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Ortiz Quantum Chemistry Group

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Electron Propagator Calculations in Gaussian

V. G. Zakrzewski and J. V. Ortiz

The OVGF (Outer Valence Green Function) key word in the Gaussian suite of codes activates electron propagator calculations in two separate approximations: OVGF and Partial Third Order (P3). This code is designed for both closed-shell Hartree-Fock (HF) and unrestricted HF (UHF) reference states and exploits Abelian point-groups, i.e. D2h, and its subgroups. Both approximations are applicable for electron detachment or attachment processes in which the frozen-orbital, single determinant picture of Koopmans's theorem is qualitatively valid. Normally, ionization energies that do not exceed 15 eV are typical for such processes in organic molecules. The pole strength (PS) is reported in the output and, in general, if it is lower than 0.8, the OVGF or P3 methods are inapplicable. In such cases, more exact approximations should be used. In the case of OVGF, even ionization energies with PS values below 0.85 should be interpreted with caution. Both OVGF and P3 approximations are based upon the diagonal matrix elements (in the canonical HF orbital basis) of the self-energy operator in electron propagator theory [1]. Perturbative expressions for the self-energy, based on a zeroth order defined by HF canonical orbital energies (Koopmans results), have been summarized in [2] and [3]. The OVGF B approximation was presented in [4] and all three OVGF approximations (A, B and C) were discussed subsequently in [5]. The OVGF procedure produces three renormalized results which are called the A, B, and C cases. An automated selection procedure suggested by W. von Niessen was reported and tested in [6]. The P3 method was derived in [7] and a review of its capabilities was given in [8]. Semidirect algorithms have been reported in [9], [10] and [11]. Recent reviews of electron propagator theory include [12], [13], [14], [15] and [16].

Bibliography

1. J. Linderberg and Y. Öhrn, Propagators in Quantum Chemistry, second edition, John Wiley and Sons, Hoboken, New Jersey (2004).

2. L. S. Cederbaum, and W. Domcke, Adv. Chem. Phys. 36, 205 (1977).

3. Y. Öhrn and G. Born, Adv. Quantum Chem. 13, 1 (1981).

4. L. S. Cederbaum, J. Phys. B 8, 280 (1975).

5. W. von Niessen, J. Schirmer and L. S. Cederbaum, Comput. Phys. Rep. 1, 57 (1984).

6. V. G. Zakrzewski, J. V. Ortiz, J. A. Nichols, D. Heryadi, D. L. Yeager and J. T. Golab, Int. J. Quant. Chem. 60, 29 (1996).

7. J. V. Ortiz, J. Chem. Phys. 104, 7599 (1996).

8. A. M. Ferreira, G. Seabra, O. Dolgounitcheva, V. G. Zakrzewski and J. V. Ortiz, Application and Testing of Diagonal, Partial Third-Order Electron Propagator Approximation, in Quantum-Mechanical Prediction of Thermochemical Data, 131, J. Cioslowski, ed., Kluwer, Dordrecht, 2001.

9. J. V. Ortiz, V. G. Zakrzewski, and O. Dolgounitcheva, One-Electron Pictures of Electronic Structure: Propagator Calculations of Photoelectron Spectra of Aromatic Molecules, in Conceptual Trends in Quantum Chemistry, Vol. 3, 465, E. S. Kryachko ed., Kluwer, Dordrecht, 1997.

10. V. G. Zakrzewski and J. V. Ortiz, Int. J. Quant. Chem., Quant. Chem. Symp. 28, 23 (1994).

11. V. G. Zakrzewski and J. V. Ortiz, Int. J. Quant. Chem. 53, 583 (1995).

12. J. V. Ortiz, The Electron Propagator Picture of Molecular Electronic Structure, in Computational Chemistry: Reviews of Current Trends, Vol. 2, 1-61, J. Leszczynski, ed., World Scientific, Singapore, 1997.

13. J. V. Ortiz, Adv. Quantum Chem. 35, 33 (1999).

14. V. G. Zakrzewski, O. Dolgounitcheva, A. V. Zakjevskii and J. V. Ortiz, Ann. Rev. Comput. Chem. 6, 79 (2010).

15. V. G. Zakrzewski, O. Dolgounitcheva, A. V. Zakjevskii and J. V. Ortiz, Adv. Quantum Chem. 62, 105 (2011).

16. J. V. Ortiz, Electron Propagator Theory: An Approach to Prediction and Interpretation in Quantum Chemistry, WIREs Comput. Mol. Sci. DOI:10.1002/wcms.1116 1-20 (2012).

Directions

  • The keyword for both OVGF and P3 calculations is OVGF
  • These calculations include SCF=tight HF calculation and integral transformation (l801,l804)
  • The default mode for integral tranformation invoked by the OVGF keyword is tran=iabc, i.e. integrals with four virtual indices are not built. The transformation can be run with the keyword tran=abcd, which will save some CPU time during the OVGF calculation but take extra disk space and more time during the transformation step.
  • G-94, 98 and 03 use direct or semidirect integral transformation. One of the main parameters in the semidirect transformation is the number of orbitals per pass. It is regulated by option 16 for link 804.
  • If link 804 is invoked directly in the additional command line (with extraoverlays in the main command line) then this is specified as 8/.....,16=n,.../1,4; where n is the number of orbitals per pass.
  • If extraoverlays are not used, iop(8/16=n) in the command line will work.
  • The OVGF and P3 options are described in detail in the source code's comments section, or in the Gaussian manual in the Options Section.
  • Integral transformation imposes a Window of orbitals sometimes called the active space. This is set by Options 10=91, and Options 37=n1, 38=n2 defining the first and the last MO included in the transformation. (This is very helpful when a system under investigation is too large for one's computer resources.) If Option 37 is 0 then an extra line (card) is read as an input specifying the first and last MOs used in transformation.
  • OVGF/P3 calculations are controlled mostly by Option 11 in l908. The default choice is OVGF. Different decimal digits have different meanings.
  • If you do not want to calculate all ionization energies by default (it takes time, you know), it is possible to specify the first and the last orbital for which the calculation is run by the option 11=100. It can be set by keyword iop(9/11=100); then the numbers of the first and the last MOs are given in the input after a blank line following previous input (such as Z-matrix, basis set, et cetera). One set of these numbers for alpha spin-orbitals and another set for beta spin-orbitals are needed. Do not forget that the number of inner MOs must be subtracted from the total number of MOs to get to these values.
  • IOp(11) ... Flags for electron propagator calculations:
    • 0 ... Normal use of MO integrals.
    • 1 ... Force direct computation of contributions.
    • 2 ... Force direct computation of contributions.
    • 00 ... Normal production of intermediates (in-core if possible).
    • 10 ... Force use of sort for intermediates (l908 only if we need it at all?).
    • 100 ... Read window of MOs to refine in the same format as 801, but with two ranges on the same line for open-shell.
    • 1000 ... Force N**3 algorithm in GFSCMA.
    • 00000 ... Default (P3 for ionization energies)
    • 10000 ... P3 for ionization energies and electron affinities.
    • 20000 ... OVGF
    • 30000 ... OVGF + P3 for ionization energies (+ P3 for electron affinities if integrals are present)
    • 40000 ... 2nd order only
    • 100000 ... Read EMin, EMax, and pole strength warning level on one line. Link 909 only.

General Recommendations

1. It is better to run jobs using #p in the command line. This choice produces more output, and, in the case of the OVGF calculations, yields all three values of the renormalized poles.
2. Basis sets: the best basis set is 6-311G**, or 6-311++G** for anions, or basis sets based upon 6-311G with additional polarization functions like 6-311G(2df),2p.
Do not use cc-pVDZ or 6-31G(d,p) basis sets. These are not reliable for propagator calculations.

Sample Inputs

test1.com

%mem=8Mw
#p ovgf 6-311G** tran=abcd iop(8/16=30)

chloro-benzene (almost default OVGF, all types of transformed
integrals are created, transformation makes 30 MOs per pass,
OVGF window is selected by default).

0 1
C,0,0.,0.,0.5001048942
C,0,0.,0.,-2.2561514014
C,0,0.,1.2044458651,-0.1771010321
C,0,0.,1.1980053753,-1.561586957
C,0,0.,-1.2044458651,-0.1771010321
C,0,0.,-1.1980053753,-1.561586957
Cl,0,0.,0.,2.2460641806
H,0,0.,0.,-3.3310796086
H,0,0.,2.1286240716,0.3686466091
H,0,0.,2.131791085,-2.0943848833
H,0,0.,-2.1286240716,0.3686466091
H,0,0.,-2.131791085,-2.0943848833


test2.com

%mem=8Mw
#p ovgf 6-311G** tran=iabc iop(9/11=100000100)

chloro-benzene (P3 calculation, partial transformation: the only kind
necessary for occupied MOs in P3, P3 Window is specified from 16 to 18 MOs,
default core MOs are already dropped at transformation stage.)

0 1
C,0,0.,0.,0.5001048942
C,0,0.,0.,-2.2561514014
C,0,0.,1.2044458651,-0.1771010321
C,0,0.,1.1980053753,-1.561586957
C,0,0.,-1.2044458651,-0.1771010321
C,0,0.,-1.1980053753,-1.561586957
Cl,0,0.,0.,2.2460641806
H,0,0.,0.,-3.3310796086
H,0,0.,2.1286240716,0.3686466091
H,0,0.,2.131791085,-2.0943848833
H,0,0.,-2.1286240716,0.3686466091
H,0,0.,-2.131791085,-2.0943848833

16 18


test3.com

%mem=8Mw
#p ovgf 6-311G** tran=iabc iop(9/11=20100)
chloro-benzene (OVGF calculation, partial transformation, OVGF window is set
from 16 to 18; core orbitals are dropped at the transformation step.)

0 1
C,0,0.,0.,0.5001048942
C,0,0.,0.,-2.2561514014
C,0,0.,1.2044458651,-0.1771010321
C,0,0.,1.1980053753,-1.561586957
C,0,0.,-1.2044458651,-0.1771010321
C,0,0.,-1.1980053753,-1.561586957
Cl,0,0.,0.,2.2460641806
H,0,0.,0.,-3.3310796086
H,0,0.,2.1286240716,0.3686466091
H,0,0.,2.131791085,-2.0943848833
H,0,0.,-2.1286240716,0.3686466091
H,0,0.,-2.131791085,-2.0943848833

16 18


test4.com

%mem=8Mw
#p ovgf 6-311G** tran=iabc iop(9/11=20100)

chloro-benzene (OVGF, partial transformation, OVGF window is set from
16 to 19, MO 19 is the LUMO when core orbitals are dropped.)

0 1
C,0,0.,0.,0.5001048942
C,0,0.,0.,-2.2561514014
C,0,0.,1.2044458651,-0.1771010321
C,0,0.,1.1980053753,-1.561586957
C,0,0.,-1.2044458651,-0.1771010321
C,0,0.,-1.1980053753,-1.561586957
Cl,0,0.,0.,2.2460641806
H,0,0.,0.,-3.3310796086
H,0,0.,2.1286240716,0.3686466091
H,0,0.,2.131791085,-2.0943848833
H,0,0.,-2.1286240716,0.3686466091
H,0,0.,-2.131791085,-2.0943848833

16 19


test5.com

%mem=8Mw
#p ovgf 6-311G** tran=iabc iop(9/11=10100)

chloro-benzene (P3 calculation for both ionization energies (MOs 16-18) and
EA into the LUMO, again core MOs are dropped by integral transformation).

0 1
C,0,0.,0.,0.5001048942
C,0,0.,0.,-2.2561514014
C,0,0.,1.2044458651,-0.1771010321
C,0,0.,1.1980053753,-1.561586957
C,0,0.,-1.2044458651,-0.1771010321
C,0,0.,-1.1980053753,-1.561586957
Cl,0,0.,0.,2.2460641806
H,0,0.,0.,-3.3310796086
H,0,0.,2.1286240716,0.3686466091
H,0,0.,2.131791085,-2.0943848833
H,0,0.,-2.1286240716,0.3686466091
H,0,0.,-2.131791085,-2.0943848833

16 19


test6.com

%mem=8Mw
#p ovgf 6-311G** tran=abcd iop(9/11=10100)

chloro-benzene (P3, same as previous test5.com but all MO transformation is
specified).

0 1
C,0,0.,0.,0.5001048942
C,0,0.,0.,-2.2561514014
C,0,0.,1.2044458651,-0.1771010321
C,0,0.,1.1980053753,-1.561586957
C,0,0.,-1.2044458651,-0.1771010321
C,0,0.,-1.1980053753,-1.561586957
Cl,0,0.,0.,2.2460641806
H,0,0.,0.,-3.3310796086
H,0,0.,2.1286240716,0.3686466091
H,0,0.,2.131791085,-2.0943848833
H,0,0.,-2.1286240716,0.3686466091
H,0,0.,-2.131791085,-2.0943848833

16 19


test7.com
Same as test5, but both OVGF and P3 are done, with partial integral transformation).

%mem=8Mw
#p ovgf 6-311G** tran=iabc iop(9/11=30100)

chloro-benzene (same as test5, but both OVGF and P3 are done, with partial
integral transformation).

0 1
C,0,0.,0.,0.5001048942
C,0,0.,0.,-2.2561514014
C,0,0.,1.2044458651,-0.1771010321
C,0,0.,1.1980053753,-1.561586957
C,0,0.,-1.2044458651,-0.1771010321
C,0,0.,-1.1980053753,-1.561586957
Cl,0,0.,0.,2.2460641806
H,0,0.,0.,-3.3310796086
H,0,0.,2.1286240716,0.3686466091
H,0,0.,2.131791085,-2.0943848833
H,0,0.,-2.1286240716,0.3686466091
H,0,0.,-2.131791085,-2.0943848833

16 19


Changes for G-09



G-09 options are the same but reading of some of them is different.
All test inputs OVGF calculations remain the same.
Test inputs for P3 calculations (test2,5,6) should look as follows.
One has to pay attention on the minus sign in option 9/11.


test2.com

%mem=8Mw
#p ovgf 6-311G** tran=iabc iop(9/11=-20100)

chloro-benzene (P3 calculation, partial transformation: the only kind
necessary for occupied MOs in P3, P3 Window is specified from 16 to 18 MOs,
default core MOs are already dropped at transformation stage.)

0 1
C,0,0.,0.,0.5001048942
C,0,0.,0.,-2.2561514014
C,0,0.,1.2044458651,-0.1771010321
C,0,0.,1.1980053753,-1.561586957
C,0,0.,-1.2044458651,-0.1771010321
C,0,0.,-1.1980053753,-1.561586957
Cl,0,0.,0.,2.2460641806
H,0,0.,0.,-3.3310796086
H,0,0.,2.1286240716,0.3686466091
H,0,0.,2.131791085,-2.0943848833
H,0,0.,-2.1286240716,0.3686466091
H,0,0.,-2.131791085,-2.0943848833

16 18

test5.com

%mem=8Mw
#p ovgf 6-311G** tran=iabc iop(9/11=-30100)

chloro-benzene (P3 calculation for both ionization energies (MOs 16-18) and
EA into the LUMO, again core MOs are dropped by integral transformation).

0 1
C,0,0.,0.,0.5001048942
C,0,0.,0.,-2.2561514014
C,0,0.,1.2044458651,-0.1771010321
C,0,0.,1.1980053753,-1.561586957
C,0,0.,-1.2044458651,-0.1771010321
C,0,0.,-1.1980053753,-1.561586957
Cl,0,0.,0.,2.2460641806
H,0,0.,0.,-3.3310796086
H,0,0.,2.1286240716,0.3686466091
H,0,0.,2.131791085,-2.0943848833
H,0,0.,-2.1286240716,0.3686466091
H,0,0.,-2.131791085,-2.0943848833

16 19

test6.com

%mem=8Mw
#p ovgf 6-311G** tran=abcd iop(9/11=-30100)

chloro-benzene (P3, same as previous test5.com but all MO transformation is
specified).

0 1
C,0,0.,0.,0.5001048942
C,0,0.,0.,-2.2561514014
C,0,0.,1.2044458651,-0.1771010321
C,0,0.,1.1980053753,-1.561586957
C,0,0.,-1.2044458651,-0.1771010321
C,0,0.,-1.1980053753,-1.561586957
Cl,0,0.,0.,2.2460641806
H,0,0.,0.,-3.3310796086
H,0,0.,2.1286240716,0.3686466091
H,0,0.,2.131791085,-2.0943848833
H,0,0.,-2.1286240716,0.3686466091
H,0,0.,-2.131791085,-2.0943848833

16 19