This is a text version of the MOPAC7 manual produced from
the LaTeX (actually DVI) version of a manual with a program
"dvi2tty". It is really useless, since it has long lines (132
characters), and all the mathematical expressions, tables,
etc., are nonexistent or messed up. However, if for some
reason you cannot process LaTeX manual from the mopac7-man.tar.Z
or cannot print the PostScript, then here it is. Do not use
is please...
Jan Labanowski
jkl@ccl.net
------------------------------------------------
MOPAC Manual (Seventh Edition)
Dr James J. P. Stewart
PUBLIC DOMAIN COPY (NOT SUITABLE FOR
PRODUCTION WORK)
January 1993
___________________________________________________________________
This document is intended for use by developers of semiempirical programs and software. It is
not intended for use as a guide to MOPAC.
All the new functionalities which have been donated to the MOPAC project during the period
1989-1993 are included in the program. Only minimal checking has been done to ensure confor-
mance with the donors' wishes. As a result, this program should not be used to judge the quality
of programming of the donors. This version of MOPAC-7 is not supported, and no attempt has
been made to ensure reliable performance.
This program and documentation have been placed entirely in the public domain, and can be
used by anyone for any purpose. To help developers, the donated code is packaged into files, each
file representing one donation.
In addition, some notes have been added to the Manual. These may be useful in understanding
the donations.
If you want to use MOPAC-7 for production work, you should get the copyrighted copy from
the Quantum Chemistry Program Exchange. That copy has been carefully written, and allows
the donors' contributions to be used in a full, production-quality program.
___________________________________________________________________
Contents
Description of MOPAC 1
1.1 Summary of MOPAC capabilities : : : : : : : : : : : : : : 1
1.2 Copyright status of MOPAC : : : : : : : : : : : : : : : : : 2
1.3 Porting MOPAC to other machines : : : : : : : : : : : : : : : 2
1.4 Relationship of AMPAC and MOPAC : : : : : : : : : : : : : 3
1.5 Programs recommended for use with MOPAC : : : : : : : : : : : 3
1.6 The data-file : : : : : : : : : : : : : : : : : : : : : @
1.6.1 Example of data for ethylene : : : : : : : : : : : : : : 5
1.6.2 Example of data for polytetrahydrofuran : : : : : : : : : : : 6
2 Keywords 9
2.1 Specification of keywords : : : : : : : : : : : : : : : : 9
2.2 Full list of keywords used in MOPAC : : : : : : : : : : : : : : 9
2.3 Definitions of keywords : : : : : : : : : : : : : : : : : : 12
2.4 Keywords that go together : : : : : : : : : : : : : : : : 39
3 Geometry specification 41
3.1 Internal coordinate definition : : : : : : : : : : : : : : : : 41
3.1.1 Constraints : : : : : : : : : : : : : : : : : : 41
3.2 Gaussian Z-matrices : : : : : : : : : : : : : : : : : : : 42
3.3 Cartesian coordinate definition : : : : : : : : : : : : : : : 43
3.4 Conversion between various formats : : : : : : : : : : : : : : 43
3.5 Definition of elements and isotopes : : : : : : : : : : : : : : : 44
3.6 Examples of coordinate definitions : : : : : : : : : : : : : : : 46
4 Examples 49
4.1 MNRSD1 test data file for formaldehyde : : : : : : : : : : : : 49
4.2 MOPAC output for test-data file MNRSD1 : : : : : : : : : : : : 50
5 Testdata 55
5.1 Data file for a force calculation : : : : : : : : : : : : : : : 55
5.2 Results file for the force calculation : : : : : : : : : : : : : : : 56
5.3 Example of reaction path with symmetry : : : : : : : : : : : : : 63
6 Background 65
6.1 Introduction : : : : : : : : : : : : : : : : : : : : @
6.2 AIDER : : : : : : : : : : : : : : : : : : : : : : @
6.3 Correction to the peptide linkage : : : : : : : : : : : : : : 66
6.4 Level of precision within MOPAC : : : : : : : : : : : : : : 67
6.5 Convergence tests in subroutine ITER : : : : : : : : : : : : : 69
6.6 Convergence in SCF calculation : : : : : : : : : : : : : : : 69
6.7 Causes of failure to achieve an SCF : : : : : : : : : : : : : : : 70
_________________________________________________________CONTENTS____________
6.8 Torsion or dihedral angle coherency : : : : : : : : : : : : : : : 71
6.9 Vibrational analysis : : : : : : : : : : : : : : : : : : : 71
6.10 A note on thermochemistry : : : : : : : : : : : : : : : : : 71
6.10.1 Basic Physical Constants : : : : : : : : : : : : : : 71
6.10.2 Thermochemistry from ab initio MO methods : : : : : : : : : 72
6.11 Reaction coordinates : : : : : : : : : : : : : : : : : : : 76
6.12 Sparkles : : : : : : : : : : : : : : : : : : : : : : @
6.13 Mechanism of the frame in FORCE calculation : : : : : : : : : : 86
6.14 Configuration interaction : : : : : : : : : : : : : : : : 87
6.15 Reduced masses in a force calculation : : : : : : : : : : : : : 91
6.16 Use of SADDLE calculation : : : : : : : : : : : : : : : : : 91
6.17 How to escape from a hilltop : : : : : : : : : : : : : : : : 93
6.17.1 EigenFollowing : : : : : : : : : : : : : : : : : 94
6.17.2 Franck-Condon considerations : : : : : : : : : : : : : : 96
6.18 Outer Valence Green's Function : : : : : : : : : : : : : : : 97
6.18.1 Example of OVGF calculation : : : : : : : : : : : : : 98
6.19 COSMO (Conductor-like Screening Model) : : : : : : : : : : : : 99
6.20 Solid state capability : : : : : : : : : : : : : : : : : : : 99
7 Program 101
7.1 Main geometric sequence : : : : : : : : : : : : : : : : : 101
7.2 Main electronic flow : : : : : : : : : : : : : : : : : : : 102
7.3 Control within MOPAC : : : : : : : : : : : : : : : : : 102
7.3.1 Subroutine GMETRY : : : : : : : : : : : : : : : : 103
8 Error messages produced by MOPAC 105
9 Criteria 113
9.1 SCF criterion : : : : : : : : : : : : : : : : : : : : : 113
9.2 Geometric optimization criteria : : : : : : : : : : : : : : : 113
10 Debugging 117
10.1 Debugging keywords : : : : : : : : : : : : : : : : : : : 117
11 Installing MOPAC 121
11.1 ESP calculation : : : : : : : : : : : : : : : : : : : : 124
A Names of FORTRAN-77 files 127
B Subroutine calls in MOPAC 129
C Description of subroutines 137
D Heats of formation 147
E References 149
CONTENTS___________________________________________________________
o New Functionalities:
- Michael B. Coolidge, The Frank J. Seiler Research Laboratory, U.S. Air Force
Academy, CO 80840, and James J. P. Stewart, Stewart Computational Chemistry,
15210 Paddington Circle, Colorado Springs, CO 80921-2512. (The Air Force code was
obtained under the Freedom of Information Act)
Symmetry is used to speed up FORCE calculations, and to facilitate the analysis of
molecular vibrations.
- David Danovich, The Fritz Haber Research Center for Molecular Dynamics, The
Hebrew University of Jerusalem, 91904 Jerusalem, Israel.
Ionization potentials are corrected using Green's Function techniques. The resulting
I.P.s are generally more accurate than the conventional I.P.s.
The point-group of the system is identified, and molecular orbitals are characterized
by irreducible representation.
- Andreas Klamt Bayer AG, Q18, D-5090 Leverkusen-Beyerwerk, Germany.
A new approach to dielectric screening in solvents with explicit expressions for the
screening energy and its gradient has been added.
o Existing Functionalities:
- Victor I. Danilov, Department of Quantum Biophysics, Academy of Sciences of
the Ukraine, Kiev 143, Ukraine.
Edited the MOPAC 7 Manual, and provided the basis for Section 6.17.2, on excited
states.
- Henry Kurtz and Prakashan Korambath, Department of Chemistry, Mem-
phis State University, Memphis TN 38152.
The Hyperpolarizability calculation, originally written by Prof Kurtz, has been im-
proved so that frequency dependent non-linear optical calculations can be performed.
(Prakashan Korambath, dissertation research)
- Frank Jensen, Department of Chemistry, Odense Universitet, Campusvej 55, DK-
5230 Odense M, Denmark.
The efficiency of Baker's EF routine has been improved.
- John M. Simmie, Chemistry Department, University College, Galway, Ireland.
The MOPAC Manual has been completely re-formatted in the LaTeX document prepa-
ration system. Equations are now much easier to read and to understand.
- Jorge A. Medrano, 5428 Falcon Ln., West Chester, OH 45069, and Roberto
Bochicchio (Universidad de Buenos Aires).
The BONDS function has been extended to allow free valence and other quantities to
be calculated.
- George Purvis III, CAChe Scientific, P.O. Box 500, Delivery Station 13-400,
Beaverton, OR 97077.
The STO-6G Gaussian expansion of the Slater orbitals has been expanded to Principal
Quantum Number 6. These expansions are used in analytical derivative calculations.
o Bug-reports/bug-fixes:
- Victor I. Danilov, Department of Quantum Biophysics, Academy of Sciences of
the Ukraine, Kiev 143, Ukraine.
Several faults in the multi-electron configuration interaction were identified, and rec-
ommendations made regarding their correction.
_________________________________________________________CONTENTS____________
Chapter 1
Description of MOPAC
MOPAC is a general-purpose semi-empirical molecular orbital package for the study of chemical
structures and reactions. The semi-empirical Hamiltonians MNDO, MINDO/3, AM1, and PM3
are used in the electronic part of the calculation to obtain molecular orbitals, the heat of formation
and its derivative with respect to molecular geometry. Using these results MOPAC calculates the
vibrational spectra, thermodynamic quantities, isotopic substitution effects and force constants
for molecules, radicals, ions, and polymers. For studying chemical reactions, a transition state
location routine and two transition state optimizing routines are available. For users to get the
most out of the program, they must understand how the program works, how to enter data, how
to interpret the results, and what to do when things go wrong.
While MOPAC calls upon many concepts in quantum theory and thermodynamics and uses
some fairly advanced mathematics, the user need not be familiar with these specialized topics.
MOPAC is written with the non-theoretician in mind. The input data are kept as simple as
possible so users can give their attention to the chemistry involved and not concern themselves
with quantum and thermodynamic exotica.
The simplest description of how MOPAC works is that the user creates a data-file which
describes a molecular system and specifies what kind of calculations and output are desired. The
user then commands MOPAC to carry out the calculation using that data-file. Finally the user
extracts the desired output on the system from the output files created by MOPAC.
1. This is the "sixth edition". MOPAC has undergone a steady expansion since its first release,
and users of the earlier editions are recommended to familiarize themselves with the changes
which are described in this manual. If any errors are found, or if MOPAC does not perform
as described, please contact Dr. James J. P. Stewart, Frank J. Seiler Research Laboratory,
U.S. Air Force Academy, Colorado Springs, CO 80840-6528.
2. MOPAC runs successfully on normal CDC, Data General, Gould, and DEC computers, and
also on the CDC 205 and CRAY-XMP "supercomputers". The CRAY version has been
partly optimized to take advantage of the CRAY architecture. Several versions exist for
microcomputers such as the IBM PC-AT and XT, Zenith, etc.
1.1 Summary of MOPAC capabilities
1. MNDO, MINDO/3, AM1, and PM3 Hamiltonians.
2. Restricted Hartree-Fock (RHF) and Unrestricted Hartree-Fock (UHF) methods.
3. Extensive Configuration Interaction
(a) 100 configurations
(b) Singlets, Doublets, Triplets, Quartets, Quintets, and Sextets
___________________________________________________Description_of_MOPAC________________
(c) Excited states
(d) Geometry optimizations, etc., on specified states
4. Single SCF calculation
5. Geometry optimization
6. Gradient minimization
7. Transition state location
8. Reaction path coordinate calculation
9. Force constant calculation
10. Normal coordinate analysis
11. Transition dipole calculation
12. Thermodynamic properties calculation
13. Localized orbitals
14. Covalent bond orders
15. Bond analysis into sigma and pi contributions
16. One dimensional polymer calculation
17. Dynamic Reaction Coordinate calculation
18. Intrinsic Reaction Coordinate calculation
1.2 Copyright status of MOPAC
At the request of the Air Force Academy Law Department the following notice has been placed
in MOPAC.
Notice of Public Domain nature of MOPAC.
"This computer program is a work of the United States Government and as such is not
subject to protection by copyright (17 U.S.C. # 105.) Any person who fraudulently
places a copyright notice or does any other act contrary to the provisions of 17 U.S.
Code 506(c) shall be subject to the penalties provided therein. This notice shall not
be altered or removed from this software and is to be on all reproductions."
I recommend that a user obtain a copy by either copying it from an existing site or ordering an
`official' copy from the Quantum Chemistry Program Exchange, (QCPE), Department of Chem-
istry, Indiana University, Bloomington, Indiana, 47405. The cost covers handling only. Contact
the Editor, Richard Counts, at (812) 855-4784 for further details.
1.3 Porting MOPAC to other machines
MOPAC is written for the DIGITAL VAX computer. However, the program has been written
with the idea that it will be ported to other machines. After such a port has been done, the new
program should be given the version number 6.10, or, if two or more versions are generated, 6.20,
6.30, etc. To validate the new copy, QCPE has a test-suite of calculations. If all tests are passed,
within the tolerances given in the tests, then the new program can be called a valid version of
MOPAC 6. Insofar as is practical, the mode of submission of a MOPAC job should be preserved,
e.g.,
1.4_Relationship_of_AMPAC_and_MOPAC____________________________________________________
(prompt) MOPAC [...]
Any changes which do not violate the FORTRAN-77 conventions, and which users believe
would be generally desirable, can be sent to the author.
1.4 Relationship of AMPAC and MOPAC
In 1985 MOPAC 3.0 and AMPAC 1.0 were submitted to QCPE for distribution. At that time,
AMPAC differed from MOPAC in that it had the AM1 algorithm. Additionally, changes in some
MNDO parameters in AMPAC made AMPAC results incompatable with MOPAC Versions 1-3.
Subsequent versions of MOPAC, in addition to being more highly debugged than Version 3.0, also
had the AM1 method. Such versions were compatible with AMPAC and with versions 1-3 of
MOPAC.
In order to avoid confusion, all versions of MOPAC after 3.0 include journal references so that
the user knows unambiguously which parameter sets were used in any given job.
Since 1985 AMPAC and MOPAC have evolved along different lines. In MOPAC I have endeav-
oured to provide a highly robust program, one with only a few new features, but which is easily
portable and which can be relied upon to give precise, if not very exciting, answers. At Austin,
the functionality of AMPAC has been enhanced by the research work of Prof. Dewar's group. The
new AMPAC 2.1 thus has functionalities not present in MOPAC. In publications, users should
cite not only the program name but also the version number.
Commercial concerns have optimized both MOPAC and AMPAC for use on supercomputers.
The quality of optimization and the degree to which the parent algorithm has been preserved differs
between MOPAC and AMPAC and also between some machine specific versions. Different users
may prefer one program to the other, based on considerations such as speed. Some modifications of
AMPAC run faster than some modifications of MOPAC, and vice versa, but if these are modified
versions of MOPAC 3.0 or AMPAC 1.0, they represent the programming prowess of the companies
doing the conversion, and not any intrinsic difference between the two programs.
Testing of these large algorithms is difficult, and several times users have reported bugs in
MOPAC or AMPAC which were introduced after they were supplied by QCPE.
Cooperative Development of MOPAC
MOPAC has developed, and hopefully will continue to develop, by the addition of contributed
code. As a policy, any supplied code which is incorporated into MOPAC will be described in the
next release of the Manual, and the author or supplier acknowledged. In the following release only
journal references will be retained. The objective is to produce a good program. This is obviously
not a one-person undertaking; if it was, then the product would be poor indeed. Instead, as we are
in a time of rapid change in computational chemistry, a time characterized by a very free exchange
of ideas and code, MOPAC has been evolving by accretion. The unstinting and generous donation
of intellectual effort speaks highly of the donors. However, with the rapid commercialization of
computational chemistry software in the past few years, it is unfortunate but it seems unlikely
that this idyllic state will continue.
1.5 Programs recommended for use with MOPAC
MOPAC is the core program of a series of programs for the theoretical study of chemical phenom-
ena. This version is the sixth in an on-going development, and efforts are being made to continue
its further evolution. In order to make using MOPAC easier, five other programs have also been
written. Users of MOPAC are recommended to use all four programs. Efforts will be made to
continue the development of these programs.
___________________________________________________Description_of_MOPAC________________
HELP
HELP is a stand-alone program which mimics the VAX HELP function. It is intended for users
on UNIX computers. HELP comes with the basic MOPAC 6.00, and is recommended for general
use.
DRAW
DRAW, written by Maj. Donn Storch, USAF, and available through QCPE, is a powerful editing
program specifically written to interface with MOPAC. Among the various facilities it offers are:
1. The on-line editing and analysis of a data file, starting from scratch or from an existing data
file, an archive file, or from a results file.
2. The option of continuous graphical representation of the system being studied. Several types
of terminals are supported, including DIGITAL, TEKTRONIX, and TERAK terminals.
3. The drawing of electron density contour maps generated by DENSITY on graphical devices.
4. The drawing of solid-state band structures generated by MOSOL.
5. The sketching of molecular vibrations, generated by a normal coordinate analysis.
DENSITY
DENSITY, written by Dr. James J. P. Stewart, and available through QCPE, is an electron-
density plotting program. It accepts data-files directly from MOPAC, and is intended to be used
for the graphical representation of electron density distribution, individual M.O.'s, and difference
maps.
MOHELP
MOHELP, also available through QCPE, is an on-line help facility, written by Maj. Donn Storch
and Dr. James J. P. Stewart, to allow non-VAX users access to the VAX HELP libraries for
MOPAC, DRAW, and DENSITY.
MOSOL
MOSOL (Distributed by QCPE) is a full solid-state MNDO program written by Dr. James J. P.
Stewart. In comparison with MOPAC, MOSOL is extremely slow. As a result, while geometry
optimization, force constants, and other functions can be carried out by MOSOL, these slow
calculations are best done using the solid-state facility within MOPAC. MOSOL should be used
for two or three dimensional solids only, a task that MOPAC cannot perform.
1.6 The data-file
This section is aimed at the complete novice _ someone who knows nothing at all about the
structure of a MOPAC data-file.
First of all, there are at most four possible types of data-files for MOPAC, but the simplest
data-file is the most commonly used. Rather than define it, two examples are shown below. An ex-
planation of the geometry definitions shown in the examples is given in the chapter "GEOMETRY
SPECIFICATION".
1.6_The_data-file____________________________________________________________
1.6.1 Example of data for ethylene
Line 1 : UHF PULAY MINDO3 VECTORS DENSITY LOCAL T=300
Line 2 : EXAMPLE OF DATA FOR MOPAC
Line 3 : MINDO/3 UHF CLOSED-SHELL D2D ETHYLENE
Line 4a: C
Line 4b: C 1.400118 1
Line 4c: H 1.098326 1 123.572063 1
Line 4d: H 1.098326 1 123.572063 1 180.000000 0 2 1 3
Line 4e: H 1.098326 1 123.572063 1 90.000000 0 1 2 3
Line 4f: H 1.098326 1 123.572063 1 270.000000 0 1 2 3
Line 5 :
As can be seen, the first three lines are textual. The first line consists of keywords (here seven
keywords are shown). These control the calculation. The next two lines are comments or titles.
The user might want to put the name of the molecule and why it is being run on these two lines.
These three lines are obligatory. If no name or comment is wanted, leave blank lines. If no
keywords are specified, leave a blank line. A common error is to have a blank line before the
keyword line: this error is quite tricky to find, so be careful not to have four lines before the start
of the geometric data (lines 4a-4f in the example). Whatever is decided, the three lines, blank or
otherwise, are obligatory.
In the example given, one line of keywords and two of documentation are shown. By use of
keywords, these defaults can be changed. Modifying keywords are +, &, and SETUP. These are
defined in the KEYWORDS chapter. The following table illustrates the allowed combinations:
Line 1 Line 2 Line 3 Line 4 Line 5 Setup used
Keys Text Text Z-matrix Z-matrix not used
Keys + Keys Text Text Z-matrix not used
Keys + Keys + Keys Text Text not used
Keys & Keys Text Z-matrix Z-matrix not used
Keys & Keys & Keys Z-matrix Z-matrix not used
Keys SETUP Text Text Z-matrix Z-matrix 1 or 2 lines used
Keys + Keys SETUP Text Text Z-matrix 1 line used
Keys & Keys SETUP Text Z-matrix Z-matrix 1 line used
No other combinations are allowed.
The proposed use of the SETUP option is to allow a frequently used set of keywords to be
defined by a single keyword. For example, if the default criteria are not suitable, SETUP might
contain:
" SCFCRT=1.D-8 SHIFT=30 ITRY=600 GNORM=0.02 ANALYT "
" "
The order of usage of a keyword is:
Line 1 > Line 2 > Line 3.
Line 1 > SETUP.
Line 2 > SETUP.
SETUP > built in default values.
The next set of lines defines the geometry. In the example, the numbers are all neatly lined up;
this is not necessary, but does make it easier when looking for errors in the data. The geometry
is defined in lines 4a to 4f; line 5 terminates both the geometry and the data-file. Any additional
data, for example symmetry data, would follow line 5.
Summarizing, then, the structure for a MOPAC data-file is:
___________________________________________________Description_of_MOPAC________________
Line 1 Keywords. (See chapter 2 on definitions of keywords)
Line 2 Title of the calculation, e.g. the name of the molecule or ion.
Line 3 Other information describing the calculation.
Lines 4 Internal or cartesian coordinates (See chapter on specification of geometry)
Line 5 Blank line to terminate the geometry definition.
Other layouts for data-files involve additions to the simple layout. These additions occur at
the end of the data-file, after line 5. The three most common additions are:
o Symmetry data: This follows the geometric data, and is ended by a blank line.
o Reaction path: After all geometry and symmetry data (if any) are read in, points on the
reaction coordinate are defined.
o Saddle data: A complete second geometry is input. The second geometry follows the first
geometry and symmetry data (if any).
1.6.2 Example of data for polytetrahydrofuran
The following example illustrates the data file for a four hour polytetrahydrofuran calculation. As
you can see the layout of the data is almost the same as that for a molecule, the main difference
is in the presence of the translation vector atom "Tv".
Line 1 :T=4H
Line 2 : POLY-TETRAHYDROFURAN (C4 H8 O)2
Line 3 :
Line 4a: C 0.000000 0 0.000000 0 0.000000 0 0 0 0
Line 4b: C 1.551261 1 0.000000 0 0.000000 0 1 0 0
Line 4c: O 1.401861 1 108.919034 1 0.000000 0 2 1 0
Line 4d: C 1.401958 1 119.302489 1 -179.392581 1 3 2 1
Line 4e: C 1.551074 1 108.956238 1 179.014664 1 4 3 2
Line 4f: C 1.541928 1 113.074843 1 179.724877 1 5 4 3
Line 4g: C 1.551502 1 113.039652 1 179.525806 1 6 5 4
Line 4h: O 1.402677 1 108.663575 1 179.855864 1 7 6 5
Line 4i: C 1.402671 1 119.250433 1 -179.637345 1 8 7 6
Line 4j: C 1.552020 1 108.665746 1 -179.161900 1 9 8 7
Line 4k: XX 1.552507 1 112.659354 1 -178.914985 1 10 9 8
Line 4l: XX 1.547723 1 113.375266 1 -179.924995 1 11 10 9
Line 4m: H 1.114250 1 89.824605 1 126.911018 1 1 3 2
Line 4n: H 1.114708 1 89.909148 1 -126.650667 1 1 3 2
Line 4o: H 1.123297 1 93.602831 1 127.182594 1 2 4 3
Line 4p: H 1.123640 1 93.853406 1 -126.320187 1 2 4 3
Line 4q: H 1.123549 1 90.682924 1 126.763659 1 4 6 5
Line 4r: H 1.123417 1 90.679889 1 -127.033695 1 4 6 5
Line 4s: H 1.114352 1 90.239157 1 126.447043 1 5 7 6
Line 4t: H 1.114462 1 89.842852 1 -127.140168 1 5 7 6
Line 4u: H 1.114340 1 89.831790 1 126.653999 1 6 8 7
Line 4v: H 1.114433 1 89.753913 1 -126.926618 1 6 8 7
Line 4w: H 1.123126 1 93.644744 1 127.030541 1 7 9 8
Line 4x: H 1.123225 1 93.880969 1 -126.380511 1 7 9 8
Line 4y: H 1.123328 1 90.261019 1 127.815464 1 9 11 10
Line 4z: H 1.123227 1 91.051403 1 -125.914234 1 9 11 10
Line 4A: H 1.113970 1 90.374545 1 126.799259 1 10 12 11
1.6_The_data-file____________________________________________________________
Line 4B: H 1.114347 1 90.255788 1 -126.709810 1 10 12 11
Line 4C: Tv 12.299490 1 0.000000 0 0.000000 0 1 11 10
Line 5 : 0 0.000000 0 0.000000 0 0.000000 0 0 0 0
Polytetrahydrofuran has a repeat unit of (C4 H8 O)2 ; i.e., twice the monomer unit. This is
necessary in order to allow the lattice to repeat after a translation through 12:3 A. See the section
on Solid State Capability for further details.
Note the two dummy atoms on lines 4k and 4l. These are useful, but not essential, for defining
the geometry. The atoms on lines 4y to 4B use these dummy atoms, as does the translation vector
on line 4C. The translation vector has only the length marked for optimization. The reason for
this is also explained in the Background chapter.
___________________________________________________Description_of_MOPAC________________
Chapter 2
Keywords
2.1 Specification of keywords
All control data are entered in the form of keywords, which form the first line of a data-file.
A description of what each keyword does is given in Section 2.3. The order in which keywords
appear is not important although they must be separated by a space. Some keywords can be
abbreviated, allowed abbreviations are noted in Section 2.3 (for example 1ELECTRON can be
entered as 1ELECT). However the full keyword is preferred in order to more clearly document the
calculation and to obviate the possibility that an abbreviated keyword might not be recognized. If
there is insufficient space in the first line for all the keywords needed, then consider abbreviating
the longer words. One type of keyword, those with an equal sign, such as, BAR=0.05, may not be
abbreviated, and the full word needs to be supplied.
Most keywords which involve an equal sign, such as SCFCRT=1.D-12 can, at the user's discretion,
be written with spaces before and after the equal sign. Thus all permutations of SCFCRT=1.D-12,
such as SCFCRT =1.D-12, SCFCRT = 1.D-12, SCFCRT= 1.D-12, SCFCRT = 1.D-12, etc. are al-
lowed. Exceptions to this are T=, T-PRIORITY=, H-PRIORITY=, X-PRIORITY=, IRC=,
DRC= and TRANS=. ` T=' cannot be abbreviated to ` T ' as many keywords start or end with
a `T'; for the other keywords the associated abbreviated keywords have specific meanings.
If two keywords which are incompatible, like UHF and C.I., are supplied, or a keyword which
is incompatible with the species supplied, for instance TRIPLET and a methyl radical, then
error trapping will normally occur, and an error message will be printed. This usually takes an
insignificant time, so data are quickly checked for obvious errors.
2.2 Full list of keywords used in MOPAC
& - TURN NEXT LINE INTO KEYWORDS
+ - ADD ANOTHER LINE OF KEYWORDS
0SCF - READ IN DATA, THEN STOP
1ELECTRON- PRINT FINAL ONE-ELECTRON MATRIX
1SCF - DO ONE SCF AND THEN STOP
AIDER - READ IN AB INITIO DERIVATIVES
AIGIN - GEOMETRY MUST BE IN GAUSSIAN FORMAT
AIGOUT - IN ARC FILE, INCLUDE AB-INITIO GEOMETRY
ANALYT - USE ANALYTICAL DERIVATIVES OF ENERGY WRT GEOMETRY
AM1 - USE THE AM1 HAMILTONIAN
BAR=n.n - REDUCE BAR LENGTH BY A MAXIMUM OF n.n
BIRADICAL- SYSTEM HAS TWO UNPAIRED ELECTRONS
BONDS - PRINT FINAL BOND-ORDER MATRIX
C.I. - A MULTI-ELECTRON CONFIGURATION INTERACTION SPECIFIED
______________________________________________________________Keywords_______
CHARGE=n - CHARGE ON SYSTEM = n (e.g. NH4 => CHARGE=1)
COMPFG - PRINT HEAT OF FORMATION CALCULATED IN COMPFG
CONNOLLY - USE CONNOLLY SURFACE
DEBUG - DEBUG OPTION TURNED ON
DENOUT - DENSITY MATRIX OUTPUT (CHANNEL 10)
DENSITY - PRINT FINAL DENSITY MATRIX
DEP - GENERATE FORTRAN CODE FOR PARAMETERS FOR NEW ELEMENTS
DEPVAR=n - TRANSLATION VECTOR IS A MULTIPLE OF BOND-LENGTH
DERIV - PRINT PART OF WORKING IN DERIV
DFORCE - FORCE CALCULATION SPECIFIED, ALSO PRINT FORCE MATRIX.
DFP - USE DAVIDON-FLETCHER-POWELL METHOD TO OPTIMIZE GEOMETRIES
DIPOLE - FIT THE ESP TO THE CALCULATED DIPOLE
DIPX - X COMPONENT OF DIPOLE TO BE FITTED
DIPY - Y COMPONENT OF DIPOLE TO BE FITTED
DIPZ - Z COMPONENT OF DIPOLE TO BE FITTED
DMAX - MAXIMUM STEPSIZE IN EIGENVECTOR FOLLOWING
DOUBLET - DOUBLET STATE REQUIRED
DRC - DYNAMIC REACTION COORDINATE CALCULATION
DUMP=n - WRITE RESTART FILES EVERY n SECONDS
ECHO - DATA ARE ECHOED BACK BEFORE CALCULATION STARTS
EF - USE EF ROUTINE FOR MINIMUM SEARCH
EIGINV -
EIGS - PRINT ALL EIGENVALUES IN ITER
ENPART - PARTITION ENERGY INTO COMPONENTS
ESP - ELECTROSTATIC POTENTIAL CALCULATION
ESPRST - RESTART OF ELECTROSTATIC POTENTIAL
ESR - CALCULATE RHF UNPAIRED SPIN DENSITY
EXCITED - OPTIMIZE FIRST EXCITED SINGLET STATE
EXTERNAL - READ PARAMETERS OFF DISK
FILL=n - IN RHF OPEN AND CLOSED SHELL, FORCE M.O. n
TO BE FILLED
FLEPO - PRINT DETAILS OF GEOMETRY OPTIMIZATION
FMAT - PRINT DETAILS OF WORKING IN FMAT
FOCK - PRINT LAST FOCK MATRIX
FORCE - FORCE CALCULATION SPECIFIED
GEO-OK - OVERRIDE INTERATOMIC DISTANCE CHECK
GNORM=n.n- EXIT WHEN GRADIENT NORM DROPS BELOW n.n
GRADIENTS- PRINT ALL GRADIENTS
GRAPH - GENERATE FILE FOR GRAPHICS
HCORE - PRINT DETAILS OF WORKING IN HCORE
HESS=N - OPTIONS FOR CALCULATING HESSIAN MATRICES IN EF
H-PRIO - HEAT OF FORMATION TAKES PRIORITY IN DRC
HYPERFINE- HYPERFINE COUPLING CONSTANTS TO BE CALCULATED
IRC - INTRINSIC REACTION COORDINATE CALCULATION
ISOTOPE - FORCE MATRIX WRITTEN TO DISK (CHANNEL 9 )
ITER - PRINT DETAILS OF WORKING IN ITER
ITRY=N - SET LIMIT OF NUMBER OF SCF ITERATIONS TO N.
IUPD - MODE OF HESSIAN UPDATE IN EIGENVECTOR FOLLOWING
K=(N,N) - BRILLOUIN ZONE STRUCTURE TO BE CALCULATED
KINETIC - EXCESS KINETIC ENERGY ADDED TO DRC CALCULATION
LINMIN - PRINT DETAILS OF LINE MINIMIZATION
LARGE - PRINT EXPANDED OUTPUT
LET - OVERRIDE CERTAIN SAFETY CHECKS
LOCALIZE - PRINT LOCALIZED ORBITALS
2.2_Full_list_of_keywords_used_in_MOPAC________________________________________________
MAX - PRINTS MAXIMUM GRID SIZE (23*23)
MECI - PRINT DETAILS OF MECI CALCULATION
MICROS - USE SPECIFIC MICROSTATES IN THE C.I.
MINDO/3 - USE THE MINDO/3 HAMILTONIAN
MMOK - USE MOLECULAR MECHANICS CORRECTION TO CONH BONDS
MODE=N - IN EF, FOLLOW HESSIAN MODE NO. N
MOLDAT - PRINT DETAILS OF WORKING IN MOLDAT
MS=N - IN MECI, MAGNETIC COMPONENT OF SPIN
MULLIK - PRINT THE MULLIKEN POPULATION ANALYSIS
NLLSQ - MINIMIZE GRADIENTS USING NLLSQ
NOANCI - DO NOT USE ANALYTICAL C.I. DERIVATIVES
NODIIS - DO NOT USE DIIS GEOMETRY OPTIMIZER
NOINTER - DO NOT PRINT INTERATOMIC DISTANCES
NOLOG - SUPPRESS LOG FILE TRAIL, WHERE POSSIBLE
NOMM - DO NOT USE MOLECULAR MECHANICS CORRECTION TO CONH BONDS
NONR -
NOTHIEL - DO NOT USE THIEL'S FSTMIN TECHNIQUE
NSURF=N - NUMBER OF SURFACES IN AN ESP CALCULATION
NOXYZ - DO NOT PRINT CARTESIAN COORDINATES
NSURF - NUMBER OF LAYERS USED IN ELECTROSTATIC POTENTIAL
OLDENS - READ INITIAL DENSITY MATRIX OFF DISK
OLDGEO - PREVIOUS GEOMETRY TO BE USED
OPEN - OPEN-SHELL RHF CALCULATION REQUESTED
ORIDE -
PARASOK - IN AM1 CALCULATIONS SOME MNDO PARAMETERS ARE TO BE USED
PI - RESOLVE DENSITY MATRIX INTO SIGMA AND PI BONDS
PL - MONITOR CONVERGENCE OF DENSITY MATRIX IN ITER
PM3 - USE THE MNDO-PM3 HAMILTONIAN
POINT=N - NUMBER OF POINTS IN REACTION PATH
POINT1=N - NUMBER OF POINTS IN FIRST DIRECTION IN GRID CALCULATION
POINT2=N - NUMBER OF POINTS IN SECOND DIRECTION IN GRID CALCULATION
POLAR - CALCULATE FIRST, SECOND AND THIRD ORDER POLARIZABILITIES
POTWRT - IN ESP, WRITE OUT ELECTROSTATIC POTENTIAL TO UNIT 21
POWSQ - PRINT DETAILS OF WORKING IN POWSQ
PRECISE - CRITERIA TO BE INCREASED BY 100 TIMES
PULAY - USE PULAY'S CONVERGER TO OBTAIN A SCF
QUARTET - QUARTET STATE REQUIRED
QUINTET - QUINTET STATE REQUIRED
RECALC=N - IN EF, RECALCULATE HESSIAN EVERY N STEPS
RESTART - CALCULATION RESTARTED
ROOT=n - ROOT n TO BE OPTIMIZED IN A C.I. CALCULATION
ROT=n - THE SYMMETRY NUMBER OF THE SYSTEM IS n.
SADDLE - OPTIMIZE TRANSITION STATE
SCALE - SCALING FACTOR FOR VAN DER WAALS DISTANCE IN ESP
SCFCRT=n - DEFAULT SCF CRITERION REPLACED BY THE VALUE SUPPLIED
SCINCR - INCREMENT BETWEEN LAYERS IN ESP
SETUP - EXTRA KEYWORDS TO BE READ OF SETUP FILE
SEXTET - SEXTET STATE REQUIRED
SHIFT=n - A DAMPING FACTOR OF n DEFINED TO START SCF
SIGMA - MINIMIZE GRADIENTS USING SIGMA
SINGLET - SINGLET STATE REQUIRED
SLOPE - MULTIPLIER USED TO SCALE MNDO CHARGES
SPIN - PRINT FINAL UHF SPIN MATRIX
STEP - STEP SIZE IN PATH
______________________________________________________________Keywords_______
STEP1=n - STEP SIZE n FOR FIRST COORDINATE IN GRID CALCULATION
STEP2=n - STEP SIZE n FOR SECOND COORDINATE IN GRID CALCULATION
STO-3G - DEORTHOGONALIZE ORBITALS IN STO-3G BASIS
SYMAVG - AVERAGE SYMMETRY EQUIVALENT ESP CHARGES
SYMMETRY - IMPOSE SYMMETRY CONDITIONS
T=n - A TIME OF n SECONDS REQUESTED
THERMO - PERFORM A THERMODYNAMICS CALCULATION
TIMES - PRINT TIMES OF VARIOUS STAGES
T-PRIO - TIME TAKES PRIORITY IN DRC
TRANS - THE SYSTEM IS A TRANSITION STATE
(USED IN THERMODYNAMICS CALCULATION)
TRIPLET - TRIPLET STATE REQUIRED
TS - USING EF ROUTINE FOR TS SEARCH
UHF - UNRESTRICTED HARTREE-FOCK CALCULATION
VECTORS - PRINT FINAL EIGENVECTORS
VELOCITY - SUPPLY THE INITIAL VELOCITY VECTOR IN A DRC CALCULATION
WILLIAMS - USE WILLIAMS SURFACE
X-PRIO - GEOMETRY CHANGES TAKE PRIORITY IN DRC
XYZ - DO ALL GEOMETRIC OPERATIONS IN CARTESIAN COORDINATES.
2.3 Definitions of keywords
The definitions below are given with some technical expressions which are not further defined.
Interested users are referred to Appendix E of this manual to locate appropriate references which
will provide further clarification.
There are three classes of keywords:
1. those which CONTROL substantial aspects of the calculation, i.e., those which affect the
final heat of formation,
2. those which determine which OUTPUT will be calculated and printed, and
3. those which dictate the WORKING of the calculation, but which do not affect the heat
of formation. The assignment to one of these classes is designated by a (C), (O) or (W),
respectively, following each keyword in the list below.
& (C)
An `_&' means `turn the next line into keywords'. Note the space before the `&' sign. Since `&'
is a keyword, it must be preceeded by a space. A `_&' on line 1 would mean that a second line
of keywords should be read in. If that second line contained a `_&', then a third line of keywords
would be read in. If the first line has a `_&' then the first description line is omitted, if the second
line has a `_&', then both description lines are omitted.
Examples: Use of one `&'
VECTORS DENSITY RESTART & NLLSQ T=1H SCFCRT=1.D-8 DUMP=30M ITRY=300
PM3 FOCK OPEN(2,2) ROOT=3 SINGLET SHIFT=30
Test on a totally weird system: Use of two `&'s
LARGE=-10 & DRC=4.0 T=1H SCFCRT=1.D-8 DUMP=30M ITRY=300 SHIFT=30
PM3 OPEN(2,2) ROOT=3 SINGLET NOANCI ANALYT T-PRIORITY=0.5 &
LET GEO-OK VELOCITY KINETIC=5.0
2.3_Definitions_of_keywords__________________________________________________
+ (C)
A `_+' sign means `read another line of keywords'. Note the space before the `+' sign. Since `+'
is a keyword, it must be preceeded by a space. A `_+' on line 1 would mean that a second line of
keywords should be read in. If that second line contains a `_+', then a third line of keywords will
be read in. Regardless of whether a second or a third line of keywords is read in, the next two
lines would be description lines.
Example of `_+' option
RESTART T=4D FORCE OPEN(2,2) SHIFT=20 PM3 +
SCFCRT=1.D-8 DEBUG + ISOTOPE FMAT ECHO singlet ROOT=3
THERMO(300,400,1) ROT=3
Example of data set with three lines of keywords. Note: There are two lines of description,
this and the previous line.
0SCF (O)
The data can be read in and output, but no actual calculation is performed when this keyword
is used. This is useful as a check on the input data. All obvious errors are trapped, and warning
messages printed.
A second use is to convert from one format to another. The input geometry is printed in
various formats at the end of a 0SCF calculation. If NOINTER is absent, cartesian coordinates
are printed. Unconditionally, MOPAC Z-matrix internal coordinates are printed, and if AIGOUT
is present, Gaussian Z-matrix internal coordinates are printed. 0SCF should now be used in place
of DDUM.
1ELECTRON (O)
The final one-electron matrix is printed out. This matrix is composed of atomic orbitals; the array
element between orbitals i and j on different atoms is given by:
H(i; j) = 0:5 x (fii + fij ) x overlap (i; j)
The matrix elements between orbitals i and j on the same atom are calculated from the electron-
nuclear attraction energy, and also from the U (i) value if i = j.
The one-electron matrix is unaffected by (a) the charge and (b) the electron density. It is only
a function of the geometry. Abbreviation: 1ELEC.
1SCF (C)
When users want to examine the results of a single SCF calculation of a geometry, 1SCF should
be used. 1SCF can be used in conjunction with RESTART, in which case a single SCF calculation
will be done, and the results printed.
When 1SCF is used on its own (that is, RESTART is not also used) then derivatives will only
be calculated if GRAD is also specified.
1SCF is helpful in a learning situation. MOPAC normally performs many SCF calculations,
and in order to minimize output when following the working of the SCF calculation, 1SCF is very
useful.
AIDER (C)
AIDER allows MOPAC to optimize an ab-initio geometry. To use it, calculate the ab-initio
gradients using, e.g., Gaussian. Supply MOPAC with these gradients, after converting them into
kcal/mol. The geometry resulting from a MOPAC run will be nearer to the optimized ab-initio
geometry than if the geometry optimizer in Gaussian had been used.
______________________________________________________________Keywords_______
AIGIN (C)
If the geometry (Z-matrix) is specified using the Gaussian-8X, then normally this will be read
in without difficulty. In the event that it is mistaken for a normal MOPAC-type Z-matrix, the
keyword AIGIN is provided. AIGIN will force the data-set to be read in assuming Gaussian
format. This is necessary if more than one system is being studied in one run.
AIGOUT (O)
The ARCHIVE file contains a data-set suitable for submission to MOPAC. If, in addition to this
data-set, the Z-matrix for Gaussian input is wanted, then AIGOUT (ab initio geometry output),
should be used.
The Z-matrix is in full Gaussian form. Symmetry, where present, will be correctly defined.
Names of symbolics will be those used if the original geometry was in Gaussian format, otherwise
`logical' names will be used. Logical names are of form **[][] where is `r'
for bond length, `a' for angle, or `d' for dihedral, **** is the atom number, **** is the atom to
which **** is related, , if present, is the atom number to which makes an angle, and ,
if present, is the atom number to which makes a dihedral.
ANALYT (W)
By default, finite difference derivatives of energy with respect to geometry are used. If ANALYT
is specified, then analytical derivatives are used instead. Since the analytical derivatives are over
Gaussian functions_a STO-6G basis set is used_the overlaps are also over Gaussian functions.
This will result in a very small (less than 0.1 kcal/mole) change in heat of formation. Use analytical
derivatives (a) when the mantissa used is less than about 51-53 bits, or (b) when comparison
with finite difference is desired. Finite difference derivatives are still used when non-variationally
optimized wavefunctions are present.
AM1 (C)
The AM1 method is to be used. By default MNDO is run.
BAR=n.nn (W)
In the SADDLE calculation the distance between the two geometries is steadily reduced until
the transition state is located. Sometimes, however, the user may want to alter the maximum
rate at which the distance between the two geometries reduces. BAR is a ratio, normally 0.15,
or 15 percent. This represents a maximum rate of reduction of the bar of 15 percent per step.
Alternative values that might be considered are BAR=0.05 or BAR=0.10, although other values
may be used. See also SADDLE.
If CPU time is not a major consideration, use BAR=0.03.
BIRADICAL (C)
Note: BIRADICAL is a redundant keyword, and represents a particular configuration interaction
calculation. Experienced users of MECI (q.v.) can duplicate the effect of the keyword BIRADICAL
by using the MECI keywords OPEN(2,2) and SINGLET.
For molecules which are believed to have biradicaloid character the option exists to optimize
the lowest singlet energy state which results from the mixing of three states. These states are, in
order, (1) the (micro)state arising from a one electron excitation from the HOMO to the LUMO,
which is combined with the microstate resulting from the time-reversal operator acting on the
parent microstate, the result being a full singlet state; (2) the state resulting from de-excitation
from the formal LUMO to the HOMO; and (3) the state resulting from the single electron in the
formal HOMO being excited into the LUMO.
2.3_Definitions_of_keywords__________________________________________________
Microstate 1 Microstate 2 Microstate 3
Alpha Beta Alpha Beta Alpha Beta Alpha Beta
LUMO * * * *
--- --- --- --- --- --- --- ---
+
HOMO * * * *
--- --- --- --- --- --- --- ---
A configuration interaction calculation is involved here. A biradical calculation done without
C.I. at the RHF level would be meaningless. Either rotational invariance would be lost, as in
the D2d form of ethylene, or very artificial barriers to rotations would be found, such as in a
methane molecule "orbiting" a D2d ethylene. In both cases the inclusion of limited configuration
interaction corrects the error. BIRADICAL should not be used if either the HOMO or LUMO
is degenerate; in this case, the full manifold of HOMO x LUMO should be included in the C.I.,
using MECI options. The user should be aware of this situation. When the biradical calculation is
performed correctly, the result is normally a net stabilization. However, if the first singlet excited
state is much higher in energy than the closed-shell ground state, BIRADICAL can lead to a
destabilization. Abbreviation: BIRAD. See also MECI, C.I., OPEN, SINGLET.
BONDS (O)
The rotationally invariant bond order between all pairs of atoms is printed. In this context a bond
is defined as the sum of the squares of the density matrix elements connecting any two atoms.
For ethane, ethylene, and acetylene the carbon-carbon bond orders are roughly 1.00, 2.00, and
3.00 respectively. The diagonal terms are the valencies calculated from the atomic terms only
and are defined as the sum of the bonds the atom makes with other atoms. In UHF and non-
variationally optimized wavefunctions the calculated valency will be incorrect, the degree of error
being proportional to the non-duodempotency of the density matrix. For an RHF wavefunction
the square of the density matrix is equal to twice the density matrix.
The bonding contributions of all M.O.'s in the system are printed immediately before the
bonds matrix. The idea of molecular orbital valency was developed by Gopinathan, Siddarth, and
Ravimohan. Just as an atomic orbital has a `valency', so has a molecular orbital. This leads to
the following relations: The sum of the bonding contributions of all occupied M.O.'s is the same
as the sum of all valencies which, in turn is equal to two times the sum of all bonds. The sum of
the bonding contributions of all M.O.'s is zero.
C.I.=n (C)
Normally configuration interaction is invoked if any of the keywords which imply a C.I. calculation
are used, such as BIRADICAL, TRIPLET or QUARTET. Note that ROOT= does not imply a
C.I. calculation: ROOT= is only used when a C.I. calculation is done. However, as these implied
C.I.'s involve the minimum number of configurations practical, the user may want to define a larger
than minimum C.I., in which case the keyword C.I.=n can be used. When C.I.=n is specified,
the n M.O.'s which `bracket' the occupied- virtual energy levels will be used. Thus, C.I.=2 will
include both the HOMO and the LUMO, while C.I.=1 (implied for odd-electron systems) will
only include the HOMO (This will do nothing for a closed-shell system, and leads to Dewar's
______________________________________________________________Keywords_______
half-electron correction for odd-electron systems). Users should be aware of the rapid increase in
the size of the C.I. with increasing numbers of M.O.'s being used. Numbers of microstates implied
by the use of the keyword C.I.=n on its own are as follows:
Keyword Even-electron systems Odd-electron systems
No. of electrons, configs No. of electrons, configs
Alpha Beta Alpha Beta
C.I.=1 1 1 1 1 0 1
C.I.=2 1 1 4 1 0 2
C.I.=3 2 2 9 2 1 9
C.I.=4 2 2 36 2 1 24
C.I.=5 3 3 100 3 2 100
C.I.=6 3 3 400 3 2 300
C.I.=7 4 4 1225 4 3 1225
C.I.=8 (Do not use unless other keywords also used, see below)
If a change of spin is defined, then larger numbers of M.O.'s can be used up to a maximum of 10.
The C.I. matrix is of size 100 x 100. For calculations involving up to 100 configurations, the spin-
states are exact eigenstates of the spin operators. For systems with more than 100 configurations,
the 100 configurations of lowest energy are used. See also MICROS and the keywords defining
spin-states.
Note that for any system, use of C.I.=5 or higher normally implies the diagonalization of a 100
by 100 matrix. As a geometry optimization using a C.I. requires the derivatives to be calculated
using derivatives of the C.I. matrix, geometry optimization with large C.I.'s will require more time
than smaller C.I.'s.
Associated keywords: MECI, ROOT=, MICROS, SINGLET, DOUBLET, etc.
C.I.=(n,m)
In addition to specifying the number of M.O.'s in the active space, the number of electrons can
also be defined. In C.I.=(n,m), n is the number of M.O.s in the active space, and m is the number
of doubly filled levels to be used. Examples:
Keywords Number of M.O.s No. Electrons
C.I.=2 2 2 (1)
C.I.=(2,1) 2 2 (3)
C.I.=(3,1) 3 2 (3)
C.I.=(3,2) 3 4 (5)
C.I.=(3,0) OPEN(2,3) 3 2 (N/A)
C.I.=(3,1) OPEN(2,2) 3 4 (N/A)
C.I.=(3,1) OPEN(1,2) 3 N/A (3)
Odd electron systems given in parentheses.
CHARGE=n (C)
When the system being studied is an ion, the charge, n, on the ion must be supplied by CHARGE=n.
For cations n can be 1, 2, 3, etc, for anions -1 or -2 or -3, etc. Examples:
ION KEYWORD ION KEYWORD
NH4(+) CHARGE=1 CH3COO(-) CHARGE=-1
C2H5(+) CHARGE=1 (COO)(=) CHARGE=-2
SO4(=) CHARGE=-2 PO4(3-) CHARGE=-3
HSO4(-) CHARGE=-1 H2PO4(-) CHARGE=-1
2.3_Definitions_of_keywords__________________________________________________
DCART (O)
The cartesian derivatives which are calculated in DCART for variationally optimized systems are
printed if the keyword DCART is present. The derivatives are in units of kcals/Angstrom, and
the coordinates are displacements in x, y, and z.
DEBUG (O)
Certain keywords have specific output control meanings, such as FOCK, VECTORS and DEN-
SITY. If they are used, only the final arrays of the relevant type are printed. If DEBUG is
supplied, then all arrays are printed. This is useful in debugging ITER. DEBUG can also increase
the amount of output produced when certain output keywords are used, e.g. COMPFG.
DENOUT (O)
The density matrix at the end of the calculation is to be output in a form suitable for input in
another job. If an automatic dump due to the time being exceeded occurs during the current run
then DENOUT is invoked automatically. (see RESTART)
DENSITY (O)
At the end of a job, when the results are being printed, the density matrix is also printed. For RHF
the normal density matrix is printed. For UHF the sum of the alpha and beta density matrices is
printed.
If density is not requested, then the diagonal of the density matrix, i.e., the electron density
on the atomic orbitals, will be printed.
DEP (O)
For use only with EXTERNAL=. When new parameters are published, they can be entered at
run-time by using EXTERNAL=, but as this is somewhat clumsy, a permanent change can be
made by use of DEP.
If DEP is invoked, a complete block of FORTRAN code will be generated, and this can be
inserted directly into the BLOCK DATA file.
Note that the output is designed for use with PM3. By modifying the names, the output can
be used with MNDO or AM1.
DEPVAR=n.nn (C)
In polymers the translation vector is frequently a multiple of some internal distance. For example,
in polythene it is the C1-C3 distance. If a cluster unit cell of C6H12 is used, then symmetry can
be used to tie together all the carbon atom coordinates and the translation vector distance. In
this example DEPVAR=3.0 would be suitable.
DFP (W)
By default the Broyden-Fletcher-Goldfarb-Shanno method will be used to optimize geometries.
The older Davidon-Fletcher-Powell method can be invoked by specifying DFP. This is intended
to be used for comparison of the two methods.
DIPOLE (C)
Used in the ESP calculation, DIPOLE will constrain the calculated charges to reproduce the
cartesian dipole moment components calculated from the density matrix and nuclear charges.
______________________________________________________________Keywords_______
DIPX (C)
Similar to DIPOLE, except the fit will be for the X-component only.
DIPY (C)
Similar to DIPOLE, except the fit will be for the Y-component only.
DIPZ (C)
Similar to DIPOLE, except the fit will be for the Z-component only.
DMAX=n.nn (W)
In the EF routine, the maximum step-size is 0:2 (Angstroms or radians), by default. This can be
changed by specifying DMAX=n.nn. Increasing DMAX can lead to faster convergence but can also
make the optimization go bad very fast. Furthermore, the Hessian updating may deteriorate when
using large stepsizes. Reducing the stepsize to 0:10 or 0:05 is recommended when encountering
convergence problems.
DOUBLET (C)
When a configuration interaction calculation is done, all spin states are calculated simultaneously,
either for component of spin=0 or 1/2. When only doublet states are of interest, then DOUBLET
can be specified, and all other spin states, while calculated, are ignored in the choice of root to be
used.
Note that while almost every odd-electron system will have a doublet ground state, DOUBLET
should still be specified if the desired state must be a doublet.
DOUBLET has no meaning in a UHF calculation.
DRC (C)
A Dynamic Reaction Coordinate calculation is to be run. By default, total energy is conserved, so
that as the `reaction' proceeds in time, energy is transferred between kinetic and potential forms.
DRC=n.nnn (C)
In a DRC calculation, the `half-life' for loss of kinetic energy is defined as n.nnn femtoseconds. If
n.nnn is set to zero, infinite damping simulating a very condensed phase is obtained.
This keyword cannot be written with spaces around the `=' sign.
DUMP (W)
Restart files are written automatically at one hour cpu time intervals to allow a long job to
be restarted if the job is terminated catastrophically. To change the frequency of dump, set
DUMP=nn to request a dump every nn seconds. Alternative forms, DUMP=nnM, DUMP=nnH,
DUMP=nnD for a dump every nn minutes, hours, or days, respectively. DUMP only works with
geometry optimization, gradient minimization, path, and FORCE calculations. It does not (yet)
work with a SADDLE calculation.
ECHO (O)
Data are echoed back if ECHO is specified. Only useful if data are suspected to be corrupt.
2.3_Definitions_of_keywords__________________________________________________
EF (C)
The Eigenvector Following routine is an alternative to the BFGS, and appears to be much faster.
To invoke the Eigenvector Following routine, specify EF. EF is particularly good in the end-game,
when the gradient is small. See also HESS, DMAX, EIGINV.
EIGINV (W)
Not recommended for normal use. Used with the EF routine. See source code for more details.
ENPART (O)
This is a very useful tool for analyzing the energy terms within a system. The total energy, in
eV, obtained by the addition of the electronic and nuclear terms, is partitioned into mono- and
bi-centric contributions, and these contributions in turn are divided into nuclear and one- and
two-electron terms.
ESP (C)
This is the ElectroStatic Potential calculation of K. M. Merz and B. H. Besler. ESP calculates
the expectation values of the electrostatic potential of a molecule on a uniform distribution of
points. The resultant ESP surface is then fitted to atom centered charges that best reproduce the
distribution, in a least squares sense.
ESPRST (W)
ESPRST restarts a stopped ESP calculation. Do not use with RESTART.
ESR (O)
The unpaired spin density arising from an odd-electron system can be calculated both RHF and
UHF. In a UHF calculation the alpha and beta M.O.'s have different spatial forms, so unpaired
spin density can naturally be present on in-plane hydrogen atoms such as in the phenoxy radical.
In the RHF formalism a MECI calculation is performed. If the keywords OPEN and C.I.= are
both absent then only a single state is calculated. The unpaired spin density is then calculated
from the state function. In order to have unpaired spin density on the hydrogens in, for example,
the phenoxy radical, several states should be mixed.
EXCITED (C)
The state to be calculated is the first excited open-shell singlet state. If the ground state is a
singlet, then the state calculated will be S(1); if the ground state is a triplet, then S(2). This
state would normally be the state resulting from a one-electron excitation from the HOMO to
the LUMO. Exceptions would be if the lowest singlet state were a biradical, in which case the
EXCITED state could be a closed shell.
The EXCITED state will be calculated from a BIRADICAL calculation in which the second
root of the C.I. matrix is selected. Note that the eigenvector of the C.I. matrix is not used in the
current formalism. Abbreviation: EXCI.
Note: EXCITED is a redundant keyword, and represents a particular configuration interaction
calculation. Experienced users of MECI can duplicate the effect of the keyword EXCITED by
using the MECI keywords OPEN(2,2), SINGLET, and ROOT=2.
______________________________________________________________Keywords_______
EXTERNAL=name (C)
Normally, PM3, AM1 and MNDO parameters are taken from the BLOCK DATA files within
MOPAC. When the supplied parameters are not suitable, as in an element recently parameterized,
and the parameters have not yet installed in the user's copy of MOPAC, then the new parameters
can be inserted at run time by use of EXTERNAL=, where is the name
of the file which contains the new parameters.
consists of a series of parameter definitions in the format:
where the possible parameters are USS, UPP, UDD, ZS, ZP, ZD, BETAS, BETAP, BETAD, GSS,
GSP, GPP, GP2, HSP, ALP, FNnm, n=1,2, or 3, and m=1 to 10, and the elements are defined by
their chemical symbols, such as Si or SI.
When new parameters for elements are published, they can be typed in as shown. This file is
ended by a blank line, the word END or nothing, i.e., no end-of-file delimiter. An example of a
parameter data file would be (put at least 2 spaces before and after parameter name):
Line 1: USS Si -34.08201495
Line 2: UPP Si -28.03211675
Line 3: BETAS Si -5.01104521
Line 4: BETAP Si -2.23153969
Line 5: ZS Si 1.28184511
Line 6: ZP Si 1.84073175
Line 7: ALP Si 2.18688712
Line 8: GSS Si 9.82
Line 9: GPP Si 7.31
Line 10: GSP Si 8.36
Line 11: GP2 Si 6.54
Line 12: HSP Si 1.32
Derived parameters do no need to be entered; they will be calculated from the optimized
parameters. All "constants" such as the experimental heat of atomization are already inserted for
all elements.
NOTE: EXTERNAL can only be used to input parameters for MNDO, AM1, or PM3. It is
unlikely, however, that any more MINDO/3 parameters will be published.
See also DEP to make a permanent change.
FILL=n (C)
The n'th M.O. in an RHF calculation is constrained to be filled. It has no effect on a UHF
calculation. After the first iteration (NOTE: not after the first SCF calculation, but after the first
iteration within the first SCF calculation) the n'th M.O. is stored, and, if occupied, no further
action is taken at that time. If unoccupied, then the HOMO and the n'th M.O.'s are swapped
around, so that the n'th M.O. is now filled. On all subsequent iterations the M.O. nearest in
character to the stored M.O. is forced to be filled, and the stored M.O. replaced by that M.O.
This is necessitated by the fact that in a reaction a particular M.O. may change its character
considerably. A useful procedure is to run 1SCF and DENOUT first, in order to identify the
M.O.'s; the complete job is then run with OLDENS and FILL=nn, so that the eigenvectors at the
first iteration are fully known. As FILL is known to give difficulty at times, consider also using
C.I.=n and ROOT=m.
FLEPO (O)
The predicted and actual changes in the geometry, the derivatives, and search direction for each
geometry optimization cycle are printed. This is useful if there is any question regarding the
efficiency of the geometry optimizer.
2.3_Definitions_of_keywords__________________________________________________
FMAT
Details of the construction of the Hessian matrix for the force calculation are to be printed.
FORCE (C)
A force-calculation is to be run. The Hessian, that is the matrix (in millidynes per Angstrom) of
second derivatives of the energy with respect to displacements of all pairs of atoms in x, y, and z
directions, is calculated. On diagonalization this gives the force constants for the molecule. The
force matrix, weighted for isotopic masses, is then used for calculating the vibrational frequencies.
The system can be characterized as a ground state or a transition state by the presence of five (for
a linear system) or six eigenvalues which are very small (less than about 30 reciprocal centimeters).
A transition state is further characterized by one, and exactly one, negative force constant.
A FORCE calculation is a prerequisite for a THERMO calculation.
Before a FORCE calculation is started, a check is made to ensure that a stationary point is
being used. This check involves calculating the gradient norm (GNORM) and if it is significant, the
GNORM will be reduced using BFGS. All internal coordinates are optimized, and any symmetry
constraints are ignored at this point. An implication of this is that if the specification of the
geometry relies on any angles being exactly 180 or zero degrees, the calculation may fail.
The geometric definition supplied to FORCE should not rely on angles or dihedrals assuming
exact values. (The test of exact linearity is sufficiently slack that most molecules that are linear,
such as acetylene and but-2-yne, should not be stopped.) See also THERMO, LET, TRANS,
ISOTOPE.
In a FORCE calculation, PRECISE will eliminate quartic contamination (part of the anhar-
monicity). This is normally not important, therefore PRECISE should not routinely be used. In
a FORCE calculation, the SCF criterion is automatically made more stringent; this is the main
cause of the SCF failing in a FORCE calculation.
GEO-OK (W)
Normally the program will stop with a warning message if two atoms are within 0:8 Angstroms of
each other, or, more rarely, the BFGS routine has difficulty optimizing the geometry. GEO-OK
will over-ride the job termination sequence, and allow the calculation to proceed. In practice, most
jobs that terminate due to these checks contain errors in data, so caution should be exercised if
GEO-OK is used. An important exception to this warning is when the system contains, or may
give rise to, a Hydrogen molecule. GEO-OK will override other geometric safety checks such as
the unstable gradient in a geometry optimization preventing reliable optimization.
See also the message "GRADIENTS OF OLD GEOMETRY, GNORM= nn.nnnn".
GNORM=n.nn (W)
The geometry optimization termination criteria in both gradient minimization and energy mini-
mization can be over-ridden by specifying a gradient norm requirement. For example, GNORM=20
would allow the geometry optimization to exit as soon as the gradient norm dropped below 20.0,
the default being 1.0.
For high-precision work, GNORM=0.0 is recommended. Unless LET is also used, the GNORM
will be set to the larger of 0.01 and the specified GNORM. Results from GNORM=0.01 are easily
good enough for all high-precision work.
GRADIENTS (O)
In a 1SCF calculation gradients are not calculated by default: in non-variationally optimized
systems this would take an excessive time. GRADIENTS allows the gradients to be calculated.
______________________________________________________________Keywords_______
Normally, gradients will not be printed if the gradient norm is less than 2.0. However, if GRA-
DIENTS is present, then the gradient norm and the gradients will unconditionally be printed.
Abbreviation: GRAD.
GRAPH (O)
Information needed to generate electron density contour maps can be written to a file by calling
GRAPH. GRAPH first calls MULLIK in order to generate the inverse-square-root of the overlap
matrix, which is required for the re-normalization of the eigenvectors. All data essential for the
graphics package DENSITY are then output.
HESS=n (W)
When the Eigenvector Following routine is used for geometry optimization, it frequently works
faster if the Hessian is constructed first. If HESS=1 is specified, the Hessian matrix will be con-
structed before the geometry is optimized. There are other, less common, options, e.g. HESS=2.
See comments in subroutine EF for details.
H-PRIORITY (O)
In a DRC calculation, results will be printed whenever the calculated heat of formation changes
by 0.1 kcal/mole. Abbreviation: H-PRIO.
H-PRIORITY=n.nn (O)
In a DRC calculation, results will be printed whenever the calculated heat of formation changes
by n.nn kcal/mole.
IRC (C)
An Intrinsic Reaction Coordinate calculation is to be run. All kinetic energy is shed at every point
in the calculation. See Background.
IRC=n (C)
An Intrinsic Reaction Coordinate calculation to be run; an initial perturbation in the direction
of normal coordinate n to be applied. If n is negative, then perturbation is reversed, i.e., initial
motion is in the opposite direction to the normal coordinate. This keyword cannot be written
with spaces around the `=' sign.
ISOTOPE (O)
Generation of the FORCE matrix is very time-consuming, and in isotopic substitution studies
several vibrational calculations may be needed. To allow the frequencies to be calculated from the
(constant) force matrix, ISOTOPE is used. When a FORCE calculation is completed, ISOTOPE
will cause the force matrix to be stored, regardless of whether or not any intervening restarts have
been made. To re-calculate the frequencies, etc. starting at the end of the force matrix calculation,
specify RESTART.
The two keywords RESTART and ISOTOPE can be used together. For example, if a normal
FORCE calculation runs for a long time, the user may want to divide it up into stages and save
the final force matrix. Once ISOTOPE has been used, it does not need to be used on subsequent
RESTART runs.
ISOTOPE can also be used with FORCE to set up a RESTART file for an IRC=n calculation.
2.3_Definitions_of_keywords__________________________________________________
ITRY=NN (W)
The default maximum number of SCF iterations is 200. When this limit presents difficulty,
ITRY=nn can be used to re-define it. For example, if ITRY=400 is used, the maximum number
of iterations will be set to 400. ITRY should normally not be changed until all other means of
obtaining a SCF have been exhausted, e.g. PULAY CAMP-KING etc.
IUPD=n (W)
IUPD is used only in the EF routine. IUPD should very rarely be touched. IUPD=1 can be used
in minimum searches if the message
"HEREDITARY POSITIVE DEFINITENESS ENDANGERED. UPDATE SKIPPED THIS CYCLE"
occurs every cycle for 10-20 iterations. Never use IUPD=2 for a TS search! For more information,
read the comments in subroutine EF.
K=(n.nn,n) (C)
Used in band-structure calculations, K=(n.nn,n) specifies the step-size in the Brillouin zone, and
the number of atoms in the monomeric unit. Two band-structure calculations are supported:
electronic and phonon. Both require a polymer to be used. If FORCE is used, a phonon spectrum
is assumed, otherwise an electronic band structure is assumed. For both calculations, a density of
states is also done. The band structure calculation is very fast, so a small step-size will not use
much time.
The output is designed to be fed into a graphics package, and is not `elegant'. For polyethylene,
a suitable keyword would be K=(0.01,6).
KINETIC=n.nnn (C)
In a DRC calculation n.nnn kcals/mole of excess kinetic energy is added to the system as soon as
the kinetic energy builds up to 0.2 kcal/mole. The excess energy is added to the velocity vector,
without change of direction.
LARGE (O)
Most of the time the output invoked by keywords is sufficient. LARGE will cause less-commonly
wanted, but still useful, output to be printed.
1. To save space, DRC and IRC outputs will, by default, only print the line with the percent
sign. Other output can be obtained by use of the keyword LARGE, according to the following
rules:
LARGE Print all internal and cartesian coordinates and cartesian velocities.
LARGE=1 Print all internal coordinates.
LARGE=-1 Print all internal and cartesian coordinates and cartesian velocities.
LARGE=n Print every n'th set of internal coordinates.
LARGE=-n Print every n'th set of internal and cartesian coordinates and cartesian velocities.
If LARGE=1 is used, the output will be the same as that of Version 5.0, when LARGE was
not used. If LARGE is used, the output will be the same as that of Version 5.0, when LARGE
was used. To save disk space, do not use LARGE.
______________________________________________________________Keywords_______
LINMIN (O)
There are two line-minimization routines in MOPAC, an energy minimization and a gradient norm
minimization. LINMIN will output details of the line minimization used in a given job.
LET (W)
As MOPAC evolves, the meaning of LET is changing.
Now LET means essentially "I know what I'm doing, override safety checks".
Currently, LET has the following meanings:
1. In a FORCE calculation, it means that the supplied geometry is to be used, even if the
gradients are large.
2. In a geometry optimization, the specified GNORM is to be used, even if it is less than 0.01.
3. In a POLAR calculation, the molecule is to be orientated along its principal moments of
inertia before the calculation starts. LET will prevent this step being done.
LOCALIZE (O)
The occupied eigenvectors are transformed into a localized set of M.O.'s by a series of 2 by 2
rotations which maximize <_4 >. The value of 1=<_4 > is a direct measure of the number of centers
involved in the MO. Thus the value of 1=<_4 > is 2.0 for H2, 3.0 for a three-center bond and 1.0
for a lone pair. Higher degeneracies than allowed by point group theory are readily obtained.
For example, benzene would give rise to a 6-fold degenerate C-H bond, a 6-fold degenerate C-C
sigma bond and a three-fold degenerate C-C pi bond. In principle, there is no single step method
to unambiguously obtain the most localized set of M.O.'s in systems where several canonical
structures are possible, just as no simple method exists for finding the most stable conformer of
some large compound. However, the localized bonds generated will normally be quite acceptable
for routine applications. Abbreviation: LOCAL.
MAX
In a grid calculation, the maximum number of points (23) in each direction is to be used. The
default is 11. The number of points in each direction can be set with POINTS1 and POINTS2.
MECI (O)
At the end of the calculation details of the Multi Electron Configuration Interaction calculation
are printed if MECI is specified. The state vectors can be printed by specifying VECTORS. The
MECI calculation is either invoked automatically, or explicitly invoked by the use of the C.I.=n
keyword.
MICROS=n (C)
The microstates used by MECI are normally generated by use of a permutation operator. When
individually defined microstates are desired, then MICROS=n can be used, where n defines the
number of microstates to be read in.
Format for Microstates
After the geometry data plus any symmetry data are read in, data defining each microstate is
read in, using format 20I1, one microstate per line. The microstate data is preceded by the word
"MICROS" on a line by itself. There is at present no mechanism for using MICROS with a
reaction path.
2.3_Definitions_of_keywords__________________________________________________
For a system with n M.O.'s in the C.I. (use OPEN=(n1,n) or C.I.=n to do this), the populations
of the n alpha M.O.'s are defined, followed by the n beta M.O.'s. Allowed occupancies are zero
and one. For n=6 the closed-shell ground state would be defined as 111000111000, meaning one
electron in each of the first three alpha M.O.'s, and one electron in each of the first three beta
M.O.'s.
Users are warned that they are responsible for completing any spin manifolds. Thus while the
state 111100110000 is a triplet state with component of spin = 1, the state 111000110100, while
having a component of spin = 0 is neither a singlet nor a triplet. In order to complete the spin
manifold the microstate 110100111000 must also be included.
If a manifold of spin states is not complete, then the eigenstates of the spin operator will not
be quantized. When and only when 100 or fewer microstates are supplied, can spin quantization
be conserved.
There are two other limitations on possible microstates. First, the number of electrons in
every microstate should be the same. If they differ, a warning message will be printed, and the
calculation continued (but the results will almost certainly be nonsense). Second, the component
of spin for every microstate must be the same, except for teaching purposes. Two microstates of
different components of spin will have a zero matrix element connecting them. No warning will
be given as this is a reasonable operation in a teaching situation. For example, if all states arising
from two electrons in two levels are to be calculated, say for teaching Russel-Saunders coupling,
then the following microstates would be used:
Microstate No. of alpha, beta electrons Ms State
1100 2 0 1 Triplet
1010 1 1 0 Singlet
1001 1 1 0 Mixed
0110 1 1 0 Mixed
0101 1 1 0 Singlet
0011 0 2 -1 Triplet
Constraints on the space manifold are just as rigorous, but much easier to satisfy. If the energy
levels are degenerate, then all components of a manifold of degenerate M.O.'s should be either
included or excluded. If only some, but not all, components are used, the required degeneracy of
the states will be missing.
As an example, for the tetrahedral methane cation, if the user supplies the microstates corre-
sponding to a component of spin = 3/2, neglecting Jahn-Teller distortion, the minimum number
of states that can be supplied is 90 = (6!=(1!5!))(6!=(4!2!)).
While the total number of electrons should be the same for all microstates, this number does
not need to be the same as the number of electrons supplied to the C.I.; thus in the example
above, a cationic state could be 110000111000.
The format is defined as 20I1 so that spaces can be used for empty M.O.'s.
MINDO/3 (C)
The default Hamiltonian within MOPAC is MNDO, with the alternatives of AM1 and MINDO/3.
To use the MINDO/3 Hamiltonian the keyword MINDO/3 should be used. Acceptable alternatives
to the keyword MINDO/3 are MINDO and MINDO3.
MMOK (C)
If the system contains a peptide linkage, then MMOK will allow a molecular mechanics correc-
tion to be applied so that the barrier to rotation is increased (to 14.00 kcal/mole in N-methyl
acetamide).
______________________________________________________________Keywords_______
MODE (C)
MODE is used in the EF routine. Normally the default MODE=1 is used to locate a transition
state, but if this is incorrect, explicitly define the vector to be followed by using MODE=n.
(MODE is not a recommended keyword). If you use the FORCE option when deciding which
mode to follow, set all isotopic masses to 1.0. The normal modes from FORCE are normally
mass-weighted; this can mislead. Alternatively, use LARGE with FORCE: this gives the force
constants and vectors in addition to the mass-weighted normal modes. Only the mass-weighted
modes can be drawn with DRAW.
MS=n
Useful for checking the MECI calculation and for teaching. MS=n overrides the normal choice
of magnetic component of spin. Normally, if a triplet is requested, an MS of 1 will be used; this
excludes all singlets. If MS=0 is also given, then singlets will also be calculated. The use of MS
should not affect the values of the results at all.
MULLIK (O)
A full Mulliken Population analysis is to be done on the final RHF wavefunction. This involves
the following steps:
1. The eigenvector matrix is divided by the square root of the overlap matrix, S.
2. The Coulson-type density matrix, P , is formed.
3. The overlap population is formed from P (i; j)S(i; j).
4. Half the off-diagonals are added onto the diagonals.
NLLSQ (C)
The gradient norm is to be minimized by Bartel's method. This is a Non-Linear Least Squares
gradient minimization routine. Gradient minimization will locate one of three possible points:
(a) A minimum in the energy surface. The gradient norm will go to zero, and the lowest five
or six eigenvalues resulting from a FORCE calculation will be approximately zero.
(b) A transition state. The gradient norm will vanish, as in (a), but in this case the system is
characterized by one, and only one, negative force constant.
(c) A local minimum in the gradient norm space. In this (normally unwanted) case the gradient
norm is minimized, but does not go to zero. A FORCE calculation will not give the five or six zero
eigenvalues characteristic of a stationary point. While normally undesirable, this is sometimes the
only way to obtain a geometry. For instance, if a system is formed which cannot be characterized
as an intermediate, and at the same time is not a transition state, but nonetheless has some
chemical significance, then that state can be refined using NLLSQ.
NOANCI (W)
RHF open-shell derivatives are normally calculated using Liotard's analytical C.I. method. If
this method is NOT to be used, specify NOANCI (NO ANalytical Configuration Interaction
derivatives).
NODIIS (W)
In the event that the G-DIIS option is not wanted, NODIIS can be used. The G-DIIS normally
accelerates the geometry optimization, but there is no guarantee that it will do so. If the heat
of formation rises unexpectedly (i.e., rises during a geometry optimization while the GNORM is
larger than about 0.3), then try NODIIS.
2.3_Definitions_of_keywords__________________________________________________
NOINTER (O)
The interatomic distances are printed by default. If you do not want them to be printed, specify
NOINTER. For big jobs this reduces the output file considerably.
NOLOG (O)
Normally a copy of the archive file will be directed to the LOG file, along with a synopsis of the
job. If this is not wanted, it can be suppressed completely by NOLOG.
NOMM (C)
All four semi-empirical methods underestimate the barrier to rotation of a peptide bond. A
Molecular Mechanics correction has been added which increases the barrier in N-methyl acetamide
to 14 kcal/mole. If you do not want this correction, specify NOMM (NO Molecular Mechanics).
NONR (W)
Not recommended for normal use. Used with the EF routine. See source code for more details.
NOTHIEL (W)
In a normal geometry optimization using the BFGS routine, Thiel's FSTMIN technique is used.
If normal line-searches are wanted, specify NOTHIEL.
NOXYZ (O)
The cartesian coordinates are printed by default. If you do not want them to be printed, specify
NOXYZ. For big jobs this reduces the output file considerably.
NSURF (C)
In an ESP calculation, NSURF=n specifies the number of surface layers for the Connolly surface.
OLDENS (W)
A density matrix produced by an earlier run of MOPAC is to be used to start the current cal-
culation. This can be used in attempts to obtain an SCF when a previous calculation ended
successfully but a subsequent run failed to go SCF.
OLDGEO (C)
If multiple geometries are to be run, and the final geometry from one calculation is to be used
to start the next calculation, OLDGEO should be specified. Example: If a MNDO, AM1, and
PM3 calculation were to be done on one system, for which only a rough geometry was available,
then after the MNDO calculation, the AM1 calculation could be done using the optimized MNDO
geometry as the starting geometry, by specifying OLDGEO.
OPEN(n1,n2) (C)
The M.O. occupancy during the SCF calculation can be defined in terms of doubly occup-
ied, empty, and fractionally occupied M.O.'s. The fractionally occupied M.O.'s are defined by
OPEN(n1,n2), where n1 = number of electrons in the open-shell manifold, and n2 = number of
open-shell M.O.'s; n1/n2 must be in the range 0 to 2. OPEN(1,1) will be assumed for odd-electron
systems unless an OPEN keyword is used. Errors introduced by use of fractional occupancy are
automatically corrected in a MECI calculation when OPEN(n1,n2) is used.
______________________________________________________________Keywords_______
ORIDE (W)
Do not use this keyword until you have read Simons' article. ORIDE is part of the EF routine,
and means "Use whatever 's are produced even if they would normally be `unacceptable'."
J. Simons, P. Jorgensen, H. Taylor, J. Ozment, J. Phys. Chem. 87:2745 (1983).
PARASOK (W)
Use this keyword with extreme caution! The AM1 method has been parameterized for only a
few elements, less than the number available to MNDO or PM3. If any elements which are not
parameterized at the AM1 level are specified, the MNDO parameters, if available, will be used.
The resulting mixture of methods, AM1 with MNDO, has not been studied to see how good the
results are, and users are strictly on their own as far as accuracy and compatibility with other
methods is concerned. In particular, while all parameter sets are referenced in the output, other
programs may not cite the parameter sets used and thus compatibility with other MNDO programs
is not guaranteed.
PI (O)
The normal density matrix is composed of atomic orbitals, that is s, px, py and pz. PI allows the
user to see how each atom-atom interaction is split into oe and ss bonds. The resulting "density
matrix" is composed of the following basis-functions:- s-oe, p-oe, p-ss, d-oe, d-ss, d-ffi. The on-diagonal
terms give the hybridization state, so that an sp2 hybridized system would be represented as s-oe:
1.0, p-oe: 2.0, p-ss: 1.0.
PM3 (C)
The PM3 method is to be used.
POINT=n (C)
The number of points to be calculated on a reaction path is specified by POINT=n. Used only
with STEP in a path calculation.
POINT1=n (C)
In a grid calculation, the number of points to be calculated in the first direction is given by
POINT1=n. `n' should be less than 24; default: 11.
POINT2=n (C)
In a grid calculation, the number of points to be calculated in the second direction is given by
POINT2=n. `n' should be less than 24, default: 11;
POTWRT (W)
In an ESP calculation, write out surface points and electrostatic potential values to UNIT 21.
POLAR (C)
The polarizability and first and second hyperpolarizabilities are to be calculated. At present this
calculation does not work for polymers, but should work for all other systems. Two different
options are implemented: the older finite field method and a new time-dependent Hartree-Fock
method.
2.3_Definitions_of_keywords__________________________________________________
Time-Dependent Hartree-Fock
This procedure is based on the detailed description given by M. Dupuis and S. Karna (J. Comp.
Chem. 12, 487 (1991)). The program is capable of calculating:
Frequency Dependent Polarizability alpha(-w;w)
Second Harmonic Generation beta(-2w;w,w)
Electrooptic Pockels Effect beta(-w;0,w)
Optical Rectification beta(0;-w,w)
Third Harmonic Generation gamma(-3w;w,w,w)
DC-EFISH gamma(-2w;0,w,w)
Optical Kerr Effect gamma(-w;0,0,w)
Intensity Dependent Index of Refraction gamma(-w;w,-w,w)
The input is given at the end of the MOPAC deck and consists of two lines of free-field input
followed by a list energies. The variables on the first line are:
Nfreq = How many energies will be used to calculate
the desired quantities.
Iwflb = Type of beta calculation to be performed.
This valiable is only important if iterative
beta calculations are chosen.
0 - static
1 - SHG
2 - EOPE
3 - OR
Ibet = Type of beta calculation:
0 - beta(0;0) static
1 - iterative calculation with type of
beta chosen by Iwflb.
1 - Noniterative calculation of SHG
-2 - Noniterative calculation of EOPE
-3 - Noniterative calculation of OR
Igam = Type of gamma calculation:
0 - No gamma calculation
1 - THG
2 - DC-EFISH
3 - IDRI
4 - OKE
The vaiables on the second line are:
Atol = Cutoff tolerance for alpha calculations
(1.0e-4 seems reasonable)
Maxitu = Maximum number of iteractions for beta
calculations
Maxita = Maximum number of iterations for alpha
calculations
Btol = Cutoff tolerance for beta calculations
Nfreq lines follow, each with an energy value in eV's at which the hyperpolarizabilites are to
be calculated.
POWSQ (C)
Details of the working of POWSQ are printed out. This is only useful in debugging.
PRECISE (W)
The criteria for terminating all optimizations, electronic and geometric, are to be increased by
a factor, normally, 100. This can be used where more precise results are wanted. If the results
______________________________________________________________Keywords_______
are going to be used in a FORCE calculation, where the geometry needs to be known quite
precisely, then PRECISE is recommended; for small systems the extra cost in CPU time is minimal.
PRECISE is not recommended for experienced users, instead GNORM=n.nn and SCFCRT=n.nn
are suggested. PRECISE should only very rarely be necessary in a FORCE calculation: all it does
is remove quartic contamination, which only affects the trivial modes significantly, and is very
expensive in CPU time.
PULAY (W)
The default converger in the SCF calculation is to be replaced by Pulay's procedure as soon as
the density matrix is sufficiently stable. A considerable improvement in speed can be achieved
by the use of PULAY. If a large number of SCF calculations are envisaged, a sample calculation
using 1SCF and PULAY should be compared with using 1SCF on its own, and if a saving in
time results, then PULAY should be used in the full calculation. PULAY should be used with
care in that its use will prevent the combined package of convergers (SHIFT, PULAY and the
CAMP-KING convergers) from automatically being used in the event that the system fails to go
SCF in (ITRY-10) iterations.
The combined set of convergers very seldom fails.
QUARTET (C)
RHF interpretation: The desired spin-state is a quartet, i.e., the state with component of spin =
1/2 and spin = 3/2. When a configuration interaction calculation is done, all spin states of spin
equal to, or greater than 1/2 are calculated simultaneously, for component of spin = 1/2. From
these states the quartet states are selected when QUARTET is specified, and all other spin states,
while calculated, are ignored in the choice of root to be used. If QUARTET is used on its own,
then a single state, corresponding to an alpha electron in each of three M.O.'s is calculated.
UHF interpretation: The system will have three more alpha electrons than beta electrons.
QUINTET (C)
RHF interpretation: The desired spin-state is a quintet, that is, the state with component of spin
= 0 and spin = 2. When a configuration interaction calculation is done, all spin states of spin
equal to, or greater than 0 are calculated simultaneously, for component of spin = 0. From these
states the quintet states are selected when QUINTET is specified, and the septet states, while
calculated, will be ignored in the choice of root to be used. If QUINTET is used on its own, then
a single state, corresponding to an alpha electron in each of four M.O.'s is calculated.
UHF interpretation: The system will have three more alpha electrons than beta electrons.
RECALC=n
RECALC=n calculates the Hessian every n steps in the EF optimization. For small n this is costly
but is also very effective in terms of convergence. RECALC=10 and DMAX=0.10 can be useful
for difficult cases. In extreme cases RECALC=1 and DMAX=0.05 will always find a stationary
point, if it exists.
RESTART (W)
When a job has been stopped, for whatever reason, and intermediate results have been stored,
then the calculation can be restarted at the point where it stopped by specifying RESTART. The
most common cause of a job stopping before completion is its exceeding the time allocated. A
saddle-point calculation has no restart, but the output file contains information which can easily
be used to start the calculation from a point near to where it stopped.
2.3_Definitions_of_keywords__________________________________________________
It is not necessary to change the geometric data to reflect the new geometry. As a result, the
geometry printed at the start of a restarted job will be that of the original data, not that of the
restarted file. A convenient way to monitor a long run is to specify 1SCF and RESTART; this
will give a normal output file at very little cost.
Note 1: In the FORCE calculation two restarts are possible. These are (a) a restart in FLEPO if
the geometry was not optimized fully before FORCE was called, and (b) the normal restart
in the construction of the force matrix. If the restart is in FLEPO within FORCE then the
keyword FORCE should be deleted, and the keyword RESTART used on its own. Forgetting
this point is a frequent cause of failed jobs.
Note 2: Two restarts also exist in the IRC calculation. If an IRC calculation stops while in the
FORCE calculation, then a normal restart can be done. If the job stops while doing the IRC
calculation itself then the keyword IRC=n should be changed to IRC, or it can be omitted if
DRC is also specified. The absence of the string "IRC=" is used to indicate that the FORCE
calculation was completed before the restart files were written.
ROOT=n (C)
The n'th root of a C.I. calculation is to be used in the calculation. If a keyword specifying the
spin-state is also present, e.g. SINGLET or TRIPLET, then the n'th root of that state will be
selected. Thus ROOT=3 and SINGLET will select the third singlet root. If ROOT=3 is used on
its own, then the third root will be used, which may be a triplet, the third singlet, or the second
singlet (the second root might be a triplet). In normal use, this keyword would not be used. It is
retained for educational and research purposes. Unusual care should be exercised when ROOT=
is specified.
ROT=n (C)
In the calculation of the rotational contributions to the thermodynamic quantities the symmetry
number of the molecule must be supplied. The symmetry number of a point group is the number of
equivalent positions attainable by pure rotations. No reflections or improper rotations are allowed.
This number cannot be assumed by default, and may be affected by subtle modifications to the
molecule, such as isotopic substitution. A list of the most important symmetry numbers follows:
---- TABLE OF SYMMETRY NUMBERS ----
C1 CI CS 1 D2 D2D D2H 4 C(INF)V 1
C2 C2V C2H 2 D3 D3D D3H 6 D(INF)H 2
C3 C3V C3H 3 D4 D4D D4H 8 T TD 12
C4 C4V C4H 4 D6 D6D D6H 12 OH 24
C6 C6V C6H 6 S6 3
SADDLE (C)
The transition state in a simple chemical reaction is to be optimized. Extra data are required.
After the first geometry, specifying the reactants, and any symmetry functions have been defined,
the second geometry, specifying the products, is defined, using the same format as that of the first
geometry.
SADDLE often fails to work successfully. Frequently this is due to equivalent dihedral angles
in the reactant and product differing by about 360 degrees rather than zero degrees. As the choice
of dihedral can be difficult, users should consider running this calculation with the keyword XYZ.
There is normally no ambiguity in the definition of cartesian coordinates. See also BAR=.
Many of the bugs in SADDLE have been removed in this version. Use of the XYZ option is
strongly recommended.
______________________________________________________________Keywords_______
SCALE (C)
SCALE=n.n specifies the scaling factor for Van der Waals' radii for the initial layer of the Connolly
surface in the ESP calculation.
SCFCRT=n.nn (W)
The default SCF criterion is to be replaced by that defined by SCFCRT=.
The SCF criterion is the change in energy in kcal/mol on two successive iterations. Other
minor criteria may make the requirements for an SCF slightly more stringent. The SCF criterion
can be varied from about 0.001 to 1.D-25, although numbers in the range 0.0001 to 1.D-9 will
suffice for most applications.
An overly tight criterion can lead to failure to achieve a SCF, and consequent failure of the
run.
SCINCR=n.nn
In an ESP calculation, SCINCR=n.nn specifies the increment between layers of the surface in the
Connolly surface. (default: 0.20)
SETUP (C)
If, on the keyword line, the word `SETUP' is specified, then one or two lines of keywords will
be read from a file with the logical name SETUP. The logical file SETUP must exist, and must
contain at least one line. If the second line is defined by the first line as a keyword line, and the
second line contains the word SETUP, then one line of keywords will be read from a file with the
logical name SETUP.
SETUP=name (C)
Same as SETUP, only the logical or actual name of the SETUP file is `name'.
SEXTET (C)
RHF interpretation: The desired spin-state is a sextet: the state with component of spin = 1/2
and spin = 5/2.
The sextet states are the highest spin states normally calculable using MOPAC in its unmodi-
fied form. If SEXTET is used on its own, then a single state, corresponding to one alpha electron
in each of five M.O.'s, is calculated. If several sextets are to be calculated, say the second or third,
then OPEN(n1,n2) should be used.
UHF interpretation: The system will have five more alpha electrons than beta electrons.
SHIFT=n.nn (W)
In an attempt to obtain an SCF by damping oscillations which slow down the convergence or
prevent an SCF being achieved, the virtual M.O. energy levels are shifted up or down in energy
by a shift technique. The principle is that if the virtual M.O.'s are changed in energy relative to
the occupied set, then the polarizability of the occupied M.O.'s will change pro rata. Normally,
oscillations are due to autoregenerative charge fluctuations.
The SHIFT method has been re-written so that the value of SHIFT changes automatically
to give a critically-damped system. This can result in a positive or negative shift of the virtual
M.O. energy levels. If a non-zero SHIFT is specified, it will be used to start the SHIFT technique,
rather than the default 15eV. If SHIFT=0 is specified, the SHIFT technique will not be used
unless normal convergence techniques fail and the automatic "ALL CONVERGERS : : :" message
is produced.
2.3_Definitions_of_keywords__________________________________________________
SIGMA (C)
The McIver-Komornicki gradient norm minimization routines, POWSQ and SEARCH are to be
used. These are very rapid routines, but do not work for all species. If the gradient norm is
low, i.e., less than about 5 units, then SIGMA will probably work; in most cases, NLLSQ is
recommended. SIGMA first calculates a quite accurate Hessian matrix, a slow step, then works
out the direction of fastest decent, and searches along that direction until the gradient norm is
minimized. The Hessian is then partially updated in light of the new gradients, and a fresh search
direction found. Clearly, if the Hessian changes markedly as a result of the line-search, the update
done will be inaccurate, and the new search direction will be faulty.
SIGMA should be avoided if at all possible when non-variationally optimized calculations are
being done.
If the Hessian is suspected to be corrupt within SIGMA it will be automatically recalculated.
This frequently speeds up the rate at which the transition state is located. If you do not want the
Hessian to be reinitialized _ it is costly in CPU time _ specify LET on the keyword line.
SINGLET (C)
When a configuration interaction calculation is done, all spin states are calculated simultaneously,
either for component of spin = 0 or 1/2. When only singlet states are of interest, then SINGLET
can be specified, and all other spin states, while calculated, are ignored in the choice of root to be
used.
Note that while almost every even-electron system will have a singlet ground state, SINGLET
should still be specified if the desired state must be a singlet.
SINGLET has no meaning in a UHF calculation, but see also TRIPLET.
SLOPE (C)
In an ESP calculation, SLOPE=n.nn specifies the scale factor for MNDO charges. (default=1.422)
SPIN (O)
The spin matrix, defined as the difference between the alpha and beta density matrices, is to be
printed. If the system has a closed-shell ground state, e.g. methane run UHF, the spin matrix
will be null.
If SPIN is not requested in a UHF calculation, then the diagonal of the spin matrix, that is
the spin density on the atomic orbitals, will be printed.
STEP (C)
In a reaction path, if the path step is constant, STEP can be used instead of explicitly specifying
each point. The number of steps is given by POINT. If the reaction coordinate is an interatomic
distance, only positive STEPs are allowed.
STEP1=n.nnn (C)
In a grid calculation the step size in degrees or Angstroms for the first of the two parameters is
given by n.nnn. By default, an 11 by 11 grid is generated. See POINT1 and POINT2 on how to
adjust this number. The first point calculated is the supplied geometry, and is in the upper left
hand corner. This is a change from Version 5.00, where the supplied geometry was the central
point.
______________________________________________________________Keywords_______
STEP2=n.nnn (C)
In a grid calculation the step size in degrees or Angstroms for the second of the two parameters is
given by n.nnn.
STO3G (W)
In an ESP calculation STO3G means "Use the STO-3G basis set to de-orthogonalize the semiem-
pirical orbitals".
SYMAVG (W)
Used by the ESP, SYMAVG will average charges which should have the same value by symmetry.
SYMMETRY (C)
Symmetry data defining related bond lengths, angles and dihedrals can be included by supplying
additional data after the geometry has been entered. If there are any other data, such as values for
the reaction coordinates, or a second geometry, as required by SADDLE, then it would follow the
symmetry data. Symmetry data are terminated by one blank line. For non-variationally optimized
systems symmetry constraints can save a lot of time because many derivatives do not need to be
calculated. At the same time, there is a risk that the geometry may be wrongly specified, e.g. if
methane radical cation is defined as being tetrahedral, no indication that this is faulty will be given
until a FORCE calculation is run. (This system undergoes spontaneous Jahn-Teller distortion.)
Usually a lower heat of formation can be obtained when SYMMETRY is specified. To see why,
consider the geometry of benzene. If no assumptions are made regarding the geometry, then all
the C-C bond lengths will be very slightly different, and the angles will be almost, but not quite
120 degrees. Fixing all angles at 120 degrees, dihedrals at 180 or 0 degrees, and only optimizing
one C-C and one C-H bond-length will result in a 2-D optimization, and exact D6h symmetry.
Any deformation from this symmetry must involve error, so by imposing symmetry some error is
removed.
The layout of the symmetry data is:
,...
where the numerical code for is given in the table of symmetry functions
below.
For example, ethane, with three independent variables, can be defined as:
SYMMETRY
ETHANE, D3D NA NB NC
C
C 1.528853 1 1
H 1.105161 1 110.240079 1 2 1
H 1.105161 0 110.240079 0 120.000000 0 2 1 3
H 1.105161 0 110.240079 0 240.000000 0 2 1 3
H 1.105161 0 110.240079 0 60.000000 0 1 2 3
H 1.105161 0 110.240079 0 180.000000 0 1 2 3
H 1.105161 0 110.240079 0 300.000000 0 1 2 3
0 0.000000 0 0.000000 0 0.000000 0 0 0 0
3, 1, 4, 5, 6, 7, 8,
3, 2, 4, 5, 6, 7, 8,
Here atom 3, a hydrogen, is used to define the bond lengths (symmetry relation 1) of atoms
4,5,6,7 and 8 with the atoms they are specified to bond with in the NA column of the data file;
2.3_Definitions_of_keywords__________________________________________________
similarly, its angle (symmetry relation 2) is used to define the bond-angle of atoms 4,5,6,7 and 8
with the two atoms specified in the NA and NB columns of the data file. The other angles are
point-group symmetry defined as a multiple of 60 degrees.
Spaces, tabs or commas can be used to separate data. Note that only three parameters are
marked to be optimized. The symmetry data can be the last line of the data file unless more data
follows, in which case a blank line must be inserted after the symmetry data.
The full list of available symmetry relations is as follows:
1 BOND LENGTH IS SET EQUAL TO THE REFERENCE BOND LENGTH
2 BOND ANGLE IS SET EQUAL TO THE REFERENCE BOND ANGLE
3 DIHEDRAL ANGLE IS SET EQUAL TO THE REFERENCE DIHEDRAL ANGLE
4 DIHEDRAL ANGLE VARIES AS 90 DEGREES - REFERENCE DIHEDRAL
5 DIHEDRAL ANGLE VARIES AS 90 DEGREES + REFERENCE DIHEDRAL
6 DIHEDRAL ANGLE VARIES AS 120 DEGREES - REFERENCE DIHEDRAL
7 DIHEDRAL ANGLE VARIES AS 120 DEGREES + REFERENCE DIHEDRAL
8 DIHEDRAL ANGLE VARIES AS 180 DEGREES - REFERENCE DIHEDRAL
9 DIHEDRAL ANGLE VARIES AS 180 DEGREES + REFERENCE DIHEDRAL
10 DIHEDRAL ANGLE VARIES AS 240 DEGREES - REFERENCE DIHEDRAL
11 DIHEDRAL ANGLE VARIES AS 240 DEGREES + REFERENCE DIHEDRAL
12 DIHEDRAL ANGLE VARIES AS 270 DEGREES - REFERENCE DIHEDRAL
13 DIHEDRAL ANGLE VARIES AS 270 DEGREES + REFERENCE DIHEDRAL
14 DIHEDRAL ANGLE VARIES AS THE NEGATIVE OF THE REFERENCE
DIHEDRAL
15 BOND LENGTH VARIES AS HALF THE REFERENCE BOND LENGTH
16 BOND ANGLE VARIES AS HALF THE REFERENCE BOND ANGLE
17 BOND ANGLE VARIES AS 180 DEGREES - REFERENCE BOND ANGLE
18 BOND LENGTH IS A MULTIPLE OF REFERENCE BOND-LENGTH
Function 18 is intended for use in polymers, in which the translation vector may be a multiple
of some bond-length. 1,2,3 and 14 are most commonly used. Abbreviation: SYM.
SYMMETRY is not available for use with cartesian coordinates.
T= (W)
This is a facility to allow the program to shut down in an orderly manner on computers with
execution time cpu limits.
The total cpu time allowed for the current job is limited to nn.nn seconds; by default this is
one hour, i.e., 3600 seconds. If the next cycle of the calculation cannot be completed without
running a risk of exceeding the assigned time the calculation will write a restart file and then stop.
The safety margin is 100 percent; that is, to do another cycle, enough time to do at least two full
cycles must remain.
Alternative specifications of the time are T=nn.nnM, this defines the time in minutes, T=nn.nnH,
in hours, and T=nn.nnD, in days, for very long jobs. This keyword cannot be written with spaces
around the `=' sign.
THERMO (O)
The thermodynamic quantities, internal energy, heat capacity, partition function, and entropy can
be calculated for translation, rotation and vibrational degrees of freedom for a single temperature,
or a range of temperatures. Special situations such as linear systems and transition states are
accommodated. The approximations used in the THERMO calculation are invalid below 100K,
______________________________________________________________Keywords_______
and checking of the lower bound of the temperature range is done to prevent temperatures of less
than 100K being used.
Another limitation, for which no checking is done, is that there should be no internal rotations.
If any exist, they will not be recognized as such, and the calculated quantities will be too low as
a result.
In order to use THERMO the keyword FORCE must also be specified, as well as the value for
the symmetry number; this is given by ROT=n.
If THERMO is specified on its own, then the default values of the temperature range are
assumed. This starts at 200K and increases in steps of 10 degrees to 400K. Three options exist
for overriding the default temperature range. These are:
THERMO(nnn) (O)
The thermodynamic quantities for a 200 degree range of temperatures, starting at nnnK and with
an interval of 10 degrees are to be calculated.
THERMO(nnn,mmm) (O)
The thermodynamic quantities for the temperature range limited by a lower bound of nnn Kelvin
and an upper bound of mmm Kelvin, the step size being calculated in order to give approximately
20 points, and a reasonable value for the step. The size of the step in Kelvin degrees will be 1, 2,
or 5, or a power of 10 times these numbers.
THERMO(nnn,mmm,lll) (O)
Same as for THERMO(nnn,mmm), only now the user can explicitly define the step size. The step
size cannot be less than 1K.
T-PRIORITY (O)
In a DRC calculation, results will be printed whenever the calculated time changes by 0.1 fem-
toseconds. Abbreviation, T-PRIO.
T-PRIORITY=n.nn (O)
In a DRC calculation, results will be printed whenever the calculated time changes by n.nn fem-
toseconds.
TRANS (C)
The imaginary frequency due to the reaction vector in a transition state calculation must not be
included in the thermochemical calculation. The number of genuine vibrations considered can be:
3N - 5 for a linear ground state system, 3N - 6 for a non-linear ground state system, or 3N - 6
for a linear transition-state complex, 3N - 7 for a non-linear transition-state complex.
This keyword must be used in conjunction with THERMO if a transition state is being calcu-
lated.
TRANS=n (C)
The facility exists to allow the THERMO calculation to handle systems with internal rotations.
TRANS=n will remove the n lowest vibrations. Note that TRANS=1 is equivalent to TRANS on
its own. For xylene, for example, TRANS=2 would be suitable.
This keyword cannot be written with spaces around the `=' sign.
2.3_Definitions_of_keywords__________________________________________________
TRIPLET (C)
The triplet state is defined. If the system has an odd number of electrons, an error message will
be printed.
UHF interpretation
The number of alpha electrons exceeds that of the beta electrons by 2. If TRIPLET is not specified,
then the numbers of alpha and beta electrons are set equal. This does not necessarily correspond
to a singlet.
RHF interpretation
An RHF MECI calculation is performed to calculate the triplet state. If no other C.I. keywords
are used, then only one state is calculated by default. The occupancy of the M.O.'s in the SCF
calculation is defined as (: : :2,1,1,0,: : :), that is, one electron is put in each of the two highest
occupied M.O.'s.
See keywords C.I.=n and OPEN(n1,n2).
TS (C)
Within the Eigenvector Following routine, the option exists to optimize a transition state. To do
this, use TS. Preliminary indications are that the TS method is much faster and more reliable
than either SIGMA or NLLSQ.
TS appears to work well with cartesian coordinates.
In the event that TS does not converge on a stationary point, try adding RECALC=5 to the
keyword line.
UHF (C)
The unrestricted Hartree-Fock Hamiltonian is to be used.
VECTORS (O)
The eigenvectors are to be printed. In UHF calculations both alpha and beta eigenvectors are
printed; in all cases the full set, occupied and virtual, are output. The eigenvectors are normalized
to unity, that is the sum of the squares of the coefficients is exactly one. If DEBUG is specified,
then ALL eigenvectors on every iteration of every SCF calculation will be printed. This is useful
in a learning context, but would normally be very undesirable.
VELOCITY (C)
The user can supply the initial velocity vector to start a DRC calculation. Limitations have to be
imposed on the geometry in order for this keyword to work. These are (a) the input geometry must
be in cartesian coordinates, (b) the first three atoms must not be coaxial, (c) triatomic systems
are not allowed (See geometry specification - triatomic systems are in internal coordinates, by
definition.)
Put the velocity vector after the geometry as three data per line, representing the x, y, and z
components of velocity for each atom. The units of velocity are centimeters per second.
The velocity vector will be rotated so as to suit the final cartesian coordinate orientation of
the molecule.
If KINETIC=n.n is also specified, the velocity vector will be scaled to equal the velocity
corresponding to n.n kcal/mole. This allows the user to define the direction of the velocity vector;
the magnitude is given by KINETIC=n.n.
______________________________________________________________Keywords_______
WILLIAMS (C)
Within the ESP calculation, the Connolly surface is used as the default. If the surface generation
procedure of Donald Williams is wanted, the keyword WILLIAMS should be used.
X-PRIORITY (O)
In a DRC calculation, results will be printed whenever the calculated geometry changes by 0.05 A.
The geometry change is defined as the linear sum of the translation vectors of motion for all atoms
in the system. Abbreviation, X-PRIO.
X-PRIORITY=n.nn (O)
In a DRC calculation, results will be printed whenever the calculated geometry changes by n.nn A.
XYZ (W)
The SADDLE calculation quite often fails due to faulty definition of the second geometry because
the dihedrals give a lot of difficulty. To make this option easier to use, XYZ was developed.
A calculation using XYZ runs entirely in cartesian coordinates, thus eliminating the problems
associated with dihedrals. The connectivity of the two systems can be different, but the numbering
must be the same. Dummy atoms can be used; these will be removed at the start of the run. A
new numbering system will be generated by the program, when necessary.
XYZ is also useful for removing dummy atoms from an internal coordinate file; use XYZ and
0SCF.
If a large ring system is being optimized, sometimes the closure is difficult, in which case XYZ
will normally work.
Except for SADDLE, do not use XYZ by default: use it only when something goes wrong!
In order for XYZ to be used, the supplied geometry must either be in cartesian coordinates
or, if internal coordinates are used, symmetry must not be used, and all coordinates must be
flagged for optimization. If dummy atoms are present, only 3N-6 coordinates need to be flagged
for optimization.
If at all possible, the first 3 atoms should be real. Except in SADDLE, XYZ will still work
if one or more dummy atoms occur before the fourth real atom, in which case more than 3N-6
coordinates will be flagged for optimization. This could cause difficulties with the EF method,
which is why dummy atoms at the start of the geometry specification should be avoided. The
coordinates to be optimized depend on the internal coordinate definition of real atoms 1, 2, and 3.
If the position of any of these atoms depends on dummy atoms, then the optimization flags will
be different from the case where the first three atoms defined are all real. The geometry is first
converted to cartesian coordinates and dummy atoms excluded. The cartesian coordinates to be
optimized are:
Atoms R R R R R X R X R X R R R X X X R X X X R X X X
X Y Z X Y Z X Y Z X Y Z X Y Z X Y Z X Y Z X Y Z
Atom 1
2 + + + + + + + + + + + + + + + + +
3 + + + + + + + + + + + + + + + + + + + + + + +
4 on + + + + + + + + + + + + + + + + + + + + + + + +
Where R and X apply to real and dummy atoms in the internal coordinate Z-matrix, and
atoms 1, 2, 3, and 4 are the real atoms in cartesian coordinates. A `+' means that the relevant
coordinate is flagged for optimization. Note that the number of flagged coordinates varies from
3N - 6 to 3N - 3, atom 1 is never optimized.
2.4_Keywords_that_go_together________________________________________________
2.4 Keywords that go together
Normally only a subset of keywords are used in any given piece of research. Keywords which are
related to each other in this way are:
1. In getting an SCF: SHIFT, PULAY, ITRY, CAMP, SCFCRT, 1SCF, PL.
2. In C.I. work: SINGLET, DOUBLET, etc., OPEN(n,m), C.I.=(n,m), LARGE, MECI, MS=n,
VECTORS, ESR, ROOT=n, MICROS.
3. In excited states: UHF with (TRIPLET, QUARTET, etc.), C.I.=n, C.I.=(n,m).
4. In geometry optimization:
(a) Using BFGS: GNORM=n.n, XYZ, PRECISE.
(b) Using EF: GNORM=n.n, XYZ, PRECISE
(c) Using NLLSQ: GNORM=n.n, XYZ, PRECISE
(d) Using SIGMA: GNORM=n.n, XYZ, PRECISE
5. In Gaussian work: AIGIN, AIGOUT, AIDER.
6. In SADDLE: XYZ, BAR=n.n
______________________________________________________________Keywords_______
Chapter 3
Geometry specification
FORMAT: The geometry is read in using essentially "Free-Format" of FORTRAN-77. In fact, a
character input is used in order to accommodate the chemical symbols, but the numeric data can
be regarded as "free-format".indexdata!free-format This means that integers and real numbers can
be interspersed, numbers can be separated by one or more spaces, a tab and/or by one comma.
If a number is not specified, its value is set to zero.
The geometry can be defined in terms of either internal or cartesian coordinates.
3.1 Internal coordinate definition
For any one atom (i) this consists of an interatomic distance in Angstroms from an already-defined
atom (j), an interatomic angle in degrees between atoms i and j and an already defined k, (k and
j must be different atoms), and finally a torsional angle in degrees between atoms i, j, k, and an
already defined atom l (l cannot be the same as k or j). See also dihedral angle coherency.
Exceptions:
1. Atom 1 has no coordinates at all: this is the origin.
2. Atom 2 must be connected to atom 1 by an interatomic distance only.
3. Atom 3 can be connected to atom 1 or 2, and must make an angle with atom 2 or 1 (thus
3-2-1 or 3-1-2); no dihedral is possible for atom 3. By default, atom 3 is connected to atom
2.
3.1.1 Constraints
1. Interatomic distances must be greater than zero. Zero Angstroms is acceptable only if the
parameter is symmetry-related to another atom, and is the dependent function.
2. Angles must be in the range 0.0 to 180.0, inclusive. This constraint is for the benefit of the
user only; negative angles are the result of errors in the construction of the geometry, and
angles greater than 180 degrees are fruitful sources of errors in the dihedrals.
3. Dihedrals angles must be definable. If atom i makes a dihedral with atoms j, k, and l, and
the three atoms j, k, and l are in a straight line, then the dihedral has no definable angle.
During the calculation this constraint is checked continuously, and if atoms j, k, and l lie
within 0.02 Angstroms of a straight line, the calculation will output an error message and
then stop. Two exceptions to this constraint are:
(a) if the angle is zero or 180 degrees, in which case the dihedral is not used.
(b) if atoms j, k, and l lie in an exactly straight line (usually the result of a symmetry
constraint), as in acetylene, acetonitrile, but-2-yne, etc.
____________________________________________________Geometry_specification_____________
If the exceptions are used, care must be taken to ensure that the program does not violate these
constraints during any optimizations or during any calculations of derivatives - see also FORCE.
Conversion to Cartesian Coordinates
By definition, atom 1 is at the origin of cartesian coordinate space_be careful, however, if atom
1 is a dummy atom. Atom 2 is defined as lying on the positive X axis _ for atom 2, Y=0 and
Z=0. Atom 3 is in the X-Y plane unless the angle 3-2-1 is exactly 0 or 180 degrees. Atom 4, 5,
6, etc. can lie anywhere in 3-D space.
3.2 Gaussian Z-matrices
With certain limitations, geometries can now be specified within MOPAC using the Gaussian
Z-matrix format.
Exceptions to the full Gaussian standard
1. The option of defining an atom's position by one distance and two angles is not allowed. In
other words, the N4 variable described in the Gaussian manual must either be zero or not
specified. MOPAC requires the geometry of atoms to be defined in terms of, at most, one
distance, one angle, and one dihedral.
2. Gaussian cartesian coordinates are not supported.
3. Chemical symbols must not be followed by an integer identifying the atom. Numbers after
a symbol are used by MOPAC to indicate isotopic mass. If labels are desired, they should
be enclosed in parentheses, thus "Cl(on C5)34.96885".
4. The connectivity (N1, N2, N3) must be integers. Labels are not allowed.
Specification of Gaussian Z-matrices
The information contained in the Gaussian Z-matrix is identical to that in a MOPAC Z-matrix.
The order of presentation is different. Atom N, (real or dummy) is specified in the format:
Element N1 Length N2 Alpha N3 Beta
where Element is the same as for the MOPAC Z-matrix. N1, N2, and N3 are the connectivity, the
same as the MOPAC Z-matrix NA, NB, and NC: bond lengths are between N and N1, angles are
between N, N1 and N2, and dihedrals are between N, N1, N2, and N3. The same rules apply to
N1, N2, and N3 as to NA, NB, and NC.
Length, Alpha, and Beta are the bond lengths, the angle, and dihedral. They can be `real',
e.g. 1.45, 109.4, 180.0, or `symbolic'. A symbolic is an alphanumeric string of up to 8 characters,
e.g. R51, A512, D5213, CH, CHO, CHOC, etc. Two or more symbolics can be the same. Dihedral
symbolics can optionally be preceeded by a minus sign, in which case the value of the dihedral is the
negative of the value of the symbolic. This is the equivalent of the normal MOPAC SYMMETRY
operations 1, 2, 3, and 14.
If an internal coordinate is real, it will not be optimized. This is the equivalent of the MOPAC
optimization flag "0". If an internal coordinate is symbolic, it can be optimized.
The Z-matrix is terminated by a blank line, after which comes the starting values of the
symbolics, one per line. If there is a blank line in this set, then all symbolics after the blank line
are considered fixed; that is, they will not be optimized. The set before the blank line will be
optimized.
Example of Gaussian Z-matrix geometry specification
3.3_Cartesian_coordinate_definition____________________________________________________
Line 1 AM1
Line 2 Ethane
Line 3
Line 4 C
Line 5 C 1 r21
Line 6 H 2 r32 1 a321
Line 7 H 2 r32 1 a321 3 d4213
Line 8 H 2 r32 1 a321 3 -d4213
Line 9 H 1 r32 2 a321 3 60.
Line 10 H 1 r32 2 a321 3 180.
Line 11 H 1 r32 2 a321 3 d300
Line 12
Line 13 r21 1.5
Line 14 r32 1.1
Line 15 a321 109.5
Line 16 d4313 120.0
Line 17
Line 18 d300 300.0
Line 19
3.3 Cartesian coordinate definition
A definition of geometry in cartesian coordinates consists of the chemical symbol or atomic number,
followed by the cartesian coordinates and optimization flags but no connectivity.
MOPAC uses the lack of connectivity to indicate that cartesian coordinates are to be used.
A unique case is the triatomics for which only internal coordinates are allowed. This is to avoid
conflict of definitions: the user does not need to define the connectivity of atom 2, and can elect to
use the default connectivity for atom 3. As a result, a triatomic may have no explicit connectivity
defined, the user thus taking advantage of the default connectivity. Since internal coordinates are
more commonly used than cartesian, the above choice was made.
If the keyword XYZ is absent every coordinate must be marked for optimization. If any
coordinates are not to be optimized, the keyword XYZ must be present. The coordinates of all
atoms, including atoms 1, 2 and 3 can be optimized. Dummy atoms should not be used, for
obvious reasons.
3.4 Conversion between various formats
MOPAC can accept any of the following formats: cartesian, MOPAC internal coordinates, and
Gaussian internal coordinates. Both MOPAC and Gaussian Z-matrices can also contain dummy
atoms. Internally, MOPAC works with either a cartesian coordinate set (if XYZ is specified) or
internal coordinates (the default). If the 0SCF option is requested, the geometry defined on input
will be printed in MOPAC Z-matrix format, along with other optional formats.
The type(s) of geometry printed at the end of a 0SCF calculation depend only on the keywords
XYZ, AIGOUT, and NOXYZ. The geometry printed is independent of the type of input geometry,
and therefore makes a convenient conversion mechanism.
If XYZ is present, all dummy atoms are removed and the internal coordinate definition remade.
All symmetry relations are lost if XYZ is used.
If NOXYZ is present, cartesian coordinates will not be printed.
If AIGOUT is present, a data set using Gaussian Z-matrix format is printed.
Note: (1) Only if the keyword XYZ is absent and the keyword SYMMETRY present in a
MOPAC internal coordinate geometry, or two or more internal coordinates in a Gaussian Z-
matrix have the same symbolic will symmetry be present in the MOPAC or Gaussian geometries
____________________________________________________Geometry_specification_____________
output. (2) This expanded use of 0SCF replaces the program DDUM, supplied with earlier copies
of MOPAC.
3.5 Definition of elements and isotopes
Elements are defined in terms of their atomic numbers or their chemical symbols, case insensitive.
Thus, chlorine could be specified as 17, or Cl. In Version 6, only main-group elements and
transition metals for which the `d' shell is full are available.
Acceptable symbols for MNDO are:
Elements Dummy atom, sparkles and
Translation Vector
H
Li * B C N O F
Na' * Al Si P S Cl + o
K' * ... Zn * Ge * * Br XX Cb ++ + -- - Tv
Rb' * ... * * Sn * * I 99 102 103 104 105 106 107
* * ... Hg * Pb *
' These symbols refer to elements which lack a basis set.
+ This is the dummy atom for assisting with geometry specification.
* Element not parameterized.
o This is the translation vector for use with polymers.
Old parameters for some elements are available. These are provided to allow compatibility with
earlier copies of MOPAC. To use these older parameters, use a keyword composed of the chemical
symbol followed by the year of publication of the parameters. Keywords currently available:
Si1978, S1978.
For AM1, acceptable symbols are:
Elements Dummy atom, sparkles and
Translation Vector
H
* * B C N O F
Na' * Al Si P S Cl + o
K' * ... Zn * Ge * * Br XX Cb ++ + -- - Tv
Rb' * ... * * Sn * * I 99 102 103 104 105 106 107
* * ... Hg * * *
If users need to use other elements, such as beryllium or lead, they can be specified, in which
case MNDO-type atoms will be used. As the behavior of such systems is not well investigated, users
are cautioned to exercise unusual care. To alert users to this situation, the keyword PARASOK
is defined.
For PM3, acceptable symbols are:
Elements Dummy atom, sparkles and
Translation Vector
H
* Be * C N O F
Na' Mg Al Si P S Cl + o
K' * ... Zn Ga Ge As Se Br XX Cb ++ + -- - Tv
Rb' * ... Cd In Sn Sb Te I 99 102 103 104 105 106 107
* * ... Hg Tl Pb Bi
3.5_Definition_of_elements_and_isotopes________________________________________________
Diatomics Parameterized within the MINDO/3 Formalism
H B C N O F Si P S Cl A star (*) indicates
----------------------------------------- that the atom-pair is
H * * * * * * * * * * parameterized within
B * * * * * * MINDO/3.
C * * * * * * * * * *
N * * * * * * * *
O * * * * * * * *
F * * * * * * *
Si * * *
P * * * * * *
S * * * * * *
Cl * * * * * *
Note: MINDO/3 should now be regarded as being of historical interest only. MOPAC contains
the original parameters. These do not reproduce the original reported results in the case of P, Si,
or S. The original work was faulty, see G. Frenking, H. Goetz, and F. Marschner, J. Am. Chem.
Soc., 100:5295 (1978). Re-optimized parameters for P-C and P-Cl were derived later which gave
better results. These are:
o Alpha(P-C): 0.8700 G. Frenking, H. Goetz, F. Marschner,
o Beta(P-C): 0.5000 J. Am. Chem. Soc., 100:5295-5296 (1978).
o Alpha(P-Cl): 1.5400 G. Frenking, F. Marschner, H. Goetz,
o Beta(P-Cl): 0.2800 Phosphorus and Sulfur, 8:337-342 (1980).
Although better than the original parameters, these have not been adopted within MOPAC
because to do so at this time would prevent earlier calculations from being duplicated. Parameters
for P-O and P-F have been added: these were abstracted from Frenking's 1980 paper. No
inconsistency is involved as MINDO/3 historically did not have P-O or P-F parameters.
Extra entities available to MNDO, MINDO/3, AM1 and PM3:
+ A 100% ionic alkali metal.
++ A 100% ionic alkaline earth metal.
- A 100% ionic halogen-like atom
-- A 100% ionic group VI-like atom.
Cb A special type of monovalent atom
Elements 103, 104, 105, and 106 are the sparkles; elements 11 and 19 are sparkles tailored to
look like the alkaline metal ions; Tv is the translation vector for polymer calculations. See "Full
description of sparkles" in Chapter 6.
Element 102, symbol Cb, is designed to satisfy valency requirements of atoms for which some
bonds are not completed. Thus in "solid" diamond the usual way to complete the normal valency
in a cluster model is to use hydrogen atoms. This approach has the defect that the electronegativity
of hydrogen is different from that of carbon. The "capped bond" atom, Cb, is designed to satisfy
these valency requirements without acquiring a net charge.
Cb behaves like a monovalent atom, with the exception that it can alter its electronegativity
to achieve an exactly zero charge in whatever environment it finds itself. It is thus all things to all
atoms. On bonding to hydrogen it behaves similar to a hydrogen atom. On bonding to fluorine it
behaves like a very electronegative atom. If several capped bond atoms are used, each will behave
independently. Thus if the two hydrogen atoms in formic acid were replaced by Cb's then each
Cb would independently become electroneutral.
Capped bonds internal coordinates should not be optimized. A fixed bond-length of 1:7 A is
recommended, if two Cb are on one atom, a contained angle of 109:471221 degrees is suggested,
and if three Cb are on one atom, a contained dihedral of -120 degrees (note sign) should be used.
____________________________________________________Geometry_specification_____________
Element 99, X, or XX is known as a dummy atom, and is used in the definition of the geometry;
it is deleted automatically from any cartesian coordinate geometry files. Dummy atoms are pure
mathematic points, and are useful in defining geometries; for example, in ammonia the definition of
C3v symmetry is facilitated by using one dummy atom and symmetry relating the three hydrogens
to it.
Output normally only gives chemical symbols.
Isotopes are used in conjunction with chemical symbols. If no isotope is specified, the average
isotopic mass is used, thus chlorine is 35.453. This is different from some earlier versions of
MOPAC, in which the most abundant isotope was used by default. This change was justified by
the removal of any ambiguity in the choice of isotope. Also, the experimental vibrational spectra
involve a mixture of isotopes. If a user wishes to specify any specific isotope it should immediately
follow the chemical symbol (no space), e.g., H2, H2.0140, C(meta)13, or C13.00335.
The sparkles ++, +, -, and - have no mass; if they are to be used in a force calculation, then
appropriate masses should be used.
Each internal coordinate is followed by an integer, to indicate the action to be taken.
Integer Action
1 Optimize the internal coordinate.
0 Do not optimize the internal coordinate.
-1 Reaction coordinate, or grid index.
Remarks: Only one reaction coordinate is allowed, but this can be made more versatile by the
use of SYMMETRY. If a reaction coordinate is used, the values of the reaction coordinate should
follow immediately after the geometry and any symmetry data. No terminator is required, and
free-format-type input is acceptable.
If two "reaction coordinates" are used, then MOPAC assumes that the two-dimensional space
in the region of the supplied geometry is to be mapped. The two dimensions to be mapped are
in the plane defined by the "-1" labels. Step sizes in the two directions must be supplied using
STEP1 and STEP2 on the keyword line.
Using internal coordinates, the first atom has three unoptimizable coordinates, the second atom
two, (the bond-length can be optimized) and the third atom has one unoptimizable coordinate.
None of these six unoptimizable coordinates at the start of the geometry should be marked for
optimization. If any are so marked, a warning is given, but the calculation will continue.
In cartesian coordinates all parameters can be optimized.
3.6 Examples of coordinate definitions
Two examples will be given. The first is formic acid, HCOOH, and is presented in the normal
style with internal coordinates. This is followed by formaldehyde, presented in such a manner as
to demonstrate as many different features of the geometry definition as possible.
MINDO/3
Formic acid
Example of normal geometry definition
O Atom 1 needs no coordinates.
C 1.20 1 Atom 2 bonds to atom 1.
O 1.32 1 116.8 1 2 1 Atom 3 bonds to atom 2 and
makes an angle with atom 1.
H 0.98 1 123.9 1 0.0 0 3 2 1 Atom 4 has a dihedral of 0.0
with atoms 3, 2 and 1.
H 1.11 1 127.3 1 180.0 0 2 1 3
0 0.00 0 0.0 0 0.0 0 0 0 0
Atom 2, a carbon, is bonded to oxygen by a bond-length of 1.20 Angstroms, and to atom 3,
an oxygen, by a bond-length of 1.32 Angstroms. The O-C-O angle is 116.8 degrees. The first
3.6_Examples_of_coordinate_definitions_________________________________________________
hydrogen is bonded to the hydroxyl oxygen and the second hydrogen is bonded to the carbon
atom. The H-C-O-O dihedral angle is 180 degrees.
MOPAC can generate data-files, both in the Archive files, and at the end of the normal output
file, when a job ends prematurely due to time restrictions. Note that the data are all neatly lined
up. This is, of course, characteristic of machine-generated data, but is useful when checking for
errors.
Format of internal coordinates in ARCHIVE file
O 0.000000 0 0.000000 0 0.000000 0 0 0 0
C 1.209615 1 0.000000 0 0.000000 0 1 0 0
O 1.313679 1 116.886168 1 0.000000 0 2 1 0
H 0.964468 1 115.553316 1 0.000000 0 3 2 1
H 1.108040 1 128.726078 1 180.000000 0 2 1 3
0 0.000000 0 0.000000 0 0.000000 0 0 0 0
Polymers are defined by the presence of a translation vector. In the following example,
polyethylene, the translation vector spans three monomeric units, and is 7.7 Angstroms long.
Note in this example the presence of two dummy atoms. These not only make the geometry defi-
nition easier but also allow the translation vector to be specified in terms of distance only, rather
than both distance and angles.
Example of polymer coordinates from ARCHIVE file:
T=20000
POLYETHYLENE, CLUSTER UNIT : C6H12
C 0.000000 0 0.000000 0 0.000000 0 0 0 0
C 1.540714 1 0.000000 0 0.000000 0 1 0 0
C 1.542585 1 113.532306 1 0.000000 0 2 1 0
C 1.542988 1 113.373490 1 179.823613 1 3 2 1
C 1.545151 1 113.447508 1 179.811764 1 4 3 2
C 1.541777 1 113.859804 1 -179.862648 1 5 4 3
XX 1.542344 1 108.897076 1 -179.732346 1 6 5 4
XX 1.540749 1 108.360151 1 -178.950271 1 7 6 5
H 1.114786 1 90.070026 1 126.747447 1 1 3 2
H 1.114512 1 90.053136 1 -127.134856 1 1 3 2
H 1.114687 1 90.032722 1 126.717889 1 2 4 3
H 1.114748 1 89.975504 1 -127.034513 1 2 4 3
H 1.114474 1 90.063308 1 126.681098 1 3 5 4
H 1.114433 1 89.915262 1 -126.931090 1 3 5 4
H 1.114308 1 90.028131 1 127.007845 1 4 6 5
H 1.114434 1 90.189506 1 -126.759550 1 4 6 5
H 1.114534 1 88.522263 1 127.041363 1 5 7 6
H 1.114557 1 88.707407 1 -126.716355 1 5 7 6
H 1.114734 1 90.638631 1 127.793055 1 6 8 7
H 1.115150 1 91.747016 1 -126.187496 1 6 8 7
Tv 7.746928 1 0.000000 0 0.000000 0 1 7 8
0 0.000000 0 0.000000 0 0.000000 0 0 0 0
____________________________________________________Geometry_specification_____________
Chapter 4
Examples
In this chapter various examples of data-files are described. With MOPAC comes two sets of data
for running calculations. One of these is called MNRSD1.DAT, and this will now be described.
4.1 MNRSD1 test data file for formaldehyde
The following file is suitable for generating the results described in the next section, and would be
suitable for debugging data.
Line 1: SYMMETRY
Line 2: Formaldehyde, for Demonstration Purposes
Line 3:
Line 4: O
Line 5: C 1.2 1
Line 6: H 1.1 1 120 1
Line 7: H 1.1 0 120 0 180 0 2 1 3
Line 8:
Line 9: 3 1 4
Line 10: 3 2 4
Line 11:
These data could be more neatly written as:
Line 1: SYMMETRY
Line 2: Formaldehyde, for Demonstration Purposes
Line 3:
Line 4: O
Line 5: C 1.20 1 1
Line 6: H 1.10 1 120.00 1 2 1
Line 7: H 1.10 0 120.00 0 180.00 0 2 1 3
Line 8:
Line 9: 3, 1, 4,
Line 10: 3, 2, 4,
Line 11:
These two data-files will produce identical results files.
In all geometric specifications, care must be taken in defining the internal coordinates to ensure
that no three atoms being used to define a fourth atom's dihedral angle ever fall into a straight
line. This can happen in the course of a geometry optimization, in a SADDLE calculation or
in following a reaction coordinate. If such a condition should develop, then the position of the
dependent atom would become ill-defined.
______________________________________________________________Examples_______
4.2 MOPAC output for test-data file MNRSD1
****************************************************************************
** FRANK J. SEILER RES. LAB., U.S. AIR FORCE ACADEMY, COLO. SPGS., CO. 80840
****************************************************************************
MNDO CALCULATION RESULTS Note 1
****************************************************************************
* MOPAC: VERSION 6.00 CALC'D. 4-OCT-90 Note 2
* SYMMETRY - SYMMETRY CONDITIONS TO BE IMPOSED
* T= - A TIME OF 3600.0 SECONDS REQUESTED
* DUMP=N - RESTART FILE WRITTEN EVERY 3600.0 SECONDS
********************************************************************043BY043
PARAMETER DEPENDENCE DATA
REFERENCE ATOM FUNCTION NO. DEPENDENT ATOM(S)
3 1 4
3 2 4
DESCRIPTIONS OF THE FUNCTIONS USED
1 BOND LENGTH IS SET EQUAL TO THE REFERENCE BOND LENGTH
2 BOND ANGLE IS SET EQUAL TO THE REFERENCE BOND ANGLE
SYMMETRY Note 3
Formaldehyde, for Demonstration Purposes
ATOM CHEMICAL BOND LENGTH BOND ANGLE TWIST ANGLE
NUMBER SYMBOL (ANGSTROMS) (DEGREES) (DEGREES)
(I) NA:I NB:NA:I NC:NB:NA:I NA NB NC
1 O Note 4
2 C 1.20000 * 1
3 H 1.10000 * 120.00000 * 2 1
4 H 1.10000 120.00000 180.00000 2 1 3
CARTESIAN COORDINATES
NO. ATOM X Y Z
1 O 0.0000 0.0000 0.0000
2 C 1.2000 0.0000 0.0000 Note 5
3 H 1.7500 0.9526 0.0000
4 H 1.7500 -0.9526 0.0000
H: (MNDO): M.J.S. DEWAR, W. THIEL, J. AM. CHEM. SOC., 99, 4899, (1977)
C: (MNDO): M.J.S. DEWAR, W. THIEL, J. AM. CHEM. SOC., 99, 4899, (1977)
O: (MNDO): M.J.S. DEWAR, W. THIEL, J. AM. CHEM. SOC., 99, 4899, (1977)
RHF CALCULATION, NO. OF DOUBLY OCCUPIED LEVELS = 6
INTERATOMIC DISTANCES
O 1 C 2 H 3 H 4
------------------------------------------------------
O 1 0.000000
C 2 1.200000 0.000000
H 3 1.992486 1.100000 0.000000 Note 6
H 4 1.992486 1.100000 1.905256 0.000000
CYCLE: 1 TIME: 0.75 TIME LEFT: 3598.2 GRAD.: 6.349 HEAT:-32.840147
CYCLE: 2 TIME: 0.37 TIME LEFT: 3597.8 GRAD.: 2.541 HEAT:-32.880103
HEAT OF FORMATION TEST SATISFIED Note 7
PETERS TEST SATISFIED Note 8
---------------------------------------------------------------------------
SYMMETRY Note 9
Formaldehyde, for Demonstration Purposes Note 10
4.2_MOPAC_output_for_test-data_file_MNRSD1_____________________________________________
PETERS TEST WAS SATISFIED IN BFGS OPTIMIZATION Note 11
SCF FIELD WAS ACHIEVED Note 12
MNDO CALCULATION Note 13
VERSION 6.00
4-OCT-90
FINAL HEAT OF FORMATION = -32.88176 KCAL Note 14
TOTAL ENERGY = -478.11917 EV
ELECTRONIC ENERGY = -870.69649 EV
CORE-CORE REPULSION = 392.57733 EV
IONIZATION POTENTIAL = 11.04198
NO. OF FILLED LEVELS = 6
MOLECULAR WEIGHT = 30.026
SCF CALCULATIONS = 15
COMPUTATION TIME = 2.740 SECONDS Note 15
ATOM CHEMICAL BOND LENGTH BOND ANGLE TWIST ANGLE
NUMBER SYMBOL (ANGSTROMS) (DEGREES) (DEGREES)
(I) NA:I NB:NA:I NC:NB:NA:I NA NB NC
1 O
2 C 1.21678 * 1 Note 16
3 H 1.10590 * 123.50259 * 2 1
4 H 1.10590 123.50259 180.00000 2 1 3
INTERATOMIC DISTANCES
O 1 C 2 H 3 H 4
------------------------------------------------------
O 1 0.000000
C 2 1.216777 0.000000
H 3 2.046722 1.105900 0.000000
H 4 2.046722 1.105900 1.844333 0.000000
EIGENVALUES
-42.98352 -25.12201 -16.95327 -16.29819 -14.17549 -11.04198 0.85804 3.6768
3.84990 7.12408 Note 17
NET ATOMIC CHARGES AND DIPOLE CONTRIBUTIONS
ATOM NO. TYPE CHARGE ATOM ELECTRON DENSITY
1 O -0.2903 6.2903
2 C 0.2921 3.7079 Note 18
3 H -0.0009 1.0009
4 H -0.0009 1.0009
DIPOLE X Y Z TOTAL
POINT-CHG. 1.692 0.000 0.000 1.692
HYBRID 0.475 0.000 0.000 0.475 Note 19
SUM 2.166 0.000 0.000 2.166
CARTESIAN COORDINATES
NO. ATOM X Y Z
1 O 0.0000 0.0000 0.0000
2 C 1.2168 0.0000 0.0000
3 H 1.8272 0.9222 0.0000
4 H 1.8272 -0.9222 0.0000
ATOMIC ORBITAL ELECTRON POPULATIONS
1.88270 1.21586 1.89126 1.30050 1.25532 0.86217 0.89095 0.69950
1.00087 1.00087 Note 20
TOTAL CPU TIME: 3.11 SECONDS
== MOPAC DONE ==
______________________________________________________________Examples_______
Note 1: The banner indicates whether the calculation uses a MNDO, MINDO/3, AM1 or PM3
Hamiltonian; here, the default MNDO Hamiltonian is used.
Note 2: The Version number is a constant for any release of MOPAC, and refers to the program,
not to the Hamiltonians used. The version number should be cited in any correspondence
regarding MOPAC. Users' own in-house modified versions of MOPAC will have a final digit
different from zero, e.g. 6.01.
All the keywords used, along with a brief explanation, should be printed at this time. If
a keyword is not printed, it has not been recognized by the program. Keywords can be in
upper or lower case letters, or any mixture. The cryptic message at the right end of the
lower line of asterisks indicates the number of heavy and light atoms this version of MOPAC
is configured for.
Note 3: Symmetry information is output to allow the user to verify that the requested symmetry
functions have in fact been recognized and used.
Note 4: The data for this example used a mixture of atomic numbers and chemical symbols, but
the internal coordinate output is consistently in chemical symbols.
The atoms in the system are, in order:
o Atom 1, an oxygen atom; this is defined as being at the origin.
o Atom 2, the carbon atom. Defined as being 1.2 Angstroms from the oxygen atom, it is
located in the +x direction. This distance is marked for optimization.
o Atom 3, a hydrogen atom. It is defined as being 1.1 Angstroms from the carbon atom,
and making an angle of 120 degrees with the oxygen atom. The asterisks indicate that
the bond length and angle are both to be optimized.
o Atom 4, a hydrogen atom. The bond length supplied has been overwritten with the
symmetry-defined C-H bond length. Atom 4 is defined as being 1.1 A from atom 2,
making a bond-angle of 120 degrees with atom 1, and a dihedral angle of 180 degrees
with atom 3.
None of the coordinates of atom 4 are marked for optimization. The bond-length and
angle are symmetry-defined by atom 3, and the dihedral is group-theory symmetry-
defined as being 180 degrees. (The molecule is flat.)
Note 5: The cartesian coordinates are calculated as follows:
Stage 1: The coordinate of the first atom is defined as being at the origin of cartesian
space, while the coordinate of the second atom is defined as being displaced by its defined
bond length along the positive x-axis. The coordinate of the third atom is defined as being
displaced by its bond length in the x-y plane, from either atom 1 or 2 as defined in the data,
or from atom 2 if no numbering is given. The angle it makes with atoms 1 and 2 is that
given by its bond angle.
The dihedral, which first appears in the fourth atom, is defined according to the IUPAC
convention. Note: This is different from previous versions of MNDO and MINDO/3, where
the dihedral had the opposite chirality to that defined by the IUPAC convention.
Stage 2: Any dummy atoms are removed. As this particular system contains no dummy
atoms, nothing is done.
Note 6: The interatomic distances are output for the user's advice, and a simple check made to
insure that the smallest interatomic distance is greater than 0:8 A.
Note 7: The geometry is optimized in a series of cycles, each cycle consisting of a line search and
calculation of the gradients. The time given is the cpu time for the cycle; time left is the
total time requested (here 100 seconds) less the cpu time since the start of the calculation
4.2_MOPAC_output_for_test-data_file_MNRSD1_____________________________________________
(which is earlier than the start of the first cycle!). These times can vary slightly from cycle
to cycle due to different options being used, for example whether or not two or more SCF
calculations need to be done to ensure that the heat of formation is lowered. The gradient
is the scalar length in kcal/mole/Angstrom of the gradient vector.
Note 8: At the end of the BFGS geometry optimization a message is given which indicates how
the optimization ended. All "normal" termination messages contain the word "satisfied";
other terminations may give acceptable results, but more care should be taken, particularly
regarding the gradient vector.
Notes 9, 10: The keywords used, titles and comments are reproduced here to remind the user
of the name of the calculation.
Notes 11, 12: Two messages are given here. The first is a reminder of how the geometry was ob-
tained, whether from the Broyden-Fletcher-Goldfarb-Shanno, Eigenvector Following, Bar-
tel's or the McIver-Komornicki methods. For any further results to be printed the second
message must be as shown; when no SCF is obtained no results will be printed.
Note 13: Again, the results are headed with either MNDO or MINDO/3 banners, and the version
number. The date has been moved to below the version number for convenience.
Note 14: The total energy of the system is the addition of the electronic and nuclear terms. The
heat of formation is relative to the elements in their standard state. The I.P. is the negative
of the energy level of the highest occupied, or highest partially occupied molecular orbital
(in accordance with Koopmans' theorem).
Note 15: Advice on time required for the calculation. This is obviously useful in estimating the
times required for other systems.
Note 16: The fully optimized geometry is printed here. If a parameter is not marked for opti-
mization, it will not be changed unless it is a symmetry-related parameter.
Note 17: The roots are the eigenvalues or energy levels in electron volts of the molecular orbitals.
There are six filled levels, therefore the HOMO has an energy of -11.041eV; analysis of the
corresponding eigenvector (not given here) shows that it is mainly lone-pair on oxygen. The
eigenvectors form an orthonormal set.
Note 18: The charge on an atom is the sum of the positive core charge; for hydrogen, carbon,
and oxygen these numbers are 1.0, 4.0, and 6.0, respectively, and the negative of the number
of valence electrons, or atom electron density on the atom, here 1.0010, 3.7079, and 6.2902
respectively.
Note 19: The dipole is the scalar of the dipole vector in cartesian coordinates. The compo-
nents of the vector coefficients are the point-charge dipole and the hybridization dipole. In
formaldehyde there is no z-dipole since the molecule is flat.
Note 20: MNDO AM1, PM3, and MINDO/3 all use the Coulson density matrix. Only the
diagonal elements of the matrix, representing the valence orbital electron populations, will
be printed, unless the keyword DENSITY is specified.
Extra lines are added as a result of user requests:
1. The total CPU time for the job, excluding loading of the executable, is printed.
2. In order to know that MOPAC has ended, the message == MOPAC DONE == is printed.
______________________________________________________________Examples_______
Chapter 5
Testdata
TESTDATA.DAT, supplied with MOPAC 6.00, is a single large job consisting of several small
systems, which are run one after the other. In order, the calculations run are:
1. A FORCE calculation on formaldehyde. The extra keywords at the start are to be used
later when TESTDATA.DAT acts as a SETUP file. This unusual usage of a data set was
made necessary by the need to ensure that a SETUP file existed. If the first two lines are
removed, the data set used in the example given below is generated.
2. The vibrational frequencies of a highly excited dication of methane are calculated. A non-
degenerate state was selected in order to preserve tetrahedral symmetry (to avoid the Jahn-
Teller effects).
3. Illustration of the use of the & in the keyword line, and of the new optional definition of
atoms 2 and 3
4. Illustration of Gaussian Z-matrix input.
5. An example of Eigenvector Following, to locate a transition state.
6. Use of SETUP. Normally, SETUP would point to a special file which would contain keywords
only. Here, the only file we can guarantee exists, is the file being run, so that is the one used.
7. Example of labelling atoms.
8. This part of the test writes the density matrix to disk, for later use.
9. A simple calculation on water.
10. The previous, optimized, geometry is to be used to start this calculation.
11. The density matrix written out earlier is now used as input to start an SCF.
This example is taken from the first data-file in TESTDATA.DAT, and illustrates the working
of a FORCE calculation.
5.1 Data file for a force calculation
Line 1 nointer noxyz + mndo dump=8
Line 2 t=2000 + thermo(298,298) force isotope
Line 3 ROT=2
Line 4 DEMONSTRATION OF MOPAC - FORCE AND THERMODYNAMICS CALCULATION
Line 5 FORMALDEHYDE, MNDO ENERGY = -32.8819 See Manual.
Line 6 O
______________________________________________________Testdata_____
Line 7 C 1.216487 1 1 0 0
Line 8 H 1.106109 1 123.513310 1 2 1 0
Line 9 H 1.106109 1 123.513310 1 180.000000 1 2 1 3
Line 10 0 0.000000 0 0.000000 0 0.000000 0 0 0 0
5.2 Results file for the force calculation
****************************************************************************
** FRANK J. SEILER RES. LAB., U.S. AIR FORCE ACADEMY, COLO. SPGS., CO. 80840
****************************************************************************
MNDO CALCULATION RESULTS
***************************************************************************
* MOPAC: VERSION 6.00 CALC'D. 12-OCT-90
* T= - A TIME OF 2000.0 SECONDS REQUESTED
* DUMP=N - RESTART FILE WRITTEN EVERY 8.0 SECONDS
* FORCE - FORCE CALCULATION SPECIFIED
* PRECISE - CRITERIA TO BE INCREASED BY 100 TIMES
* NOINTER - INTERATOMIC DISTANCES NOT TO BE PRINTED Note 1
* ISOTOPE - FORCE MATRIX WRITTEN TO DISK (CHAN. 9 )
* NOXYZ - CARTESIAN COORDINATES NOT TO BE PRINTED
* THERMO - THERMODYNAMIC QUANTITIES TO BE CALCULATED
* ROT - SYMMETRY NUMBER OF 2 SPECIFIED
*******************************************************************040BY040
NOINTER NOXYZ + MNDO DUMP=8
T=2000 + THERMO(298,298) FORCE ISOTOPE
ROT=2 PRECISE
DEMONSTRATION OF MOPAC - FORCE AND THERMODYNAMICS CALCULATION
FORMALDEHYDE, MNDO ENERGY = -32.8819 See Manual.
ATOM CHEMICAL BOND LENGTH BOND ANGLE TWIST ANGLE
NUMBER SYMBOL (ANGSTROMS) (DEGREES) (DEGREES)
(I) NA:I NB:NA:I NC:NB:NA:I NA NB NC
ATOM CHEMICAL BOND LENGTH BOND ANGLE TWIST ANGLE
1 O
2 C 1.21649 * 1
3 H 1.10611 * 123.51331 * 2 1
4 H 1.10611 * 123.51331 * 180.00000 * 2 1 3
H: (MNDO): M.J.S. DEWAR, W. THIEL, J. AM. CHEM. SOC., 99, 4899, (1977)
C: (MNDO): M.J.S. DEWAR, W. THIEL, J. AM. CHEM. SOC., 99, 4899, (1977)
O: (MNDO): M.J.S. DEWAR, W. THIEL, J. AM. CHEM. SOC., 99, 4899, (1977)
RHF CALCULATION, NO. OF DOUBLY OCCUPIED LEVELS = 6
HEAT OF FORMATION = -32.881900 KCALS/MOLE
5.2_Results_file_for_the_force_calculation_____________________________________________
INTERNAL COORDINATE DERIVATIVES
ATOM AT. NO. BOND ANGLE DIHEDRAL
1 O
2 C 0.000604
3 H 0.000110 -0.000054
4 H 0.000110 -0.000054 0.000000
GRADIENT NORM = 0.00063 Note 2
TIME FOR SCF CALCULATION = 0.45
TIME FOR DERIVATIVES = 0.32 Note 3
MOLECULAR WEIGHT = 30.03
PRINCIPAL MOMENTS OF INERTIA IN CM(-1)
A = 9.832732 B = 1.261998 C = 1.118449
PRINCIPAL MOMENTS OF INERTIA IN UNITS OF 10**(-40)*GRAM-CM**2
A = 2.846883 B = 22.181200 C = 25.028083
ORIENTATION OF MOLECULE IN FORCE CALCULATION
NO. ATOM X Y Z
1 8 -0.6093 0.0000 0.0000
2 6 0.6072 0.0000 0.0000
3 1 1.2179 0.9222 0.0000
4 1 1.2179 -0.9222 0.0000
FIRST DERIVATIVES WILL BE USED IN THE CALCULATION OF SECOND DERIVATIVES
ESTIMATED TIME TO COMPLETE CALCULATION = 36.96 SECONDS
STEP: 1 TIME = 2.15 SECS, INTEGRAL = 2.15 TIME LEFT: 1997.08
STEP: 2 TIME = 2.49 SECS, INTEGRAL = 4.64 TIME LEFT: 1994.59
STEP: 3 TIME = 2.53 SECS, INTEGRAL = 7.17 TIME LEFT: 1992.06
STEP: 4 TIME = 2.31 SECS, INTEGRAL = 9.48 TIME LEFT: 1989.75
STEP: 5 RESTART FILE WRITTEN, INTEGRAL = 11.97 TIME LEFT: 1987.26
STEP: 6 TIME = 2.43 SECS, INTEGRAL = 14.40 TIME LEFT: 1984.83
STEP: 7 TIME = 2.32 SECS, INTEGRAL = 16.72 TIME LEFT: 1982.51
STEP: 8 TIME = 2.30 SECS, INTEGRAL = 19.02 TIME LEFT: 1980.21
STEP: 9 RESTART FILE WRITTEN, INTEGRAL = 22.17 TIME LEFT: 1977.06
STEP: 10 TIME = 2.52 SECS, INTEGRAL = 24.69 TIME LEFT: 1974.54
______________________________________________________Testdata_____
STEP: 11 TIME = 2.25 SECS, INTEGRAL = 26.94 TIME LEFT: 1972.29
STEP: 12 TIME = 3.15 SECS, INTEGRAL = 30.09 TIME LEFT: 1969.14
FORCE MATRIX IN MILLIDYNES/ANGSTROM
0
O 1 C 2 H 3 H 4
------------------------------------------------------
O 1 9.557495
C 2 8.682982 11.426823
H 3 0.598857 2.553336 3.034881
H 4 0.598862 2.553344 0.304463 3.034886
HEAT OF FORMATION = -32.881900 KCALS/MOLE
ZERO POINT ENERGY 18.002 KILOCALORIES PER MOLE Note 4
THE LAST 6 VIBRATIONS ARE THE TRANSLATION AND ROTATION MODES
THE FIRST THREE OF THESE BEING TRANSLATIONS IN X, Y, AND Z, RESPECTIVELY
NORMAL COORDINATE ANALYSIS
Note 5
ROOT NO. 1 2 3 4 5 6
1209.90331 1214.67040 1490.52685 2114.53841 3255.93651 3302.12319
1 0.00000 0.00000 -0.04158 -0.25182 0.00000 0.00067
2 0.06810 0.00001 0.00000 0.00000 0.00409 0.00000
3 0.00000 -0.03807 0.00000 0.00000 0.00000 0.00000
4 0.00000 0.00000 -0.03819 0.32052 0.00000 -0.06298
5 -0.13631 -0.00002 0.00000 0.00000 0.08457 0.00000
6 -0.00002 0.15172 0.00000 0.00000 0.00000 0.00000
7 -0.53308 -0.00005 0.55756 0.08893 -0.39806 0.36994
8 0.27166 0.00003 -0.38524 0.15510 -0.53641 0.57206
9 0.00007 -0.60187 0.00001 0.00000 0.00000 0.00000
10 0.53307 0.00006 0.55757 0.08893 0.39803 0.36997
11 0.27165 0.00003 0.38524 -0.15509 -0.53637 -0.57209
12 0.00007 -0.60187 0.00001 0.00000 0.00000 0.00000
ROOT NO. 7 8 9 10 11 12
-0.00019 -0.00044 -0.00016 3.38368 2.03661 -0.76725
1 0.25401 0.00000 0.00000 0.00000 0.00000 0.00000
2 0.00000 -0.25401 0.00000 0.00000 0.00000 -0.17792
5.2_Results_file_for_the_force_calculation_____________________________________________
3 0.00000 0.00000 -0.25401 0.00000 -0.19832 0.00000
4 0.25401 0.00000 0.00000 0.00000 0.00000 0.00000
5 0.00000 -0.25401 0.00000 0.00000 0.00000 0.17731
6 0.00000 0.00000 -0.25401 0.00000 0.19764 0.00000
7 0.25401 0.00000 0.00000 0.00000 0.00000 -0.26930
8 0.00000 -0.25401 0.00000 0.00000 0.00000 0.35565
9 0.00000 0.00000 -0.25401 0.70572 0.39642 0.00000
10 0.25401 0.00000 0.00000 0.00000 0.00000 0.26930
11 0.00000 -0.25401 0.00000 0.00000 0.00000 0.35565
12 0.00000 0.00000 -0.25401 -0.70572 0.39642 0.00000
MASS-WEIGHTED COORDINATE ANALYSIS
Note 6
ROOT NO. 1 2 3 4 5 6
1209.90331 1214.67040 1490.52685 2114.53841 3255.93651 3302.12319
1 0.00000 0.00000 -0.16877 -0.66231 0.00000 0.00271
2 0.26985 0.00003 0.00000 0.00000 0.01649 0.00000
3 0.00002 -0.15005 0.00000 0.00000 0.00000 0.00000
4 0.00000 0.00000 -0.13432 0.73040 0.00001 -0.22013
5 -0.46798 -0.00005 0.00000 0.00000 0.29524 0.00001
6 -0.00006 0.51814 0.00000 0.00000 0.00000 0.00000
7 -0.53018 -0.00005 0.56805 0.05871 -0.40255 0.37455
8 0.27018 0.00003 -0.39249 0.10238 -0.54246 0.57918
9 0.00007 -0.59541 0.00001 0.00000 0.00000 0.00000
10 0.53018 0.00006 0.56806 0.05871 0.40252 0.37457
11 0.27018 0.00003 0.39249 -0.10238 -0.54242 -0.57922
12 0.00007 -0.59541 0.00001 0.00000 0.00000 0.00000
Note 7
ROOT NO. 7 8 9 10 11 12
-0.00025 -0.00022 -0.00047 3.38368 2.03661 -0.76725
1 0.72996 0.00000 0.00000 0.00000 0.00000 0.00000
2 0.00000 -0.72996 0.00000 0.00000 0.00000 -0.62774
3 0.00000 0.00000 -0.72996 0.00000 -0.66681 0.00000
4 0.63247 0.00000 0.00000 0.00000 0.00000 0.00000
5 0.00000 -0.63247 0.00000 0.00000 0.00000 0.54204
6 0.00000 0.00000 -0.63247 0.00000 0.57578 0.00000
7 0.18321 0.00000 0.00000 0.00000 0.00000 -0.23848
8 0.00000 -0.18321 0.00000 0.00000 0.00000 0.31495
9 0.00000 0.00000 -0.18321 0.70711 0.33455 0.00000
10 0.18321 0.00000 0.00000 0.00000 0.00000 0.23848
11 0.00000 -0.18321 0.00000 0.00000 0.00000 0.31495
12 0.00000 0.00000 -0.18321 -0.70711 0.33455 0.00000
DESCRIPTION OF VIBRATIONS
______________________________________________________Testdata_____
VIBRATION 1 ATOM PAIR ENERGY CONTRIBUTION RADIAL
FREQ. 1209.90 C 2 -- H 3 42.7% ( 79.4%) 12.6%
T-DIPOLE 0.8545 C 2 -- H 4 42.7% 12.6%
TRAVEL 0.1199 O 1 -- C 2 14.6% 0.0%
RED. MASS 1.9377
VIBRATION 2 ATOM PAIR ENERGY CONTRIBUTION RADIAL
FREQ. 1214.67 C 2 -- H 3 45.1% ( 62.3%) 0.0%
T-DIPOLE 0.1275 C 2 -- H 4 45.1% 0.0%
TRAVEL 0.1360 O 1 -- C 2 9.8% 0.0%
RED. MASS 1.5004
VIBRATION 3 ATOM PAIR ENERGY CONTRIBUTION RADIAL
FREQ. 1490.53 C 2 -- H 4 49.6% ( 61.5%) 0.6%
T-DIPOLE 0.3445 C 2 -- H 3 49.6% 0.6%
TRAVEL 0.1846 O 1 -- C 2 0.9% 100.0%
RED. MASS 0.6639
VIBRATION 4 ATOM PAIR ENERGY CONTRIBUTION RADIAL
FREQ. 2114.54 O 1 -- C 2 60.1% (100.5%) 100.0%
T-DIPOLE 3.3662 C 2 -- H 4 20.0% 17.7%
TRAVEL 0.0484 C 2 -- H 3 20.0% 17.7%
RED. MASS 6.7922
VIBRATION 5 ATOM PAIR ENERGY CONTRIBUTION RADIAL
FREQ. 3255.94 C 2 -- H 3 49.5% ( 72.2%) 98.1%
T-DIPOLE 0.7829 C 2 -- H 4 49.5% 98.1%
TRAVEL 0.1174 O 1 -- C 2 1.0% 0.0%
RED. MASS 0.7508
VIBRATION 6 ATOM PAIR ENERGY CONTRIBUTION RADIAL
FREQ. 3302.12 C 2 -- H 4 49.3% ( 69.8%) 95.5%
T-DIPOLE 0.3478 C 2 -- H 3 49.3% 95.5%
TRAVEL 0.1240 O 1 -- C 2 1.4% 100.0%
RED. MASS 0.6644
SYSTEM IS A GROUND STATE
FORMALDEHYDE, MNDO ENERGY = -32.8819 See Manual.
DEMONSTRATION OF MOPAC - FORCE AND THERMODYNAMICS CALCULATION
MOLECULE IS NOT LINEAR
THERE ARE 6 GENUINE VIBRATIONS IN THIS SYSTEM
THIS THERMODYNAMICS CALCULATION IS LIMITED TO
MOLECULES WHICH HAVE NO INTERNAL ROTATIONS
Note 8
CALCULATED THERMODYNAMIC PROPERTIES
5.2_Results_file_for_the_force_calculation_____________________________________________
*
TEMP. (K) PARTITION FUNCTION H.O.F. ENTHALPY HEAT CAPACITY ENTROPY
KCAL/MOL CAL/MOLE CAL/K/MOL CAL/K/MOL
298 VIB. 1.007 23.39484 0.47839 0.09151
ROT. 709. 888.305 2.981 16.026
INT. 714. 911.700 3.459 16.117
TRA. 0.159E+27 1480.509 4.968 36.113
TOT. -32.882 2392.2088 8.4274 52.2300
* NOTE: HEATS OF FORMATION ARE RELATIVE TO THE
ELEMENTS IN THEIR STANDARD STATE AT 298K
TOTAL CPU TIME: 32.26 SECONDS
== MOPAC DONE ==
Note 1: All three words, ROT, FORCE, and THERMO are necessary in order to obtain thermo-
dynamic properties. In order to obtain results for only one temperature, THERMO has the
first and second arguments identical. The symmetry number for the C2v point-group is 2.
Note 2: Internal coordinate derivatives are in kcal/Angstrom or kcal/radian. Values of less than
about 0.2 are quite acceptable.
Note 3: In larger calculations, the time estimates are useful. In practice they are pessimistic,
and only about 70% of the time estimated will be used, usually. The principal moments of
inertia can be directly related to the microwave spectrum of the molecule. They are simple
functions of the geometry of the system, and are usually predicted with very high accuracy.
Note 4: Zero point energy is already factored into the MNDO parameterization. Force constant
data are not printed by default. If you want this output, specify LARGE in the keywords.
Note 5: Normal coordinate analysis has been extensively changed. The first set of eigenvectors
represent the `normalized' motions of the atoms. The sum of the speeds (not the velocities)
of the atoms adds to unity. This is verified by looking at the motion in the `z' direction of
the atoms in vibration 2. Simple addition of these terms, unsigned, adds to 1.0, whereas to
get the same result for mode 1 the scalar of the motion of each atom needs to be calculated
first.
Users might be concerned about reproducibility. As can be seen from the vibrational fre-
quencies from Version 3.00 to 6.00 given below, the main difference over earlier FORCE
calculations is in the trivial frequencies.
Real Frequencies of Formaldehyde
Version 3.00 1209.96 1214.96 1490.60 2114.57 3255.36 3301.57
Version 3.10 1209.99 1215.04 1490.59 2114.57 3255.36 3301.58
Version 4.00 1209.88 1214.67 1490.52 2114.52 3255.92 3302.10
Version 5.00 1209.89 1214.69 1490.53 2114.53 3255.93 3302.10
Version 6.00 1209.90 1214.67 1490.53 2114.54 3255.94 3302.12
Trivial Frequencies of Formaldehyde
T(x) T(y) T(z) R(x) R(y) R(z)
______________________________________________________Testdata_____
Version 3.00 -0.00517 -0.00054 -0.00285 57.31498 11.59518 9.01619
Version 3.10 -0.00557 0.00049 -0.00194 87.02506 11.18157 10.65295
Version 4.00 -0.00044 -0.00052 -0.00041 12.99014 -3.08110 -3.15427
Version 5.00 0.00040 -0.00044 -0.00062 21.05654 2.80744 3.83712
Version 6.00 -0.00025 -0.00022 -0.00047 3.38368 2.03661 -0.76725
Note 6: Normal modes are not of much use in assigning relative importance to atoms in a mode.
Thus in iodomethane it is not obvious from an examination of the normal modes which
mode represents the C-I stretch. A more useful description is provided by the energy or
mass-weighted coordinate analysis. Each set of three coefficients now represents the relative
energy carried by an atom. (This is not strictly accurate as a definition, but is believed (by
JJPS) to be more useful than the stricter definition.)
Note 7: The following description of the coordinate analysis is given without rigorous justifica-
tion. Again, the analysis, although difficult to understand, has been found to be more useful
than previous descriptions.
On the left-hand side are printed the frequencies and transition dipoles. Underneath these
are the reduced masses and idealized distances traveled which represent the simple harmonic
motion of the vibration. The mass is assumed to be attached by a spring to an infinite mass.
Its displacement is the travel.
The next column is a list of all pairs of atoms that contribute significantly to the energy of
the mode. Across from each pair (next column) is the percentage energy contribution of the
pair to the mode, calculated according to the formula described below.
Formula for energy contribution
The total vibrational energy, T , carried by all pairs of bonded atoms in a molecule is first
calculated. For any given pair of atoms, A and B, the relative contribution, R(A; B), as a
percentage, is given by the energy of the pair, P (A; B), times 100 divided by T , i.e.,
R(A; B) = 100_x_P_(A;_B)_____T
As an example, for formaldehyde the energy carried by the pair of atoms (C,O) is added to
the energy of the two (C,H) pairs to give a total, T . Note that this total cannot be related
to anything which is physically meaningful (there is obvious double-counting), but it is a
convenient artifice. For mode 4, the C=O stretch, the relative contribution of the carbon-
oxygen pair is 60.1%. It might be expected to be about 100% (after all, we envision the C=O
bond as absorbing the photon); however, the fact that the carbon atom is vibrating implies
that it is changing its position relative to the two hydrogen atoms. If the total vibrational
energy, Ev (the actual energy of the absorbed photon, as distinct from T ), were carried
equally by the carbon and oxygen atoms, then the relative contributions to the mode would
be C=O, 50% ; C-H, 25% ; C-H, 25%, respectively. This leads to the next entry, which is
given in parentheses.
For the pair with the highest relative contribution (in mode 4, the C=O stretch), the energy
of that pair divided by the total energy of the mode, Ev , is calculated as a percentage. This
is the absolute contribution, A as a percentage, to the total energy of the mode.
A(A; B) = 100_x_P_(A;_B)_____E
v
Now the C=O is seen to contribute 100.5 percent of the energy. For this sort of partitioning
only the sum of all A's must add to 100%, each pair can contribute more or less than 100%.
5.3_Example_of_reaction_path_with_symmetry_____________________________________________
In the case of a free rotator, e.g. ethane, the A of any specific bonded pair to the total
energy can be very high (several hundred percent).
It may be easier to view P=Ev as a contribution to the total energy of the mode, Ev . In this
case the fact that P=Ev can be greater than unity can be explained by the fact that there
are other relative motions within the molecule which make a negative contribution to Ev .
From the R's an idea can be obtained of where the energy of the mode is going; from the A
value the significance of the highest contribution can be inferred. Thus, in mode 4 all three
bonds are excited, but because the C=O bond carries about 100% of the energy, it is clear
that this is really a C=O bond stretch mode, and that the hydrogens are only going along
for the ride.
In the last column the percentage radial motion is printed. This is useful in assigning the
mode as stretching or bending. Any non-radial motion is de-facto tangential or bending.
To summarize: The new analysis is more difficult to understand, but is considered by the
author (JJPS) to be the easiest way of describing what are often complicated vibrations.
Note 8: In order, the thermodynamic quantities calculated are:
1. The vibrational contribution,
2. The rotational contribution,
3. The sum of (1) and (2), this gives the internal contribution,
4. The translational contribution.
For partition functions the various contributions are multiplied together.
A new quantity is the heat of formation at the defined temperature. This is intended
for use in calculating heats of reaction. Because of a limitation in the data available, the
H.o.F. at T Kelvin is defined as "The heat of formation of the compound at T Kelvin
from it's elements in their standard state at 298 Kelvin". Obviously, this definition
of heat of formation is incorrect, but should be useful in calculating heats of reaction,
where the elements in their standard state at 298 Kelvin drop out.
5.3 Example of reaction path with symmetry
In this example, one methyl group in ethane is rotated relative to the other and the geometry
is optimized at each point. As the reaction coordinate involves three hydrogen atoms moving,
symmetry is imposed to ensure equivalence of all hydrogens.
Line 1: SYMMETRY T=600
Line 2: ROTATION OF METHYL GROUP IN ETHANE
Line 3: EXAMPLE OF A REACTION PATH CALCULATION
Line 4: C
Line 5: C 1.479146 1
Line 6: H 1.109475 1 111.328433 1
Line 7: H 1.109470 0 111.753160 0 120.000000 0 2 1 3
Line 8: H 1.109843 0 110.103163 0 240.000000 0 2 1 3
Line 9: H 1.082055 0 121.214083 0 60.000000 -1 1 2 3
Line 10: H 1.081797 0 121.521232 0 180.000000 0 1 2 3
Line 11: H 1.081797 0 121.521232 0 -60.000000 0 1 2 3
Line 12: 0 0.000000 0 0.000000 0 0.000000 0 0 0 0
Line 13: 3 1 4 5 6 7 8
Line 14: 3 2 4 5 6 7 8
Line 15: 6 7 7
Line 16: 6 11 8
Line 17:
Line 18: 70 80 90 100 110 120 130 140 150
______________________________________________________Testdata_____
Points to note:
1. The dihedrals of the second and third hydrogens are not marked for optimization: the
dihedrals follow from point-group symmetry.
2. All six C-H bond lengths and H-C-C angles are related by symmetry: see lines 13 and 14.
3. The dihedral on line 9 is the reaction coordinate, while the dihedrals on lines 10 and 11 are
related to it by symmetry functions on lines 15 and 16. The symmetry functions are defined
by the second number on lines 13 to 16 (see SYMMETRY for definitions of functions 1, 2,
7, and 11).
4. Symmetry data are ended by a blank line.
5. The reaction coordinate data are ended by the end of file. Several lines of data are allowed.
6. Whenever symmetry is used in addition to other data below the geometry definition it will
always follow the "blank line" immediately following the geometry definition. The other
data will always follow the symmetry data.
Chapter 6
Background
6.1 Introduction
While all the theory used in MOPAC is in the literature, so that in principle one could read and
understand the algorithm, many parts of the code involve programming concepts or constructions
which, while not of sufficient importance to warrant publication, are described here in order to
facilitate understanding.
6.2 AIDER
AIDER will allow gradients to be defined for a system. MOPAC will calculate gradients, as usual,
and will then use the supplied gradients to form an error function. This error function is: (supplied
gradients - initial calculated gradients), which is then added to the computed gradients, so that
for the initial SCF, the apparent gradients will equal the supplied gradients.
A typical data-set using AIDER would look like this:
PM3 AIDER AIGOUT GNORM=0.01 EF
Cyclohexane
X
X 1 1.0
C 1 CX 2 CXX
C 1 CX 2 CXX 3 120.000000
C 1 CX 2 CXX 3 -120.000000
X 1 1.0 2 90.0 3 0.000000
X 1 1.0 6 90.0 2 180.000000
C 1 CX 7 CXX 3 180.000000
C 1 CX 7 CXX 3 60.000000
C 1 CX 7 CXX 3 -60.000000
H 3 H1C 1 H1CX 2 0.000000
H 4 H1C 1 H1CX 2 0.000000
H 5 H1C 1 H1CX 2 0.000000
H 8 H1C 1 H1CX 2 180.000000
H 9 H1C 1 H1CX 2 180.000000
H 10 H1C 1 H1CX 2 180.000000
H 3 H2C 1 H2CX 2 180.000000
H 4 H2C 1 H2CX 2 180.000000
H 5 H2C 1 H2CX 2 180.000000
H 8 H2C 1 H2CX 2 0.000000
___________________________________________________________Background________
H 9 H2C 1 H2CX 2 0.000000
H 10 H2C 1 H2CX 2 0.000000
CX 1.46613
H1C 1.10826
H2C 1.10684
CXX 80.83255
H1CX 103.17316
H2CX 150.96100
AIDER
0.0000
13.7589 -1.7383
13.7589 -1.7383 0.0000
13.7589 -1.7383 0.0000
0.0000 0.0000 0.0000
0.0000 0.0000 0.0000
13.7589 -1.7383 0.0000
13.7589 -1.7383 0.0000
13.7589 -1.7383 0.0000
-17.8599 -2.1083 0.0000
-17.8599 -2.1083 0.0000
-17.8599 -2.1083 0.0000
-17.8599 -2.1083 0.0000
-17.8599 -2.1083 0.0000
-17.8599 -2.1083 0.0000
-17.5612 -0.6001 0.0000
-17.5612 -0.6001 0.0000
-17.5612 -0.6001 0.0000
-17.5612 -0.6001 0.0000
-17.5612 -0.6001 0.0000
-17.5612 -0.6001 0.0000
Each supplied gradient goes with the corresponding internal coordinate. In the example given,
the gradients came from a 3-21G calculation on the geometry shown. Symmetry will be taken into
account automatically. Gaussian prints out gradients in atomic units; these need to be converted
into kcal/mol/Angstrom or kcal/mol/radian for MOPAC to use. The resulting geometry from
the MOPAC run will be nearer to the optimized 3-21G geometry than if the normal geometry
optimizers in Gaussian had been used.
6.3 Correction to the peptide linkage
The residues in peptides are joined together by peptide linkages, -HNCO-. These linkages are
almost flat, and normally adopt a trans configuration; the hydrogen and oxygen atoms being
on opposite sides of the C-N bond. Experimentally, the barrier to interconversion in N-methyl
acetamide is about 14 kcal/mole, but all four methods within MOPAC predict a significantly lower
barrier, PM3 giving the lowest value.
The low barrier can be traced to the tendency of semiempirical methods to give pyramidal
nitrogens. The degree to which pyramidalization of the nitrogen atom is preferred can be seen in
the following series of compounds.
Compound MINDO/3 MNDO AM1 PM3 Exp
Ammonia Py Py Py Py Py
Aniline Py Py Py Py Py
6.4_Level_of_precision_within_MOPAC____________________________________________________
Formamide Py Py Flat Py Py
Acetamide Flat Py Flat Py Flat
N-methyl formamide Flat Py Flat Py Flat
N-methyl acetamide Flat Flat Flat Py Flat
To correct this, a molecular-mechanics correction has been applied. This consists of identifying
the -R-HNCO- unit, and adding a torsion potential of form:
k x sin `2
where ` is the X-N-C-O angle, X=R or H, and k varies from method to method. This has two
effects: there is a force constraining the nitrogen to be planar, and HNCO barrier in N-methyl
acetamide is raised to 14.00 kcal/mole. When the MM correction is in place, the nitrogen atom
for all methods for the last three compounds shown above is planar. The correction should be
user-transparent.
Cautions
1. This correction will lead to errors of 0.5-1.5 kcal/mole if the peptide linkage is made or
broken in a reaction calculation.
2. If the correction is applied to formamide the nitrogen will be flat, contrary to experiment.
3. When calculating rotation barriers, take into account the rapid rehybridization which occurs.
When the dihedral is 0 or 180 degrees the nitrogen will be planar (sp2), but at 90 degrees
the nitrogen should be pyramidal, as the partial double bond is broken. At that geometry
the true transition state involves motion of the nitrogen substituent so that the nitrogen
in the transition state is more nearly sp2. In other words, a simple rotation of the HNCO
dihedral will not yield the activation barrier, however it will be within 2 kcal/mole of the
correct answer. The 14 kcal barrier mentioned earlier refers to the true transition state.
4. Any job involving a CONH group will require either the keyword NOMM or MMOK. If
you do not want the correction to be applied, use the keyword "NOMM" (NO Molecular
Mechanics).
6.4 Level of precision within MOPAC
Several users have criticised the tolerances within MOPAC. The point made is that significantly
different results have been obtained when different starting conditions have been used, even when
the same conformer should have resulted. Of course, different results must be expected _ there
will always be small differences _ nonetheless any differences should be small, e.g. heats of
formation (HoF) differences should be less than about 0.1 kcal/mole. MOPAC has been modified
to allow users to specify a much higher precision than the default when circumstances warrant it.
Reasons for low precision
There are several reasons for obtaining low quality results. The most obvious cause of such errors
is that for general work the default criteria will result in a difference in HoF of less than 0.1
kcal/mole. This is only true for fairly rigid systems, e.g. formaldehyde and benzene. For systems
with low barriers to rotation or flat potential surfaces, e.g. aniline or water dimer, quite large HoF
errors can result.
___________________________________________________________Background________
Various precision levels
In normal (non-publication quality) work the default precision of MOPAC is recommended. This
will allow reasonably precise results to be obtained in a reasonable time. Unless this precision
proves unsatisfactory, use this default for all routine work.
The best way of controlling the precision of the geometry optimization and gradient mini-
mization is by specifying a gradient norm which must be satisfied. This is done via the keyword
GNORM=. Altering the GNORM automatically disables the other termination tests resulting in
the gradient norm dominating the calculation. This works both ways: a GNORM of 20 will give a
very crude optimization while a GNORM of 0.01 will give a very precise optimization. The default
GNORM is 1.0.
When the highest precision is needed, such as in exacting geometry work, or when you
want results which cannot be improved, then use the combination keywords GNORM=0.0 and
SCFCRT=1.D-NN; NN should be in the range 2-15. Increasing the SCF criterion (the default is
SCFCRT=1.D-4) helps the line search routines by increasing the precision of the heat of formation
calculation; however, it can lead to excessive run times, so take care. Also, there is an increased
chance of not achieving an SCF when the SCF criterion is excessively increased.
Superficially, requesting a GNORM of zero might seem excessively stringent, but as soon as
the run starts, it will be cut back to 0.01. Even that might seem too stringent. The geometry
optimization will continue to lower the energy, and hopefully the GNORM, but frequently it will
not prove possible to lower the GNORM to 0.01. If, after 10 cycles, the energy does not drop then
the job will be stopped. At this point you have the best geometry that MOPAC, in its current
form, can give.
If a slightly less than highest precision is needed, such as for normal publication quality work,
set the GNORM to the limit wanted. For example, for a flexible system, a GNORM of 0.1 to 0.5
will normally be good enough for all but the most demanding work.
If higher than the default, but still not very high precision is wanted, then use the keyword
PRECISE. This will tighten up various criteria so that higher than routine precision will be given.
If high precision is used, so that the printed GNORM is 0.000, and the resulting geometry
resubmitted for one SCF and gradients calculation, then normally a GNORM higher than 0.000
will result. This is NOT an error in MOPAC: the geometry printed is only precise to six figures
after the decimal point. Geometries need to be specified to more than six decimals in order to
drive the GNORM to less than 0.000.
If you want to test MOPAC, or use it for teaching purposes, the GNORM lower limit of 0.01 can
be overridden by specifying LET, in which case you can specify any limit for GNORM. However,
if it is too low the job may finish due to an irreducible minimum in the heat of formation being
encountered. If this happens, the "STATIONARY POINT" message will be printed.
Finally there is a full analytical derivative function within MOPAC. These use STO-6G Gaus-
sian wavefunctions because the derivatives of the overlap integral are easier to calculate in Gaus-
sians than in STO's. Consequently, there will be a small difference in the calculated HoFs when
analytical derivatives are used. If there is any doubt about the accuracy of the finite derivatives,
try using the analytical derivatives. They are a bit slower than finite derivatives but are more
precise (a rough estimate is 12 figures for finite difference, 14 for analytical).
Some calculations, mainly open shell RHF or closed shell RHF with C.I. have untracked errors
which prevent very high precision. For these systems GNORM should be in the range 1.0 to 0.1.
How large can a gradient be and still be acceptable?
A common source of confusion is the limit to which the GNORM should be reduced in order to
obtain acceptable results. There is no easy answer, however a few guidelines can be given.
First of all reducing the GNORM to an arbitarily small number is not sensible. If the keywords
GNORM=0.000001, LET, and EF are used, a geometry con be obtained which is precise to about
0.000001 A. If ANALYT is also used, the results obtained will be slightly different. Chemically,
this change is meaningless, and no significance should be attached to such numbers. In addition,
6.5_Convergence_tests_in_subroutine_ITER_______________________________________________
any minor change to the algorithm, such as porting it to a new machine, will give rise to small
changes in the optimized geometry. Even the small changes involved in going from MOPAC 5.00
to MOPAC 6.00 caused small changes in the optimized geometry of test molecules.
As a guide, a GNORM of 0.1 is sufficient for all heat-of-formation work, and a GNORM of 0.01
for most geometry work. If the system is large, you may need to settle for a GNORM of 1.0-0.5.
This whole topic was raised by Dr. Donald B. Boyd of Lilly Research Laboratories, who pro-
vided unequivocal evidence for a failure of MOPAC and convinced me of the importance of in-
creasing precision in certain circumstances.
6.5 Convergence tests in subroutine ITER
Self-consistency test
The SCF iterations are stopped when two tests are satisfied. These are (1) when the difference
in electronic energy, in eV, between any two consecutive iterations drops below the adjustable
parameter, SELCON, and the difference between any three consecutive iterations drops below ten
times SELCON, and (2) the difference in density matrix elements on two successive iterations falls
below a preset limit, which is a multiple of SELCON.
SELCON is set initially to 0.0001 kcal/mole; this can be made 100 times smaller by spec-
ifying PRECISE or FORCE. It can be over-ridden by explicitly defining the SCF criterion via
SCFCRT=1.D-12.
SELCON is further modified by the value of the gradient norm, if known. If GNORM is large,
then a more lax SCF criterion is acceptable, and SCFCRT can be relaxed up to 50 times it's
default value. As the gradient norm drops, the SCF criterion returns to its default value.
The SCF test is performed using the energy calculated from the Fock matrix which arises from
a density matrix, and not from the density matrix which arises from a Fock. In the limit, the
two energies would be identical, but the first converges faster than the second, without loss of
precision.
6.6 Convergence in SCF calculation
A brief description of the convergence techniques used in subroutine ITER follows.
ITER, the SCF calculation, employs six methods to achieve a self-consistent field. In order of
usage, these are:
1. Intrinsic convergence by virtue of the way the calculation is carried out. Thus a trial Fock
gives rise to a trial density matrix, which in turn is used to generate a better Fock matrix.
This is normally convergent, but many exceptions are known. The main situations when the
intrinsic convergence does not work are:
(a) A bad starting density matrix. This normally occurs when the default starting density
matrix is used. This is a very crude approximation, and is only used to get the calcu-
lation started. A large charge is generated on an atom in the first iteration, the second
iteration overcompensates, and an oscillation is generated.
(b) The equations are only very slowly convergent. This can be due to a long-lived oscilla-
tion or to a slow transfer of charge.
2. Oscillation damping. If, on any two consecutive iterations, a density matrix element changes
by more than 0.05, then the density matrix element is set equal to the old element shifted
by 0.05 in the direction of the calculated element. Thus, if on iterations 3 and 4 a certain
density matrix element was 0.55 and 0.78, respectively, then the element would be set to
0.60 (=0.55+0.05) on iteration 4. The density matrix from iteration 4 would then be used
in the construction of the next Fock matrix. The arrays which hold the old density matrices
___________________________________________________________Background________
are not filled until after iteration 2. For this reason they are not used in the damping before
iteration 3.
3. Three-point interpolation of the density matrix. Subroutine CNVG monitors the number
of iterations, and if this is exactly divisible by three, and certain other conditions relating
to the density matrices are satisfied, a three-point interpolation is performed. This is the
default converger, and is very effective with normally convergent calculations. It fails in
certain systems, usually those where significant charge build-up is present.
4. Energy-level shift technique. The virtual M.O. energy levels are normally shifted to more
positive energy. This has the effect of damping oscillations, and intrinsically divergent equa-
tions can often be changed to intrinsically convergent form. With slowly-convergent systems
the virtual M.O. energy levels can be moved to a more negative value.
The precise value of the shift used depends on the behavior of the iteration energy. If it is
dropping, then the HOMO-LUMO gap is reduced, if the iteration energy rises, the gap is
increased rapidly.
5. Pulay's method. If requested, when the largest change in density matrix elements on two
consecutive iterations has dropped below 0.1, then routine CNVG is abandoned in favor of a
multi-Fock matrix interpolation. This relies on the fact that the eigenvectors of the density
and Fock matrices are identical at self-consistency, so [P.F]=0 at SCF. The extent to which
this condition does not occur is a measure of the deviance from self-consistency. Pulay's
method uses this relationship to calculate that linear combination of Fock matrices which
minimize [P.F]. This new Fock matrix is then used in the SCF calculation.
Under certain circumstances, Pulay's method can cause very slow convergence, but some-
times it is the only way to achieve a self-consistent field. At other times the procedure gives
a ten-fold increase in speed, so care must be exercised in its use. (invoked by the keyword
PULAY)
6. The Camp-King converger. If all else fails, the Camp-King converger is just about guaranteed
to work every time. However, it is time-consuming, and therefore should only be invoked as
a last resort.
It evaluates that linear combination of old and current eigenvectors which minimize the total
energy. One of its strengths is that systems which otherwise oscillate due to charge surges,
e.g. CHO-H, the C-H distance being very large, will converge using this very sophisticated
converger.
6.7 Causes of failure to achieve an SCF
In a system where a biradical can form, such as ethane decomposing into two CH3 units, the normal
RHF procedure can fail to go self-consistent. If the system has marked biradicaloid character,
then BIRADICAL or UHF and TRIPLET can often prove successful. These options rely on the
assumption that two unpaired electrons can represent the open shell part of the wave-function.
Consider H-Cl, with the interatomic distance being steadily increased. At first the covalent
bond will be strong, and a self-consistent field is readily obtained. Gradually the bond will
become more ionic, and eventually the charge on chlorine will become very large. The hydrogen,
meanwhile, will become very electropositive, and there will be an increased energy advantage to
any one electron to transfer from chlorine to hydrogen. If this in fact occurred, the hydrogen
would suddenly become very electron-rich and would, on the next iteration, lose its extra electron
to the chlorine. A sustained oscillation would then be initiated. To prevent this, if BIRADICAL
is specified, exactly one electron will end up on hydrogen. A similar result can be obtained by
specifying TRIPLET in a UHF calculation.
6.8_Torsion_or_dihedral_angle_coherency________________________________________________
6.8 Torsion or dihedral angle coherency
MOPAC calculations do not distinguish between enantiomers, consequently the sign of the dihe-
drals can be multiplied by -1 and the calculations will be unaffected. However, if chirality is
important, a user should be aware of the sign convention used.
The dihedral angle convention used in MOPAC is that defined by Klyne and Prelog in Ex-
perientia 16, 521 (1960). In this convention, four atoms, AXYB, with a dihedral angle of 90
degrees, will have atom B rotated by 90 degrees clockwise relative to A when X and Y are lined
up in the direction of sight, X being nearer to the eye. In their words, "To distinguish between
enantiomeric types the angle `tau' is considered as positive when it is measured clockwise from the
front substituent A to the rear substituent B, and negative when it is measured anticlockwise."
The alternative convention was used in all earlier programs, including QCPE 353.
6.9 Vibrational analysis
Analyzing normal coordinates is very tedious. Users are normally familiar with the internal co-
ordinates of the system they are studying, but not familiar with the cartesian coordinates. To
help characterize the normal coordinates, a very simple analysis is done automatically, and users
are strongly encouraged to use this analysis first, and then to look at the normal coordinate
eigenvectors.
In the analysis, each pair of bonded atoms is examined to see if there is a large relative motion
between them. By bonded is meant within the Van der Waals' distance. If there is such a motion,
the indices of the atoms, the relative distance in Angstroms, and the percentage radial motion are
printed. Radial plus tangential motion adds to 100%, but as there are two orthogonal tangential
motions and only one radial, the radial component is printed.
6.10 A note on thermochemistry
By
Tsuneo Hirano
Department of Synthetic Chemistry
Faculty of Engineering
University of Tokyo
Hongo, Bunkyo-ku, Tokyo, Japan
6.10.1 Basic Physical Constants
Taken from: "Quantities, Units and Symbols in Physical Chemistry," Blackwell Scientific Publi-
cations Ltd, Oxford OX2 0EL, UK, 1987 (IUPAC, based on CODATA of ICSU, 1986). pp 81-82.
_______________________________________________________________10
| Speed of light, c = 2:99792458 x 10 cm/s (Definition)-23 -16 |
| Boltzmann constant, k = R=N a = 1:380658-x3104 J/K = 1:380658-x2107 erg/K |
| Planck constant, h = 6:6260755 x 10 J s = 6:6260755 x 10 erg s |
| Gas constant, R = 8:314510 J/mol/K = 1:9872162cal/mol/K3 |
| Avogadro number, Na = 6:0221367 x 10 /mol |
| Volume of 1 mol7of gas, V0 = 22:41410 l/mol (at 1 atm, 25 C) |
| 1 J = 1: x 10 erg |
| 1 kcal = 4:184 kJ (Definition) |
| 1 eV = 23:0606 kcal/mol |
| 1 a.u.-1= 27:21135 eV/mol = 627.509 6 kcal/mol7 |
| 1 cm = 2:859144 cal/mol5= Na hc=4:1846 2 |
|__1_atm_=_1:01325_x_10___Pa_=_1:01325_x_10___dyn/cm___(Definition)_________________|__________________
___________________________________________________________Background________
Moment of inertia: I 1 amu angstrom2 = 1:660540 x 10-40 g cm2 .
Rotational constants: A, B, and C (e.g. A = h=(8ss2 I))
With I in amu angstroms2 then: A (in MHz) = 5:053791 x 105 =I
A (in cm-1 ) = 5:053791 x 105 =cI = 16:85763=I
6.10.2 Thermochemistry from ab initio MO methods
Ab initio MO methods provide total energies, Eeq , as the sum of electronic and nuclear-nuclear
repulsion energies for molecules, isolated in vacuum, without vibration at 0 K.
Eeq = Eel + Enuclear-nuclear (6:1)
>From the 0 K potential surface and using the harmonic oscillator approximation, we can calculate
the vibrational frequencies, i, of the normal modes of vibration. Using these, we can calculate
vibrational, rotational and translational contributions to the thermodynamic quantities such as
the partition function and heat capacity which arise from heating the system from 0 to T K.
Q: partition function, E: energy, S: entropy, and C: heat capacity.
[Vibration]
X 1
Qvib = ________________ (6:2)
i [1 - exp (-h i=kT )]
Evib , for a molecule at the temperature T as:
X aeh i h i exp (-h i=kT ) oe
Evib = _____ + ________________ (6:3)
i 2 [1 - exp (-h i=kT )]
where h is the Planck constant, i the i-th normal vibration frequency, and k the Boltzmann
constant. For 1 mole of molecules, Evib should be multiplied by the Avogadro number Na = R=k.
Thus: X ae oe
Evib = Na h_i__+ _h_i_exp_(-h_i=kT_)_______ (6:4)
i 2 [1 - exp (-h i=kT )]
Note that the first term in equation (6.4) is the Zero-point vibration energy. Hence, the second
term in eq. (6.4) is the additional vibrational contribution due to the temperature increase from
0 K to T K. Namely,
Evib = Ezero + Evib (0 ! T ) (6.5)
X h i
Ezero = Na _____ (6.6)
i 2
X h i exp (-h i=kT )
Evib (0 ! T ) = Na ________________ (6.7)
i [1 - exp (-h i=kT )]
The value of Evib from GAUSSIAN 82 and 86 includes Ezero as defined by Eqs. (6.4,6.7).
X ae(h i=kT ) exp (-h i=kT ) oe
Svib = R _____________________ - ln[1 - exp (-h i=kT )] (6.8)
i [1 - exp (-h ii=kT )]
X ae(h i=kT )2 exp (-h i=kT ) oe
Cvib = R _______________________2 (6.9)
i [1 - exp (-h i=kT )]
At temperature T > 0 K, a molecule rotates about the x, y, and z-axes and translates in x, y,
and z-directions. By assuming the equipartition of energy, energies for rotation and translation,
Erot and Etr, are calculated.
6.10_A_note_on_thermochemistry_______________________________________________
[Rotation]
oe is symmetry number. I is moment of inertia. IA , IB , and IC are moments of inertia about A,
B, and C axes.
Linear molecule
2 IkT
Qrot = 8ss_______oeh2 (6.10)
Erot = (2=2)RT (6.11)
~ 2 ~
Srot = R ln 8ss__IkT__oeh2+ R (6.12)
= R ln I + R ln T - R ln oe - 4:349203
where -4:349203 = R ln[8 x 10-16 ss2 k=(Na h2 )] + R.
Crot = (2=2)R (6:13)
Non-linear molecule
` p __' ~ 2 ~ 3=2 p __________
Qrot = ___ss_oe 8ss__kT__h2 IA IB IC
` p __' ~ ` 2 ' ` 2 ' ` 2 ' ~ 1=2 ` ' 3=2
= ___ss_oe 8ss__cIA__h 8ss__cIB__h 8ss__cIC__h kT__hc (6.14)
Erot = (3=2)RT (6.15)
( ` ' ` 2 ' ` 2 ' ` 2 ' ` ' 3)
Srot = R__2ln _ss__p_ 8ss__cIA__ 8ss__cIB__ 8ss__cIC__ kT__ + (3=2)R (6.16)
oe h h h hc
= (R=2) ln (IA IB IC ) + (3=2)R ln T - R ln oe - 5:3863921
Here, -5:3863921 is calculated as:
( ` -16 ' 3=2 )
p _____________
R ln 1___h310______N (3 x 29 x ss7 x k) + (3=2)R:
a
Crot = (3=2)R (6:17)
[Translation]
M is Molecular weight.
_ p ________________! 3
2ssM kT =Na
Qtra = _________h (6.18)
Etra = (3=2)RT (6.19)
ae ` ' ` ' oe
Stra = R 5_2+ 3_2ln 2ssk_h2 + ln k + 3_2ln M___N + 5_ ln T - ln p (6.20)
a 2
= (5=2)R ln T + (3=2)R ln M - R ln p - 2:31482 (6.21)
Ctra = (5=2)R (6.22)
or Htra = (5=2)RT due to the pV term (cf. H = U + pV ). The internal energy U at T is:
U = Eeq + [Evib + Erot + Etra] (6:23)
___________________________________________________________Background________
or
U = Eeq + [(Ezero + Evib (0 ! T )) + Erot + Etra] (6:24)
Enthalpy H for one mole of gas is defined as
H = U + pV (6:25)
Assumption of an ideal gas (i.e., pV = RT ) leads to
H = U + pV = U + RT (6:26)
Thus, Gibbs free energy G can be calculated as:
G = H - T S(0 ! T ) (6:27)
Thermochemistry in MOPAC
It should be noted that MO parameters for MINDO/3, MNDO, AM1 and PM3 are optimized so
as to reproduce the experimental heat of formation (i.e., standard enthalpy of formation or the
enthalpy change to form a mole of compound at 25 degrees C from its elements in their standard
state) as well as observed geometries (mostly at 25 degrees C), and not to reproduce the Eeq and
equilibrium geometry at 0 K.
In this sense, Escf (defined as Heat of formation), force constants, normal vibration frequencies
etc are all related to the values at 25 degree C, not to 0 K!!!!! Therefore, the Ezero calculated in
FORCE is not the true Ezero . Its use as Ezero should be made at your own risk, bearing in mind
the situation discussed above.
Since Escf is standard enthalpy of formation (at 25 degree C):
X
Escf = Eeq +Ezero +Evib (0 ! 298:15)+Erot +Etra +pV + [-Eelec(atom ) + Hf (atom )] (6:28)
To avoid the complication arising from the definition of Escf, within the thermodynamics calcula-
tion the Standard Enthalpy of Formation, H, is calculated by
H = Escf + (HT - H298 ) (6:29)
Here, Escf is the heat of formation (at 25 degree C) given in the output list, and HT and
H298 are the enthalpy contributions for the increase of the temperature from 0 K to T and 298.15,
respectively. In other words, the enthalpy of formation is corrected for the difference in temperature
from 298.15 K to T . The method of calculation for T and H298 will be given below.
In MOPAC, the variables defined below are used:
C1 = _hc_kT (6:30)
The wavenumber, !i, in cm-1 :
i = !ic (6:31)
EWJ = exp (-h i=kT ) = exp (-!ihc=kT ) = exp (-!iC1 ) (6:32)
The rotational constants A, B, and C in cm-1 :
A = _____h______(8ss2 cI (6:33)
A )
Energy and Enthalpy in cal/mol, and Entropy in cal/mol/K. Thus, eqs. (6.2-6.27) can be
written as follows.
6.10_A_note_on_thermochemistry_______________________________________________
[Vibration]
X 1
Qvib = ss ______________ (6.34)
i (1 - EWJ )
X
E0 = __0:5Na_hc_____4:184!xi107 (6.35)
X i
= 1:429572 !i (6.36)
i
X !iEWJ X WiEWJ
Evib (0 ! T ) = Na hc ____________= (R=k)hc ____________ (6.37)
i 1 - EWJ i 1 - EWJ
X ae !iEWJ oe X
Svib = R(hc=kT ) ______________ - R ln(1 - EWJ )
i (1 - EWJ ) i
X ae !iEWJ oe X
= RC1 ______________ - R ln(1 - EWJ ) (6.38)
i (1 - EWJ ) i
X ae !2 EWJ oe
Cvib = R(hc=kT )2 ____i__________2
i (1 - EWJ )
X ae !2 EWJ oe
= RC21 ___i___________2 (6.39)
i (1 - EWJ )
[Rotation]
Linear molecule
Qrot = (1=oe)(1=A)(kT =hc) = ___1____oeAC (6.40)
1
Erot = (2=2)RT (6.41)
` ' ` ' ` '
Srot = R ln __kT____oehcA+ R = R ln ___1____oeAC+ R = R ln __kT____ + R (6.42)
1 oehcA
Crot = (2=2)R (6.43)
Non-linear molecule
~ ~1=2
Qrot = 1_oe _____ss______(ABCC3 (6.44)
1 )
Erot = (3=2)RT (6.45)
( ` ' 3)
Srot = R__2ln ____ss_____oe2kABCT_hc + (3=2)R
i ss j
= 0:5R3 ln(kT =hc) - 2 ln oe + ln _______ABC+ 3 (6.46)
i ss j
= 0:5R-3 ln C1 - 2 ln oe + ln _______ABC+ 3
Crot = (3=2)R (6.47)
[Translation]
_ p ________________! 3 _ p ______________________ ! 3
2ssM kT =Na 1:660540 x-24 x2ssM kT
Qtra = _________h = _________________________h (6.48)
___________________________________________________________Background________
Etra = (3=2)RT (6.49)
Htra = (3=2)RT + pV = (5=2)RT cf: pV = RT (6.50)
Stra = (R=2)[5 ln T + 3 ln M ] - 2:31482 cf: p = 1atm
= 0:993608[5 ln T + 3 ln M ] - 2:31482 (6.51)
In MOPAC:
Hvib = Evib (0 ! T ) (6:52)
(Note: Ezero is not included in Hvib !i is not derived from force-constants at 0 K) and for T :
HT = [Hvib + Hrot + Htra] (6:53)
while for T = 298:15 K:
H298 = [Hvib + Hrot + Htra] (6:54)
Note that HT (and H298 ) is equivalent to:
(Evib - Ezero ) + Erot + (Etra + pV ) (6:55)
except that the normal frequencies are those obtained from force constants at 25 degree C, or at
least not at 0 K.
Thus, Standard Enthalpy of Formation, H, can be calculated according to Eqs. (6.24,6.25)
and (6.28), as shown in Eq. (6.29);
H = Escf + (HT - H298 ) (6:56)
Note that Ezero is already counted in Escf, see Eq. (6.28).
By using Eq. (6.26), Standard Internal Energy of Formation, U , can be calculated as:
U = H - R(T - 298:15) (6:57)
Standard Gibbs Free-Energy of Formation, G, can be calculated by taking the difference
from that for the isomer or that at different temperature:
G = [ H - T S] (for the state under consideration ) - [ H - T S] (for reference state ) (6:58)
Taking the difference is necessary to cancel the unknown values of standard entropy of formation
for the constituent elements.
6.11 Reaction coordinates
The Intrinsic Reaction Coordinate method pioneered and developed by Mark Gordon has been
incorporated in a modified form into MOPAC. As this facility is quite complicated all the keywords
associated with the IRC have been grouped together in this section.
DRC
The Dynamic Reaction Coordinate is the path followed by all the atoms in a system assuming
conservation of energy, i.e., as the potential energy changes the kinetic energy of the system
changes in exactly the opposite way so that the total energy (kinetic plus potential) is a constant.
If started at a ground state geometry, no significant motion should be seen. Similarly, starting at
a transition state geometry should not produce any motion - after all it is a stationary point and
during the lifetime of a calculation it is unlikely to accumulate enough momentum to travel far
from the starting position.
In order to calculate the DRC path from a transition state, either an initial deflection is
necessary or some initial momentum must be supplied.
Because of the time-dependent nature of the DRC the time elapsed since the start of the
reaction is meaningful, and is printed.
6.11_Reaction_coordinates____________________________________________________
Description
The course of a molecular vibration can be followed by calculating the potential and kinetic
energy at various times. Two extreme conditions can be identified: (a) gas phase, in which the
total energy is a constant through time, there being no damping of the kinetic energy allowed,
and (b) liquid phase, in which kinetic energy is always set to zero, the motion of the atoms being
infinitely damped.
All possible degrees of damping are allowed. In addition, the facility exists to dump energy
into the system, appearing as kinetic energy. As kinetic energy is a function of velocity, a vector
quantity, the energy appears as energy of motion in the direction in which the molecule would
naturally move. If the system is a transition state, then the excess kinetic energy is added after
the intrinsic kinetic energy has built up to at least 0.2 kcal/mole.
For ground-state systems, the excess energy sometimes may not be added; if the intrinsic
kinetic energy never rises above 0.2kcal/mole then the excess energy will not be added.
Equations used
Force acting on any atom:
2 E d3 E
g(i) + g0(i)t + g00(i)t2 = __dE___dx(i)+ __d_____dx(i)2+ ________dx(i)3
Acceleration due to force acting on each atom:
a(i) = ___1___M((i)g(i) + g0(i)t + g00(i)t2 )
New velocity:
2 0 3 00
V (o) + ___1___M (i)Dtg(i) + (1=2)Dt g (i) + (1=3)Dt g (i)
or:
V (i) = V (i) + V 0(i)t + V 00(i)t2 + V 000(i)t3
That is, the change in velocity is equal to the integral over the time interval of the acceleration.
New position of atoms:
X(i) = X(o) + V (o)t + (1=2)V 0t2 + (1=3)V 00t3 + (1=4)V 000t4
That is, the change in position is equal to the integral over the time interval of the velocity.
The velocity vector is accurate to the extent that it takes into account the previous velocity,
the current acceleration, the predicted acceleration, and the change in predicted acceleration over
the time interval. Very little error is introduced due to higher order contributions to the velocity;
those that do occur are absorbed in a re-normalization of the magnitude of the velocity vector
after each time interval.
The magnitude of Dt, the time interval, is determined mainly by the factor needed to re-
normalize the velocity vector. If it is significantly different from unity, Dt will be reduced; if it is
very close to unity, Dt will be increased.
Even with all this, errors creep in and a system, started at the transition state, is unlikely to
return precisely to the transition state unless an excess kinetic energy is supplied, for example
0.2kcal/mole.
The calculation is carried out in cartesian coordinates, and converted into internal coordinates
for display. All cartesian coordinates must be allowed to vary, in order to conserve angular and
translational momentum.
___________________________________________________________Background________
IRC
The Intrinsic Reaction Coordinate is the path followed by all the atoms in a system assuming all
kinetic energy is completely lost at every point, i.e., as the potential energy changes the kinetic
energy generated is annihilated so that the total energy (kinetic plus potential) is always equal to
the potential energy only.
The IRC is intended for use starting with the transition state geometry. A normal coordinate
is chosen, usually the reaction coordinate, and the system is displaced in either the positive
or negative direction along this coordinate. The internal modes are obtained by calculating the
mass-weighted Hessian matrix in a force calculation and translating the resulting cartesian normal
mode eigenvectors to conserve momentum. That is, the initial cartesian coordinates are displaced
by a small amount proportional to the eigenvector coefficients plus a translational constant; the
constant is required to ensure that the total translational momentum of the system is conserved
as zero. At the present time there may be small residual rotational components which are not
annihilated; these are considered unimportant.
General description of the DRC and IRC
As the IRC usually requires a normal coordinate, a force constant calculation normally has to be
done first. If IRC is specified on its own a normal coordinate is not used and the IRC calculation
is performed on the supplied geometry.
A recommended sequence of operations to start an IRC calculation is as follows:
1. Calculate the transition state geometry. If the T/S is not first optimized, then the IRC
calculation may give very misleading results. For example, if NH3 inversion is defined as the
planar system but without the N-H bond length being optimized the first normal coordinate
might be for N-H stretch rather than inversion. In that case the IRC will relax the geometry
to the optimized planar structure.
2. Do a normal FORCE calculation, specifying ISOTOPE in order to save the FORCE matri-
ces. Do not attempt to run the IRC directly unless you have confidence that the FORCE
calculation will work as expected. If the IRC calculation is run directly, specify ISOTOPE
anyway: that will save the FORCE matrix and if the calculation has to be re-done then
RESTART will work correctly.
3. Using IRC=n and RESTART run the IRC calculation. If RESTART is specified with IRC=n
then the restart is assumed to be from the FORCE calculation. If RESTART is specified
without IRC=n, say with IRC on its own, then the restart is assumed to be from an earlier
IRC calculation that was shut down before going to completion.
A DRC calculation is simpler in that a force calculation is not a prerequisite; however, most
calculations of interest normally involve use of an internal coordinate. For this reason IRC=n can
be combined with DRC to give a calculation in which the initial motion (0.3kcal worth of kinetic
energy) is supplied by the IRC, and all subsequent motion obeys conservation of energy. The DRC
motion can be modified in three ways:
1. It is possible to calculate the reaction path followed by a system in which the generated
kinetic energy decays with a finite half-life. This can be defined by DRC=n.nnn, where
n.nnn is the half-life in femtoseconds. If n.nn is 0.0 this corresponds to infinite damping
simulating the IRC. A limitation of the program is that time only has meaning when DRC
is specified without a half-life.
2. Excess kinetic energy can be added to the calculation by use of KINETIC=n.nn. After
the kinetic energy has built up to 0.2kcal/mole or if IRC=n is used then n.nn kcal/mole of
kinetic energy is added to the system. The excess kinetic energy appears as a velocity vector
in the same direction as the initial motion.
6.11_Reaction_coordinates____________________________________________________
3. The RESTART file .RES can be edited to allow the user to modify the velocity
vector or starting geometry. This file is formatted.
Frequently DRC leads to a periodic, repeating orbit. One special type _ the orbit in which
the direction of motion is reversed so that the system retraces its own path _ is sensed for and if
detected the calculation is stopped after exactly one cycle. If the calculation is to be continued,
the keyword GEO-OK will allow this check to be by-passed.
Due to the potentially very large output files that the DRC can generate extra keywords are
provided to allow selected points to be printed. After the system has changed by a preset amount
the following keywords can be used to invoke a print of the geometry.
KeyWord Default User Specification
X-PRIO 0.05 Angstroms X-PRIORITY=n.nn
T-PRIO 0.10 Femtoseconds T-PRIORITY=n.nn
H-PRIO 0.10 kcal/mole H-PRIORITY=n.nn
Option to allow only extrema to be output
In the geometry specification, if an internal coordinate is marked for optimization then when
that internal coordinate passes through an extremum a message will be printed and the geometry
output.
Difficulties can arise from the way internal coordinates are processed. The internal coordinates
are generated from the cartesian coordinates, so an internal coordinate supplied may have an
entirely different meaning on output. In particular the connectivity may have changed. For
obvious reasons dummy atoms should not be used in the supplied geometry specification. If there
is any doubt about the internal coordinates or if the starting geometry contains dummy atoms
then run a 1SCF calculation specifying XYZ. This will produce an ARC file with the "ideal"
numbering _ the internal numbering system used by MOPAC. Use this ARC file to construct a
data file suitable for the DRC or IRC.
Notes:
1. Any coordinates marked for optimization will result in only extrema being printed.
2. If extrema are being printed then kinetic energy extrema will also be printed.
Keywords for use with the IRC and DRC
1. Setting up the transition state: NLLSQ SIGMA TS.
2. Constructing the FORCE matrix: FORCE or IRC=n, ISOTOPE, LET.
3. Starting an IRC: RESTART and IRC=n, T-PRIO, X-PRIO, H-PRIO.
4. Starting a DRC: DRC or DRC=n.nn, KINETIC=n.nn.
5. Starting a DRC from a transition state: (DRC or DRC=n) and IRC=n, KINETIC=n.
6. Restarting an IRC: RESTART and IRC.
7. Restarting a DRC: RESTART and (DRC or DRC=n.nn).
8. Restarting a DRC starting from a transition state: RESTART and (DRC or DRC=n.nn).
Other keywords, such as T=nnn or GEO-OK can be used anytime.
___________________________________________________________Background________
Examples of DRC/IRC data
Use of the IRC/DRC facility is quite complicated. In the following examples various `reasonable'
options are illustrated for a calculation on water. It is assumed that an optimized transition-state
geometry is available.
Example 1: A Dynamic Reaction Coordinate, starting at the transition state for water invert-
ing, initial motion opposite to the transition normal mode, with 6kcal of excess kinetic energy
added in. Every point calculated is to be printed (Note all coordinates are marked with a zero,
and T-PRIO, H-PRIO and X-PRIO are all absent). The results of an earlier calculation using
the same keywords is assumed to exist. The earlier calculation would have constructed the force
matrix. While the total cpu time is specified, it is in fact redundant in that the calculation will
run to completion in less than 600 seconds.
KINETIC=6 RESTART IRC=-1 DRC T=600
WATER
H 0.000000 0 0.000000 0 0.000000 0 0 0 0
O 0.911574 0 0.000000 0 0.000000 0 1 0 0
H 0.911574 0 180.000000 0 0.000000 0 2 1 0
0 0.000000 0 0.000000 0 0.000000 0 0 0 0
Example 2: An Intrinsic Reaction Coordinate calculation. Here the restart is from a previous
IRC calculation which was stopped before the minimum was reached. Recall that RESTART with
IRC=n implies a restart from the FORCE calculation. Since this is a restart from within an IRC
calculation the keyword IRC=n has been replaced by IRC. IRC on its own (without the "=n")
implies an IRC calculation from the starting position _ here the RESTART position _ without
initial displacement.
RESTART IRC T=600
WATER
H 0.000000 0 0.000000 0 0.000000 0 0 0 0
O 0.911574 0 0.000000 0 0.000000 0 1 0 0
H 0.911574 0 180.000000 0 0.000000 0 2 1 0
0 0.000000 0 0.000000 0 0.000000 0 0 0 0
Output format for IRC and DRC
The IRC and DRC can produce several different forms of output. Because of the large size of
these outputs, users are recommended to use search functions to extract information. To facilitate
this, specific lines have specific characters. Thus, a search for the "%" symbol will summarize the
energy profile while a search for "AA" will yield the coordinates of atom 1, whenever it is printed.
The main flags to use in searches are:
SEARCH FOR YIELDS
'% ' Energies for all points calculated,
excluding extrema
'%M' Energies for all turning points
'%MAX' Energies for all maxima
'%MIN' Energies for all minima
'%' Energies for all points calculated
'AA*' Internal coordinates for atom 1 for every point
'AE*' Internal coordinates for atom 5 for every point
'123AB*' Internal coordinates for atom 5 for point 123
6.11_Reaction_coordinates____________________________________________________
As the keywords for the IRC/DRC are interdependent, the following list of keywords illustrates
various options.
KEYWORD RESULTING ACTION
DRC The Dynamic Reaction Coordinate is calculated.
Energy is conserved, and no initial impetus.
DRC=0.5 In the DRC kinetic energy is lost with a half-
life of 0.5 femtoseconds.
DRC=-1.0 Energy is put into a DRC with an half-life of
-1.0 femtoseconds, i.e., the system gains
energy.
IRC The Intrinsic Reaction Coordinate is
calculated. No initial impetus is given.
Energy not conserved.
IRC=-4 The IRC is run starting with an impetus in the
negative of the 4th normal mode direction. The
impetus is one quantum of vibrational energy.
IRC=1 KINETIC=1 The first normal mode is used in an IRC, with
the initial impetus being 1.0kcal/mole.
DRC KINETIC=5 In a DRC, after the velocity is defined, 5 kcal
of kinetic energy is added in the direction of
the initial velocity.
IRC=1 DRC KINETIC=4 After starting with a 4 kcal impetus in the
direction of the first normal mode, energy is
conserved.
DRC VELOCITY KINETIC=10 Follow a DRC trajectory which starts with an
initial velocity read in, normalized to a
kinetic energy of 10 kcal/mol.
Instead of every point being printed, the option exists to print specific points determined by the
keywords T-PRIORITY, X-PRIORITY and H-PRIORITY. If any one of these words is specified,
then the calculated points are used to define quadratics in time for all variables normally printed.
In addition, if the flag for the first atom is set to T then all kinetic energy turning points are
printed. If the flag for any other internal coordinate is set to T then, when that coordinate passes
through an extremum, that point will be printed. As with the PRIORITYs, the point will be
calculated via a quadratic to minimize non-linear errors.
N.B.: Quadratics are unstable in the regions of inflection points, in these circumstances linear
interpolation will be used. A result of this is that points printed in the region of an inflection may
not correspond exactly to those requested. This is not an error and should not affect the quality
of the results.
Test of DRC_verification of trajectory path
Introduction: Unlike a single-geometry calculation or even a geometry optimization, verification
of a DRC trajectory is not a simple task. In this section a rigorous proof of the DRC trajectory is
presented; it can be used both as a test of the DRC algorithm and as a teaching exercise. Users
of the DRC are asked to follow through this proof in order to convince themselves that the DRC
works as it should.
Part 1: The nitrogen molecule
For the nitrogen molecule and using MNDO, the equilibrium distance is 1:103802 A, the heat
of formation is 8.276655 kcal/mole and the vibrational frequency is 2739:6 cm-1 . For small dis-
placements, the energy curve versus distance is parabolic and the gradient curve is approximately
___________________________________________________________Background________
linear, as is shown in the following table. A nitrogen molecule is thus a good approximation to a
harmonic oscillator.
STRETCHING CURVE FOR NITROGEN MOLECULE
N--N DIST HoF GRADIENT
(Angstroms) (kcal/mole) (kcal/mole/Angstrom)
1.1180 8.714564 60.909301
1.1170 8.655723 56.770564
1.1160 8.601031 52.609237
1.1150 8.550512 48.425249
1.1140 8.504188 44.218525
1.1130 8.462082 39.988986
1.1120 8.424218 35.736557
1.1110 8.390617 31.461161
1.1100 8.361303 27.162720
1.1090 8.336299 22.841156
1.1080 8.315628 18.496393
1.1070 8.299314 14.128353
1.1060 8.287379 9.736959
1.1050 8.279848 5.322132
1.1040 8.276743 0.883795
1.1030 8.278088 -3.578130
1.1020 8.283907 -8.063720
1.1010 8.294224 -12.573055
1.1000 8.309061 -17.106213
1.0990 8.328444 -21.663271
1.0980 8.352396 -26.244309
1.0970 8.380941 -30.849404
1.0960 8.414103 -35.478636
1.0950 8.451906 -40.132083
1.0940 8.494375 -44.809824
1.0930 8.541534 -49.511939
1.0920 8.593407 -54.238505
1.0910 8.650019 -58.989621
1.0900 8.711394 -63.765330
Period of vibration
The period of vibration (time taken for the oscillator to undertake one complete vibration, re-
turning to its original position and velocity) can be calculated in three ways. Most direct is
the calculation from the energy curve; using the gradient constitutes a faster, albeit less direct,
method, while calculating it from the vibrational frequency is very fast but assumes that the
vibrational spectrum has already been calculated.
1. From the energy curve. For a simple harmonic oscillator the period r is given by:
r ____
r = 2ss m__k
where m is the reduced mass and k is the force constant. The reduced mass (in amu) of a
nitrogen molecule is 14:0067=2 = 7:00335, and the force-constant can be calculated from:
E - c = (1=2)k(R - Ro )2
6.11_Reaction_coordinates____________________________________________________
Given Ro = 1:1038, R = 1:092, c = 8:276655 and E = 8:593407 kcal/mol then:
= 4548:2 kcal/mole/A 2
= 4545 x 4:184 x 103 x 107 x 1016 ergs/cm 2
= 1:9029 x 1030 ergs/cm 2
Therefore:
r _________
r = 2 x 3:14159 x ____7:0035________1:9029sxe1030conds= 12:054 x 10-15 s = 12:054 fs
2. From the gradient curve. The force constant is the derivative of the gradient wrt distance:
k = dG__dx
Since we are using discrete points, the force constant is best obtained from finite differences:
k = (G2_-_G1_)____(x
2 - x1 )
For x2 = 1:1100, G2 = 27:163 and for x1 = 1:0980, G1 = -26:244, giving rise to k = 4450
kcal/mole/A2 and a period of 12:186 fs.
3. From the vibrational frequency. Given a "frequency" (wavenumber) of vibration of N2 of
~ = 2739:6 cm-1 , the period of oscillation, in seconds, is given directly by:
r = _1_c~= ______________1_____________2739:6 x 2:998 x 1010
or as 12:175 femtoseconds.
Summarizing, by three different methods the period of oscillation of N2 is calculated to be
12:054, 12:186 and 12:175 fs, average 12:138 fs.
Initial dynamics of N2 with N-N distance = 1.094 A
A useful check on the dynamics of N2 is to calculate the initial acceleration of the two nitrogen
atoms after releasing them from a starting interatomic separation of 1.094 A.
At R(N-N) = 1.094 A, G = -44:810 kcal/mole/A or -18:749 x 1019 erg/cm. Therefore
acceleration, f = -18:749 x 1019 =14:0067 cm/sec/sec or -13:386 x 1018 cm/s2 which is -13:386 x
1015 x Earth surface gravity!
Distance from equilibrium = 0:00980 A. After 0:1 fs, velocity is 0:110-15 (-13:3861018 ) cm/sec
or 1338:6 cm/s.
In the DRC the time-interval between points calculated is a complicated function of the curva-
ture of the local surface. By default, the first time-interval is 0.105fs, so the calculated velocity at
this time should be 0:105 x 1338:6 = 1405:6 cm/s, in the DRC calculation the predicted velocity
is 1405:6 cm/s.
The option is provided to allow sampling of the system at constant time-intervals, the default
being 0:1 fs. For the first few points the calculated velocities are as follows.
TIME CALCULATED LINEAR DIFF.
VELOCITY VELOCITY VELOCITY
0.000 0.0 0.0 0.0
0.100 1338.6 1338.6 0.0
0.200 2673.9 2677.2 -3.3
___________________________________________________________Background________
0.300 4001.0 4015.8 -14.8
0.400 5317.3 5354.4 -37.1
0.500 6618.5 6693.0 -74.5
0.600 7900.8 8031.6 -130.8
As the calculated velocity is a fourth-order polynomial of the acceleration, and the acceleration,
its first, second and third derivatives, are all changing, the predicted velocity rapidly becomes a
poor guide to future velocities.
For simple harmonic motion the velocity at any time is given by:
v = v0 sin (2sst=r)
By fitting the computed velocities to simple harmonic motion, a much better fit is obtained:
Calculated Simple Harmonic Diff
Time Velocity 25316.Sin(0.529t)
0.000 0.0 0.0 0.0
0.100 1338.6 1338.6 0.0
0.200 2673.9 2673.4 +0.5
0.300 4001.0 4000.8 +0.2
0.400 5317.3 5317.0 +0.3
0.500 6618.5 6618.3 +0.2
0.600 7900.8 7901.0 -0.2
The repeat-time required for this motion is 11:88 fs, in good agreement with the three values
calculated using static models. The repeat time should not be calculated from the time required
to go from a minimum to a maximum and then back to a minimum - only half a cycle. For all
real systems the potential energy is a skewed parabola, so that the potential energy slopes are
different for both sides; a compression (as in this case) normally leads to a higher force-constant,
and shorter apparent repeat time (as in this case). Only the addition of the two half-cycles is
meaningful.
Conservation of normal coordinate
So far this analysis has only considered a homonuclear diatomic. A detailed analysis of a large
polyatomic is impractical, and for simplicity a molecule of formaldehyde will be studied.
In polyatomics, energy can transfer between modes. This is a result of the non-parabolic nature
of the potential surface. For small displacements the surface can be considered as parabolic. This
means that for small displacements interconversion between modes should occur only very slowly.
Of the six normal modes, mode 1, at 1204.5 cm-1 , the in-plane C-H asymmetric bend, is the most
unsymmetric vibration, and is chosen to demonstrate conservation of vibrational purity.
Mode 1 has a frequency corresponding to 3.44 kcal/mole and a predicted vibrational time of
27:69 fs. By direct calculation, using the DRC, the cycle time is 27:55 fs. The rate of decay of
this mode has an estimated half-life of a few thousands femtoseconds.
Rate of decay of starting mode
For trajectories initiated by an IRC=n calculation, whenever the potential energy is a minimum
the current velocity is compared with the supplied velocity. The square of the cosine of the angle
between the two velocity vectors is a measure of the intensity of the original mode in the current
vibration.
Half-Life for decay of initial mode
Vibrational purity is assumed to decay according to zero'th order kinetics. The half-life is thus
-0:6931472t= log (_2 ) fs, where _2 is the square of the overlap integral of the original vibration
6.12_Sparkles______________________________________________________
with the current vibration. Due to the very slow rate of decay of the starting mode, several
half-life calculations should be examined. Only when successive half-lives are similar should any
confidence be placed in their value.
DRC print options
The amount of output in the DRC is controlled by three sets of options. These sets are:
o Equivalent Keywords H-PRIORITY, T-PRIORITY, and X-PRIORITY
o Potential Energy Turning Point option.
o Geometry Maxima Turning Point options.
If T-PRIORITY is used then turning points cannot be monitored. Currently H-PRIORITY and
X-PRIORITY are not implemented, but will be as soon as practical.
To monitor geometry turning points, put a "T" in place of the geometry optimization flag for
the relevant geometric variable.
To monitor the potential energy turning points, put a "T" for the flag for atom 1 bond length
(Do not forget to put in a bond-length (zero will do)!).
The effect of these flags together is as follows.
1. No options: All calculated points will be printed. No turning points will be calculated.
2. Atom 1 bond length flagged with a "T": If T-PRIO, etc. are NOT specified, then potential
energy turning points will be printed.
3. Internal coordinate flags set to "T": If T-PRIO, etc. are NOT specified, then geometry
extrema will be printed. If only one coordinate is flagged, then the turning point will be
displayed in chronologic order; if several are flagged then all turning points occuring in a
given time-interval will be printed as they are detected. In other words, some may be out of
chronologic order. Note that each coordinate flagged will give rise to a different geometry:
minimize flagged coordinates to minimize output.
4. Potential and geometric flags set: The effect is equivalent to the sum of the first two options.
5. T-PRIO set: No turning points will be printed, but constant time-slices (by default 0:1 fs)
will be used to control the print.
6.12 Sparkles
Four extra `elements" have been put into MOPAC. These represent pure ionic charges, roughly
equivalent to the following chemical entities:
Chemical Symbol Equivalent to
+ Tetramethyl ammonium radical, Potassium
atom or Cesium atom.
++ Barium atom.
- Borohydride radical, Halogen, or
Nitrate radical
-- Sulfate, oxalate.
For the purposes of discussion these entities are called `sparkles': the name arises from consid-
eration of their behavior.
___________________________________________________________Background________
Behavior of sparkles in MOPAC
Sparkles have the following properties:
1. Their nuclear charge is integer, and is +1, +2, -1, or -2; there are an equivalent number
of electrons to maintain electroneutrality, +1, +2, -1, and -2 respectively. For example, a
`+' sparkle consists of a unipositive nucleus and an electron. The electron is donated to the
quantum mechanics calculation.
2. They all have an ionic radius of 0:7 A. Any two sparkles of opposite sign will form an ion-pair
with a interatomic separation of 1:4 A.
3. They have a zero heat of atomization, no orbitals, and no ionization potential.
They can be regarded as unpolarizable ions of diameter 1:4A. They do not contribute to the
orbital count, and cannot accept or donate electrons.
Since they appear as uncharged species which immediately ionize, attention should be given to
the charge on the whole system. For example, if the alkaline metal salt of formic acid was run, the
formula would be: HCOO+ where `+' is the unipositive sparkle. The charge on the system would
then be zero.
A water molecule polarized by a positive sparkle would have the formula H2 O+ , and the charge
on the system would be +1.
At first sight, a sparkle would appear to be too ionic to be a point charge and would combine
with the first charge of opposite sign it encountered.
This representation is faulty, and a better description would be of an ion, of diameter 1:4A,
and the charge delocalized over its surface. Computationally, a sparkle is an integer charge at
the center of a repulsion sphere of form exp (-ffr). The hardness of the sphere is such that other
atoms or sparkles can approach within about 2A quite easily, but only with great difficulty come
closer than 1:4A.
Uses of Sparkles
1. They can be used as counterions, e.g. for acid anions or for cations. Thus, if the ionic form
of an acid is wanted, then the moieties H.X, H.-, and +.X could be examined.
2. Two sparkles of equal and opposite sign can form a dipole for mimicking solvation effects.
Thus water could be surrounded by six dipoles to simulate the solvent cage. A dipole of
value D can be made by using the two sparkles + and -, or using ++ and --. If + and
- are used, the inter-sparkle separation would be D=4:803A. If ++ and -- are used, the
separation would be D=9:606A. If the inter-sparkle separation is less than 1:0A (a situation
that cannot occur naturally) then the energy due to the dipole on its own is subtracted from
the total energy.
3. They can operate as polarization functions. A controlled, shaped electric field can easily be
made from two or more sparkles. The polarizability in cubic Angstroms of a molecule in any
particular orientation can then easily be calculated.
6.13 Mechanism of the frame in FORCE calculation
The FORCE calculation uses cartesian coordinates, and all 3N modes are calculated, where N is the
number of atoms in the system. Clearly, there will be 5 or 6 "trivial" vibrations, which represent
the three translations and two or three rotations. If the molecule is exactly at a stationary point,
then these "vibrations" will have a force constant and frequency of precisely zero. If the force
calculation was done correctly, and the molecule was not exactly at a stationary point, then the
three translations should be exactly zero, but the rotations would be non-zero. The extent to
which the rotations are non-zero is a measure of the error in the geometry.
6.14_Configuration_interaction_______________________________________________
If the distortions are non-zero, the trivial vibrations can interact with the low-lying genuine
vibrations or rotations, and with the transition vibration if present.
To prevent this the analytic form of the rotations and vibrations is calculated, and arbitrary
eigenvalues assigned; these are 500, 600, 700, 800, 900, and 1000 millidynes/angstrom for Tx,
Ty, Tz, Rx, Ry and Rz (if present), respectively. The rotations are about the principal axes of
inertia for the system, taking into account isotopic masses. The "force matrix" for these trivial
vibrations is determined, and added on to the calculated force matrix. After diagonalization the
arbitrary eigenvalues are subtracted off the trivial vibrations, and the resulting numbers are the
"true" values. Interference with genuine vibrations is thus avoided.
6.14 Configuration interaction
MOPAC contains a very large Multi-Electron Configuration Interaction calculation, MECI, which
allows almost any configuration interaction calculation to be performed. Because of its complexity,
two distinct levels of input are supported; the default values will be of use to the novice while an
expert has available an exhaustive set of keywords from which a specific C.I. can be tailored.
A MECI calculation involves the interaction of microstates representing specific permutations
of electrons in a set of M.O.'s. Starting with a set electronic configuration, either closed shell or
open shell, but unconditionally restricted Hartree-Fock, the first step in a MECI calculation is the
removal from the M.O.'s of the electrons to be used in the C.I.
Each microstate is then constructed from these empty M.O.'s by adding in electrons according
to a prescription. The energy of the configuration is evaluated, as is the energy of interaction with
all previously-defined configurations. Diagonalization then results in state functions. From the
eigenvectors the expectation value of s2 is calculated, and the spin-states of the state functions
calculated.
General overview of keywords
Keywords associated with the operations of MECI are:
SINGLET DOUBLET EXCITED
TRIPLET QUARTET BIRADICAL
QUINTET SEXTET ESR
OPEN(n1,n2) C.I.=n MECI
ROOT=n
Each keyword may imply others; thus TRIPLET implies an open-shell system, therefore
OPEN(2,2), and C.I.=2 are implied, if not user specified.
Starting electronic configuration
MECI is restricted to RHF calculations, but with that single restriction any starting configuration
will be supported. Examples of starting configurations would be
System KeyWords used Starting Configuration
Methane 2.00 2.00 2.00 2.00 2.00
Methyl Radical 2.00 2.00 2.00 2.00 1.00
Twisted Ethylene TRIPLET 2.00 2.00 2.00 1.00 1.00
Twisted Ethylene OPEN(2,2) 2.00 2.00 2.00 1.00 1.00
Twisted Ethylene Cation OPEN(1,2) 2.00 2.00 2.00 0.50 0.50
Methane Cation CHARGE=1 OPEN(5,3) 2.00 2.00 1.67 1.67 1.67
Choice of starting configuration is important. For example, if twisted ethylene, a ground-
state triplet, is not defined using TRIPLET or OPEN(2,2), then the closed-shell ground-state
___________________________________________________________Background________
structure will be calculated. Obviously, this configuration is a legitimate microstate, but from the
symmetry of the system a better choice would be to define one electron in each of the two formally
degenerate pi-type M.O.'s. The initial SCF calculation does not distinguish between OPEN(2,2)
and TRIPLET since both keywords define the same starting configuration. This can be verified
by monitoring the convergence using PL, for which both keywords give the same SCF energy.
Removal of electrons from starting configuration
For a starting configuration of alpha M.O. occupancies O(i), O(i) being in the range 0.0 to 1.0,
the energies of the M.O.'s involved in the MECI can be calculated from:
X
E(i) = {[2J (i; j) - K(i; j)]O(j)}
j
where J (i; j) and K(i; j) are the coulomb and exchange integrals between M.O.'s i and j. The
M.O. index j runs over those M.O.'s involved in the MECI only. Most MECI calculations will
involve between 1 and 5 M.O.'s, so a system with about 30 filled or partly filled M.O.'s could
have M.O.'s 25-30 involved. The resulting eigenvalues correspond to those of the cationic system
resulting from removal of n electrons, where n is twice the sum of the orbital occupancies of those
M.O.'s involved in the C.I.
The arbitrary zero of energy in a MECI calculation is the starting ground state, without any
correction for errors introduced by the use of fractional occupancies. In order to calculate the
energy of the various configurations, the energy of the vacuum state (i.e., the state resulting from
removal of the electrons used in the C.I.) needs to be evaluated. This energy is defined by:
2 3
X X
GSE = 4 E(i)O(i) + J (i; i) x O(i) x O(i) + {2[2J (i; j) - K(i; j)] x O(i) x O(j)}5
i j*** - )[Occa(k) - Occg(k)] + ()[Occb(k) - Occg(k)]}
k
E(p; q) may need to be multiplied by -1, if the number of two electron permutations required
to bring M.O.'s i and j into coincidence is odd.
Where Occa(k) is the alpha molecular orbital occupancy in the configuration interaction.
3. Determinants differing by exactly two M.O.'s: The two M.O.'s can have the same or opposite
spins. Three cases can be identified:
(a) Both M.O.'s have alpha spin: For the first microstate having M.O.'s i and j, and
the second microstate having M.O.'s k and l, the matrix element connecting the two
microstates is given by:
Q(p; q) = -
E(p; q) may need to be multiplied by -1, if the number of two electron permutations
required to bring M.O. i into coincidence with M.O. k and M.O. j into coincidence with
M.O. l is odd.
(b) Both M.O.'s have beta spin: The matrix element is calculated in the same manner as
in the previous case.
(c) One M.O. has alpha spin, and one beta spin: For the first microstate having M.O.'s
alpha(i) and beta(j), and the second microstate having M.O.'s alpha(k) and beta(l),
the matrix element connecting the two microstates is given by:
Q(p; q) =
E(p; q) may need to be multiplied by -1, if the number of two electron permutations
required to bring M.O. i into coincidence with M.O. k and M.O. j into coincidence with
M.O. l is odd.
States arising from various calculations
Each MECI calculation invoked by use of the keyword C.I.=n normally gives rise to states of
quantized spins. When C.I. is used without any other modifying keywords, the following states
will be obtained.
No. of M.O.'s States Arising States Arising From
From Odd Electron Systems Even Electron Systems
in MECI Doublets Singlets Triplets
1 1 1
2 2 3 1
3 8 1 6 3
4 20 4 20 15 1
5 75 24 1 50 45 5
These numbers of spin states will be obtained irrespective of the chemical nature of the system.
6.15_Reduced_masses_in_a_force_calculation_____________________________________________
Calculation of spin-states
In order to calculate the spin-state, the expectation value of S2 is calculated.
where N e is the no. of electrons in C.I., C(i; k) is the coefficient of microstate i in State k,
Nff(i) is the number of alpha electrons in microstate i, Nfi(i) is the number of beta electrons in
microstate i, Off(l; k) is the occupancy of alpha M.O. l in microstate k, Ofi(l; k) is the occupancy
of beta M.O. l in microstate k, S(+) is the spin shift up or step up operator, S(-) is the spin shift
down or step down operator, the Kroneker delta is 1 if the two terms in brackets following it are
identical.
The spin state is calculated from:
p __
S = (1=2)[ (1 + 4S2) - 1]
In practice, S is calculated to be exactly integer, or half integer. That is, there is insignificant
error due to approximations used. This does not mean, however, that the method is accurate.
The spin calculation is completely precise, in the group theoretic sense, but the accuracy of the
calculation is limited by the Hamiltonian used, a space-dependent function.
Choice of state to be optimized
MECI can calculate a large number of states of various total spin. Two schemes are provided to
allow a given state to be selected. First, ROOT=n will, when used on its own, select the n'th
state, irrespective of its total spin. By default n=1. If ROOT=n is used in conjunction with a
keyword from the set SINGLET, DOUBLET, TRIPLET, QUARTET, QUINTET, or SEXTET,
then the n'th root of that spin-state will be used. For example, ROOT=4 and SINGLET will
select the 4th singlet state. If there are two triplet states below the fourth singlet state then this
will mean that the sixth state will be selected.
Calculation of unpaired spin density
Starting with the state functions as linear combinations of configurations, the unpaired spin den-
sity, corresponding to the alpha spin density minus the beta spin density, will be calculated for
the first few states. This calculation is straightforward for diagonal terms, and only those terms
are used.
6.15 Reduced masses in a force calculation
Reduced masses for a diatomic are given by:
m1_x_m2_____
m1 + m2
For a Hydrogen molecule the reduced mass is thus 0.5; for heavily hydrogenated systems, e.g.
methane, the reduced mass can be very low. A vibration involving only heavy atoms , e.g. a C-N
in cyanide, should give a large reduced mass.
For the `trivial' vibrations the reduced mass is ill-defined, and where this happens the reduced
mass is set to zero.
6.16 Use of SADDLE calculation
A SADDLE calculation uses two complete geometries, as shown on the following data file for the
ethyl radical hydrogen migration from one methyl group to the other.
___________________________________________________________Background________
Line 1: UHF SADDLE
Line 2: ETHYL RADICAL HYDROGEN MIGRATION
Line 3:
Line 4: C 0.000000 0 0.000000 0 0.000000 0 0 0 0
Line 5: C 1.479146 1 0.000000 0 0.000000 0 1 0 0
Line 6: H 1.109475 1 111.328433 1 0.000000 0 2 1 0
Line 7: H 1.109470 1 111.753160 1 120.288410 1 2 1 3
Line 8: H 1.109843 1 110.103163 1 240.205278 1 2 1 3
Line 9: H 1.082055 1 121.214083 1 38.110989 1 1 2 3
Line 10: H 1.081797 1 121.521232 1 217.450268 1 1 2 3
Line 11: 0 0.000000 0 0.000000 0 0.000000 0 0 0 0
Line 12: C 0.000000 0 0.000000 0 0.000000 0 0 0 0
Line 13: C 1.479146 1 0.000000 0 0.000000 0 1 0 0
Line 14: H 1.109475 1 111.328433 1 0.000000 0 2 1 0
Line 15: H 1.109470 1 111.753160 1 120.288410 1 2 1 3
Line 16: H 2.109843 1 30.103163 1 240.205278 1 2 1 3
Line 17: H 1.082055 1 121.214083 1 38.110989 1 1 2 3
Line 18: H 1.081797 1 121.521232 1 217.450268 1 1 2 3
Line 19: 0 0.000000 0 0.000000 0 0.000000 0 0 0 0
Line 20:
Details of the mathematics of SADDLE appeared in print in 1984, (M. J. S. Dewar, E. F.
Healy, J. J. P. Stewart, J. Chem. Soc. Faraday Trans. II , 3, 227, (1984)) so only a superficial
description will be given here.
The main steps in the saddle calculation are as follows:
1. The heats of formation of both systems are calculated.
2. A vector R of length 3N - 6 defining the difference between the two geometries is calculated.
3. The scalar P of the difference vector is reduced by some fraction, normally about 5 to 15
percent.
4. Identify the geometry of lower energy; call this G.
5. Optimize G, subject to the constraint that it maintains a constant distance P from the other
geometry.
6. If the newly-optimized geometry is higher in energy then the other geometry, then go to 1.
If it is higher, and the last two steps involved the same geometry moving, make the other
geometry G without modifying P , and go to 5.
7. Otherwise go back to 2.
The mechanism of 5 involves the coordinates of the moving geometry being perturbed by an
amount equal to the product of the discrepancy between the calculated and required P and the
vector R.
As the specification of the geometries is quite difficult, in that the difference vector depends
on angles (which are, of necessity ill-defined by 360 degrees) SADDLE can be made to run in
cartesian coordinates using the keyword XYZ. If this option is chosen then the initial steps of the
calculation are as follows:
1. Both geometries are converted into cartesian coordinates.
2. Both geometries are centered about the origin of cartesian space.
3. One geometry is rotated until the difference vector is a minimum _ this minimum is within
1 degree of the absolute bottom.
4. The SADDLE calculation then proceeds as described above.
6.17_How_to_escape_from_a_hilltop______________________________________________________
Limitations:
The two geometries must be related by a continuous deformation of the coordinates. By default,
internal coordinates are used in specifying geometries, and while bond lengths and bond angles
are unambiguously defined (being both positive), the dihedral angles can be positive or negative.
Clearly 300 degrees could equally well be specified as -60 degrees. A wrong choice of dihedral
would mean that instead of the desired reaction vector being used, a completely incorrect vector
was used, with disastrous results.
To correct this, ensure that one geometry can be obtained from the other by a continuous
deformation, or use the XYZ option.
6.17 How to escape from a hilltop
A particularly irritating phenomenon sometimes occurs when a transition state is being refined.
A rough estimate of the geometry of the transition state has been obtained by either a SADDLE
or reaction path or by good guesswork. This geometry is then refined by SIGMA or by NLLSQ,
and the system characterized by a force calculation. It is at this point that things often go
wrong. Instead of only one negative force constant, two or more are found. In the past, the
recommendation has been to abandon the work and to go on to something less masochistic. It is
possible, however, to systematically progress from a multiple maximum to the desired transition
state. The technique used will now be described.
If a multiple maximum is identified, most likely one negative force constant corresponds to the
reaction coordinate, in which case the objective is to render the other force constants positive.
The associated normal mode eigenvalues are complex, but in the output are printed as negative
frequencies, and for the sake of simplicity will be described as negative vibrations. Use DRAW-2 to
display the negative vibrations, and identify which mode corresponds to the reaction coordinate.
This is the one we need to retain.
Hitherto, simple motion in the direction of the other modes has proved difficult. However
the DRC provides a convenient mechanism for automatically following a normal coordinate. Pick
the largest of the negative modes to be annihilated, and run the DRC along that mode until a
minimum is reached. At that point, refine the geometry once more using SIGMA and repeat the
procedure until only one negative mode exists.
To be on the safe side, after each DRC+SIGMA sequence do the DRC+SIGMA operation
again, but use the negative of the initial normal coordinate to start the trajectory. After both
stationary points are reached, choose the lower point as the starting point for the next elimina-
tion. The lower point is chosen because the transition state wanted is the highest point on the
lowest energy path connecting reactants to products. Sometimes the two points will have equal
energy: this is normally a consequence of both trajectories leading to the same point or symmetry
equivalent points.
After all spurious negative modes have been eliminated, the remaining normal mode corre-
sponds to the reaction coordinate, and the transition state has been located.
This technique is relatively rapid, and relies on starting from a stationary point to begin each
trajectory. If any other point is used, the trajectory will not be even roughly simple harmonic.
If, by mistake, the reaction coordinate is selected, then the potential energy will drop to that
of either the reactants or products, which, incidentally, forms a handy criterion for selecting the
spurious modes: if the potential energy only drops by a small amount, and the time evolution is
roughly simple harmonic, then the mode is one of the spurious modes. If there is any doubt as to
whether a minimum is in the vicinity of a stationary point, allow the trajectory to continue until
one complete cycle is executed. At that point the geometry should be near to the initial geometry.
Superficially, a line-search might appear more attractive than the relatively expensive DRC.
However, a line-search in cartesian space will normally not locate the minimum in a mode. An
obvious example is the mode corresponding to a methyl rotation.
___________________________________________________________Background________
Keyword Sequences to be Used
1. To locate the starting stationary point given an approximate transition state:- SIGMA
2. To define the normal modes:- FORCE ISOTOPE
At this point, copy all the files to a second filename, for use later.
3. Given vibrational frequencies of -654, -123, 234, and 456, identify via DRAW-2 the nor-
mal coordinate mode, let's say that is the -654 mode. Eliminate the second mode by:
IRC=2 DRC T=30M RESTART LARGE
Use is made of the FORCE restart file.
4. Identify the minimum in the potential energy surface by inspection or using the VAX
SEARCH command, of form: SEARCH .OUT %
5. Edit out of the output file the data file corresponding to the lowest point, and refine the
geometry using: SIGMA
6. Repeat the last three steps but for the negative of the normal mode, using the copied files.
The keywords for the first of the two jobs are: IRC=-2 DRC T=30M RESTART LARGE
7. Repeat the last four steps as often as there are spurious modes.
8. Finally, carry out a DRC to confirm that the transition state does, in fact, connect the
reactants and products. The drop in potential energy should be monotonic. If you are
unsure whether this last operation will work successfully, do it at any time you have a
stationary point. If it fails at the very start, then we are back where we were last year - give
up and go home!!
6.17.1 EigenFollowing
Description of the EF and TS function
by
Dr Frank Jensen
Department of Chemistry
Odense University
5230 Odense
Denmark
The current version of the EF optimization routine is a combination of the original EF algo-
rithm of Simons et al. (J. Phys. Chem. 89, 52) as implemented by Baker (J. Comp. Chem. 7,
385) and the QA algorithm of Culot et al. (Theo. Chim. Acta 82, 189), with some added features
for improving stability.
The geometry optimization is based on a second order Taylor expansion of the energy around
the current point. At this point the energy, the gradient and some estimate of the Hessian are
available. There are three fundamental steps in determining the next geometry based on this
information:
o finding the "best" step within or on the hypersphere with the current trust radius.
o possibly reject this step based on various criteria.
o update the trust radius.
6.17_How_to_escape_from_a_hilltop______________________________________________________
1. For a minimum search the correct Hessian has only positive eigenvalues. For a Transition
State (TS) search the correct Hessian should have exactly one negative eigenvalue, and the
corresponding eigenvector should be in the direction of the desired reaction coordinate. The
geometry step is parameterized as g=(s - H), where s is a shift factor which ensure that
the step-length is within or on the hypersphere. If the Hessian has the correct structure,
a pure Newton-Raphson step is attempted. This corresponds to setting the shift factor to
zero. If this step is longer than the trust radius, a P-RFO step is attempted. If this is also
too long, then the best step on the hypersphere is made via the QA formula. This three step
procedure is the default. The pure NR step can be skipped by giving the keyword NONR.
An alternative to the QA step is to simply scale the P-RFO step down to the trust radius
by a multiplicative constant, this can be accomplished by specifying RSCAL.
2. Using the step determined from 1), the new energy and gradient are evaluated. If it is a TS
search, two criteria are used in determining whether the step is "appropriate". The ratio
between the actual and predicted energy change should ideally be 1. If it deviates substan-
tially from this value, the second order Taylor expansion is no longer accurate. RMIN and
RMAX (default values 0 and 4) determine the limits on how far from 1 the ratio can be
before the step is rejected. If the ratio is outside the RMIN and RMAX limits, the step
is rejected, the trust radius reduced by a factor of two and a new step is determined. The
second criteria is that the eigenvector along which the energy is being maximized should
not change substantially between iterations. The minimum overlap of the TS eigenvector
with that of the previous iteration should be larger than OMIN, otherwise the step is re-
jected. Such a step rejection can be recognized in the output by the presence of (possibly
more) lines with the same CYCLE number. The default OMIN value is 0.8, which allows
fairly large changes to occur, and should be suitable for most uncomplicated systems. See
below for a discussion of how to use RMIN, RMAX and OMIN for difficult cases. The
selection of which eigenvector to follow towards the TS is given by MODE=n, where n is
the number of the Hessian eigenvector to follow. The default is MODE=1. These features
can be turned off by giving suitable values as keywords, e.g. RMIN=-100 RMAX=100
effectively inhibits step rejection. Similarly setting OMIN=0 disables step rejection based
on large changes in the structure of the TS mode. The default is to use mode following even
if the TS mode is the lowest eigenvector. This means that the TS mode may change to some
higher mode during the optimization. To turn of mode following, and thus always follow
the mode with lowest eigenvalue, set MODE=0. If it is a minimum search the new energy
should be lower than the previous.
The acceptance criteria used is that the actual/predicted ratio should be larger than RMIN,
which for the default value of RMIN=0 is equivalent to a lower energy. If the ratio is below
RMIN, the step is rejected, the trust radius reduced by a factor of two and a new step is
predicted. The RMIN, RMAX and OMIN features has been introduced in the current
version of EF to improve the stability of TS optimizations. Setting RMIN and RMAX
close to one will give a very stable, but also very slow, optimization. Wide limits on RMIN
and RMAX may in some cases give a faster convergence, but there is always the risk that
very poor steps are accepted, causing the optimization to diverge. The default values of
0 and 4 rarely rejects steps which would lead to faster convergence, but may occasionally
accept poor steps. If TS searches are found to cause problems, the first try should be to
lower the limits to 0.5 and 2. Tighter limits like 0.8 and 1.2, or even 0.9 and 1.1, will almost
always slow the optimization down significantly but may be necessary in some cases.
In minimum searches it is usually desirable that the energy decreases in each iteration.
In certain very rigid systems, however, the initial diagonal Hessian may be so poor that
the algorithm cannot find an acceptable step larger than DDMIN, and the optimization
terminates after only a few cycles with the "TRUST RADIUS BELOW DDMIN" warning
long before the stationary point is reached. In such cases the user can specify RMIN to
some negative value, say -10, thereby allowing steps which increases the energy.
___________________________________________________________Background________
The algorithm has the capability of following Hessian eigenvectors other than the one with
the lowest eigenvalue toward a TS. Such higher mode following are always much more difficult
to make converge. Ideally, as the optimization progresses, the TS mode should at some point
become the lowest eigenvector. Care must be taken during the optimization, however, that
the nature of the mode does not change all of a sudden, leading to optimization to a different
TS than the one desired. OMIN has been designed for ensuring that the nature of the TS
mode only changes gradually, specifically the overlap between to successive TS modes should
be higher than OMIN. While this concept at first appears very promising, it is not without
problems when the Hessian is updated.
As the updated Hessian in each step is only approximately correct, there is a upper limit on
how large the TS mode overlap between steps can be. To understand this, consider a series
of steps made from the same geometry (e.g. at some point in the optimization), but with
steadily smaller step-sizes. The update adds corrections to the Hessian to make it a better
approximation to the exact Hessian. As the step-size become small, the updated Hessian
converges toward the exact Hessian, at least in the direction of the step. The old Hessian is
constant, thus the overlap between TS modes thus does not converge toward 1, but rather to
a constant value which indicate how well the old approximate Hessian resembles the exact
Hessian. Test calculations suggest a typical upper limit around 0.9, although cases have been
seen where the limit is more like 0.7. It appears that an updated Hessian in general is not
of sufficient accuracy for reliably rejecting steps with TS overlaps much greater than 0.80.
The default OMIN of 0.80 reflects the typical use of an updated Hessian. If the Hessian
is recalculated in each step, however, the TS mode overlap does converge toward 1 as the
step-size goes toward zero, and in this cases there is no problems following high lying modes.
Unfortunately setting RECALC=1 is very expensive in terms of computer time, but used in
conjecture with OMIN=0.90 (or possibly higher), and maybe also tighter limits on RMIN
and RMAX, it represents an option of locating transitions structures that otherwise might
not be possible. If problems are encountered with many step rejections due to small TS
mode overlaps, try reducing OMIN, maybe all the way down to 0. This most likely will
work if the TS mode is the lowest Hessian eigenvector, but it is doubtful that it will produce
any useful results if a high lying mode is followed. Finally, following modes other than the
lowest toward a TS indicates that the starting geometry is not "close" to the desired TS.
In most cases it is thus much better to further refined the starting geometry, than to try
following high lying modes. There are cases, however, where it is very difficult to locate a
starting geometry which has the correct Hessian, and mode following may be of some use
here
6.17.2 Franck-Condon considerations
This section was written based on discussions with
Victor I. Danilov
Department of Quantum Biophysics
Academy of Sciences of the Ukraine
Kiev 143
Ukraine
The Frank-Condon principle states that electronic transitions take place in times that are very
short compared to the time required for the nuclei to move significantly. Because of this, care
must be taken to ensure that the calculations actually do reflect what is wanted.
Examples of various phenomena which can be studied are:
Photoexcitation If the purpose of a calculation is to predict the energy of photoexcitation, then
the ground-state should first be optimized. Once this is done, then a C.I. calculation can be
carried out using 1SCF. With the appropriate keywords (MECI C.I.=n etc.), the energy
of photoexcitation to the various states can be predicted.
6.18_Outer_Valence_Green's_Function____________________________________________________
A more expensive, but more rigorous, calculation, would be to optimize the geometry using
all the C.I. keywords. This is unlikely to change the results significantly, however.
Fluorescence If the excited state has a sufficiently long lifetime, so that the geometry can relax,
then if the system returns to the ground state by emission of a photon, the energy of the
emitted photon will be less (it will be red-shifted) than that of the exciting photon. To do
such a calculation, proceed as follows:
o Optimize the ground-state geometry using all the keywords for the later steps, but
specify the ground state, e.g. C.I.=3 EF GNORM=0.01 MECI.
o Optimize the excited state, e.g. C.I.=3 ROOT=2 EF GNORM=0.01 MECI.
o Calculate the Franck-Condon excitation energy, using the results of the ground-state
calculation only.
o Calculate the Franck-Condon emission energy, using the results of the excited state
calculation only.
o If indirect emission energies are wanted, these can be obtained from the Hf of the
optimized excited and optimized ground-state calculations.
In order for fluorescence to occur, the photoemission probability must be quite large, there-
fore only transitions of the same spin are allowed. For example, if the ground state is S0 ,
then the fluorescing state would be S1 .
Phosphorescence If the photoemission probability is very low, then the lifetime of the excited
state can be very long (sometimes minutes). Such states can become populated by S1 ! T1
intersystem crossing. Of course, the geometry of the system will relax before the photoemis-
sion occurs.
Indirect emission If the system relaxes from the excited electronic, ground vibrational state
to the ground electronic, ground vibrational state, then a more complicated calculation is
called for. The steps of such a calculation are:
o Optimize the geometry of the excited state.
o Using the same keywords, except that the ground state is specified, optimize the geom-
etry of the ground state.
o Take the difference in Hf of the optimized excited and optimized ground-state calcu-
lations.
o Convert this difference into the appropriate units.
Excimers An excimer is a pair of molecules, one of which is in an electronic excited state. Such
systems are usually stabilized relative to the isolated systems. Optimization of the geometries
of such systems is difficult. Suggestions on how to improve this type of calculation would be
appreciated.
6.18 Outer Valence Green's Function
This section is based on materials supplied by
Dr David Danovich
The Fritz Haber Research Center for Molecular Dynamics
The Hebrew University of Jerusalem
91904 Jerusalem
Israel
___________________________________________________________Background________
The OVGF technique was used with the self-energy part extended to include third order per-
turbation corrections, [?]. The higher order contributions were estimatedPby the renormalization
procedure. The actual expression used to calculate the self-energy part, pp(w), chosen in the
P (2) P (3)
diagonal form, is given in equation (6.59), where pp (w) and pp (w) are the second- and third-
order corrections, and A is the screening factor accounting for all the contributions of higher
orders.
X X(2) X 3
(w) = (w) + (1 - A)-1 (w) (6:59)
pp pp pp
The particular expression which was used for the second-order corrections is given in equa-
tion (6.60).
X(2) X X (2V - V )V X X (2V - V )V
(w) = ___paij_____paji___paij____ + ___piab____piba___piab_____ (6:60)
pp a i;j w + ea - ei - ej a;b i w + ei - ea - eb
where Z Z
Vpqrs = OE*p(1)OE*q(2)(1=r12 )OE*r(1)OE*s(2)do1 do2
In equation (6.60), i and j denote occupied orbitals, a and b denote virtual orbitals, p denotes
orbitals of unspecified occupancy, and e denotes an orbital energy. The equations are solved by
an iterative procedure, represented in equation (6.61).
X
wi+1p = ep + (wi) (6:61)
pp
The SCF energies and the corresponding integrals, which were calculated by one of the semiem-
pirical methods (MNDO, AM1, or PM3), were taken as the zero'th approximation and all M.O.s
may be included in the activePspace for the OVGF calculations.
The expressions used for (3)ppand A are given in [?].
The OVGF method itself, is described in detail in [?].
6.18.1 Example of OVGF calculation
Because Danovich's OVGF method is new to MOPAC, users will want to see how well it works. The
data-set test__green.dat will calculate the first 8 I.P.s for dimethoxy-s-tetrazine. This calculation
is discussed in detail in [?]. The experimental and calculated I.P.s are shown in Table 6.1.
Table 6.1: OVGF Calculation, Comparison with Experiment
M.O. Expt* PM3 Error OVGF(PM3) Error
n1 9.05 10.15 1.10 9.46 0.41
ss1 9.6 10.01 0.41 9.65 0.05
n2 11.2 11.96 0.76 11.13 -0.07
ss2 11.8 12.27 0.47 11.43 -0.37
*: R. Gleiter, V. Schehlmann, J. Spanget-Larsen, H. Fischer and F. A. Neugebauer, J. Org.
Chem., 53, 5756 (1988).
From this, we see that for PM3 the average error is 0.69eV, but after OVGF correction, the
error drops to 0.22eV. This is typical of nitrogen heterocycle calculations.
6.19_COSMO_(Conductor-like_Screening_Model)____________________________________________
6.19 COSMO (Conductor-like Screening Model)
This section was written based on material provided by:
Andreas Klamt
Bayer AG
Q18, D-5090 Leverkusen-Bayerwerk
Germany
Unlike the Self-Consistent Reaction Field model [?], the Conductor-like Screening Model
(COSMO) is a new continuum approach which, while more complicated, is computationally quite
efficient. The expression for the total screening energy is simple enough to allow the first derivatives
of the energy with respect to atomic coordinates to be easily evaluated.
Details of the procedure have been submitted for publication: A. Klamt and G. Schuurmann,
COSMO: A New Approach to Dielectric Screening in Solvents with Explicit Expressions for the
Screening Energy and its Gradient, J. Chem. Soc., Perkin Trans. 2, 1993. (in press).
The COSMO procedure generates a conducting polygonal surface around the system (ion or
molecule), at the van der Waals' distance. By introducing a "-dependent correction factor,
f (") = _("_-_1)__1;
(" + __2)
into the expressions for the screening energy and its gradient, the theory can be extended to finite
dielectric constants with only a small error.
The accuracy of the method can be judged by how well it reproduces known quantities, such
as the heat of solution in water (water has a dielectric constant of 78.4 at 25O C), Table 6.2. Here,
the keywords used were
NSPA=60 GRADIENTS 1SCF EPS=78.4 AM1 CHARGE=1
From the Table we see that the glycine zwitterion becomes the stable form in water, while the
neutral species is the stable gas-phase form.
The COSMO method is easy to use, and the derivative calculation is of sufficient precision to
allow gradients of 0.1 to be readily achieved.
_________Table_6.2:__Calculated_and_Observed_Hydration_Energies____________________
Compound Method Hf (kcal/mol) Hydration
________________________gas_phase_______solution_phase_________H(calc.)________Enthalpy(exp.)_y________
NH+4 AM1 150.6 59.5 91.1 88.0
N(Me)+4 AM1 157.1 101.1 56.0 59.9
N(Et)+4 AM1 132.1 84.2 47.9 57.0
Glycine
neutral AM1 -101.6 -117.3 15.7 --
__zwitterion________AM1_______________-59.2_____________-125.6________________66.4_______________--______________
y : Y. Nagano, M. Sakiyama, T. Fujiwara, Y. Kondo, J. Phys. Chem., 92, 5823 (1988).
6.20 Solid state capability
Currently MOPAC can only handle up to one-dimensional extended systems. As the solid-state
method used is unusual, details are given at this point.
If a polymer unit cell is large enough, then a single point in k-space, the Gamma point,
is sufficient to specify the entire Brillouin zone. The secular determinant for this point can be
constructed by adding together the Fock matrix for the central unit cell plus those for the adjacent
___________________________________________________________Background________
unit cells. The Born-von Karman cyclic boundary conditions are satisfied, and diagonalization
yields the correct density matrix for the Gamma point.
At this point in the calculation, conventionally, the density matrix for each unit cell is con-
structed. Instead, the Gamma-point density and one-electron density matrices are combined with
a "Gamma-point-like" Coulomb and exchange integral strings to produce a new Fock matrix. The
calculation can be visualized as being done entirely in reciprocal space, at the Gamma point.
Most solid-state calculations take a very long time. These calculations, called "Cluster" cal-
culations after the original publication, require between 1.3 and 2 times the equivalent molecular
calculation.
A minor `fudge' is necessary to make this method work. The contribution to the Fock matrix
element arising from the exchange integral between an atomic orbital and its equivalent in the
adjacent unit cells is ignored. This is necessitated by the fact that the density matrix element
involved is invariably large.
The unit cell must be large enough that an atomic orbital in the center of the unit cell has an
insignificant overlap with the atomic orbitals at the ends of the unit cell. In practice, a translation
vector of more that about 7 or 8A is sufficient. For one rare group of compounds a larger translation
vector is needed. Polymers with delocalized ss-systems, and polymers with very small band-gaps
will require a larger translation vector, in order to accurately sample k-space. For these systems,
a translation vector in the order of 15-20 Angstroms is needed.
Chapter 7
Program
The logic within MOPAC is best understood by use of flow-diagrams.
There are two main sequences, geometric and electronic. These join only at one common
subroutine COMPFG. It is possible, therefore, to understand the geometric or electronic sections
in isolation, without having studied the other section.
7.1 Main geometric sequence
``````
_ _
_ MAIN _
_ _
_``````_
`````````````````````_``````````````````````````````
_ _ ```_``` ````_````` _ ```_```
_ ```_``` _ _ _ _ _ _ _
_ _IRC/DRC_ _ FORCE _ _ REACT1 _ _ _ PATHS _
_ _ or _ _ _ _ _ _ _ _
_ _ EF _ _```````_``` _``````````_ _ _```````_
_ _ or _ _ _ _ _ _ _
_ _ POLAR _ _ _ _ _ _ _
_ _```````_ _ _`` _ _`````````_``````_
`_````` _ `_```` _ _ ```_```
_ NLLSQ _ _ _ _ _ _````````````_ _
_ and _ _ _ FMAT _ _ _ FLEPO _
_ POWSQ _ _ _ _ _ _ _
_```````_ _ _``````_ _ _```````_
````_``` _ _ _ _ `````_`` _
_ SEARCH _ _ _ _ _ _ _ _
_ or _ _ _ _ _ _ LINMIN _ _
_ LOCMIN _ _ _ _ _ _ _ _
_````````_ _ _ _ _ _````````_ _
_``````_```_`````````_`````_``````````````_``````_
````_```
_ _
_ COMPFG _ (See ELECTRONIC SEQUENCE)
_ _
_````````_
_______________________________________________________________Program_______
7.2 Main electronic flow
````````
_ _
_ COMPFG _ (See GEOMETRIC SEQUENCE)
_ _
_````````_
```````````````_````````````````````
```_``` ```_``` ```_```` _
_ _ _ _ _ _ _
_ HCORE _```````_ DERIV _````_ GMETRY _ _
_ _ _ _ _ _ _
_```````_ _```````_ _ SYMTRY _ _
_ _ _ _ _ _
_ ````_`` _ _````````_ _
_ _ _ _ _
_ _ DCART _ _ _
_ _ _ _ _
_ _```````_ _`````` ```````_
_ ``_`` `_``_` `````````
_ _ _ _ _ _ _
_ _ DHC _ ````_ ITER _````_ RSP _
_ _ _ _ _ _ _ _
_ _`````_ _ _``````_ _`````````_
_ _ _ _ _ _
_``` ``_ _ _ _ _ ````````
_ _ _ _ _ _ _ _
`_````_` _````_` _ _``````_ DENSIT _
_ _ _ _ _ _ _
_ ROTATE _ _ FOCK1 _ _ _ CNVG _
_ _ _ _ _ _ PULAY _
_ H1ELEC _ _ FOCK2 _ _ _````````_
_ _ _ _ _
_````````_ _```````_ _`````
_ _ _
```_`` _ MECI _
_ _ _ _
_ DIAT _ _``````_
_ _
_``````_
_
``_`
_ _
_ SS _
_````_
7.3 Control within MOPAC
Almost all the control information is passed via the single datum "KEYWRD", a string of 80
characters, which is read in at the start of the job.
Each subroutine is made independent, as far as possible, even at the expense of extra code
or calculation. Thus, for example, the SCF criterion is set in subroutine ITER, and nowhere
else. Similarly, subroutine DERIV has exclusive control of the step size in the finite-difference
7.3_Control_within_MOPAC_____________________________________________________
calculation of the energy derivatives. If the default values are to be reset, then the new value is
supplied in KEYWRD, and extracted via INDEX and READA. The flow of control is decided by
the presence of various keywords in KEYWRD.
When a subroutine is called, it assumes that all data required for its operation are available
in either common blocks or arguments. Normally no check is made as to the validity of the data
received. All data are "owned" by one, and only one, subroutine. Ownership means the implied
permission and ability to change the data. Thus MOLDAT "owns" the number of atomic orbitals,
in that it calculates this number, and stores it in the variable NORBS. Many subroutines use
NORBS, but none of them is allowed to change it. For obvious reasons no exceptions should be
made to this rule. To illustrate the usefulness of this convention, consider the eigenvectors, C and
CBETA. These are owned by ITER. Before ITER is called, C and CBETA are not calculated,
after ITER has been called C and CBETA are known, so any subroutine which needs to use the
eigenvectors can do so in the certain knowledge that they exist.
Any variables which are only used within a subroutine are not passed outside the subroutine
unless an overriding reason exists. This is found in PULAY and CNVG, among others where arrays
used to hold spin-dependent data are used, and these cannot conveniently be defined within the
subroutines. In these examples, the relevant arrays are "owned" by ITER.
A general subroutine, of which ITER is a good example, handles three kinds of data: First,
data which the subroutine is going to work on, for example the one and two electron matrices;
second, data necessary to manipulate the first set of data, such as the number of atomic orbitals;
third, the calculated quantities, here the electronic energy, and the density and Fock matrices.
Reference data are entered into a subroutine by way of the common blocks. This is to emphasize
their peripheral role. Thus the number of orbitals, while essential to ITER, is not central to the
task it has to perform, and is passed through a common block.
Data the subroutine is going to work on are passed via the argument list. Thus the one and
two electron matrices, which are the main reason for ITER's existence, are entered as two of the
four arguments. As ITER does not own these matrices it can use them but may not change their
contents. The other argument is EE, the electronic energy. EE is owned by ITER even though it
first appears before ITER is called.
Sometimes common block data should more correctly appear in an argument list. This is
usually not done in order to prevent obscuring the main role the subroutine has to perform. Thus
ITER calculates the density and Fock matrices, but these are not represented in the argument list
as the calling subroutine never needs to know them; instead, they are stored in common.
7.3.1 Subroutine GMETRY
Description for programmers
GMETRY has two arguments, GEO and COORD. On input GEO contains either (a) internal
coordinates or (b) cartesian coordinates. On exit COORD contains the cartesian coordinates.
The normal mode of usage is to supply the internal coordinates, in which case the connectivity
relations are found in common block GEOKST.
If the contents of NA(1) is zero, as required for any normal system, then the normal internal
to cartesian conversion is carried out.
If the contents of NA(1) is 99, then the coordinates found in GEO are assumed to be cartesian,
and no conversion is made. This is the situation in a FORCE calculation.
A further option exists within the internal to cartesian conversion. If STEP, stored in common
block REACTN, is non-zero, then a reaction path is assumed, and the internal coordinates are
adjusted radially in order that the "distance" in internal coordinate space from the geometry
specified in GEO is STEPP away from the geometry stored in GEOA, stored in REACTN.
During the internal to cartesian conversion, the angle between the three atoms used in defining
a fourth atom is checked to ensure that it is not near to 0 or 180 degrees. If it is near to these
angles, then there is a high probability that a faulty geometry will be generated and to prevent
this the calculation is stopped and an error message printed.
_______________________________________________________________Program_______
Note:
1. If the angle is exactly 0 or 180 degrees, then the calculation is not terminated: This is the
normal situation in a high-symmetry molecule such as propyne.
2. The check is only made if the fourth atom has a bond angle which is not zero or 180 degrees.
Chapter 8
Error messages produced by
MOPAC
MOPAC produces several hundred messages, all of which are intended to be self-explanatory.
However, when an error occurs it is useful to have more information than is given in the standard
messages.
The following alphabetical list gives more complete definitions of the messages printed.
AN UNOPTIMIZABLE GEOMETRIC PARAMETER : : :
When internal coordinates are supplied, six coordinates cannot be optimized. These are the three
coordinates of atom 1, the angle and dihedral on atom 2 and the dihedral on atom 3. An attempt
has been made to optimize one of these. This is usually indicative of a typographic error, but
might simply be an oversight. Either way, the error will be corrected and the calculation will not
be stopped here.
ATOM NUMBER nn IS ILLDEFINED
The rules for definition of atom connectivity are:
1. Atom 2 must be connected to atom 1 (default - no override)
2. Atom 3 must be connected to atom 1 or 2, and make an angle with 2 or 1.
3. All other atoms must be defined in terms of already-defined atoms: these atoms must all
be different. Thus atom 9 might be connected to atom 5, make an angle with atom 6, and
have a dihedral with atom 7. If the dihedral was with atom 5, then the geometry definition
would be faulty.
If any of these rules is broken, a fatal error message is printed, and the calculation stopped.
ATOMIC NUMBER nn IS NOT AVAILABLE : : :
An element has been used for which parameters are not available. Only if a typographic error has
been made can this be rectified. This check is not exhaustive, in that even if the elements are
acceptable there are some combinations of elements within MINDO/3 that are not allowed. This
is a fatal error message.
ATOMIC NUMBER OF nn ?
An atom has been specified with a negative or zero atomic number. This is normally caused by
forgetting to specify an atomic number or symbol. This is a fatal error message.
________________________________________Error_messages_produced_by_MOPAC_______________
ATOMS nn AND nn ARE SEPARATED BY nn.nnnn ANGSTROMS
Two genuine atoms (not dummies) are separated by a very small distance. This can occur when a
complicated geometry is being optimized, in which case the user may wish to continue. This can
be done by using the keyword GEO-OK. More often, however, this message indicates a mistake,
and the calculation is, by default, stopped.
ATTEMPT TO GO DOWNHILL IS UNSUCCESSFUL : : :
A quite rare message, produced by Bartel's gradient norm minimization. Bartel's method attempts
to minimize the gradient norm by searching the gradient space for a minimum. Apparently a
minimum has been found, but not recognized as such. The program has searched in all (3N - 6)
directions, and found no way down, but the criteria for a minimum have not been satisfied. No
advice is available for getting round this error.
BOTH SYSTEMS ARE ON THE SAME SIDE : : :
A non-fatal message, but still cause for concern. During a SADDLE calculation the two geometries
involved are on opposite sides of the transition state. This situation is verified at every point by
calculating the cosine of the angle between the two gradient vectors. For as long as it is negative,
then the two geometries are on opposite sides of the T/S. If, however, the cosine becomes positive,
then the assumption is made that one moiety has fallen over the T/S and is now below the other
geometry. That is, it is now further from the T/S than the other, temporarily fixed, geometry. To
correct this, identify geometries corresponding to points on each side of the T/S. (Two geometries
on the output separated by the message "SWAPPING...") and make up a new data-file using these
geometries. This corresponds to points on the reaction path near to the T/S. Run a new job
using these two geometries, but with BAR set to a third or a quarter of its original value, e.g.
BAR=0.05. This normally allows the T/S to be located.
C.I. NOT ALLOWED WITH UHF
There is no UHF configuration interaction calculation in MOPAC. Either remove the keyword
that implies C.I. or the word UHF.
CALCULATION ABANDONED AT THIS POINT
A particularly annoying message! In order to define an atom's position, the three atoms used in
the connectivity table must not accidentally fall into a straight line. This can happen during a
geometry optimization or gradient minimization. If they do, and if the angle made by the atom
being defined is not zero or 180 degrees, then its position becomes ill-defined. This is not desirable,
and the calculation will stop in order to allow corrective action to be taken. Note that if the three
atoms are in an exactly straight line, this message will not be triggered. The good news is that the
criterion used to trigger this message was set too coarsely. The criterion has been tightened so that
this message now does not often appear. Geometric integrity does not appear to be compromized.
CARTESIAN COORDINATES READ IN, AND CALCULATION : : :
If cartesian coordinates are read in, but the calculation is to be carried out using internal coordi-
nates, then either all possible geometric variables must be optimized, or none can be optimized. If
only some are marked for optimization then ambiguity exists. For example, if the "X" coordinate
of atom 6 is marked for optimization, but the "Y" is not, then when the conversion to internal
coordinates takes place, the first coordinate becomes a bond-length, and the second an angle.
These bear no relationship to the "X" or "Y" coordinates. This is a fatal error.
Error_messages_produced_by_MOPAC_____________________________________________
CARTESIAN COORDINATES READ IN, AND SYMMETRY : : :
If cartesian coordinates are read in, but the calculation is to be carried out using internal coordi-
nates, then any symmetry relationships between the cartesian coordinates will not be reflected in
the internal coordinates. For example, if the "Y" coordinates of atoms 5 and 6 are equal, it does
not follow that the internal coordinate angles these atoms make are equal. This is a fatal error.
ELEMENT NOT FOUND
When an external file is used to redefine MNDO, AM1, or PM3 parameters, the chemical symbols
used must correspond to known elements. Any that do not will trigger this fatal message.
ERROR DURING READ AT ATOM NUMBER : : :
Something is wrong with the geometry data. In order to help find the error, the geometry already
read in is printed. The error lies either on the last line of the geometry printed, or on the next
(unprinted) line. This is a fatal error.
FAILED IN SEARCH, SEARCH CONTINUING
Not a fatal error. The McIver-Komornicki gradient minimization involves use of a line-search
to find the lowest gradient. This message is merely advice. However, if SIGMA takes a long
time, consider doing something else, such as using NLLSQ, or refining the geometry a bit before
resubmitting it to SIGMA.
<<<<----**** FAILED TO ACHIEVE SCF. ****---->>>>
The SCF calculation failed to go to completion; an unwanted and depressing message that unfor-
tunately appears every so often.
To date three unconditional convergers have appeared in the literature: the SHIFT technique,
Pulay's method, and the Camp-King converger. It would not be fair to the authors to condemn
their methods. In MOPAC all sorts of weird and wonderful systems are calculated, systems the
authors of the convergers never dreamed of. MOPAC uses a combination of all three convergers
at times. Normally only a quadratic damper is used.
If this message appears, suspect first that the calculation might be faulty, then, if you feel
confident, use PL to monitor a single SCF. Based on the SCF results either increase the number
of allowed iterations, default: 200, or use PULAY, or Camp-King, or a mixture.
If nothing works, then consider slackening the SCF criterion. This will allow heats of formation
to be calculated with reasonable precision, but the gradients are likely to be imprecise.
GEOMETRY TOO UNSTABLE FOR EXTRAPOLATION : : :
In a reaction path calculation the initial geometry for a point is calculated by quadratic extrapo-
lation using the previous three points.
If a quadratic fit is likely to lead to an inferior geometry, then the geometry of the last point
calculated will be used. The total effect is to slow down the calculation, but no user action is
recommended.
** GRADIENT IS TOO LARGE TO ALLOW : : :
Before a FORCE calculation can be performed the gradient norm must be so small that the
third and higher order components of energy in the force field are negligible. If, in the system
under examination, the gradient norm is too large, the gradient norm will first be reduced using
FLEPO, unless LET has been specified. In some cases the FORCE calculation may be run only
to decide if a state is a ground state or a transition state, in which case the results have only two
interpretations. Under these circumstances, LET may be warranted.
________________________________________Error_messages_produced_by_MOPAC_______________
GRADIENT IS VERY LARGE : : :
In a calculation of the thermodynamic properties of the system, if the rotation and translation
vibrations are non-zero, as would be the case if the gradient norm was significant, then these
`vibrations' would interfere with the low-lying genuine vibrations. The criteria for THERMO are
much more stringent than for a vibrational frequency calculation, as it is the lowest few genuine
vibrations that determine the internal vibrational energy, entropy, etc.
ILLEGAL ATOMIC NUMBER
An element has been specified by an atomic number which is not in the range 1 to 107. Check
the data: the first datum on one of the lines is faulty. Most likely line 4 is faulty.
IMPOSSIBLE NUMBER OF OPEN SHELL ELECTRONS
The keyword OPEN(n1,n2) has been used, but for an even-electron system n1 was specified as
odd or for an odd-electron system n1 was specified as even. Either way, there is a conflict which
the user must resolve.
IMPOSSIBLE OPTION REQUESTED
A general catch-all. This message will be printed if two incompatible options are used, such as
both MINDO/3 and AM1 being specified. Check the keywords, and resolve the conflict.
INTERNAL COORDINATES READ IN, AND CALCULATION : : :
If internal coordinates are read in, but the calculation is to be carried out using cartesian coordi-
nates, then either all possible geometric variables must be optimized, or none can be optimized.
If only some are marked for optimization, then ambiguity exists. For example, if the bond-length
of atom 6 is marked for optimization, but the angle is not, then when the conversion to cartesian
coordinates takes place, the first coordinate becomes the `X' coordinate and the second the `Y'
coordinate. These bear no relationship to the bond length or angle. This is a fatal error.
INTERNAL COORDINATES READ IN, AND SYMMETRY : : :
If internal coordinates are read in, but the calculation is to be carried out using cartesian coordi-
nates, then any symmetry relationships between the internal coordinates will not be reflected in
the cartesian coordinates. For example, if the bond-lengths of atoms 5 and 6 are equal, it does
not follow that these atoms have equal values for their `X' coordinates. This is a fatal error.
JOB STOPPED BY OPERATOR
Any MOPAC calculation, for which the SHUTDOWN command works, can be stopped by a user
who issues the command "$SHUT , from the directory which contains .DAT.
MOPAC will then stop the calculation at the first convenient point, usually after the current
cycle has finished. A restart file will be written and the job ended. The message will be printed
as soon as it is detected, which would be the next time the timer routine is accessed.
**** MAX. NUMBER OF ATOMS ALLOWED: : : :
At compile time the maximum sizes of the arrays in MOPAC are fixed. The system being run
exceeds the maximum number of atoms allowed. To rectify this, modify the file DIMSIZES.DAT
to increase the number of heavy and light atoms allowed. If DIMSIZES.DAT is altered, then the
whole of MOPAC should be re-compiled and re-linked.
Error_messages_produced_by_MOPAC_____________________________________________
**** MAX. NUMBER OF ORBITALS: : : :
At compile time the maximum sizes of the arrays in MOPAC are fixed. The system being run
exceeds the maximum number of orbitals allowed. To rectify this, modify the file DIMSIZES.DAT
to change the number of heavy and light atoms allowed. If DIMSIZES.DAT is altered, then the
whole of MOPAC should be re-compiled and re-linked.
**** MAX. NUMBER OF TWO ELECTRON INTEGRALS : : :
At compile time the maximum sizes of the arrays in MOPAC are fixed. The system being run
exceeds the maximum number of two-electron integrals allowed. To rectify this, modify the file
DIMSIZES.DAT to modify the number of heavy and light atoms allowed. If DIMSIZES.DAT is
altered, then the whole of MOPAC should be re-compiled and re-linked.
NAME NOT FOUND
Various atomic parameters can be modified in MOPAC by use of EXTERNAL=. These comprise:
Uss Betas Gp2 GSD
Upp Betap Hsp GPD
Udd Betad AM1 GDD
Zs Gss Expc FN1
Zp Gsp Gaus FN2
Zd Gpp Alp FN3
Thus to change the Uss of hydrogen to -13:6 the line USS H -13.6 could be used. If
an attempt is made to modify any other parameters, then an error message is printed, and the
calculation terminated.
NUMBER OF PARTICLES, nn GREATER THAN : : :
When user-defined microstates are not used, the MECI will calculate all possible microstates that
satisfy the space and spin constraints imposed. This is done in PERM, which permutes N electrons
in M levels. If N is greater than M, then no possible permutation is valid. This is not a fatal error
- the program will continue to run, but no C.I. will be done.
NUMBER OF PERMUTATIONS TOO GREAT, LIMIT 60
The number of permutations of alpha or beta microstates is limited to 60. Thus if 3 alpha electrons
are permuted among 5 M.O.'s, that will generate 10 = 5!=(3!2!) alpha microstates, which is an
allowed number. However if 4 alpha electrons are permuted among 8 M.O.'s, then 70 alpha
microstates result and the arrays defined will be insufficient. Note that 60 alpha and 60 beta
microstates will permit 3600 microstates in all, which should be more than sufficient for most
purposes. (An exception would be for excited radical icosohedral systems.)
SYMMETRY SPECIFIED, BUT CANNOT BE USED IN DRC
This is self explanatory. The DRC requires all geometric constraints to be lifted. Any symmetry
constraints will first be applied, to symmetrize the geometry, and then removed to allow the
calculation to proceed.
SYSTEM DOES NOT APPEAR TO BE OPTIMIZABLE
This is a gradient norm minimization message. These routines will only work if the nearest
minimum to the supplied geometry in gradient-norm space is a transition state or a ground state.
Gradient norm space can be visualized as the space of the scalar of the derivative of the energy
________________________________________Error_messages_produced_by_MOPAC_______________
space with respect to geometry. To a first approximation, there are twice as many minima in
gradient norm space as there are in energy space.
It is unlikely that there exists any simple way to refine a geometry that results in this message.
While it is appreciated that a large amount of effort has probably already been expended in
getting to this point, users should steel themselves to writing off the whole geometry. It is not
recommended that a minor change be made to the geometry and the job re-submitted.
Try using SIGMA instead of POWSQ.
TEMPERATURE RANGE STARTS TOO LOW, : : :
The thermodynamics calculation assumes that the statistical summations can be replaced by
integrals. This assumption is only valid above 100K, so the lower temperature bound is set to 100,
and the calculation continued.
THERE IS A RISK OF INFINITE LOOPING : : :
The SCF criterion has been reset by the user, and the new value is so small that the SCF test
may never be satisfied. This is a case of user beware!
THIS MESSAGE SHOULD NEVER APPEAR, CONSULT A PROGRAMMER!
This message should never appear; a fault has been introduced into MOPAC, most probably as a
result of a programming error. If this message appears in the vanilla version of MOPAC (a version
ending in 00), please contact JJPS as I would be most interested in how this was achieved.
THREE ATOMS BEING USED TO DEFINE : : :
If the cartesian coordinates of an atom depend on the dihedral angle it makes with three other
atoms, and those three atoms fall in an almost straight line, then a small change in the cartesian
coordinates of one of those three atoms can cause a large change in its position. This is a potential
source of trouble, and the data should be changed to make the geometric specification of the atom
in question less ambiguous.
This message can appear at any time, particularly in reaction path and saddle-point calcula-
tions.
An exception to this rule is if the three atoms fall into an exactly straight line. For example,
if, in propyne, the hydrogens are defined in terms of the three carbon atoms, then no error will
be flagged. In such a system the three atoms in the straight line must not have the angle between
them optimized, as the finite step in the derivative calculation would displace one atom off the
straight line and the error-trap would take effect.
Correction involves re-defining the connectivity. LET and GEO-OK will not allow the calcu-
lation to proceed.
- - - - - - - TIME UP - - - - - - -
The time defined on the keywords line or 3,600 seconds, if no time was specified, is likely to be
exceeded if another cycle of calculation were to be performed. A controlled termination of the
run would follow this message. The job may terminate earlier than expected: this is ordinarily
due to one of the recently completed cycles taking unusually long, and the safety margin has been
increased to allow for the possibility that the next cycle might also run for much longer than
expected.
TRIPLET SPECIFIED WITH ODD NUMBER OF ELECTRONS
If TRIPLET has been specified the number of electrons must be even. Check the charge on the
system, the empirical formula, and whether TRIPLET was intended.
Error_messages_produced_by_MOPAC_____________________________________________
""""""""""""""UNABLE TO ACHIEVE SELF-CONSISTENCY
See the error-message: <<<<----**** FAILED TO ACHIEVE SCF. ****---->>>>.
UNDEFINED SYMMETRY FUNCTION USED
Symmetry operations are restricted to those defined, i.e., in the range 1-18. Any other symmetry
operations will trip this fatal message.
UNRECOGNIZED ELEMENT NAME
In the geometric specification a chemical symbol which does not correspond to any known element
has been used. The error lies in the first datum on a line of geometric data.
**** WARNING ****
Don't pay too much attention to this message. Thermodynamics calculations require a higher
precision than vibrational frequency calculations. In particular, the gradient norm should be very
small. However, it is frequently not practical to reduce the gradient norm further, and to date
no-one has determined just how slack the gradient criterion can be before unacceptable errors
appear in the thermodynamic quantities. The 0.4 gradient norm is only a suggestion.
WARNING: INTERNAL COORDINATES : : :
Triatomics are, by definition, defined in terms of internal coordinates. This warning is only a
reminder. For diatomics, cartesian and internal coordinates are the same. For tetra-atomics
and higher, the presence or absence of a connectivity table distinguishes internal and cartesian
coordinates, but for triatomics there is an ambiguity. To resolve this, cartesian coordinates are
not allowed for the data input for triatomics.
________________________________________Error_messages_produced_by_MOPAC_______________
Chapter 9
Criteria
MOPAC uses various criteria which control the precision of its stages. These criteria are chosen
as the best compromise between speed and acceptable errors in the results. The user can override
the default settings by use of keywords; however, care should be exercised as increasing a criterion
can introduce the potential for infinite loops, and decreasing a criterion can result in unacceptably
imprecise results. These are usually characterized by `noise' in a reaction path, or large values for
the trivial vibrations in a force calculation.
9.1 SCF criterion
Name: SCFCRT.
Defined in ITER.
Default value 0.0001 kcal/mole
Basic Test Change in energy in kcal/mole on successive
iterations is less than SCFCRT.
Exceptions: If PRECISE is specified, SCFCRT=0.000001
If a polarization calculation SCFCRT=1.D-11
If a FORCE calculation SCFCRT=0.0000001
If SCFCRT=n.nnn is specified SCFCRT=n.nnn
If a BFGS optimization, SCFCRT becomes a function
of the difference between the current energy and
the lowest energy of previous SCFs.
Secondary tests: (1) Change in density matrix elements on two
successive iterations must be less than 0.001
(2) Change in energy in eV on three successive
iterations must be less than 10 x SCFCRT.
9.2 Geometric optimization criteria
Name: TOLERX "Test on X Satisfied"
Defined in FLEPO
Default value 0.0001 Angstroms
Basic Test The projected change in geometry is less than
TOLERX Angstroms.
Exceptions If GNORM is specified, the TOLERX test is not used.
Name: DELHOF "Herbert's Test Satisfied"
_______________________________________________________Criteria____
Defined in FLEPO
Default value 0.001
Basic Test The projected decrease in energy is less than
DELHOF kcals/mole.
Exceptions If GNORM is specified, the DELHOF test is not used.
Name: TOLERG "Test on Gradient Satisfied"
Defined in FLEPO
Default value 1.0
Basic Test The gradient norm in kcals/mole/Angstrom is less
than TOLERG multiplied by the square root of the
number of coordinates to be optimized.
Exceptions If GNORM=n.nnn is specified, TOLERG=n.nnn divided
by the square root of the number of coordinates
to be optimized, and the secondary tests are not
done. If LET is not specified, n.nnn is reset to
0.01, if it was smaller than 0.01.
If PRECISE is specified, TOLERG=0.2
If a SADDLE calculation, TOLERG is made a function
of the last gradient norm.
Name: TOLERF "Heat of Formation Test Satisfied"
Defined in FLEPO
Default value 0.002 kcal/mole
Basic Test The calculated heats of formation on two successive
cycles differ by less than TOLERF.
Exceptions If GNORM is specified, the TOLERF test is not used.
Secondary Tests For the TOLERG, TOLERF, and TOLERX tests, a
second test in which no individual component of the
gradient should be larger than TOLERG must be
satisfied.
Other Tests If, after the TOLERG, TOLERF, or TOLERX test has been
satisfied three consecutive times the heat of
formation has dropped by less than 0.3kcal/mole, then
the optimization is stopped.
Exceptions If GNORM is specified, then this test is not performed.
Name: TOL2
Defined in POWSQ
Default value 0.4
Basic Test The absolute value of the largest component of the
gradient is less than TOL2
Exceptions If PRECISE is specified, TOL2=0.01
If GNORM=n.nn is specified, TOL2=n.nn
If LET is not specified, TOL2 is reset to
0.01, if n.nn was smaller than 0.01.
9.2_Geometric_optimization_criteria____________________________________________________
Name: TOLS1
Defined in NLLSQ
Default Value 0.000 000 000 001
Basic Test The square of the ratio of the projected change in the
geometry to the actual geometry is less than TOLS1.
Name:
Defined in NLLSQ
Default Value 0.2
Basic Test Every component of the gradient is less than 0.2.
_______________________________________________________Criteria____
Chapter 10
Debugging
There are three potential sources of difficulty in using MOPAC, each of which requires special
attention. There can be problems with data, due to errors in the data, or MOPAC may be called
upon to do calculations for which it was not designed. There are intrinsic errors in MOPAC which
extensive testing has not yet revealed, but which a user's novel calculation uncovers. Finally there
can be bugs introduced by the user modifying MOPAC, either to make it compatible with the
host computer, or to implement local features.
For whatever reason, the user may need to have access to more information than the normal
keywords can provide, and a second set, specifically for debugging, is provided. These keywords
give information about the working of individual subroutines, and do not affect the course of the
calculation.
10.1 Debugging keywords
A full list of keywords for debugging subroutines:
1ELEC the one-electron matrix. Note 1
COMPFG Heat of Formation.
DCART Cartesian derivatives.
DEBUG Note 2
DEBUGPULAY Pulay matrix, vector, and error-function. Note 3
DENSITY Every density matrix. Note 1
DERI1 Details of DERI1 calculation
DERI2 Details of DERI2 calculation
DERITR Details of DERITR calculation
DERIV All gradients, and other data in DERIV.
DERNVO Details of DERNVO calculation
DFORCE Print Force Matrix.
DIIS Details of DIIS calculation
EIGS All eigenvalues.
FLEPO Details of BFGS minimization.
FMAT
FOCK Every Fock matrix Note 1
HCORE The one electron matrix, and two electron integrals.
ITER Values of variables and constants in ITER.
LARGE Increases amount of output generated by other keywords.
LINMIN Details of line minimization (LINMIN, LOCMIN, SEARCH)
MOLDAT Molecular data, number of orbitals, "U" values, etc.
MECI C.I. matrices, M.O. indices, etc.
PL Differences between density matrix elements Note 4
_____________________________________________________________Debugging_______
in ITER.
LINMIN Function values, step sizes at all points in the
line minimization (LINMIN or SEARCH).
TIMES Times of stages within ITER.
VECTORS All eigenvectors on every iteration. Note 1
Notes
1. These keywords are activated by the keyword DEBUG. Thus if DEBUG and FOCK are both
specified, every Fock matrix on every iteration will be printed.
2. DEBUG is not intended to increase the output, but does allow other keywords to have a
special meaning.
3. PULAY is already a keyword, so DEBUGPULAY was an obvious alternative.
4. PL initiates the output of the value of the largest difference between any two density matrix
elements on two consecutive iterations. This is very useful when investigating options for
increasing the rate of convergence of the SCF calculation.
Suggested procedure for locating bugs
Users are supplied with the source code for MOPAC, and, while the original code is fairly bug-free,
after it has been modified there is a possibility that bugs may have been introduced. In these
circumstances the author of the changes is obviously responsible for removing the offending bug,
and the following ideas might prove useful in this context.
First of all, and most important, before any modifications are done a back-up copy of the
standard MOPAC should be made. This will prove invaluable in pinpointing deviations from the
standard working. This point cannot be over-emphasized _ make a back-up before modifying
MOPAC!.
Clearly, a bug can occur almost anywhere, and a logical search sequence is necessary in order
to minimize the time taken to locate it.
If possible, perform the debugging with a small molecule, in order to save time (debugging is,
of necessity, time consuming) and to minimize output.
The two sets of subroutines in MOPAC, those involved with the electronics and those involved
in the geometrics, are kept strictly separate, so the first question to be answered is which set
contains the bug. If the heats of formation, derivatives, I.P.s, and charges, etc., are correct, the
bug lies in the geometrics; if faulty, in the electronics.
Bug in the Electronics Subroutines
Use formaldehyde for this test. The supplied data-file MNRSD1.DAT could be used as a template
for this operation. Use keywords 1SCF, DEBUG, and any others necessary.
The main steps are:
1. Check the starting one-electron matrix and two-electron integral string, using the keyword
HCORE. It is normally sufficient to verify that the two hydrogen atoms are equivalent, and
that the pi system involves only pz on oxygen and carbon. Note that numerical values are
not checked, but only relative values.
If an error is found, use MOLDAT to verify the orbital character, etc.
If faulty the error lies in READ, GETGEO or MOLDAT.
Otherwise the error lies in HCORE, H1ELEC or ROTATE.
If the starting matrices are correct, go on to step (2).
10.1_Debugging_keywords______________________________________________________
2. Check the density or Fock matrix on every iteration, with the words FOCK or DENSITY.
Check the equivalence of the two hydrogen atoms, and the pi system, as in (1).
If an error is found, check the first Fock matrix. If faulty, the bug lies in ITER, probably in
the Fock subroutines FOCK1 or FOCK2. or in the (guessed) density matrix (MOLDAT).
An exception is in the UHF closed-shell calculation, where a small asymmetry is introduced
to initiate the separation of the alpha and beta UHF wavefunctions.
If no error is found, check the second Fock matrix. If faulty, the error lies in the density
matrix DENSIT, or the diagonalization RSP.
If the Fock matrix is acceptable, check all the Fock matrices. If the error starts in iterations
2 to 4, the error probably lies in CNVG, if after that, in PULAY, if used.
If SCF is achieved, and the heat of formation is faulty, check HELECT. If C.I. was used
check MECI.
If the derivatives are faulty, use DCART to verify the cartesian derivatives. If these are
faulty, check DCART and DHC. If they are correct, or not calculated, check the DERIV finite
difference calculation. If the wavefunction is non-variationally optimized, check DERNVO.
If the geometric calculation is faulty, use FLEPO to monitor the optimization, DERIV may
also be useful here.
For the FORCE calculation, DCART or DERIV are useful for variationally optimized func-
tions, COMPFG for non-variationally optimized functions.
For reaction paths, verify that FLEPO is working correctly; if so, then PATHS is faulty.
For saddle-point calculations, verify that FLEPO is working correctly; if so, then REACT1
is faulty.
Keep in mind the fact that MOPAC is a large calculation, and while intended to be versatile,
many combinations of options have not been tested. If a bug is found in the original code,
please communicate details to the Academy, to Dr. James J. P. Stewart, Frank J. Seiler Research
Laboratory, U.S. Air Force Academy, Colorado Springs, CO 80840-6528.
_____________________________________________________________Debugging_______
Chapter 11
Installing MOPAC
MOPAC is distributed on a magnetic tape as a set of FORTRAN-77 files, along with ancillary
documents such as command, help, data and results files. The format of the tape is that of
DIGITAL'S VAX computers. The following instructions apply only to users with VAX computers:
users with other machines should use the following instructions as a guide to getting MOPAC up
and running.
1. Put the magnetic tape on the tape drive, write protected.
2. Allocate the tape drive with a command such as $ALLOCATE MTA0:
3. Go into an empty directory which is to hold MOPAC
4. Mount the magnetic tape with the command $MOUNT MTA0: MOPAC
5. Copy all the files from the tape with the command $COPY MTA0:*.* *
A useful operation after this would be to make a hard copy of the directory. You should now
have the following sets of files in the directory:
1. A file, AAAINVOICE.TXT, summarizing this list.
2. A set of FORTRAN-77 files, see Appendix A.
3. The command files COMPILE, MOPACCOM, MOPAC, RMOPAC, and SHUT.
4. A file, MOPAC.OPT, which lists all the object modules used by MOPAC.
5. Help files MOPAC.HLP and HELP.FOR
6. A text file MOPAC.MAN.
7. A manual summarizing the updates, called UPDATE.MAN.
8. Two test-data files: TESTDATA.DAT and MNRSD1.DAT, and corresponding results files,
TESTDATA.OUT and MNRSD1.OUT.
Structure of command files: COMPILE
The parameter file DIMSIZES.DAT should be read and, if necessary, modified before COMPILE
is run.
DO NOT RUN COMPILE AT THIS TIME!!
_________________________________________________Installing_MOPAC____________
COMPILE should be run once only. It assigns DIMSIZES.DAT, the block of FORTRAN
which contains the PARAMETERS for the dimension sizes to the logical name "SIZES". This is
a temporary assignment, but the user is strongly recommended to make it permanent by suitably
modifying LOGIN file(s). COMPILE is a modified version of Maj Donn Storch's COMPILE for
DRAW-2.
All the FORTRAN files are then compiled, using the array sizes given in DIMSIZES.DAT: these
should be modified before COMPILE is run. If, for whatever reason, DIMSIZES.DAT needs to be
changed, then COMPILE should be re-run, as modules compiled with different DIMSIZES.DAT
will be incompatible.
The parameters within DIMSIZES.DAT that the user can modify are MAXLIT, MAXHEV,
MAXTIM and MAXDMP. MAXLIT is assigned a value equal to the largest number of hydrogen
atoms that a MOPAC job is expected to run, MAXHEV is assigned the corresponding number of
heavy (non-hydrogen) atoms. The ratio of light to heavy atoms should not be less than 1/2. Do
not set MAXHEV or MAXLIT less than 7. If you do, some subroutines will not compile correctly.
Some molecular orbital eigenvector arrays are overlapped with Hessian arrays, and to prevent
compilation time error messages, the number of allowed A.O.'s must be greater than, or equal to
three times the number of allowed real atoms. MAXTIM is the default maximum time in seconds
a job is allowed to run before either completion or a restart file being written. MAXDMP is the
default time in seconds for the automatic writing of the restart files. If your computer is very
reliable, and disk space is at a premium, you might want to set MAXDMP as MAXDMP=999999.
If SYBYL output is wanted, set ISYBYL to 1, otherwise set it to zero.
If you want, NMECI can be changed. Setting it to 1 will save some space, but will prevent all
C.I. calculations except simple radicals.
If you want, NPULAY can be set to 1. This saves memory, but also disables the PULAY
converger.
If you want, MESP can be varied. This is only meaningful if ESP is installed.
Compile MOPAC. This operation takes about 7 minutes, and should be run "on-line", as a
question and answer session is involved.
When everything is successfully compiled, the object files will then be assembled into an
executable image called MOPAC.EXE. Once the image exists, there is no reason to keep the
object files, and if space is at a premium these can be deleted at this time.
If you need to make any changes to any of the files, COMPILE followed by the names of the
changed files will reconstruct MOPAC, provided all the other OBJ files exist. For example, if you
change the version number in DIMSIZES.DAT, then READ.FOR and WRITE.FOR are affected
and will need to be recompiled. This can be done using the command @COMPILE WRITE,READ
In the unlikely event that you want to link only, use the command @COMPILE LINK
Sometimes the link stage will fail, and give the message
"%LINK-E-INSVIRMEM, insufficient virtual memory for 2614711. pages
-LINK-E-NOIMGFIL, image file not created",
or your MOPAC will not run due to the size of the image. In these cases you should ask the
system manager to alter your PGFLQUO and WSEXTENT limits. Possibly the system limits,
VIRTUALPAGECNT CURRENT and MAX will need to be changed. As an example, on a
Microvax 3600 with 16Mb of memory:
PGFLQUO=50000, WSEXTENT=16000, VIRTUALPAGECNT CURRENT=40768,
VIRTUALPAGECNT MAX=600000
are sufficient for the default MOPAC values of 43 heavy and 43 light atoms.
In order for users to have access to MOPAC they must insert in their individual LOGIN.COM
files the line:
$@ MOPACCOM
where is the name of the disk and directory which holds all the MOPAC files.
For example:
Installing_MOPAC_____________________________________________________________
DRA0:[MOPAC]
thus: $@ DRA0:[MOPAC]MOPAC
MOPACCOM.COM should be modified once to accommodate local definitions of the di-
rectory which is to hold MOPAC. This change must also be made to RMOPAC.COM and to
MOPAC.COM.
MOPAC
This command file submits a MOPAC job to a queue. Before use, MOPAC.COM should be
modified to suit local conditions. The user's VAX is assumed to run three queues, called QUEUE3,
QUEUE2, and QUEUE1. The user should substitute the actual names of the VAX queues for these
symbolic names. Thus, for example, if the local names of the queues are "TWELVEHOUR", for
jobs of length up to 12 hours, "ONEHOUR", for jobs of less than one hour, and "30MINS" for quick
jobs, then in place of "QUEUE3", "QUEUE2", and "QUEUE1" the words "TWELVEHOUR",
"ONEHOUR", and "30MINS" should be inserted.
RMOPAC
RMOPAC is the command file for running MOPAC. It assigns all the data files that MOPAC
uses to the channels. If the user wants to use other file-name endings than those supplied, the
modifications should be made to RMOPAC.
When a long job ends, RMOPAC will also send a mail message to the user giving a brief
description of the job. You may want to change the default definition of "a long job"; currently it
is 12 hours. This feature was written by Dr. James Petts of Kodak Ltd Research Labs.
A recommended sequence of operations to get MOPAC up and running would be:
1. Modify the file DIMSIZES.DAT. The default sizes are 40 heavy atoms and 40 light atoms.
Do not make the size less than 7 by 7.
2. Read through the COMMAND files to familiarize yourself with what is being done.
3. Edit the file MOPAC.COM to use the local queue names.
4. Edit the file RMOPAC.COM if the default file-names are not acceptable.
5. Edit MOPACCOM.COM to assign MOPACDIRECTORY to the disk and directory which
will hold MOPAC.
6. Edit the individual LOGIN.COM files to insert the following line:
$@ MOPACCOM
Note that MOPACDIRECTORY cannot be used, as the definition of MOPACDIRECTORY
is made in MOPACCOM.COM
7. Execute the modified LOGIN command so that the new commands are effective.
8. Run COMPILE.COM. This takes about 8 minutes to execute.
9. Enter the command $MOPAC
You will receive the message What file? : to which the reply should be the actual data-file
name. For example, "MNRSD1", the file is assumed to end in .DAT, e.g. MNRSD1.DAT.
You will then be prompted for the queue:
What queue? :
_________________________________________________Installing_MOPAC____________
Any queue defined in MOPAC.COM will suffice: "SYS$BATCH"
Finally, the priority will be requested: What priority? [5]: To which any value between 1
and 5 will suffice. Note that the maximum priority is limited by the system (manager).
11.1 ESP calculation
As supplied, MOPAC will not do the ESP calculation because of the large memory requirement
of the ESP. To install the ESP, make the following changes:
1. Rename ESP.ROF to ESP.FOR
2. Add to the first line of MOPAC.OPT the string " ESP, " (without the quotation marks).
3. Edit MNDO.FOR to uncomment the line C# CALL ESP.
4. Compile ESP and MNDO, and relink MOPAC using, e.g. @COMPILE ESP,MNDO.
5. If the resulting executable is too large, modify DIMSIZES.DAT to reduce MAXHEV and
MAXLIT, then recompile everything and relink MOPAC with @COMPILE.
To familiarize yourself with the system, the following operations might be useful.
1. Run the (supplied) test molecules, and verify that MOPAC is producing "acceptable" results.
2. Make some simple modifications to the datafiles supplied in order to test your understanding
of the data format
3. When satisfied that MOPAC is working, and that data files can be made, begin production
runs.
Working of SHUTDOWN command
If, for whatever reason, a run needs to be stopped prematurely, the command $SHUT
can be issued. This will execute a small command-language file, which copies the data-file to form
a new file called .END.
The next time MOPAC calls function SECOND, the presence of a readable file called SHUT-
DOWN, logically identified with .END, is checked for, and if it exists, the apparent
elapsed CPU time is increased by 1,000,000 seconds, and a warning message issued. No further
action is taken until the elapsed time is checked to see if enough time remains to do another cycle.
Since an apparently very long time has been used, there is not enough time left to do another
cycle, and the restart files are generated and the run stopped.
SHUTDOWN is completely machine-independent.
Specific instructions for mounting MOPAC on other computers have been left out due to
limitations of space in the Manual; however, the following points may prove useful:
1. Function SECOND is machine-specific. SECOND is double-precision, and should return the
CPU time in seconds, from an arbitary zero of time. If the SHUT command has been issued,
the value returned by SECOND should be increased by 1,000,000.
2. On UNIX-based and other machines, on-line help can be provided by using help.f. Docu-
mentation on help.f is in help.f.
3. OPEN and CLOSE statements are a fruitful source of problems. If MOPAC does not work,
most likely the trouble lies in these statements.
4. RMOPAC.COM should be read to see what files are attached to what logical channel.
11.1_ESP_calculation_________________________________________________________
How to use MOPAC
The COM file to run the MOPAC can be accessed using the command "MOPAC" followed by
none, one, two or three arguments. Possible options are:
MOPAC MYDATAFILE 120 4
MOPAC MYDATAFILE 120
MOPAC MYDATAFILE
In the latter case it is assumed that the shortest queue will be adequate. The COM file to
run the MOPAC can be accessed using the command "MOPAC" followed by none, one or two
arguments. Possible options are:
MOPAC MYDATAFILE 120
MOPAC MYDATAFILE
In the latter case it is assumed that the default time (15 seconds) will be adequate.
MOPAC
In this case you will be prompted for the datafile, and then for the queue. Restarts should be user
transparent. If MOPAC does make any restart files, do not change them (It would be hard to do
anyhow, as they're in machine code), as they will be used when you run a RESTART job. The
files used by MOPAC are:
File Description Logical name
.DAT Data FOR005
.OUT Results FOR006
.RES Restart FOR009
.DEN Density matrix (in binary) FOR010
SYS$OUTPUT LOG file FOR011
.ARC Archive or summary FOR012
.GPT Data for program DENSITY FOR013
.SYB SYBYL data FOR016
SETUP.DAT SETUP data SETUP
Short version
For various reasons it might not be practical to assemble the entire MOPAC program. For example,
your computer may have memory limitations, or you may have very large systems to be run, or
some options may never be wanted. For whatever reason, if using the entire program is undesirable,
an abbreviated version, which lacks the full range of options of the whole program, can be specified
at compile time.
At the bottom of the DIMSIZES.DAT file the programmer is asked for various options to be
used in compiling. These options allow arrays of MECI, PULAY, and ESP to assume their correct
size.
As long as no attempt is made to use the reduced subroutines, the program will function
normally. If an attempt is made to use an option which has been excluded then the program will
error.
Size of MOPAC
The amount of storage required by MOPAC depends mainly on the number of heavy and light
atoms. As it is useful for programmers to have an idea of how large various MOPACs are, the
following data are presented as a guide.
Sizes of various MOPAC Version 6.00 executables in which the number of heavy atoms is equal
to the number of light atoms, assembled on a VAX computer, are:
_________________________________________________Installing_MOPAC____________
No. of heavy atoms Size of Executable (Kbytes)
MOPAC 5.00 MOPAC 6.00 (AMPAC 2.00)
10 1,653 2,054 N/A
20 3,442 4,689 4,590
30 6,356 8,990 9,150
40 10,400 14,955 15,588
50 15,572 22,586 23,944
60 21,872 31,880 34,145
100 58,361 87,519
200 228,602 336.867
300 511,723 754,540
The size, S, of any given MOPAC executable, in Kbytes, may be estimated for MOPAC 5.00
as:
S = 9939 + N * 9:57 + N * N * 5:64
and for MOPAC 6.00 as:
S = 1091 + N * 13:40 + N * N * 8:33
The large increase in size of MOPAC was caused mainly by the inclusion of the analytical
C.I. derivatives. Because they are so much more efficient and accurate than finite differences, and
because computer memory is becoming more available, this increase was accepted as the lesser of
two evils.
The size of MOPAC executables will vary from machine to machine, due to the different sizes of
the code. For a VAX, this amounts to approximately 0.1Mb. Most machines use a 64 bit or 8 byte
double precision real number, so the multipliers of N and N*N should apply to them. For large
jobs, 0.1Mb is negligible, therefore the above expression should be applicable to most computers.
No. of lines in program in Version 5.00 = 22,084 = 17,718 code + 4,366 comment. Version
6.00 = 31,857 = 22,526 code + 9,331 comment.
Appendix A
Names of FORTRAN-77 files
AABABC ANALYT ANAVIB AXIS BLOCK BONDS BRLZON
CALPAR CAPCOR CDIAG CHRGE CNVG COMPFG DATIN
DCART DELMOL DELRI DENROT DENSIT DEPVAR DERI0
DERI1 DERI2 DERI21 DERI22 DERI23 DERITR DERIV
DERNVO DERS DFOCK2 DFPSAV DIAG DIAT DIAT2
DIIS DIJKL1 DIJKL2 DIPIND DIPOLE DOFS DOT
DRC DRCOUT EF ENPART EXCHNG FFHPOL FLEPO
FMAT FOCK1 FOCK2 FORCE FORMXY FORSAV FRAME
FREQCY GEOUT GEOUTG GETGEG GETGEO GETSYM GETTXT
GMETRY GOVER GRID H1ELEC HADDON HCORE HELECT
HQRII IJKL INTERP ITER JCARIN LINMIN LOCAL
LOCMIN MAMULT MATOUT MATPAK MECI MECID MECIH
MECIP MNDO MOLDAT MOLVAL MULLIK MULT NLLSQ
NUCHAR PARSAV PARTXY PATHK PATHS PERM POLAR
POWSAV POWSQ PRTDRC QUADR REACT1 READ READA
REFER REPP ROTAT ROTATE RSP SEARCH SECOND
SETUPG SOLROT SWAP SYMTRY THERMO TIMER UPDATE
VECPRT WRITE WRTKEY WRTTXT XYZINT
___________________________________________Names_of_FORTRAN-77_files_________
Appendix B
Subroutine calls in MOPAC
A list of the program segments which call various subroutines.
SUBROUTINE CALLS
AABABC
AABACD
AABBCD
AINTGS
ANALYT DERS DELRI DELMOL
ANAVIB
AXIS RSP
BABBBC
BABBCD
BANGLE
BFN
BINTGS
BKRSAV GEOUT
BONDS VECPRT MPCBDS
BRLZON CDIAG DOFS
CALPAR
CAPCOR
CDIAG ME08A EC08C SORT
CHRGE
CNVG
COE
COMPFG SETUPG SYMTRY GMETRY TIMER HCORE ITER
DIHED DERIV MECIP
DANG
DATIN UPDATE MOLDAT CALPAR
DCART ANALYT DHC DIHED
DELMOL ROTAT
DELRI
DENROT GMETRY COE
DENSIT
DEPVAR
DERI0
DERI1 TIMER DHCORE SCOPY DFOCK2 SUPDOT MTXM MXM
DIJKL1 MECID MECIH SUPDOT TIMER
DERI2 DERI21 DERI22 MXM OSINV MTXM SCOPY DERI23
____________________________________________Subroutine_calls_in_MOPAC__________________
DIJKL2 MECID MECIH SUPDOT
DERI21 MTXMC HQRII MXM
DERI22 MXM MXMT FOCK2 FOCK1 SUPDOT
DERI23 SCOPY
DERITR SYMTRY GMETRY HCORE ITER DERIV DERNVO DCART
JCARIN MXM GEOUT DERITR
DERNVO DERI0 DERI1 DERI2
DERS
DFOCK2 JAB KAB
DFPSAV XYZINT GEOUT
DHC H1ELEC ROTATE SOLROT FOCK2
DHCORE H1ELEC ROTATE
DIAG EPSETA
DIAGI
DIAT COE GOVER DIAT2
DIAT2 SET
DIHED DANG
DIIS SPACE VECPRT MINV
DIJKL1 FORMXY
DIJKL2
DIPIND CHRGE GMETRY
DIPOLE
DOFS
DRC GMETRY COMPFG PRTDRC
DRCOUT
EA08C EA09C
EA09C
EC08C EA08C
EF BKRSAV COMPFG BKRSAV UPDHES HQRII FORMD SYMTRY
ENPART
EPSETA
EXCHNG
FFHPOL COMPFG DIPIND VECPRT RSP MATOUT
FLEPO DFPSAV COMPFG SCOPY GEOUT SUPDOT LINMIN DIIS
FMAT FORSAV COMPFG CHRGE
FOCK2 JAB KAB
FOCK2D
FORCE GMETRY COMPFG NLLSQ FLEPO WRITE XYZINT AXIS
FMAT VECPRT FRAME RSP MATOUT FREQCY MATOUT
DRC ANAVIB THERMO
FORMD OVERLP
FORMXY
FORSAV
FRAME AXIS
FREQCY BRLZON FRAME RSP
GEOUT XYZINT WRTTXT CHRGE
GEOUTG XXX
GETDAT
GETGEG GETVAL GETVAL GETVAL
GETGEO GEOUT NUCHAR XYZINT
GETSYM
GETTXT UPCASE
GMETRY GEOUT
GOVER
Subroutine_calls_in_MOPAC____________________________________________________
GRID DFPSAV FLEPO GEOUT WRTTXT
H1ELEC DIAT
HADDON DEPVAR
HCORE H1ELEC ROTATE SOLROT VECPRT
HELECT
HQRII
IJKL PARTXY
INTERP HQRII SCHMIT SCHMIB SPLINE
ITER EPSETA VECPRT FOCK2 FOCK1 WRITE INTERP PULAY
HQRII DIAG MATOUT SWAP DENSIT CNVG
JAB
JCARIN SYMTRY GMETRY
KAB
LINMIN COMPFG EXCHNG
LOCAL MATOUT
LOCMIN COMPFG EXCHNG
MNDO GETDAT READ MOLDAT DATIN REACT1 GRID PATHS
PATHK FORCE DRC NLLSQ COMPFG POWSQ EF
FLEPO WRITE POLAR
MAMULT
MATOUT
ME08A ME08B
ME08B
MECI IJKL PERM MECIH VECPRT HQRII MATOUT
MECIH
MECIP MXM
MINV
MOLDAT REFER GMETRY VECPRT
MOLVAL
MPCBDS
MPCPOP
MPCSYB
MTXM
MTXMC MXM
MULLIK RSP GMETRY MULT DENSIT VECPRT
MULT
MXM
MXMT
NLLSQ PARSAV COMPFG GEOUT LOCMIN PARSAV
NUCHAR
OSINV
OVERLP
PARSAV XYZINT GEOUT
PARTXY FORMXY
PATHK DFPSAV FLEPO GEOUT WRTTXT
PATHS DFPSAV FLEPO WRITE
PERM
POLAR GMETRY AXIS COMPFG FFHPOL
POWSAV XYZINT GEOUT
POWSQ POWSAV COMPFG VECPRT RSP SEARCH
PRTDRC CHRGE XYZINT QUADR
PULAY MAMULT OSINV
QUADR
REACT1 GETGEO SYMTRY GEOUT GMETRY FLEPO COMPFG WRITE
____________________________________________Subroutine_calls_in_MOPAC__________________
READ GETTXT GETGEG GETGEO DATE GEOUT WRTKEY GETSYM
SYMTRY NUCHAR WRTTXT GMETRY
REFER
REPP
ROTAT
ROTATE REPP
RSP EPSETA TRED3 TQLRAT TQL2 TRBAK3
SAXPY
SCHMIB
SCHMIT
SCOPY
SEARCH COMPFG
SECOND
SET AINTGS BINTGS
SETUPG
SOLROT ROTATE
SORT
SPACE
SPLINE BFN
SUPDOT
SWAP
SYMTRY HADDON
THERMO
TIMCLK
TIMER
TIMOUT
TQL2
TQLRAT
TRBAK3
TRED3
UPCASE
UPDATE
UPDHES
VECPRT
WRITE DATE WRTTXT GEOUT DERIV TIMOUT SYMTRY GMETRY GEOUT
VECPRT MATOUT CHRGE BRLZON MPCSYB DENROT MOLVAL BONDS
LOCAL ENPART MULLIK MPCPOP GEOUTG
WRTKEY
WRTTXT
XXX
XYZGEO BANGLE DIHED
XYZINT DIHED BANGLE XYZGEO
A list of subroutines called by various segments (the inverse of the first list)
Subroutine Called by
AABABC MECIH
AABACD MECIH
AABBCD MECIH
AINTGS SET
ANALYT DCART
ANAVIB FORCE
AXIS FORCE FRAME POLAR
BABBBC MECIH
BABBCD MECIH
Subroutine_calls_in_MOPAC____________________________________________________
BANGLE XYZGEO XYZINT
BFN SPLINE
BINTGS SET
BKRSAV EF
BONDS WRITE
BRLZON FREQCY WRITE
CALPAR DATIN
CAPCOR ITER
CDIAG BRLZON
CHRGE DIPIND FMAT GEOUT PRTDRC WRITE
CNVG ITER
COE DENROT DIAT
COMPFG DRC EF FFHPOL FLEPO FMAT
FORCE LINMIN LOCMIN MNDO NLLSQ
POLAR POWSQ REACT1 SEARCH
DANG DIHED
DATIN MNDO
DCART DERITR
DELMOL ANALYT
DELRI ANALYT
DENROT WRITE
DENSIT ITER MULLIK
DEPVAR HADDON
DERI0 DERNVO
DERI1 DERNVO
DERI2 DERI2 DERNVO
DERI21 DERI2
DERI22 DERI2
DERI23 DERI2
DERITR DERITR
DERNVO DERITR
DERS ANALYT
DFOCK2 DERI1
DFPSAV FLEPO GRID PATHK PATHS
DHC DCART DERI1
DHCORE DERI1
DIAG DERI21 ITER
DIAGI DERI21
DIAT DIAT H1ELEC
DIAT2 DIAT
DIHED COMPFG DCART XYZGEO XYZINT
DIIS FLEPO
DIJKL1 DERI1
DIJKL2 DERI2
DIPIND FFHPOL
DIPOLE FMAT WRITE
DOFS BRLZON
DRC FORCE MNDO
DRCOUT PRTDRC
EA08C EC08C
EA09C EA08C
EC08C CDIAG
EF MNDO
ENPART WRITE
____________________________________________Subroutine_calls_in_MOPAC__________________
EPSETA DIAG ITER RSP
EXCHNG LINMIN LOCMIN
FFHPOL POLAR
FLEPO FORCE GRID MNDO PATHK PATHS
REACT1
FMAT FORCE
FOCK2 DERI22 DHC ITER
FORCE MNDO
FORMD EF
FORMXY DIJKL1 PARTXY
FORSAV FMAT
FRAME FORCE FREQCY
FREQCY FORCE
GEOUT BKRSAV DERITR DFPSAV FLEPO GETGEO
GMETRY GRID NLLSQ PARSAV PATHK
POWSAV REACT1 READ
WRITE WRITE
GEOUTG WRITE
GETDAT MNDO
GETGEG READ
GETGEO REACT1 READ
GETSYM READ
GETTXT READ
GMETRY COMPFG DENROT DERITR DIPIND DRC
FORCE JCARIN MOLDAT MULLIK POLAR
REACT1 READ WRITE
GOVER DIAT
GRID MNDO
H1ELEC DHC DHCORE HCORE
HADDON SYMTRY
HCORE COMPFG DERITR
HELECT DCART DERI2 ITER
HQRII EF INTERP ITER MECI
IJKL MECI
INTERP ITER
ITER COMPFG DERITR
JAB DFOCK2 FOCK2
JCARIN DERITR
KAB DFOCK2 FOCK2
LINMIN FLEPO
LOCAL WRITE
LOCMIN NLLSQ
MNDO (main segment)
MAMULT PULAY
MATOUT FFHPOL FORCE ITER LOCAL MECI
WRITE
ME08A CDIAG
ME08B ME08A
MECI COMPFG DERI1 DERI2 MECI
MECIH DERI1 DERI2 MECI
MECIP COMPFG
MINV DIIS
MOLDAT DATIN MNDO
MOLVAL WRITE
Subroutine_calls_in_MOPAC____________________________________________________
MPCBDS BONDS
MPCPOP WRITE
MPCSYB WRITE
MTXM DERI1 DERI2 DERI21
MTXMC DERI21
MULLIK WRITE
MULT MULLIK
MXM DERI1 DERI2 DERI21 DERI22 DERITR
MECIP MTXMC
MXMT DERI22
NLLSQ FORCE MNDO
NUCHAR GETGEO READ
OSINV DERI2 PULAY
OVERLP FORMD
PARSAV NLLSQ
PARTXY IJKL
PATHK MNDO
PATHS MNDO
PERM MECI
POLAR MNDO
POWSAV POWSQ
POWSQ MNDO
PRTDRC DRC
PULAY ITER
QUADR PRTDRC
REACT1 MNDO
READ MNDO
REFER MOLDAT
REPP ROTATE
ROTAT DELMOL DHC DHCORE HCORE SOLROT
ROTATE DHC DHCORE HCORE SOLROT
RSP AXIS FFHPOL FORCE FREQCY MULLIK
POWSQ
SCHMIB INTERP
SCHMIT INTERP
SCOPY DERI1 DERI2 DERI23 FLEPO
SEARCH POWSQ
SECOND DERI2 DRC EF ESP FLEPO
FMAT FORCE GRID ITER MNDO
NLLSQ PATHK PATHS POWSQ REACT1
TIMER WRITE
SET COMPFG DIAT2
SETUPG COMPFG
SOLROT DHC HCORE
SORT CDIAG
SPACE DIIS
SPLINE INTERP
SUPDOT DERI1 DERI1 DERI2 DERI22 FLEPO
SWAP ITER
SYMTRY COMPFG DERITR EF JCARIN REACT1
READ WRITE
THERMO FORCE
TIMCLK SECOND
TIMER COMPFG DERI1 DERI1
____________________________________________Subroutine_calls_in_MOPAC__________________
TIMOUT WRITE
TQL2 RSP
TQLRAT RSP
TRBAK3 RSP
TRED3 RSP
UPCASE GETTXT
UPDATE DATIN
UPDHES EF
VECPRT BONDS DIIS FFHPOL FORCE HCORE
ITER MECI MOLDAT MULLIK POWSQ
WRITE
WRITE FORCE ITER MNDO PATHS REACT1
WRTKEY READ
WRTTXT GEOUT GRID PATHK READ WRITE
XXX GEOUTG
XYZGEO XYZINT
XYZINT DFPSAV FORCE GEOUT GETGEO PARSAV
POWSAV PRTDRC
Appendix C
Description of subroutines
o AABABC Utility: Calculates the configuration interaction matrix element between two
configurations differing by exactly one alpha M.O. Called by MECI only.
o AABACD Utility: Calculates the configuration interaction matrix element between two
configurations differing by exactly two alpha M.O.'s. Called by MECI only.
o AABBCD Utility: Calculates the configuration interaction matrix element between two
configurations differing by exactly two M.O.'s; one configuration has alpha M.O. "A" and
beta M.O. "C" while the other configuration has alpha M.O. "B" and beta M.O. "D". Called
by MECI only.
o AINTGS Utility: Within the overlap integrals, calculates the A-integrals. Dedicated to
function SS within DIAT.
o ANALYT Main Sequence: Calculates the analytical derivatives of the energy with respect
to cartesian coordinates for all atoms. Use only if the mantissa is short (less than 52 bits)
or out of interest. Should not be used for routine work on a VAX.
o ANAVIB Utility: Gives a brief interpretation of the modes of vibration of the molecule. The
principal pairs of atoms involved in each vibration are identified, and the mode of motion
(tangential or radial) is output.
o AXIS Utility: Works out the three principal moments of inertia of a molecule. If the system
is linear, one moment of inertia is zero. Prints moments in units of cm-1 and 10-40 g cm2 .
o BABBBC Utility: Calculates the configuration interaction matrix element between two con-
figurations differing by exactly one beta M.O. Called by MECI only.
o BABBCD Utility: Calculates the configuration interaction matrix element between two
configurations differing by exactly two beta M.O.'s. Called by MECI only.
o BANGLE Utility: Given a set of coordinates, BANGLE will calculate the angle between any
three atoms.
o BFN Utility: Calculates the B-functions in the Slater overlap.
o BINTGS Utility: Calculates the B-functions in the Slater overlap.
o BKRSAV Utility: Saves and restores data used by the eigenvector following subroutine.
Called by EF only.
o BONDS Utility: Evaluates and prints the valencies of atoms and bond-orders between atoms.
Main argument: density matrix. No results are passed to the calculation, and no data are
changed. Called by WRITE only.
_______________________________________________Description_of_subroutines______________
o BRLZON Main Sequence: BRLZON generates a band structure, or phonon structure, for
high polymers. Called by WRITE and FREQCY.
o CALPAR Utility: When external parameters are read in via EXTERNAL=, the derived
parameters are worked out using CALPAR. Note that all derived parameters are calculated
for all parameterized elements at the same time.
o CAPCOR Utility: Capping atoms, of type Cb, should not contribute to the energy of a
system. CAPCOR calculates the energy contribution due to the Cb and subtracts it from
the electronic energy.
o CDIAG Utility: Complex diagonalization. Used in generating eigenvalues of complex Her-
mitian secular determinant for band structures. Called by BRLZON only.
o CHRGE Utility: Calculates the total number of valence electrons on each atom. Main
arguments: density matrix, array of atom charges (empty on input). Called by ITER only.
o CNVG Utility: Used in SCF cycle. CNVG does a three-point interpolation of the last three
density matrices. Arguments: Last three density matrices, Number of iterations, measure of
self-consistency (empty on input). Called by ITER only.
o COE Utility: Within the general overlap routine COE calculates the angular coefficients for
the s, p and d real atomic orbitals given the axis and returns the rotation matrix.
o COMPFG Main Sequence: Evaluates the total heat of formation of the supplied geometry,
and the derivatives, if requested. This is the nodal point connecting the electronic and
geometric parts of the program. Main arguments: on input: geometry, on output: heat of
formation, gradients.
o DANG Utility: Called by XYZINT, DANG computes the angle between a point, the origin,
and a second point.
o DATIN Utility: Reads in external parameters for use within MOPAC. Originally used for the
testing of new parameters, DATIN is now a general purpose reader for parameters. Invoked
by the keyword EXTERNAL.
o DCART Utility: Called by DERIV, DCART sets up a list of cartesian derivatives of the
energy wrt coordinates which DERIV can then use to construct the internal coordinate
derivatives.
o DELMOL Utility: Part of analytical derivates. Two-electron.
o DELRI Utility: Part of analytical derivates. Two-electron.
o DENROT Utility: Converts the ordinary density matrix into a condensed density matrix
over basis functions s (sigma), p (sigma) and p (pi), i.e., three basis functions. Useful in
hybridization studies. Has capability to handling "d" functions, if present.
o DENSIT Utility: Constructs the Coulson electron density matrix from the eigenvectors.
Main arguments: Eigenvectors, No. of singly and doubly occupied levels, density matrix
(empty on input) Called by ITER.
o DEPVAR Utility: A symmetry-defined "bond length" is related to another bond length by a
multiple. This special symmetry function is intended for use in Cluster calculations. Called
by HADDON.
o DERI0 Utility: Part of the analytical C.I. derivative package. Calculates the diagonal dom-
inant part of the super-matrix.
Description_of_subroutines___________________________________________________
o DERI1 Utility: Part of the analytical C.I. derivative package. Calculates the frozen density
contribution to the derivative of the energy wrt cartesian coordinates, and the derivatives of
the frozen Fock matrix in M.O. basis. It's partner is DERI2.
o DERI2 Utility: Part of the analytical C.I. derivative package. Calculates the relaxing density
contribution to the derivative of the energy wrt cartesian coordinates. Uses the results of
DERI1.
o DERI21 Utility: Part of the analytical C.I. derivative package. Called by DERI2 only.
o DERI22 Utility: Part of the analytical C.I. derivative package. Called by DERI2 only.
o DERI23 Utility: Part of the analytical C.I. derivative package. Called by DERI2 only.
o DERITR Utility: Calculates derivatives of the energy wrt internal coordinates using full
SCF's. Used as a foolproof way of calculating derivatives. Not recommended for normal use.
o DERIV Main Sequence: Calculates the derivatives of the energy with respect to the geomet-
ric variables. This is done either by using initially cartesian derivatives (normal mode), by
analytical C.I. RHF derivatives, or by full SCF calculations (NOANCI in half-electron and
C.I. mode). Arguments: on input: geometry, on output: derivatives. Called by COMPFG.
o DERNVO Analytical C.I. Derivative main subroutine. Calculates the derivative of the energy
wrt geometry for a non-variationally optimized wavefunction (a SCF-CI wavefunction).
o DERS Utility: Called by ANALYT, DERS calculates the analytical derivatives of the overlap
matrix within the molecular frame.
o DEX2 Utility: A function called by ESP.
o DFOCK2 Utility: Part of the analytical C.I. derivative package. Called by DERI1, DFOCK2
calculates the frozen density contribution to the derivative of the energy wrt cartesian coor-
dinates.
o DFPSAV Utility: Saves and restores data used by the BFGS geometry optimization. Main
arguments: parameters being optimized, gradients of parameters, last heat of formation,
integer and real control data. Called by FLEPO.
o DHC Utility: Called by DCART and calculates the energy of a pair of atoms using the SCF
density matrix. Used in the finite difference derivatve calculation.
o DHCORE Utility: Part of the analytical C.I. derivative package. Called by DERI1, DHCORE
calculates the derivatives of the 1 and 2 electron integrals wrt cartesian coordinates.
o DIAG Utility: Rapid pseudo-diagonalization. Given a set of vectors which almost block-
diagonalize a secular determinant, DIAG modifies the vectors so that the block-diagonalization
is more exact. Main arguments: Old vectors, Secular Determinant, New vectors (on output).
Called by ITER.
o DIAGI Utility: Calculates the electronic energy arising from a given configuration. Called
by MECI.
o DIAT Utility: Calculates overlap integrals between two atoms in general cartesian space.
Principal quantum numbers up to 6, and angular quantum numbers up to 2 are allowed.
Main arguments: Atomic numbers and cartesian coordinates in Angstroms of the two atoms,
Diatomic overlaps (on exit). Called by H1ELEC.
o DIAT2 Utility: Calculates reduced overlap integrals between atoms of principal quantum
numbers 1, 2, and 3, for s and p orbitals. Faster than the SS in DIAT. This is a dedicated
subroutine, and is unable to stand alone without considerable backup. Called by DIAT.
_______________________________________________Description_of_subroutines______________
o DIGIT Utility: Part of READA. DIGIT assembles numbers given a character string.
o DIHED Utility: Calculates the dihedral angle between four atoms. Used in converting from
cartesian to internal coordinates.
o DIIS Utility: Pulay's Geometric Direct Inversion of the Iterative Subspace (G-DIIS) accel-
erates the rate at which the BFGS locates an energy minimum. (In MOPAC 6.00, the DIIS
is only partially installed _ several capabilities of the DIIS are not used)
o DIJKL1 Utility: Part of the analytical C.I. derivative package. Called by DERI1, DIJKL1
calculates the two-electron integrals over M.O. bases, e.g. **/.
o DIJKL2 Utility: Part of the analytical C.I. derivative package. Called by DERI2, DIJKL2
calculates the derivatives of the two-electron integrals over M.O. bases, e.g. **/,
wrt cartesian coordinates.
o DIPIND Utility: Similar to DIPOLE, but used by the POLAR calculation only.
o DIPOLE Utility: Evaluates and, if requested, prints dipole components and dipole for the
molecule or ion. Arguments: Density matrix, Charges on every atom, coordinates, dipoles
(on exit). Called by WRITE and FMAT.
o DIST2 Utility: Called by ESP only, DIST2 works out the distance between two points in
3D space.
o DOFS Main Sequence: Calculates the density of states within a Brillouin zone. Used in
polymer work only.
o DOT Utility: Given two vectors, X and Y, of length N, function DOT returns with the dot
product X.Y. I.e., if X=Y, then DOT = the square of X. Called by FLEPO.
o DRC Main Sequence: The dynamic and intrinsic reaction coordinates are calculated by
following the mass-weighted trajectories.
o DRCOUT Utility: Sets up DRC and IRC data in quadratic form preparatory to being
printed.
o EA08C Part of the diagonalizer RSP.
o EA09C Part of the diagonalizer RSP.
o EC08C Part of the diagonalizer RSP.
o EF Main Sequence: EF is the Eigenvector Following routine. EF implements the keywords
EF and TS.
o ELESP Utility: Within the ESP, ELESP calculates the electronic contribution to the elec-
trostatic potential.
o ENPART Utility: Partitions the energy of a molecule into its monatomic and diatomic
components. Called by WRITE when the keyword ENPART is specified. No data are
changed by this call.
o EPSETA Utility: Calculates the machine precision and dynamic range for use by the two
diagonalizers.
o ESP Main Sequence: ESP is not present in the default copy of MOPAC. ESP calculates the
atomic charges which would reproduce the electrostatic potential of the nuclii and electronic
wavefunction.
o ESPBLO Block Data: Used by the ESP calculation, ESPBLO fills two small arrays!
Description_of_subroutines___________________________________________________
o ESPFIT Utility: Part of the ESP. ESP fits the quantum mechanical potential to a classical
point charge model
o EXCHNG Utility: Dedicated procedure for storing 3 parameters and one array in a store.
Used by SEARCH.
o FFHPOL Utility: Part of the POLAR calculation. Evaluates the effect of an electric field
on a molecule.
o FLEPO Main Sequence: Optimizes a geometry by minimizing the energy. Makes use of
the first and estimated second derivatives to achieve this end. Arguments: Parameters to
be optimized, (overwritten on exit with the optimized parameters), Number of parameters,
final optimized heat of formation. Called by MAIN, REACT1, and FORCE.
o FM06AS Utility: Part of CDIAG.
o FM06BS Utility: part of CDIAG.
o FMAT Main sequence: Calculates the exact Hessian matrix for a system This is done by
either using differences of first derivatives (normal mode) or by four full SCF calculations
(half electron or C.I. mode). Called by FORCE.
o FOCK1 Utility: Adds on to Fock matrix the one-center two electron terms. Called by ITER
only.
o FOCK2 Utility: Adds on to Fock matrix the two-center two electron terms. Called by ITER
and DERIV. In ITER the entire Fock matrix is filled; in DERIV, only diatomic Fock matrices
are constructed.
o FOCK2D Written out of MOPAC 6.00.
o FORCE Main sequence: Performs a force-constant and vibrational frequency calculation on
a given system. If the starting gradients are large, the geometry is optimized to reduce the
gradient norm, unless LET is specified in the keywords. Isotopic substitution is allowed.
Thermochemical quantities are calculated. Called by MAIN.
o FORMD Main Sequence: Called by EF. FORMD constructs the next step in the geometry
optimization or transition state location.
o FORMXY Utility: Part of DIJKL1. FORMXY constructs part of the two- electron integral
over M.O.'s.
o FORSAV Utility: Saves and restores data used in FMAT in FORCE calculation. Called by
FMAT.
o FRAME Utility: Applies a very rigid constraint on the translations and rotations of the
system. Used to separate the trivial vibrations in a FORCE calculation.
o FREQCY Main sequence: Final stage of a FORCE calculation. Evaluates and prints the
vibrational frequencies and modes.
o FSUB Utility: Part of ESP.
o GENUN Utility: Part of ESP. Generates unit vectors over a sphere. called by SURFAC only.
o GEOUT Utility: Prints out the current geometry. Can be called at any time. Does not
change any data.
o GEOUTG Utility: Prints out the current geometry in Gaussian Z-matrix format.
o GETDAT Utility: Reads in all the data, and puts it in a scratch file on channel 5.
_______________________________________________Description_of_subroutines______________
o GETGEG Utility: Reads in Gaussian Z-matrix geometry. Equivalent to GETGEO and
GETSYM combined.
o GETGEO Utility: Reads in geometry in character mode from specified channel, and stores
parameters in arrays. Some error-checking is done. Called by READ and REACT1.
o GETSYM Utility: Reads in symmetry data. Used by READ.
o GETTXT Utility: Reads in KEYWRD, KOMENT and TITLE.
o GETVAL Utility: Called by GETGEG, GETVAL either gets an internal coordinate or a
logical name for that coordinate.
o GMETRY Utility: Fills the cartesian coordinates array. Data are supplied from the array
GEO, GEO can be (a) in internal coordinates, or (b) in cartesian coordinates. If STEP is
non-zero, then the coordinates are modified in light of the other geometry and STEP. Called
by HCORE, DERIV, READ, WRITE, MOLDAT, etc.
o GOVER Utility: Calculates the overlap of two Slater orbitals which have been expanded
into six gaussians. Calculates the STP-6G overlap integrals.
o GRID Main Sequence: Calculates a grid of points for a 2-D search in coordinate space.
Useful when more information is needed about a reaction surface.
o H1ELEC Utility: Given any two atoms in cartesian space, H1ELEC calculates the one-
electron energies of the off-diagonal elements of the atomic orbital matrix.
H(i; j) = -S(i; j)[fi(i) + fi(j)]=2
Called by HCORE and DERIV.
o HADDON Utility: The symmetry operation subroutine, HADDON relates two geometric
variables by making one a dependent function of the other. Called by SYMTRY only.
o HCORE Main sequence: Sets up the energy terms used in calculating the SCF heat of
formation. Calculates the one and two electron matrices, and the nuclear energy. Called by
COMPFG.
o HELECT Utility: Given the density matrix, and the one electron and Fock matrices, calcu-
lates the electronic energy. No data are changed by a call of HELECT. Called by ITER and
DERIV.
o HQRII Utility: Rapid diagonalization routine. Accepts a secular determinant, and produces
a set of eigenvectors and eigenvalues. The secular determinant is destroyed.
o IJKL Utility: Fills the large two-electron array over a M.O. basis set. Called by MECI.
o INTERP Utility: Runs the Camp-King converger. q.v.
o ITER Main sequence: Given the one and two electron matrices, ITER calculates the Fock
and density matrices, and the electronic energy. Called by COMPFG.
o JAB Utility: Calculates the coulomb contribution to the Fock matrix in NDDO formalism.
Called by FOCK2.
o JCARIN Utility: Calculates the difference vector in cartesian coordinates corresponding to
a small change in internal coordinates.
o KAB Utility: Calculates the exchange contribution to the Fock matrix in NDDO formalism.
Called by FOCK2.
Description_of_subroutines___________________________________________________
o LINMIN Main sequence: Called by the BFGS geometry optimized FLEPO, LINMIN takes
a step in the search-direction and if the energy drops, returns. Otherwise it takes more steps
until if finds one which causes the energy to drop.
o LOCAL Utility: Given a set of occupied eigenvectors, produces a canonical set of localized
bonding orbitals, by a series of 2 x 2 rotations which maximize <_4 >. Called by WRITE.
o LOCMIN Main sequence: In a gradient minimization, LOCMIN does a line- search to find
the gradient norm minimum. Main arguments: current geometry, search direction, step,
current gradient norm; on exit: optimized geometry, gradient norm.
o MAMULT Utility: Matrix multiplication. Two matrices, stored as lower half triangular
packed arrays, are multiplied together, and the result stored in a third array as the lower
half triangular array. Called from PULAY.
o MATOUT Utility: Matrix printer. Prints a square matrix, and a row-vector, usually eigen-
vectors and eigenvalues. The indices printed depend on the size of the matrix: they can
be either over orbitals, atoms, or simply numbers, thus M.O.'s are over orbitals, vibrational
modes are over numbers. Called by WRITE, FORCE.
o ME08A, ME08B Utilities: Part of the complex diagonalizer, and called by CDIAG.
o MECI Main sequence: Main function for Configuration Interaction, MECI constructs the
appropriate C.I. matrix, and evaluates the roots, which correspond to the electronic energy
of the states of the system. The appropriate root is then returned. Called by ITER only.
o MECID Utility: Constructs the differential C.I. secular determinant.
o MECIH Utility: Constructs the normal C.I. secular determinant.
o MECIP Utility: Reforms the density matrix after a MECI calculation.
o MINV Utility: Called by DIIS. MINV inverts the Hessian matrix.
o MNDO Main sequence: MAIN program. MNDO first reads in data using READ, then calls
either FLEPO to do geometry optimization, FORCE to do a FORCE calculation, PATHS
for a reaction with a supplied coordinate, NLLSQ for a gradient minimization or REACT1
for locating the transition state. Starts the timer.
o MOLDAT Main Sequence: Sets up all the invariant parameters used during the calculation,
e.g. number of electrons, initial atomic orbital populations, number of open shells, etc.
Called once by MNDO only.
o MOLVAL Utility: Calculates the contribution from each M.O. to the total valency in the
molecule. Empty M.O.'s normally have a negative molecular valency.
o MTXM Utility: Part of the matrix package. Multiplies together two rectangular packed
arrays, i.e., C = A.B.
o MTXMC Utility: Part of the matrix package. Similar to MTXM.
o MULLIK Utility: Constructs and prints the Mulliken Population Analysis. Available only
for RHF calculations. Called by WRITE.
o MULT Utility: Used by MULLIK only, MULT multiplies two square matrices together.
o MXM Utility: Part of the matrix package. Similar to MTXM.
o MXMT Utility: Part of the matrix package. Similar to MTXM.
_______________________________________________Description_of_subroutines______________
o MYWORD Utility: Called in WRTKEY, MYWORD checks for the existance of a specific
string. If it is found, MYWORD is set true, and the all occurances of string are deleted.
Any words not recognised will be flagged and the job stopped.
o NAICAP Utility: Called by ESP.
o NAICAP Utility: Called by ESP.
o NLLSQ Main sequence: Used in the gradient norm minimization.
o NUCHAR Takes a character string and reads all the numbers in it and stores these in an
array.
o OSINV Utility: Inverts a square matrix. Called by PULAY only.
o OVERLP Utility: Part of EF. OVERLP decides which normal mode to follow.
o OVLP Utility: Called by ESP only. OVLP calculates the overlap over Gaussian STO's.
o PARSAV Utility: Stores and restores data used in the gradient-norm minimization calcula-
tion.
o PARTXY Utility: Called by IJKL only, PARTXY calculates the partial product **/.
o PATHK Main sequence: Calculates a reaction coordinate which uses a constant step-size.
Invoked by keywords STEP and POINTS.
o PATHS Main sequence: Given a reaction coordinate as a row-vector, PATHS performs a
FLEPO geometry optimization for each point, the later geometries being initially guessed
from a knowledge of the already optimized geometries, and the current step. Called by
MNDO only.
o PDGRID Utility: Part of ESP. Calculates the Williams surface.
o PERM Utility: Permutes n1 electrons of alpha or beta spin among n2 M.O.'s.
o POLAR Utility: Calculates the polarizability volumes for a molecule or ion. Uses 19 SCF
calculations, so appears after WRITE has finished. Cannot be used with FORCE, but can
be used anywhere else. Called by WRITE.
o POWSAV Utility: Calculation store and restart for SIGMA calculation. Called by POWSQ.
o POWSQ Main sequence: The McIver - Komornicki gradient minimization routine. Con-
structs a full Hessian matrix and proceeds by line-searches Called from MAIN when SIGMA
is specified.
o PRTDRC Utility: Prints DRC and IRC results according to instructions. Output can be
(a) every point calculated (default), (b) in constant steps in time, space or energy.
o PULAY Utility: A new converger. Uses a powerful mathematical non-iterative method for
obtaining the SCF Fock matrix. Principle is that at SCF the eigenvectors of the Fock and
density matrices are identical, so [F.P] is a measure of the non-self consistency. While very
powerful, PULAY is not universally applicable. Used by ITER.
o QUADR: Utility: Used in printing the IRC - DRC results. Sets up a quadratic in time of
calculated quantities so that PRTDRC can select specific reaction times for printing.
o REACT1 Main sequence: Uses reactants and products to find the transition state. A hy-
persphere of N dimensions is centered on each moiety, and the radius steadily reduced. The
entity of lower energy is moved, and when the radius vanishes, the transition state is reached.
Called by MNDO only.
Description_of_subroutines___________________________________________________
o READ Main sequence: Almost all the data are read in through READ. There is a lot of
data-checking in READ, but very little calculation. Called by MNDO.
o READA Utility: General purpose character number reader. Used to enter numerical data in
the control line as =n.nnn where is a mnemonic such as SCFCRT
or CHARGE. Called by READ, FLEPO, ITER, FORCE, and many other subroutines.
o REFER Utility: Prints the original references for atomic data. If an atom does not have a
reference, i.e., it has not been parameterized, then a warning message will be printed and
the calculation stopped.
o REPP Utility: Calculates the 22 two-electron reduced repulsion integrals, and the 8 electron-
nuclear attraction integrals. These are in a local coordinate system. Arguments: atomic
numbers of the two atoms, interatomic distance, and arrays to hold the calculated integrals.
Called by ROTATE only.
o ROTAT Utility: Rotates analytical two-electron derivatives from atomic to molecular frame.
o ROTATE Utility: All the two-electron repulsion integrals, the electron- nuclear attraction
integrals, and the nuclear-nuclear repulsion term between two atoms are calculated here.
Typically 100 two- electron integrals are evaluated.
o RSP Utility: Rapid diagonalization routine. Accepts a secular determinant, and produces a
set of eigenvectors and eigenvalues. The secular determinant is destroyed.
o SAXPY Utility: Called by the utility SUPDOT only!
o SCHMIB Utility: Part of Camp-King converger.
o SCHMIT Utility: Part of Camp-King converger.
o SCOPY Utility: Copies an array into another array.
o SDOT Utility: Forms the scalar of the product of two vectors.
o SEARCH Utility: Part of the SIGMA and NLLSQ gradient minimizations. The line-search
subroutine, SEARCH locates the gradient minimum and calculates the second derivative of
the energy in the search direction. Called by POWSQ and NLLSQ.
o SECOND Utility: Contains VAX specific code. Function SECOND returns the number of
CPU seconds elapsed since an arbitrary starting time. If the SHUTDOWN command has
been issued, the CPU time is in error by exactly 1,000,000 seconds, and the job usually
terminates with the message "time exceeded".
o SET Utility: Called by DIAT2, evaluates some terms used in overlap calculation.
o SETUP3 Utility: Sets up the Gaussian expansion of Slater orbitals using a STO-3G basis
set.
o SETUPG Utility: Sets up the Gaussian expansion of Slater orbitals using a STO-6G basis
set.
o SOLROT Utility: For Cluster systems, adds all the two-electron integrals of the same type,
between different unit cells, and stores them in a single array. Has no effect on molecules.
o SORT Utility: Part of CDIAG, the complex diagonalizer.
o SPACE Utility: Called by DIIS only.
o SPCG Written out of Version 6.00.
_______________________________________________Description_of_subroutines______________
o SPLINE Utility: Part of Camp-King converger.
o SS Utility: An almost general Slater orbital overlap calculation. Called by DIAT.
o SUPDOT Utility: Matrix mutiplication A=B.C
o SURFAC Utility: Part of the ESP.
o SWAP Utility: Used with FILL=, SWAP ensures that a specified M.O. is filled. Called by
ITER only.
o SYMTRY Utility: Calculates values for geometric parameters from known geometric param-
eters and symmetry data. Called whenever GMETRY is called.
o THERMO Main sequence: After the vibrational frequencies have been calculated, THERMO
calculates thermodynamic quantities such as internal energy, heat capacity, entropy, etc, for
translational, vibrational, and rotational, degrees of freedom.
o TIMCLK Utility: Vax-specific code for determining CPU time.
o TIMER Utility: Prints times of various steps.
o TIMOUT Utility: Prints total CPU time in elegant format.
o TQL2 Utility: Part of the RSP.
o TQLRAT Utility: Part of the RSP.
o TRBAK3 Utility: Part of the RSP.
o TRED3 Utility: Part of the RSP.
o UPDATE Utility: Given a set of new parameters, stores these in their appropriate arrays.
Invoked by EXTERNAL.
o UPDHES Utility: Called by EF, UPDHES updates the Hessian matrix.
o VECPRT Utility: Prints out a packed, lower-half triangular matrix. The labeling of the
sides of the matrix depend on the matrix's size: if it is equal to the number of orbitals,
atoms, or other. Arguments: The matrix to be printed, size of matrix. No data are changed
by a call of VECPRT.
o WRITE Main sequence: Most of the results are printed here. All relevant arrays are assumed
to be filled. A call of WRITE only changes the number of SCF calls made, this is reset to
zero. No other data are changed. Called by MAIN, FLEPO, FORCE.
o WRTKEY Main Sequence: Prints all keywords and checks for compatability and to see if
any are not recognised. WRTKEY can stop the job if any errors are found.
o WRTTXT Main Sequence: Writes out KEYWRD, KOMENT and TITLE. The inverse of
GETTXT.
o XXX Utility: Forms a unique logical name for a Gaussian Z-matrix logical. Called by
GEOUTG only.
o XYZINT Utility: Converts from cartesian coordinates into internal.
o XYZGEO XYZINT sets up its own numbering system, so no connectivity is needed.
Appendix D
Heats of formation
Test MNDO, PM3 and AM1 compounds
In order to verify that MOPAC is working correctly, a large number of tests need to be done. These
take about 45 minutes on a VAX 11-780, and even then many potential bugs remain undetected.
It is obviously impractical to ask users to test MOPAC. However, users must be able to verify the
basic working of MOPAC, and to do this the following tests for the elements have been provided.
Each element can be tested by making up a data-file using estimated geometries and running
that file using MOPAC. The optimized geometries should give rise to heats of formation as shown.
Any difference greater than 0.1 kcal/mole indicates a serious error in the program.
Caveats
1. Geometry definitions must be correct.
2. Heats of formation may be too high for certain compounds. This is due to a poor starting
geometry trapping the system in an excited state. (Affects ICl at times)
Element Test Compound Heat of Formation
MINDO/3 MNDO AM1 PM3
Hydrogen CH4 -6.3 -11.9 -8.8 -13.0
Lithium LiH +23.2
Beryllium BeO +38.6 +53.0
Boron BF3 -270.2 -261.0 -272.1*
Carbon CH4 -6.3 -11.9 -8.8 -13.0
Nitrogen NH3 -9.1 -6.4 -7.3 -3.1
Oxygen CO2 -95.7 -75.1 -79.8 -85.0
Fluorine CF4 -223.9 -214.2 -225.7 -225.1
Magnesium MgF2 -160.7
Aluminium AlF -83.6 -77.9 -50.1
Silicon SiH +82.9 +90.2 +84.5 +94.6
Phosphorus PH3 +2.5 +3.9 +10.2 +0.2
Sulfur H2S -2.6 +3.8 +1.2 -0.9
Chlorine HCl -21.1 -15.3 -24.6 -20.5
Zinc ZnMe2 +19.9 +19.8 8.2
Gallium GaCl3 -79.7
Germanium GeF -16.4 -19.7 -3.3
Arsenic AsH3 +12.7
Selenium SeCl2 -38.0
Bromine HBr +3.6 -10.5 +5.3
________________________________________________Heats_of_formation___________
Cadmium CdCl2 -48.6
Indium InCl3 -72.8
Tin SnF -20.4 -17.5
Antimony SbCl3 -72.4
Tellurium TeH2 +23.8
Iodine ICl -6.7 -4.6 +10.8
Mercury HgCl2 -36.9 -44.8 -32.7
Thallium TlCl -13.4
Lead PbF -22.6 -21.0
Bismuth BiCl3 -42.6
* Not an exhaustive test of AM1 boron.
Appendix E
References
On G-DIIS
"Computational Strategies for the Optimization of Equilibrium Geometry and Transition-State
Structures at the Semiempirical Level", Peter L. Cummings, Jill E. Gready, J. Comp. Chem.,
10:939-950 (1989).
On Analytical C.I. Derivatives
"An Efficient Procedure for Calculating the Molecular Gradient, using SCF-CI Semiempirical
Wavefunctions with a Limited Number of Configurations", M. J. S. Dewar, D. A. Liotard, J. Mol.
Struct. (Theochem), 206:123-133 (1990).
On Eigenvector Following
J. Baker, J. Comp. Chem., 7:385 (1986).
On ElectroStatic Potentials (ESP)
"Atomic Charges Derived from Semiempirical Methods", B. H. Besler, K. M. Merz, Jr., P. A.
Kollman, J. Comp. Chem., 11:431-439 (1990).
On MNDO
"Ground States of Molecules. 38. The MNDO Method. Approximations and Parameters.", M.J.S.
Dewar, W.Thiel, J. Am. Chem. Soc., 99:4899, (1977).
Original References for Elements Parameterized in MNDO:
H M.J.S. Dewar, W. Thiel, J. Am. Chem. Soc., 99, 4907, (1977).
Li Parameters taken from the MNDOC program, written by Walter Thiel, Quant. Chem. Prog.
Exch. No. 438; 2:63, (1982).
Be M.J.S. Dewar, H.S. Rzepa, J. Am. Chem. Soc., 100:777, (1978).
B M.J.S. Dewar, M.L. McKee, J. Am. Chem. Soc., 99:5231, (1977).
C M.J.S. Dewar, W. Thiel, J. Am. Chem. Soc., 99:4907, (1977).
N M.J.S. Dewar, W. Thiel, J. Am. Chem. Soc., 99:4907, (1977).
O M.J.S. Dewar, W. Thiel, J. Am. Chem. Soc., 99:4907, (1977).
F M.J.S. Dewar, H.S. Rzepa, J. Am. Chem. Soc., 100:58, (1978).
____________________________________________________________References_______
Al L.P. Davis, R.M. Guidry, J.R. Williams, M.J.S. Dewar, H.S. Rzepa J. Comp. Chem., 2:433,
(1981).
Si (a) M.J.S. Dewar, M.L. McKee, H.S. Rzepa, J. Am. Chem. Soc., 100:3607 (1978). z
(c) M.J.S. Dewar, J. Friedheim, G. Grady, E.F. Healy, J.J.P. Stewart, Organometallics, 5:375
(1986).
P M.J.S. Dewar, M.L. McKee, H.S. Rzepa, J. Am. Chem. Soc., 100: 3607 (1978).
S (a) M.J.S. Dewar, M.L. McKee, H.S. Rzepa, J. Am. Chem. Soc., 100:3607 (1978). z
(b) M.J.S. Dewar, C. H. Reynolds, J. Comp. Chem., 7:140 (1986).
Cl (a) M.J.S. Dewar, M.L. McKee, H.S. Rzepa, J. Am. Chem. Soc., 100, 3607 (1978). z
(b) M.J.S. Dewar, H.S. Rzepa, J. Comp. Chem., 4, 158, (1983)
Zn M.J.S. Dewar, K. M. Merz, Organometallics, 5:1494 (1986).
Ge M.J.S. Dewar, G.L. Grady, E.F. Healy, Organometallics, 6:186 (1987).
Br M.J.S. Dewar, E.F. Healy, J. Comp. Chem., 4:542, (1983).
I M.J.S. Dewar, E.F. Healy, J.J.P. Stewart, J. Comp. Chem., 5:358, (1984).
Sn M.J.S. Dewar, G.L. Grady, J.J.P. Stewart, J. Am. Chem. Soc., 106:6771 (1984).
Hg M.J.S. Dewar, G.L. Grady, K. Merz, J.J.P. Stewart, Organometallics, 4:1964, (1985).
Pb M.J.S. Dewar, M. Holloway, G.L. Grady, J.J.P. Stewart, Organometallics, 4:1973, (1985).
N.B.: z_ Parameters defined here are obsolete.
On MINDO/3
Part XXVI, Bingham, R.C., Dewar, M.J.S., Lo, D.H, J. Am. Chem. Soc., 97, (1975).
On AM1
"AM1: A New General Purpose Quantum Mechanical Molecular Model", M.J.S. Dewar, E.G.
Zoebisch, E.F. Healy, J.J.P. Stewart, J. Am. Chem. Soc., 107:3902-3909 (1985).
On PM3
"Optimization of Parameters for Semi-Empirical Methods I-Method", J.J.P. Stewart, J. Comp.
Chem., 10:221 (1989).
"Optimization of Parameters for Semi-Empirical Methods II-Applications, J.J.P. Stewart, J.
Comp. Chem., 10:221 (1989). (These two references refer to H, C, N, O, F, Al, Si, P, S, Cl,
Br, and I).
"Optimization of Parameters for Semi-Empirical Methods III-Extension of PM3 to Be, Mg,
Zn, Ga, Ge, As, Se, Cd, In, Sn, Sb, Te, Hg, Tl, Pb, and Bi", J.J.P. Stewart, J. Comp. Chem. (In
press, expected date of publication, Feb. 1991).
Original References for Elements Parameterized in AM1:
H M.J.S. Dewar, E.G. Zoebisch, E.F. Healy, J.J.P. Stewart, J. Am. Chem. Soc., 107:3902-3909
(1985).
B M.J.S. Dewar, C Jie, E. G. Zoebisch, Organometallics, 7:513-521 (1988).
C M.J.S. Dewar, E.G. Zoebisch, E.F. Healy, J.J.P. Stewart, J. Am. Chem. Soc., 107:3902-3909
(1985).
References_________________________________________________________
N M.J.S. Dewar, E.G. Zoebisch, E.F. Healy, J.J.P. Stewart, J. Am. Chem. Soc., 107:3902-3909
(1985).
O M.J.S. Dewar, E.G. Zoebisch, E.F. Healy, J.J.P. Stewart, J. Am. Chem. Soc., 107:3902-3909
(1985).
F M.J.S. Dewar, E.G. Zoebisch, Theochem., 180:1 (1988).
Al M.J.S. Dewar, A.J. Holder, Organometallics, 9:508 (1990).
Si M.J.S. Dewar, C. Jie, Organometallics, 6:1486-1490 (1987).
P M.J.S. Dewar, C.Jie, Theochem., 187:1 (1989)
S (No reference)
Cl M.J.S. Dewar, E.G. Zoebisch, Theochem., 180:1 (1988).
Zn M.J.S. Dewar, K.M. Merz, Jr., Organometallics, 7:522 (1988).
Ga M.J.S. Dewar, C. Jie, Organometallics, 8:1544 (1989).
Br M.J.S. Dewar, E.G. Zoebisch, Theochem., 180:1 (1988).
I M.J.S. Dewar, E.G. Zoebisch, Theochem., 180:1 (1988).
Hg M. J. S. Dewar, C. Jie, Organometallics, 8:1547 (1989). (see also PARASOK for the use of
MNDO parameters for other elements)
On Shift
"The Dynamic `Level Shift' Method for Improving the Convergence of the SCF Procedure", A.
V. Mitin, J. Comp. Chem., 9:107-110 (1988).
On Half-Electron
"Ground States of Conjugated Molecules. IX. Hydrocarbon Radicals and Radical Ions", M.J.S.
Dewar, J.A. Hashmall, C.G. Venier, J.A.C.S., 90:1953 (1968).
"Triplet States of Aromatic Hydrocarbons", M.J.S. Dewar, N. Trinajstic, Chem. Comm., 646,
(1970).
"Semiempirical SCF-MO Treatment of Excited States of Aromatic Compounds", M.J.S. Dewar,
N. Trinajstic, J. Chem. Soc., (A), 1220, (1971).
On Pulay's Converger
"Convergence Acceleration of Iterative Sequences. The Case of SCF Iteration", Pulay, P., Chem.
Phys. Lett., 73:393, (1980).
On Pseudodiagonalization
"Fast Semiempirical Calculations", Stewart. J.J.P., Csaszar, P., Pulay, P., J. Comp. Chem.,
3:227, (1982).
On Localization
"A New Rapid Method for Orbital Localization.", P.G. Perkins and J.J.P. Stewart,J.C.S. Faraday
(II), 77:000, (1981).
____________________________________________________________References_______
On Diagonalization
Beppu, Y., Computers and Chemistry, Vol.6 (1982).
On MECI
"Molecular Orbital Theory for the Excited States of Transition Metal Complexes", D.R. Arm-
strong, R. Fortune, P.G. Perkins, and J.J.P. Stewart, J. Chem. Soc., Faraday II, 68:1839-1846
(1972).
On Broyden-Fletcher-Goldfarb-Shanno Method
Broyden, C. G., Journal of the Institute for Mathematics and Applications, Vol. 6, pp 222-231,
1970.
Fletcher, R., Computer Journal, Vol. 13, pp 317-322, 1970. Goldfarb, D., Mathematics of Com-
putation, Vol. 24, pp 23-26, 1970.
Shanno, D. F., Mathematics of Computation, Vol. 24, pp 647-656 1970. See also summary in:
Shanno, D. F., J. of Optimization Theory and Applications, Vol.46, No 1 pp 87-94 1985.
On Polarizability
"Calculation of Nonlinear Optical Properties of Molecules", H. A. Kurtz, J. J. P. Stewart, K. M.
Dieter, J. Comp. Chem., 11:82 (1990). See also "Semiempirical Calculation of the Hyperpolariz-
ability of Polyenes", H. A. Kurtz, I. J. Quant. Chem. Symp., 24, xxx (1990).
On Thermodynamics
"Ground States of Molecules. 44 MINDO/3 Calculations of Absolute Heat Capacities and En-
tropies of Molecules without Internal Rotations. Dewar, M.J.S., Ford, G.P., J. Am. Chem. Soc.,
99:7822 (1977).
On SIGMA Method
Komornicki, A., McIver, J. W., Chem. Phys. Lett., 10:303, (1971).
Komornicki, A., McIver, J. W., J. Am. Chem. Soc., 94:2625 (1971).
On Molecular Orbital Valency
"Valency and Molecular Structure", Gopinathan, M. S., Siddarth, P., Ravimohan, C., Theor.
Chim. Acta , 70:303 (1986).
On Bonds
"Bond Indices and Valency", Armstrong, D.R., Perkins, P.G., Stewart, J.J.P., J. Chem. Soc.,
Dalton, 838 (1973). For a second, equivalent, description, see also: Gopinathan, M. S., and Jug,
K., Theor. Chim. Acta, 63:497 (1983).
On Locating Transition States
"Location of Transition States in Reaction Mechanisms", M.J.S. Dewar, E.F. Healy, J.J.P. Stewart,
J. Chem. Soc., Faraday Trans. II, 3:227, (1984).
On Dipole Moments for Ions
"Molecular Quadrupole Moments", A.D. Buckingham, Quarterly Reviews, 182 (1958 or 1959).
References_________________________________________________________
On Polymers
"MNDO Cluster Model Calculations on Organic Polymers", J.J.P. Stewart, New Polymeric Ma-
terials, 1:53-61 (1987).
"Calculation of Elastic Moduli using Semiempirical Methods", H. E. Klei, J.J.P. Stewart, Int. J.
Quant. Chem., 20:529-540 (1986).
Index
+, 13 CRAY-XMP, 1
&, 12 CYCLE, 95
0SCF, 13
1ELECTRON, 13 Danilof, V. I., v
1SCF, 13 data
commas in, 41
Ab initio total energies, 72 for ethene, 5
AIDER, 13 for polytetrahydrofuran, 6
AIGIN, 14 for polythene, 47
AIGOUT, 14 layout, 6
AM1, 14 MNRSD1
elements in, 44 input, 49
references, 150 output, 50
ANALYT, 14 tabs in, 41
analytical derivatives, 68 TESTDATA
input, 55
BAR, 14 output, 56
BIRADICAL, 14 Data General, 1
Boltzmann constant, 71 DCART, 17
BONDS, 15 DEBUG, 17
Born-von Karman, 100 DEC, 1
Boyd, Donald B., 69 definitions
bugs Boltzmann constant, 71
locating, 118 velocity of light, 71
DELHOF, 113
C.I., 15 DENOUT, 17
capped bonds, 45 DENSITY, 4
CDC, 1 DENSITY (0), 17
CHARGE, 16 Dewar research group, 3
cluster model, 100 dihedral angle coherency, 71
command file dipole moments
COMPILE, 121 of ions, 152
MOPAC, 123 DRAW program, 4
RMOPAC, 123 DRC
CONH linkage, 67 background, 76
constants conservation of momentum, 77
physical, 71 definition, 76
coordinates dummy atoms in, 79
Cartesian, 42 keyword options, 81
examples, 46
Gaussian Eigenvector
example, 66 following, 94
internal to Cartesian, 42 elements
reaction, 76 specification of, 44
COSMO, 99 energy, 72
INDEX______________________________________________________________
entropy, 72 Kurtz, Henry, A., v
error messages, 105
ESP LaTeX, v
installing, 124 liquids, 77
Excimers, 97 Localized orbitals, 2
Fluorescence, 97 mass-weighted coordinates, 62
force constant, 82 MECI
force constants, 1, 61 description of, 87
frame messages, 105
description of, 86 MNDO
Franck-Condon, 96 elements in, 44
MODE, 95
gas constant, R, 71 MOHELP, 4
Gaussian coordinates, 42 molecular orbitals, 1
geometry MOPAC
flags for, 43 geometric structure, 101
Gibbs free energy, 74 copyright, 2
GMETRY cost, 2
description, 103 criteria, 113
Gordon, Mark, 76 development, 3
Gould, 1 electronic structure, 102
grid map, 46 error messages, 105
installing, 121
H-PRIORITY, 85 programming policy, 102
heat capacity, 72 size of, 126
heat of formation, 74 using, 125
criteria, 113 version number, 52
molecular standards, 147 MOSOL, 4
HELP, 4
Hessian, 94 NONR, 94
Hirano, Tsuneo, 71 normal coordinate analysis, 62
IBM PC-AT, 1 OMIN, 94
internal coordinate definition, 41
ions, 1 partition function, 72
IRC PATH calculation, 63
definition, 78 Petts, Dr. J., 123
example of, 80 Phosphorescence, 97
example of restart, 80 Photoemission, 97
keywords for, 79 Photoexcitation energy, 96
isotopes POLAR, 28
specification of, 44 polymers, 1
data for, 6
Jensen, Frank, 94 Program
DENSITY, 4
keywords MOHELP, 4
debugging, 117 MOSOL, 4
specification, 6
KINETIC, 81 QCPE address, 2
kinetic energy
damping, 77 radicals, 1
Klamt, Andreas, v reaction coordinate
Klyne and Prelog, 71 specification, 46
Korambath, Prakashan, v Red-shift, 97
_______________________________________________________INDEX_______
reduced mass, 82 version number
references of MOPAC, 52
AM1, 150 vibrational analysis, 62
BFGS method, 152
bonds, 152 zero point energy, 61
CI derivatives, 149
diagonalization, 152
dipole moments of ions, 152
eigenvector following, 149
ESP, 149
half-electron, 151
localization, 151
MECI, 152
MINDO/3, 150
MNDO, 149
MO valency, 152
on G-DIIS, 149
PM3, 150
polarizability, 152
polymers, 153
pseudo-diagonalization, 151
Pulay's converger, 151
SHIFT, 151
SIGMA method, 152
thermodynamics, 152
transition state location, 152
RMAX, 95
RMIN, 95
RSCAL, 94
SCFCRT, 113
SHUTDOWN, 124
sparkles, 45
subroutines
calls in MOPAC, 129
description of, 137
full list of, 127
supercomputers, 1
symmetry functions
defined, 35
Taylor expansion, 94
THERMO
example of, 55
TOL2, 113
TOLERG, 113
TOLERX, 113
TOLS1, 113
transition state, 1
UNIX
on-line help, 124
VAX, 2, 4
*