# SPARTAN and CI

• From: "Michael E. Beck" <mbeck' at \`oci.unizh.ch>
• Subject: SPARTAN and CI
• Date: Tue, 1 Sep 1998 10:58:27 +0200 (MEST)

``` Dear CCLs,
I've got a problem understanding SPARTANS CI--output.  Imagine you are
performing a MNDO calculation on water. Orbitals 1 to 4 are doubly
occupied. Now you want to do singles and doubles configuration
interaction with orbitals 3 to 6 active.
For the ground state, Spartan gives the following CI-wavefunction
(the complete output is given below):
0         -0.998742     => that's the ground state (HF) determinant
1          0.003359     => a singly excited determinant
3          0.003359     => a singly excited determinant
9          0.017222     => a doubly excited determinant
12         0.032083     => a doubly excited determinant
23         0.031287     => a doubly excited determinant
26         0.013703     => a doubly excited determinant
Thus the _singly_ excited determinants 1 and 3 enter the groundstate
wavefunction with 0.003359. How's that possible?
Michael
___________________________________________________________________
Dr. Michael E. Beck                  |  privat:
Organisch--Chemisches Institut       |  Zschokkestr. 12a
Theoretische Gruppe, Prof. W. Thiel  |  CH--8037 Zuerich
Universitaet Zuerich                 |  +41-1-271-54-39
Winterthurerstr. 190                 |___________________________
CH--8057 Zuerich
Tel.: +41-1-635-6117          web : www.unizh.ch/oci/group.pages/
thiel/persons/beck/
Fax.:           6836          mail: mbeck' at \`oci.unizh.ch
___________________________________________________________________
Here's the complete SPARTAN output
SPARTAN SEMIEMPIRICAL PROGRAM: SGI/R10K       Release 5.0.3
(Job run on ocisgi30)
Calculation started: Fri Aug 14 12:23:03 1998
Run type: Single point energy
Model: RHF/MNDO
Number of shells:   4
3 S shells
1 P shells
Number of basis functions:   6
Number of electrons:   8
Use of molecular symmetry enabled
Molecular charge:   0
Spin multiplicity:  1
Cartesian Coordinates (Angstroms)
Atom Label         X             Y             Z
-- --------  ------------- ------------- -------------
H  H1           0.0000000    -0.7570569     0.1874133
O  O1           0.0000000     0.0000000    -0.3748267
H  H2           0.0000000     0.7570569     0.1874133
Point Group = CNV Order =  2 Nsymop =  4
This system has   2 degrees of freedom
Interatomic distances (Angstroms)
1           2           3
1      0.000000    0.943000    1.514114
2      0.943000    0.000000    0.943000
3      1.514114    0.943000    0.000000
Angle            3  2  1    is  106.800 degrees
Angle            3  1  2    is   36.600 degrees
Angle            2  3  1    is   36.600 degrees
Highest occupied MO = #4
Huckel Guess...
Guess energy = -474.011396062
cycle # 1	Energy = -499.548338849
cycle # 2	Energy = -500.382719238
cycle # 3	Energy = -500.467977346
cycle # 4	Energy = -500.482152185
cycle # 5	Energy = -500.484942669	pseudo
cycle # 6	Energy = -500.485511347	pseudo
cycle # 7	Energy = -500.485628130	pseudo
cycle # 8	Energy = -500.485652173	pseudo
cycle # 9	Energy = -500.485657128	pseudo
Final Energy = -500.485658153 (rechecking after pseudodiagonalization)
Converged in 9 cycles
Convergence critera met in 9 cycles ...
Electronic energy = -500.485658 eV
Core repulsion energy = 149.060825 eV
Total Energy = -351.424834 eV
Performing integral transformation ...
Constructing singles ...
Constructing doubles ...
CI calculation performed using orbitals 3 to 6
Slater Determinants
State   type           configuration
-----------------------------------------------------------------
0 Ground state     11  00
11  00
1   Single         01  10
11  00
2   Single         01  01
11  00
3   Single         11  00
01  10
4   Single         11  00
01  01
5   Single         10  10
11  00
6   Single         10  01
11  00
7   Single         11  00
10  10
8   Single         11  00
10  01
9   Double         01  10
01  10
10   Double         01  10
01  01
11   Double         01  01
01  10
12   Double         01  01
01  01
13   Double         00  11
11  00
14   Double         01  10
10  10
15   Double         01  10
10  01
16   Double         01  01
10  10
17   Double         01  01
10  01
18   Double         10  10
01  10
19   Double         10  10
01  01
20   Double         10  01
01  10
21   Double         10  01
01  01
22   Double         11  00
00  11
23   Double         10  10
10  10
24   Double         10  10
10  01
25   Double         10  01
10  10
26   Double         10  01
10  01
Heats of Formation:   HF    -60.938 kcal/mol
CI    -62.320 kcal/mol
Eigenvalues and eigenvectors of the CI matrix ...
0          1          2          3          4          5
eig:      -0.059920   6.310075   7.511671   7.528376   8.243903   9.449156
OS:                   0.123017   0.146661   0.000000   0.000000   0.758494
nm:                 196.511126 165.076454 164.710152 150.414189 131.228648
spin:                   no         yes        no         yes        no
---------------------------------------------------------------------------
0         -0.998742   0.000000   0.000000   0.000000   0.000000   0.000000
1          0.003359   0.000000   0.000000   0.000000   0.000000  -0.707107
2          0.000000   0.000000   0.000000   0.000000   0.000000   0.000000
3          0.003359   0.000000   0.000000   0.000000   0.000000   0.707107
4          0.000000   0.000000   0.000000   0.000000   0.000000   0.000000
5          0.000000   0.705760   0.706022   0.000000   0.000000   0.000000
6          0.000000   0.000000   0.000000   0.704836  -0.705693   0.000000
7          0.000000  -0.705760   0.706022   0.000000   0.000000   0.000000
8          0.000000   0.000000   0.000000  -0.704836  -0.705693   0.000000
9          0.017222   0.000000   0.000000   0.000000   0.000000   0.000000
10         0.000000   0.000000   0.000000   0.000000   0.000000   0.000000
11         0.000000   0.000000   0.000000   0.000000   0.000000   0.000000
12         0.032083   0.000000   0.000000   0.000000   0.000000   0.000000
13         0.000000   0.000000   0.000000  -0.010847   0.009463   0.000000
14         0.000000  -0.019114   0.009315   0.000000   0.000000   0.000000
15         0.000000   0.000000   0.000000  -0.029136  -0.025788   0.000000
16         0.000000   0.000000   0.000000   0.047322   0.035251   0.000000
17         0.000000  -0.039215   0.038023   0.000000   0.000000   0.000000
18         0.000000  -0.019114  -0.009315   0.000000   0.000000   0.000000
19         0.000000   0.000000   0.000000  -0.047322   0.035251   0.000000
20         0.000000   0.000000   0.000000   0.029136  -0.025788   0.000000
21         0.000000  -0.039215  -0.038023   0.000000   0.000000   0.000000
22         0.000000   0.000000   0.000000   0.010847   0.009463   0.000000
23         0.031287   0.000000   0.000000   0.000000   0.000000   0.000000
24         0.000000   0.000000   0.000000   0.000000   0.000000   0.000000
25         0.000000   0.000000   0.000000   0.000000   0.000000   0.000000
26         0.013703   0.000000   0.000000   0.000000   0.000000   0.000000
6          7          8          9         10         11
eig:      10.257741  10.323881  11.782136  15.801429  16.092334  16.430589
OS:        2.631401   0.813497   2.937839   0.000000   0.000000   0.000000
nm:      120.884315 120.109872 105.244074  78.473915  77.055325  75.468995
spin:        no         yes        yes        no         no         yes
---------------------------------------------------------------------------
0	   0.000000  -0.007135   0.000000   0.000000   0.000000   0.018663
1	   0.000000  -0.703839   0.000000   0.000000   0.000000   0.014371
2	  -0.706960   0.000000  -0.701960   0.000000   0.012296   0.000000
3	   0.000000  -0.703839   0.000000   0.000000   0.000000   0.014371
4	   0.706960   0.000000  -0.701960   0.000000  -0.012296   0.000000
5	   0.000000   0.000000   0.000000   0.000000   0.000000   0.000000
6	   0.000000   0.000000   0.000000   0.000000   0.000000   0.000000
7	   0.000000   0.000000   0.000000   0.000000   0.000000   0.000000
8	   0.000000   0.000000   0.000000   0.000000   0.000000   0.000000
9	   0.000000  -0.066444   0.000000   0.000000   0.000000  -0.112892
10	   0.009163   0.000000  -0.083163   0.000000   0.100365   0.000000
11	   0.009163   0.000000   0.083163   0.000000   0.100365   0.000000
12	   0.000000  -0.064357   0.000000   0.000000   0.000000   0.082687
13	   0.000000   0.000000   0.000000  -0.408248   0.000000   0.000000
14	   0.000000   0.000000   0.000000   0.000000   0.000000   0.000000
15	   0.000000   0.000000   0.000000   0.408248   0.000000   0.000000
16	   0.000000   0.000000   0.000000   0.408248   0.000000   0.000000
17	   0.000000   0.000000   0.000000   0.000000   0.000000   0.000000
18	   0.000000   0.000000   0.000000   0.000000   0.000000   0.000000
19	   0.000000   0.000000   0.000000   0.408248   0.000000   0.000000
20	   0.000000   0.000000   0.000000   0.408248   0.000000   0.000000
21	   0.000000   0.000000   0.000000   0.000000   0.000000   0.000000
22	   0.000000   0.000000   0.000000  -0.408248   0.000000   0.000000
23	   0.000000   0.024536   0.000000   0.000000   0.000000   0.815618
24	  -0.011107   0.000000   0.018348   0.000000  -0.699840   0.000000
25	  -0.011107   0.000000  -0.018348   0.000000  -0.699840   0.000000
26	   0.000000   0.003261   0.000000   0.000000   0.000000  -0.560736
12         13         14         15         16         17
eig:      17.333535  18.020974  19.015929  19.183426  19.365041  19.379897
OS:        0.000000   0.000000   0.000000   0.000000   0.000015   0.000000
nm:       71.537628  68.808711  65.208489  64.639131  64.032912  63.983829
spin:        no         no         no         yes        yes        yes
---------------------------------------------------------------------------
0	   0.000000   0.000000   0.000000   0.000000   0.000000   0.000000
1	   0..000000   0.000000   0.000000   0.000000   0.000000   0.000000
2	   0.000000   0.000000   0.000000   0.000000   0.029411   0.000000
3	   0.000000   0.000000   0.000000   0.000000   0.000000   0.000000
4	   0.000000   0.000000   0.000000   0.000000   0.029411   0.000000
5	   0.007689   0.000000   0.000000   0.000000   0.000000  -0.014835
6	   0.000000   0.006805   0.001475  -0.004125   0.000000   0.000000
7	  -0.007689   0.000000   0.000000   0.000000   0.000000  -0.014835
8	   0.000000  -0.006805  -0.001475  -0.004125   0.000000   0.000000
9	   0.000000   0.000000   0.000000   0.000000   0.000000   0.000000
10	   0.000000   0.000000   0.000000   0.000000  -0.093752   0.000000
11	   0.000000   0.000000   0.000000   0.000000   0.093752   0.000000
12	   0.000000   0.000000   0.000000   0.000000   0.000000   0.000000
13	   0.000000   0.674224   0.207141  -0.569009   0.000000   0.000000
14	  -0.571169   0.000000   0.000000   0.000000   0.000000  -0.571916
15	   0.000000   0.153504  -0.586804  -0.369139   0.000000   0.000000
16	   0.000000   0.147691  -0.335784  -0.199871   0.000000   0.000000
17	   0.416782   0.000000   0.000000   0.000000   0.000000   0.415562
18	  -0.571169   0.000000   0.000000   0.000000   0.000000   0.571916
19	   0.000000  -0.147691   0.335784  -0.199871   0.000000   0.000000
20	   0.000000  -0.153504   0.586804  -0.369139   0.000000   0.000000
21	   0.416782   0.000000   0.000000   0.000000   0.000000  -0.415562
22	   0.000000  -0.674224  -0.207141  -0.569009   0.000000   0.000000
23	   0.000000   0.000000   0.000000   0.000000   0.000000   0.000000
24	   0.000000   0.000000   0.000000   0.000000   0.700247   0.000000
25	   0.000000   0.000000   0.000000   0.000000  -0.700247   0.000000
26	   0.000000   0.000000   0.000000   0.000000   0.000000   0.000000
18         19         20         21         22         23
eig:      19.943584  20.380517  20.803840  22.406845  22.832961  23.342782
OS:        0.000001   0.000000   0.000006   0.000000   0.000003   0.000000
nm:       62.175385  60.842420  59.604381  55.340231  54.307455  53.121346
spin:        yes        no         no         yes        yes        no
---------------------------------------------------------------------------
0	  -0.023708   0.000000   0.000000   0.000000   0.000000   0.000000
1	  -0.020550   0.000000   0.000000   0.000000   0.000000   0.000000
2	   0.000000   0.000000   0.000000   0.000000   0.000000   0.007492
3	  -0.020550   0.000000   0.000000   0.000000   0.000000   0.000000
4	   0.000000   0.000000   0.000000   0.000000   0.000000  -0.007492
5	   0.000000   0.000000   0.042943   0.000000   0.036228   0.000000
6	   0.000000   0.056191   0.000000  -0.044499   0.000000   0.000000
7	   0.000000   0.000000  -0.042943   0.000000   0.036228   0.000000
8	   0.000000  -0.056191   0.000000  -0.044499   0.000000   0.000000
9	   0.071421   0.000000   0.000000   0.000000   0.000000   0.000000
10	   0.000000   0.000000   0.000000   0.000000   0.000000   0.699888
11	   0.000000   0.000000   0.000000   0.000000   0.000000   0.699888
12	   0.123133   0.000000   0.000000   0.000000   0.000000   0.000000
13	   0.000000   0.048965   0.000000  -0.097326   0.000000   0.000000
14	   0.000000   0.000000   0.416415   0.000000  -0.415722   0.000000
15	   0.000000   0.362282   0.000000   0.443176   0.000000   0.000000
16	   0.000000  -0.602658   0.000000  -0.540502   0.000000   0.000000
17	   0.000000   0.000000   0.569873   0.000000  -0.570844   0.000000
18	   0.000000   0.000000   0.416415   0.000000   0.415722   0.000000
19	   0.000000   0.602658   0.000000  -0.540502   0.000000   0.000000
20	   0.000000  -0.362282   0.000000   0.443176   0.000000   0.000000
21	   0.000000   0.000000   0.569873   0.000000   0.570844   0.000000
22	   0.000000  -0.048965   0.000000  -0.097326   0.000000   0.000000
23	  -0.561260   0.000000   0.000000   0.000000   0.000000   0.000000
24	   0.000000   0.000000   0.000000   0.000000   0.000000   0.100504
25	   0.000000   0.000000   0.000000   0.000000   0.000000   0.100504
26	  -0.814443   0.000000   0.000000   0.000000   0.000000   0.000000
24         25         26
eig:      23.750830  26.793754  27.275329
OS:        0.000000   0.001123   0.000135
nm:       52.208701  46.279442  45.462329
spin:        yes        yes        yes
---------------------------------------------------------------------------
0	   0.004494   0.000000  -0.039162
1	   0.006874   0.000000   0.062632
2	   0.000000  -0.079923   0.000000
3	   0.006874   0.000000   0.062632
4	   0.000000  -0.079923   0.000000
5	   0.000000   0.000000   0.000000
6	   0.000000   0.000000   0.000000
7	   0.000000   0.000000   0.000000
8	   0.000000   0.000000   0.000000
9	  -0.775560   0.000000  -0.613148
10	   0.000000   0.695913   0.000000
11	   0.000000  -0.695913   0.000000
12	   0.615096   0.000000  -0.771030
13	   0.000000   0.000000   0.000000
14	   0.000000   0.000000   0.000000
15	   0.000000   0.000000   0.000000
16	   0.000000   0.000000   0.000000
17	   0.000000   0.000000   0.000000
18	   0.000000   0.000000   0.000000
19	   0.000000   0.000000   0.000000
20	   0.000000   0.000000   0.000000
21	   0.000000   0.000000   0.000000
22	   0.000000   0.000000   0.000000
23	  -0.103953   0.000000  -0.085839
24	   0.000000   0.096529   0.000000
25	   0.000000  -0.096529   0.000000
26	   0.096143   0.000000  -0.113204
eigenvalue 0 = -500.545578
eigenvalue 1 = -494.175583
eigenvalue 2 = -492.973987
eigenvalue 3 = -492.957282
eigenvalue 4 = -492.241755
eigenvalue 5 = -491.036502
eigenvalue 6 = -490.227917
eigenvalue 7 = -490.161777
eigenvalue 8 = -488.703522
eigenvalue 9 = -484.684229
eigenvalue 10 = -484.393324
eigenvalue 11 = -484.055070
eigenvalue 12 = -483.152123
eigenvalue 13 = -482.464684
eigenvalue 14 = -481.469729
eigenvalue 15 = -481.302232
eigenvalue 16 = -481.120617
eigenvalue 17 = -481.105761
eigenvalue 18 = -480.542074
eigenvalue 19 = -480.105141
eigenvalue 20 = -479.681818
eigenvalue 21 = -478.078813
eigenvalue 22 = -477.652697
eigenvalue 23 = -477.142876
eigenvalue 24 = -476.734828
eigenvalue 25 = -473.691904
eigenvalue 26 = -473.210329
Spin-allowed singlet excitations
State    Energy        OS         nm
-----------------------------------------
2    7.511671    0.146661  165.076454
7   10.323881    0.813497  120.109872
8   11.782136    2.937839  105.244074
Ground State Dipole Moment:
u(x) = 0.000000  u(y) = 0.000000  u(z) = 1.773507   u(tot) = 1.773507
Ground State Atomic Charges
Atom    Population    Charge
------------------------------
H    1    0.838358    0.161642
O    2    6.323284   -0.323284
H    3    0.838358    0.161642
Ground State Bond Order Matrix
1          2          3
---------------------------------------------------------------------------
1        0.000000   0.966988   0.003462
2        0.966988   0.000000   0.966988
3        0.003462   0.966988   0.000000
State 2 Dipole Moment:
u(x) = 0.000000  u(y) = 0.000000  u(z) = -0.321723   u(tot) = 0.321723
State 2 Atomic Charges
------------------------------
H    1    1.143015   -0.143015
O    2    5.713970    0.286030
H    3    1.143015   -0.143015
State 2 Bond Order Matrix
1          2          3
---------------------------------------------------------------------------
1        0.000000   0.610875   0.059521
2        0.610875   0.000000   0.610875
3        0.059521   0.610875   0.000000
Gross electron populations over atoms (HF wavefunction):
Atom   Population  Net charge
------------------------------
1       0.837       0.163
2       6.326      -0.326
3       0.837       0.163
Bond Order Matrix
1          2          3
---------------------------------------------------------------------------
1        0.000000   0.970036   0.003445
2        0.970036   0.000000   0.970036
3        0.003445   0.970036   0.000000
Dipole Moment:
u(x) = 0.000000  u(y) = 0.000000  u(z) = 1.783296   u(tot) = 1.783296
Heat of Formation:      -62.320 kcal/mol
** Archive file written to unit 12 **
Total Cpu time:        0 mins.  0.04 secs.
Total Wall time:       0 mins.  0.18 secs.
Calculation started: Fri Aug 14 12:23:03 1998
SPARTAN PROPERTIES PACKAGE: SGI/R10K       Release 5.0.3
Total Cpu time:   0 mins.  0.00 secs.
```