 


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 closedshell HartreeFock (HF) and unrestricted HF (UHF) reference states and exploits
Abelian pointgroups,
i.e. D_{2h}, and its subgroups. Both approximations
are applicable for electron detachment or attachment processes in which the frozenorbital,
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 selfenergy operator in electron propagator theory [1]. Perturbative expressions for the
selfenergy, 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 ThirdOrder Electron Propagator Approximation,
in QuantumMechanical Prediction of Thermochemical Data, 131, J. Cioslowski, ed., Kluwer,
Dordrecht, 2001.
9. J. V. Ortiz, V. G. Zakrzewski, and O. Dolgounitcheva, OneElectron 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, 161, 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 120 (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.
 G94, 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
Zmatrix, basis set, et cetera). One set of these numbers for alpha spinorbitals and another
set for beta spinorbitals 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 (incore 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 openshell.
 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 6311G**, or 6311++G** for anions, or basis sets based
upon 6311G with additional polarization functions like 6311G(2df),2p.
Do not use ccpVDZ or 631G(d,p) basis sets. These are not reliable for propagator calculations.
Sample Inputs
test1.com
%mem=8Mw
#p ovgf 6311G** tran=abcd iop(8/16=30)
chlorobenzene (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 6311G** tran=iabc iop(9/11=10100)
chlorobenzene (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 6311G** tran=iabc iop(9/11=20100)
chlorobenzene (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 6311G** tran=iabc iop(9/11=20100)
chlorobenzene (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 6311G** tran=iabc iop(9/11=10100)
chlorobenzene (P3 calculation for both ionization energies (MOs 1618) 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 6311G** tran=abcd iop(9/11=10100)
chlorobenzene (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 6311G** tran=iabc iop(9/11=30100)
chlorobenzene (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 G09
G09 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 6311G** tran=iabc iop(9/11=20100)
chlorobenzene (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 6311G** tran=iabc iop(9/11=30100)
chlorobenzene (P3 calculation for both ionization energies (MOs 1618) 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 6311G** tran=abcd iop(9/11=30100)
chlorobenzene (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
 