These method keywords request an electron propagator theory [Migdal67] calculation of correlated electron affinities and ionization potentials [Cederbaum75, Cederbaum77, Ohrn81, vonNiessen84, Ortiz88, Ortiz88a, Ortiz89, Zakrzewski93, Zakrzewski94a, Zakrzewski95, Ortiz96, Zakrzewski96, Ortiz97, Ferreira01, Linderberg04]. Gaussian 16 includes the renormalized partial third order approximation—P3+—method of Ortiz [Ortiz05]. It also includes algorithmic improvements for significant speedup of the diagonal, second-order self-energy approximation (D2) component of composite electron propagator (CEP) methods as described in [DiazTinoco16]. These models combine a relatively inexpensive D2-level calculation using a large basis set (e.g., augmented quadruple or triple zeta) with a more expensive P3+ or OVGF calculation with a smaller basis set (e.g., triple or double zeta) to produce high accuracy predictions.

For reviews of EPT methods and applications, see [Scholes03, Zakrzewski11].

EPT calculations default to storage of <ia||bc> integrals, but can be run with Trans=Full to save CPU time at the expense of disk usage or with Trans=IJAB to save on disk space at the expense of CPU time. In the latter case, electron affinities are not computed.

By default, only ionization potentials which are < 20 eV are computed.

Use the ReadOrbitals option to specify the starting and ending orbitals to refine as input.

OVGF is a synonym for this keyword.

#### OVGF

Use the Outer Valence Green's Function propagator. This is the default.

#### P3

Use the P3 and P3+ propagators.

#### OVGF+P3

Use both propagator methods.

#### D2

Perform the second-order electron propagator using code that is very efficient for this case. D2 does both attachment (electron affinities) and detachment (ionization potentials) from all orbitals, while the D2IA does only ionization from active (non-frozen-core) orbitals, (which is even less expensive). Often used as part of a compound method in conjection with a higher-order EPT calculation using a smaller basis set. EP2 and EP2IA are synonyms for these options (respectively).

#### FC

All frozen core options are available with this keyword; a frozen core calculation is the default. See the discussion of the FC options for full information.

#### ReadOrbitals

Specify starting and ending orbitals to refine, in a separate, blank-terminated input section. For unrestricted calculations, separate ranges are specified for alpha and beta orbitals (on the same input line). Orbital numbering starts with the first active orbital after the frozen core. For example, using the default frozen core for ethene, the input 3 8 will skip the two 2s valence orbitals (in addition to the two frozen 1s cores), resulting in the HOMO being labeled as orbital 6 in the output.

#### ForceSort

Forces sorting of intermediate quantities to be done even when it is not necessary. This option appears in some Gaussian test jobs, but it is not useful for production calculations.

Single-point energy calculations using HF for the reference method.

For EPT=OVGF calculations, the results for each orbital appear as follows:

3 OVGF renormalized results based on the 3rd order
Method Orbital HF-eigenvalue 3rd-order Pole strength
A: 2 -14.81277 -14.16283 0.93047 OVGF-A results
B: 2 -14.81277 -14.26825 0.92594 OVGF-B results
C: 2 -14.81277 -14.28318 0.92723 OVGF-C results
Summary of results for alpha spin-orbital 2 OVGF:
Koopmans theorem: -0.54436D+00 au -14.813 eV
Converged second order pole: -0.51494D+00 au -14.012 eV 0.921 (PS)
Converged third order pole: -0.52613D+00 au -14.317 eV 0.929 (PS)
Outer Valence Approximation: -0.52435D+00 au -14.268 eV 0.926 (PS) OVGF-von Niessen (OVGF-N) result

The second section gives the estimate of ionization potential/electron affinity for the specified orbital (which property is given depends on whether the orbital is occupied or not, respectively) with the specified propagator. The pole strength is a measure of how easy it is to make this excitation, with 1.0 as the maximum value. Note that orbitals are listed in the output in order of symmetry (and not necessarily in numerical order).

For EPT=P3 calculations, the results for each orbital appear as follows:

Summary of results for alpha spin-orbital 5 P3:
Koopmans theorem: 0.16053D+00 au 4.368 eV
Converged second order pole: 0.13657D+00 au 3.716 eV 0.978 (PS)
Converged 3rd order P3 pole: 0.13578D+00 au 3.695 eV 0.974 (PS) P3 propagator result
Renormalized (P3+) P3 pole: 0.13584D+00 au 3.696 eV 0.974 (PS) P3+ propagator result

Results are given for both the original and renormalized formulations of P3.

For EPT=D2 calculations, the results for each orbital appear as follows:

Converged second order pole for alpha spin-orbital 2 -0.857776 au -23.341 eV
Converged second order pole for alpha spin-orbital 3 -0.514940 au -14.012 eV
Converged second order pole for alpha spin-orbital 4 -0.514940 au -14.012 eV
Converged second order pole for alpha spin-orbital 5 -0.514940 au -14.012 eV
…