| Chapter 21. A Simple Example of Using Configuration Interaction | ||
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Part II. AMPAC™ 10 Examples |  |
| Chapter 21. A Simple Example of Using Configuration Interaction | ||
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Part II. AMPAC™ 10 Examples | |
Table of Contents
AMPAC has a very powerful and robust configuration interaction (CI) engine, so it is worthwhile to present a simple example of its use. (A complete description of CI theory and keywords can be found in Chapter 11, Configuration Interaction.) In this example, ethylene is being optimized with a very limited CI. Many more CI examples can be found in the AMPAC test stuite.
am1 c.i.=2 cistate=3 cimax=100 singlet t=auto truste lforce bonds 
D2h Ethylene, AM1/CI, HOMO LUMO Active, S0 (Singlet Ground State)
Opt+LowFreq, Active MOs and Bonds, Calc 3 Lowest States
C 0.000000 0 0.000000 0 0.000000 0 0 0 0
C 1.325916 1 0.000000 0 0.000000 0 1 0 0
H 1.098266 1 122.715971 1 0.000000 0 1 2 0
H 1.098266 1 122.715971 1 -180.000000 1 1 2 3
H 1.098266 1 122.715971 1 0.000000 1 2 1 4
H 1.098266 1 122.715971 1 180.000000 1 2 1 4
0 0.000000 0 0.000000 0 0.000000 0 0 0 0
Timestamp: 2011-08-31-12-35-20-0000001734-win64
User Info: John Millam, Nahum,
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AM1 CALCULATION RESULTS
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* AMPAC Version 10.0.1
* Presented by:
*
* Semichem, Inc.
* www.semichem.com
*
* AM1 - THE AM1 HAMILTONIAN TO BE USED
* RHF - RESTRICTED HARTREE-FOCK CALCULATION
* TRUSTE - MINIMIZE ENERGY USING TRUST REGION METHOD
* LFORCE - LOWEST IR FREQUENCIES CALCULATION SPECIFIED
* T=AUTO - AUTOMATIC DETERMINATION OF ALLOWED TIME
* C.I.=N - 2 M.O.S TO BE USED IN C.I.
* CIMAX= 100 - ALLOWED SIZE FOR CI MATRIX
* CISTATE= 3 - EIGENSTATES CALCULATED IN CI
* BONDS - PRINT NON-ZERO ELEMENTS OF FINAL BOND-ORDER MATRIX
* SINGLET - IS THE REQUIRED SPIN MULTIPLICITY
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AM1 C.I.=2 CISTATE=3 CIMAX=100 SINGLET T=AUTO TRUSTE LFORCE BONDS
D2h Ethylene, AM1/CI, HOMO LUMO Active, S0 (Singlet Ground State)
Opt+LowFreq, Active MOs and Bonds, Calc 3 Lowest States
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 C
2 C 1.32592 * 1
3 H 1.09827 * 122.71597 * 1 2
4 H 1.09827 * 122.71597 * -180.00000 * 1 2 3
5 H 1.09827 * 122.71597 * 0.00000 * 2 1 4
6 H 1.09827 * 122.71597 * 180.00000 * 2 1 4
MOLECULAR POINT GROUP SYMMETRY CRITERIA
D2h 0.10000000
SINGLET STATE CALCULATION
RHF CALCULATION, NO. OF DOUBLY OCCUPIED LEVELS = 6
** REFERENCES TO PARAMETERS **
H (AM1): M.J.S. DEWAR ET AL, J. AM. CHEM. SOC. 107 3902-3909 (1985).
C (AM1): M.J.S. DEWAR ET AL, J. AM. CHEM. SOC. 107 3902-3909 (1985).
CARTESIAN COORDINATES
ATOM X Y Z
1 C 0.00000000 0.00000000 0.00000000
2 C 1.32591600 0.00000000 0.00000000
3 H -0.59358517 0.92403726 0.00000000
4 H -0.59358517 -0.92403726 0.00000000
5 H 1.91950117 -0.92403726 0.00000000
6 H 1.91950117 0.92403726 0.00000000
STANDARD DEVIATION ON ENERGY (KCAL) 0.00000055519
STANDARD DEVIATION ON GRADIENT (KCAL/A,RD,RD) 0.00008233 0.00007642 0.00008301
LOWEST IR FREQUENCIES CALCULATION (MARCH 1999)
HEAT OF FORMATION= 8.261408 kcal/mole
RMS GRADIENT NORM= 0.020640 kcal/mole/A
HESSIAN SPANNED BY 12 INTERNAL COORDINATES.
1 LOWEST EIGENVALUES OF THE HESSIAN HAVE BEEN ACCURATELY CALCULATED.
NON ZERO EIGENVALUES, (STD DEV) AND ASSOCIATED EIGENVECTORS: (Angstroms or radians)
1.51D+01 0.000 0.000 0.000 0.000 0.000 -0.703 0.000 0.000 -0.599 0.000
(1.61D-03) 0.000 -0.384
NOTE: WAVE NUMBERS ARE BIASED WITH RESPECT TO EXACT VALUES,
BUT SIGNS ARE ASCERTAINED (UNLESS A ERROR BAR TOO LARGE).
VIBRATIONAL FREQUENCIES AND ERRORS (CM-1),
REDUCED FORCE CONSTANTS (MILLIDYNES/ANGSTROMS),
DIPOLE DERIVATIVES (DEBYE/ANGSTROMS),
IR INTENSITIES (DEBYE**2/ANGSTROMS**2),
AND NORMAL MODES (CARTESIAN COORDINATES):
FREQ : 0.000 0.000 0.000 0.000 0.000 0.000 965.219
ERROR : 0.000 0.000 0.000 0.000 0.000 0.000 0.155
F-CST : 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.27443
DIP(X): 0.000 0.000 0.000 0.000 0.000 0.000 0.000
DIP(Y): 0.000 0.000 0.000 0.000 0.000 0.000 0.000
DIP(Z): 0.000 0.000 0.000 0.000 0.000 0.000 0.000
DIP TOT 0.000 0.000 0.000 0.000 0.000 0.000 0.000
IR ITEN 0.000 0.000 0.000 0.000 0.000 0.000 0.000
1C (x) -0.0043 0.0000 0.0000 0.0000 0.1888 0.0000 0.0000
1C (y) -0.1256 -0.0465 -0.1542 -0.0091 -0.0029 -0.1249 0.0000
1C (z) 0.0442 0.0642 -0.1598 -0.1073 0.0010 0.1367 0.1244
2C (x) -0.0043 0.0000 0.0000 0.0000 0.1888 0.0000 0.0000
2C (y) 0.1630 -0.0474 -0.1029 0.0239 0.0037 -0.1321 0.0000
2C (z) 0.0126 0.1237 0.0401 -0.1893 0.0003 -0.0944 -0.1244
3H (x) -0.2036 0.0006 -0.0354 -0.0228 0.1842 0.0049 0.0000
3H (y) -0.2523 -0.0460 -0.1768 -0.0236 -0.0057 -0.1217 0.0000
3H (z) 0.0402 0.4418 -0.3240 0.2038 0.0009 0.1806 -0.3947
4H (x) 0.1950 -0.0006 0.0354 0.0228 0.1933 -0.0049 0.0000
4H (y) -0.2523 -0.0460 -0.1768 -0.0236 -0.0057 -0.1217 0.0000
4H (z) 0.0761 -0.3655 -0.1709 -0.3463 0.0017 0.2956 -0.3947
5H (x) 0.1950 -0.0006 0.0354 0.0228 0.1933 -0.0049 0.0000
5H (y) 0.2896 -0.0478 -0.0804 0.0384 0.0066 -0.1352 0.0000
5H (z) 0.0166 -0.2538 0.2043 -0.5003 0.0004 -0.1383 0.3948
6H (x) -0.2036 0.0006 -0.0354 -0.0228 0.1842 0.0049 0.0000
6H (y) 0.2896 -0.0478 -0.0804 0.0384 0.0066 -0.1352 0.0000
6H (z) -0.0193 0.5534 0.0512 0.0498 -0.0004 -0.2533 0.3948
AM1 C.I.=2 CISTATE=3 CIMAX=100 SINGLET T=AUTO TRUSTE LFORCE BONDS
D2h Ethylene, AM1/CI, HOMO LUMO Active, S0 (Singlet Ground State)
Opt+LowFreq, Active MOs and Bonds, Calc 3 Lowest States
GEOMETRY OPTIMIZED : ENERGY MINIMIZED
SCF FIELD WAS ACHIEVED
AM1 CALCULATION
VERSION 10.0.1
Aug-31-2011
FINAL HEAT OF FORMATION = 8.261408 kcal (CI SINGLET No 1)
= 34.573991 kJ
ELECTRONIC ENERGY = -736.450184 eV
CORE-CORE REPULSION = 425.733187 eV
TOTAL ENERGY = -310.716996 eV
GRADIENT NORM = 0.071497
RMS GRADIENT NORM = 0.020639
UNSTABLE MODE(S) = 0 ( ACCURATE )
MOLECULAR WEIGHT = 28.053600
MOLECULAR POINT GROUP = D2h 0.100000
NO. OF FILLED LEVELS = 6 (OCC = 2)
TOTAL NUMBER OF ORBITALS = 12
SCF + CI CALCULATIONS = 16
COMPUTATION TIME = 0.23 SECONDS
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 C
2 C 1.34092 * 1
3 H 1.09708 * 122.43943 * 1 2
4 H 1.09708 * 122.43943 * -180.00000 * 1 2 3
5 H 1.09708 * 122.43943 * 0.00000 * 2 1 4
6 H 1.09708 * 122.43943 * 180.00000 * 2 1 4
MOLECULAR POINT GROUP SYMMETRY CRITERIA
D2h 0.10000000
RHF EIGENVALUES
-32.96035 -21.92659 -15.75830 -14.25910 -11.89512 -10.45383
1.37797 4.05778 4.39209 5.06914 5.56126 5.74277
CONFIGURATION INTERACTION CALCULATION 
4 MICRO-STATES GENERATED BY CAS-CI VS 44 ROOM AVAILABLE.
4 MICRO-STATES FINALLY KEPT.
CI-ACTIVE MOLECULAR ORBITALS:
ROOT NO. 6 7 
-10.454 1.378
1 C S 0.0000 0.0000
1 C Px 0.0000 0.0000
1 C Py 0.0000 0.0000
1 C Pz 0.7071 -0.7071
2 C S 0.0000 0.0000
2 C Px 0.0000 0.0000
2 C Py 0.0000 0.0000
2 C Pz 0.7071 0.7071
3 H S 0.0000 0.0000
4 H S 0.0000 0.0000
5 H S 0.0000 0.0000
6 H S 0.0000 0.0000
DETAILED COUNT OF THE 4 CALCULATED LOWEST EIGENSTATES: 
SINGLET TRIPLET
CSF 3 1
STATES 3 1
THE EIGENSTATE SELECTED IS No 1 (SINGLET)
ROW: MAIN MICRO-STATES OVER THE 4 SELECTED IN C.I. 
COLUMN: EIGENSTATES FROM 1 TO 3
MO: 00 1:SINGLET 2:TRIPLET 3:SINGLET
: 67 eV: 0.0000 2.9456 6.6045
1 20 96% 0% 0%
( 0.9807) ( 0.0000) ( 0.0000)
2 +- 0% 50% 50%
( 0.0000) ( 0.7071) (-0.7071)
3 -+ 0% 50% 50%
( 0.0000) ( 0.7071) ( 0.7071)
4 02 4% 0% 0%
(-0.1953) ( 0.0000) ( 0.0000)
TRANSITION DIPOLE (A.U.) AND OSC. STRENGTHS FROM STATE 1 (SINGLET) TO OTHERS 
STATE eV nm X Y Z STRENGTH
2 2.946 420.9 FORBIDDEN TO TRIPLET
3 6.605 187.7 1.4073 0.0000 0.0000 0.3205
SUM OF STRENGTHS: 0.9615 0.0000 0.0000
NET ATOMIC CHARGES AND DIPOLE CONTRIBUTIONS 
ATOM CHARGE ATOM ELECTRON DENSITY
1 C -0.2193 4.2193
2 C -0.2193 4.2193
3 H 0.1097 0.8903
4 H 0.1097 0.8903
5 H 0.1097 0.8903
6 H 0.1097 0.8903
DIPOLE (DEBYE) X Y Z TOTAL
POINT-CHG. 0.000 0.000 0.000 0.000
HYBRID 0.000 0.000 0.000 0.000
SUM 0.000 0.000 0.000 0.000
CARTESIAN COORDINATES 
ATOM X Y Z
1 C 0.00000000 0.00000000 0.00000000
2 C 1.34092452 0.00000000 0.00000000
3 H -0.58848034 0.92588760 0.00000000
4 H -0.58848034 -0.92588760 0.00000000
5 H 1.92940486 -0.92588760 0.00000000
6 H 1.92940486 0.92588760 0.00000000
ATOMIC ORBITAL ELECTRON POPULATIONS 
1.24839 0.95422 1.01669 1.00000 1.24839 0.95422
1.01669 1.00000 0.89035 0.89035 0.89035 0.89035
BOND ORDERS AND VALENCIES 
| 1 C
1 C | 3.928231
| 1 C 2 C
2 C | 1.852496 3.928231
| 1 C 2 C 3 H
3 H | 0.957752 0.006722 0.987976
| 1 C 2 C 3 H 4 H
4 H | 0.957752 0.006722 0.008643 0.987976
| 1 C 2 C 3 H 4 H 5 H
5 H | 0.006722 0.957752 0.013244 0.001615 0.987976
| 1 C 2 C 3 H 4 H 5 H 6 H
6 H | 0.006722 0.957752 0.001615 0.013244 0.008643 0.987976
ELAPSED WALL CLOCK TIME : 0.24 SECONDS
FULL COMPUTATION TIME : 0.23 SECONDS
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The primary CI eigenstate is, as requested, the ground state singlet, S0. For reference, the AM1/SCF and experimental heats of formation are 16.5 kcal/mol and 12.5 kcal/mol, respectively. There is a significant decrease in energy in going from AM1/SCF to even this “minimal” AM1/CAS-CI. Since AM1 (and all of the semi-empirical models in AMPAC) was parameterized against experiment at the SCF level, absolute heats of formation at the corresponding CI level are generally too low, especially at higher levels of CI. |
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This Z-matrix shows the AM1 optimized geometry of Ethylene in the primary CI eigenstate. All of the results in AMPAC output file, including those for the secondary CI eigenstates, are calculated at this geometry. The transition energies between the primary and secondary CI eigenstates are thus “vertical” transition energies. |
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As requested, the number of CI-active MOs was 2, the HOMO and LUMO. There are six possible microstates, given below in terms of the SO occupancies of the HOMO and LUMO, where + means the alpha SO is occupied, - means the beta SO is occupied and 0 means the corresponding SO is unoccupied: Table 21.1. Possible microstates with 2 CI-active MOs
This “minimal” CAS-CI for a singlet state uses the first four 4 microstates, which have Sz = 0. The 5th and 6th microstates, with Sz = 1 and -1, are degenerate with the linear combination of the 3rd and 4th microstates and so are not used, even for the triplet CI eigenstates (they cannot be used for the singlet states, of course). |
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The AO coefficients of the two CI-active MOs show that the first (the HOMO) is a π MO while the second (the LUMO) is a corresponding π* MO. |
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The 3 lowest secondary CI eigenstates were calculated in addition to the primary one S0. One of the secondary CI eigenstates is a triplet, the others being singlets. The “CSF” row in the table refers to the number of spin-adapted configurations used in the expansion of the CI eigenstates. |
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This table gives the contribution - as both a percentage and as a normalized
coefficient - of each microstate to each of the 3 requested CI eigenstates, whose energies
are given (in eV) relative to the primary eigenstate. The SO occupancies of the CI-active
MOs for each microstate are also given. Thus, the first excited state, “
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This table gives the transition energies, transition wavelengths, transition dipoles and oscillator strengths between the primary CI eigenstate and the two secondary CI eigenstates. Since the primary CI eigenstate is a singlet, the transition dipole and corresponding oscillator strength for the triplet CI eigenstate is identically zero. The first excited singlet state (S1) has a significant transition dipole parallel to the C-C bond and the corresponding oscillator strength of 0.3025 indicates there should be a significant absorption intensity around 187 nm for gas phase ethylene. |
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The atomic Mulliken charges and dipole moments given in this section are for the primary CI eigenstate. Values for the secondary eigenstates can be calculated with the AMPAC keyword CIDIP. |
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This table gives the atoms’ Cartesian coordinates for the geometry optimized in the primary CI eigenstate. |
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These tables of AO electron populations, bond orders and valencies are calculated from the first-order density matrix of the primary CI eigenstate. |
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Copyright © 1992-2013 Semichem, Inc. All rights reserved. |
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| Chapter 20. Analyzing the Lewis Dot Structure of a Molecule (LEWIS) |  |
Chapter 22. Solvation (COSMO, SM5.2, SM5C) |