From:	"Leif Haldor Bjerkeseth . Organisk Kjemi" <bjerkese #*at*# kj
Date:	Sun, 21 Feb 1993 20:51:19 +0100 (MET)
Subject:	Summary. Scaled freq for S and H

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## S U M M A R Y   O F   R E S P O N S E S :  ##
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Warning: long!

Here is the summary of the responses I received. Thank you very much
to all that responded.


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## Original posting: ##
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## From: "Leif Haldor Bjerkeseth . Organisk Kjemi" 
Subject: G90/92. Scaled Freq. Correct. for H and S.
To: chemistry &$at$& ccl.net
Date: Wed, 10 Feb 1993 16:55:05 +0100 (MET)

You have to scale the frequencies you get from Gaussian by about 0.9.
The enthalphy, entropy and ZPE among other thermodynamical properties
calculated by Gaussian depend upon the frequencies. Does someone on this
list know how you can compute the thermodynamical properties using scaled
frequencies in Gaussian? Probably not possible? If so, has someone written
a program to extract the frequencies from the outputfile or chk-file,
correct for the scaling and then compute the thermodynamical properties?
Or do I have to use Lotus 1-2-3 or Excel after looking up the litterature
references for all the formulas.

Leif Haldor
--
 Leif Haldor Bjerkeseth, Dept.Org.Chem., NTH, UNIT, N-7034 TRONDHEIM
 Phone: +47 7 59 39 67  //  Prefered E-mail address: bjerkese $#at#$
kjemi.unit.no
 Fax:   +47 7 59 42 56  //

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## Responses: ##
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## From: culmer "-at-" stardent.chem.UTOLEDO.edu (Charles Ulmer)

Leif:
  I would be greatful if you could summarize for the list any of the
responces that you receive concerning programs which use scaled freq.
to estimate thermodynamic properties.  I too am tired of entering all
the data into Excel...
--

 Charles W. Ulmer
 D.A.Smith Group
 University of Toledo
 Toledo, OH, 43606
 culmer : at : stardent.chem.utoledo.edu

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## From: Louis.Grace -AatT- um.cc.umich.edu

I have been editing my gaussian output files in Word.  When I have the
sections I want (frequencies and displacements, for example) I then
change all the spaces into tabs.  I then use Excel to manipulate the data.
One can probably use Lotus 1-2-3 or a host of other programs, too.
Depending on what you wish to extract from the file and in what format
you would like to have it, you may need to make a set of macros for
transposing and rearranging things.  Have fun!

                                             Louis Grace
                                             Department of Chemistry
                                             The University of Michigan
                                             Ann Arbor, Michigan   48104

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## From: zheng # - at - # violet.berkeley.edu

  Hi, I remember that in one paper Prof. Pople demonstrated scaling of
frequencies has little effect on thermodynamical properties calculated. If you
wnat to compare the calculated frequencies with experiemntal data, scaling is
usefull. Otherwise, scaling is not needed.

     Yajun Zheng

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## From: Bundens Jeanne W 

	There is a derivation from Hehre's book for scaling freq and
correcting for zpve and to standard temp. If you don't get other
responses I could send you the short code that does that much and you
can modify it. As for extracting frequencies from Gaussian output, we
get by in UNIX with the convenient grep command and pipe the results to
a file to be read by the program. I'd be interested in your other
responses.

		Jeanne Bundens
		jbundens;at;cc.brynmawr.edu

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From: jan "-at-" si.fi.ameslab.gov (Jan Jensen)

Dear Dr. Bjerkeseth,

	With regard to using scaled frequencies to calculate thermodynamical
properties I have one suggestion.  The US version of the quantum chemistry
program GAMESS allows the input of a scale factor for the frequencies,
and the scaled frequencies are then used to calculate the ZPE, etc.  It
is also possible to type in the frequencies in the input, if you don't
want to recalculate a hessian or have done so with another program.
All this is done in $FORCE, in case you are familiar with GAMESS input. If you
have access to this code this may be a good solution.  If not, it may be
too much work to to set up the code to scale a few frequencies.  However, I
would be happy to let you know how to get it, if you are interested.

			Best regards,
					Jan H. Jensen (grad. student)

					Department of Chemistry
					Iowa State University
					Ames, Iowa

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## From: "J.S. Kwiatkowski" 

Hi Leif,
 I just read your e-mail concerning the calculation of thermodynamic
properties using the scaled frequencies from Gaussian.
 It is my pleasure to inform you that I wrote a short program
to compute these properties using frequencies given as the input
data (so you can use scaled, unscaled, experimental frequencies etc.).
The program is written in fortran, it is a very short (the program
reproduce exactly the results from the Gaussian programs at T = 298.15
K). Using my program you can compute the thermodynamic properties at
any temperature.
 If you are interested in this program, please reply me this
 message
Yours   Staszek (J.S. Kwiatkowski)

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## From: "J.S. Kwiatkowski" 

[FORTRAN-CODE, FOR PC. LH]

Program THERM calculate thermodynamic functions: capacity Cp and enrtopies
(trans,rot,vibr,tot) at any temperature. To prepare input data it is necessary
to know the rotational constants (A,B,C), molecular mass, and frequencies
of a molecule.

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## From: ckf &$at$& f16.cray.com (Charles Foley)

Leif -

You should contact Lee Bartolotti at the North Carolina Supercomputing
Center here in the U.S.  Lee has written a program that will calculate
thermodynamice properties at a given temperature using a starting geometry
and frequencies.  The program has been modified by Dave Deerfield at the
Pittsburgh Supercomputing Center to read frequency and geometry information
directly from a Gaussian 90/92 output file.  I'm not sure if the frequencies
are scaled however.

You can reach Lee Bartolotti at e-mail address: bartolot -x- at -x-
flyer.ncsc.org

Regards,

Charles K. Foley, Ph.D.
Cray Research, Inc.
P.O. Box 12746
Research Triangle Park, NC 27709
(919) 544-6267 							o
							      <(
ckf -8 at 8- f16.cray.com					       [\.

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## From: Lee Bartolotti 

[Response from Dr. Bartolotti to E-mail from me. LH]
[FORTRAN-CODE FOR PROGRAM THERMAL. LH]

Hi,
In response to your e-mail request, I am sending you a copy of the program
which will read Gaussian output files and calculated various thermodynamic
properties.  It was just thrown together and could be made cleaner but
it is functional.  Not all output is well documented. For instance, the
zero point energy is output as "ev0", and "delta h" is the change in
enthalpy going from OK to the temperature of interest ("delta h" equation
is given in the book by Hehre et al).

This program will also read input from the following file format
(which makes compatable with other programs)

[format deleted. LH]

Here, the first line tells the program if the molecule is linear or not,
the symmetry number (1 in this case) and the temperature.  The next set
of data gives the Cartesian coordinates (in Angstroms).  A blank line
separates the the input of the vibrational frequencies (in 1/cm).

If you want to scale the frequencies, you can do in subroutine thermo,
at the "do 10" loop.  Just multiply "FREQ(i)" by the scale factor.

 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 ||  Lee Bartolotti                   North Carolina Supercomputing Center   ||
 ||  Computational Scientist          3021 Cornwallis Rd.                    ||
 ||  Research Institute               Research Triangle Park, NC 27709       ||
 ||  bartolot &$at$& ncsc.org
||
 ||  (919) 248-1185                                                          ||
 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

      PROGRAM THERMAL
c*******************************************************************************
c
c     This program calculates the thermo-chemical properties of a molecule
c     given its Cartesian coordinates and vibrational spectrum.
C
C     The program was originally written by:
C
C              Dr. Lee Bartolotti
C              North Carolina Supercomputing Center
C              bartolot -AatT- ncsc.org
C              919-248-1185
C
C     Bastardized by:
C
C              Dr. David W. Deerfield II
C              Pittsburgh Supercomputing Center
C              deerfiel "at@at" psc.edu
C              412-268-6102

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## From: topper' at \`HAYDN.CHM.URI.EDU (Robert Q. Topper)

Dear Leif,

You can certainly estimate thermochemical properties from the frequencies
you get from Gaussian. However, you will have to use the rigid-rotator/
harmonic oscillator (RRHO) approximation to the partition function, which
requires the three principal moments of inertia as well as the
harmonic frequencies. These can be calculated from the molecular
geometry and masses.  Also, the calculation may only
be semi-quantitative, unless you have a fancy way of estimating the
partition function.

My coworkers and I have recently written a paper on the calculation of
thermochemical properties from potential energy surfaces
using various methods, and the article will appear soon in
the Journal of Chemical Physics (March 15 is the approximate date).
In that paper, we compare the RRHO approximation of the free energy
to calculations made using perturbation theory to treat the vibrations
and to (exact) Fourier path-integral quantum Monte Carlo calculations
for potential energy models of gas-phase H2O, D2O, H2S, and H2Se.
However, we did not use "scaled" frequencies; we used the actual normal-
mode harmonic oscillator frequencies. These resulted in partition
functions which were off by as much as 30% from "exact" values
(looking at temperatures between 200 and 4000 K).
There's no telling whether using scaled frequencies would make
the partition functions more accurate or less accurate, at least not
from first principles.
I would be glad to send you a preprint of our work if you are interested
(this is the same article that many people on the list have asked for
in the context of coordinate transformations).

Also, Martin, Francois and Gijbels have recently calculated thermochemical
properties for H2O using Gaussian. A good reference is:

Martin, Francois, and Gijbels, J. Chem. Phys. 96, 7633 (1992)

Our work indicates that their calculations (which use vibrational
perturbation theory in combination with a quantum non-rigid rotator
calculation) are quite accurate up to 2400K.  However, for molecules
which can undergo internal rotations at the temperature of interest,
all bets are off! Also, beware of very low-frequency (floppy) vibrations.

A very useful approximate "harmonic" form for the vibrational
partition function (if you know the zero-point energy and the
fundamentals) is given in

D.G. Truhlar and A.D. Isaacson, J. Chem. Phys. 94, 357 (1991)

and you may also want to look at the JANAF tables;

M.W. Chase Jr. et.al., JANAF Thermochemical Tables, 3rd ed. (ACS and APS
for the National Bureau of Standards, New York, 1985).

-Hope this helps!
robert


            ********************************
            *  Robert Q. Topper, Ph.D.     *
            *  Department of Chemistry     *
            *  University of Rhode Island  *
            *  Kingston, RI 02881 USA      *
            ********************************
            *  rtopper &$at$& chm.uri.edu OR      *
            *  topper ^at^ haydn.chm.uri.edu    *
            *  (401) 792-2597 [office]     *
            *  (401) 792-5072 [FAX]        *
            ********************************

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## From: topper.,at,.haydn.chm.uri.edu (Robert Q. Topper)

Leif, you may also want to look at

J. Gao, J.Am. Chem. Soc. 113, 7796 (1991)

for thermochemical calculations of the Menshutkin reaction in solution
using Gaussian.

-Robert

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## From: "DR. DOUGLAS A. SMITH, UNIVERSITY OF TOLEDO" 

[original posting deleted. LH]

Robert Topper responds:

>You can certainly estimate thermochemical properties from the frequencies
>you get from Gaussian. However, you will have to use the rigid-rotator/
>harmonic oscillator (RRHO) approximation to the partition function, which
>requires the three principal moments of inertia as well as the
>harmonic frequencies. These can be calculated from the molecular
>geometry and masses.  Also, the calculation may only
>be semi-quantitative, unless you have a fancy way of estimating the
>partition function.  (Significantly more and detailed information has
been deleted from this response - DAS.)

In a recent manuscript we wrote:

"Each HF/6-31G* optimization, and for the monomers the MP2/6-31G*
optimizations, were followed by normal frequency analysis to make sure an
energy minimum was obtained and for calculating free energies at 298
K and one atmosphere.  In the free energy calculations the thermal
correction to the enthalpy, H(T) and entropy, S(T) were calculated in the
rigid rotor, harmonic oscillator approximation.  Ideal gas behavior
was accepted in the imidazole protonation reaction and for the formation
of monohydrates.  The thermal energy contributions were calculated using
classical statistical thermodynamic functions.  The total entropy
for PyW(pi) and Im(3)W without any molecular symmetry contain a term
of RTln2 due to the entropy of mixing."

Taken from:  Nagy, P. I.; Durant, G. J.; Smith, D. A. "Theoretical Studies
on Hydration of Pyrrole, Imidazole and Protonated Imidazole in the Gas
Phase and Aqueous Solution," J. Am. Chem. Soc., in press.

Doug

Douglas A. Smith
Assistant Professor of Chemistry
The University of Toledo
Toledo, OH  43606-3390

voice    419-537-2116
fax      419-537-4033
email    dsmith(-(at)-)uoft02.utoledo.edu

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## From: topper # - at - # haydn.chm.uri.edu (Robert Q. Topper)

[In response to the message above Robert Topper responded: LH]

Doug, Please understand that I have nothing agains the classical
rigid-rotator/quantum harmonic-oscillator approximation,
which enjoys widespread use. (A paper I saw by J. Gao on the
Menshutskin reaction [JACS 113, 7796 (1991)] comes to mind). Also,
Don Truhlar (with whom I did the quantum Monte Carlo work) and
Bruce Garrett have been using this approximation for many years
in rate constant and isotope effect calculations for polyatomic molecules,
often with great success. However, if a molecule can undergo internal
rotations at room temperature, or the molecule is an ionic complex
of some kind (large-amplitude, low-frequency stretches),
the CRR/QHO approximation has less chance of working well.
Moreover, anharmonicities can sometimes have a big effect on the
zero-point energy, and thus affect the quality of the thermochemical
calculations. This is my main point...and the point of our JCP article.

My second point is that the use of scaled freqencies may be numerically
justified, but has never been actually tested against exact calculations
of free energies, at least not to my knowledge. Personally, if I were going
to calculate thermochemical properties from a Gaussian calculation, I'd
use the classical rigid rotator for the rotations, calculate some cubic
and quartic force constants using Gaussian (assuming I had enough
computer time), and use the expression given for the vibrational partition
function in Truhlar and Issacson, JCP 94, 357 (1991). At least then
the zero-point energy would be accurate, and so then presumably would be
the room-temperature thermochemical values (again, assuming no internal
rotations....). Moreover, only a subset of the force field is needed
for the aforementioned approximate form.

-rqt

            ********************************
            *  Robert Q. Topper, Ph.D.     *
            *  Department of Chemistry     *
            *  University of Rhode Island  *
            *  Kingston, RI 02881 USA      *
            ********************************
            *  rtopper %! at !% chm.uri.edu OR      *
            *  topper #*at*# haydn.chm.uri.edu    *
            *  (401) 792-2597 [office]     *
            *  (401) 792-5072 [FAX]        *
            ********************************

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I think I will mention another solution to the problem mentioned in my
original posting. If I could scale the frequencies in Gaussian that
would be the best. It should be possible to take a copy of the link
that performs the thermo-calculations, modify the procedure THERMO to
calculate both scaled and unscaled thermodynamical properties (include
the scale factor in the code) and recompile the link under another
name and then change the route to use this new link instead of the
standard one.

Such a procedure is something that would have been very nice to
have in the original Gaussian. Probably something to put into
it in the next version, Mike Frisch ? (e.g in combination with the
READISOTOPES keyword.)


Again, thank you very much to all that responded.

Leif Haldor
---
 Leif Haldor Bjerkeseth, Dep.Org.Chem., NTH, UNIT, N-7034 TRONDHEIM, Norway
 Phone: +47 7 59 39 67  //  Prefered E-mail adress: bjerkese ^at^ kjemi.unit.no
 Fax:   +47 7 59 42 56  //




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05/25/1995:  Summary: Imaginary freq. and rate constant
01/10/1995:  Summary - Scaling of vibrational frequencies
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