Further Modifications of G2 and G3 Theories

Further Modifications of Gaussian Theories

1) G2+ theory for charged species
Negatively as well as positively charged systems are often better described, when diffuse functions
are included in the basis set. An appropriately modified G2 procedure was therefore designed by
S. Gronert including augmented basis sets at all steps of the G2 procedure:

(1) geometry optimizations are performed at the MP2(FULL)/6-31+G(d,p) level of theory
(instead of MP2(FULL)/6-31G(d));
(2) zero point vibrational energies are computed at the HF/6-31+G(d,p)
(instead of HF/6-31G(d))) level of theory and scaled by 0.9;
(3) the highest level single point calculation is performed at the
QCISD(T)/6-311+G(d,p) (instead of QCISD(T)/6-311G(d,p)) level;
(4) the "2df" correction is calculated as the difference between
MP4(SDTQ,FC)/6-311+G(2df,p) and MP4(SDTQ,FC)/6-311G(d,p) energies;
(5) the "3df,2p" correction is calculated as the difference between
MP2(FC)/6-311+G(3df,2p) and MP2(FC)/6-311+G(2df,p) energies.

The higher level correction is kept unchanged with respect to the original G2 scheme
as E(HLC) = - 0.00481*N_B - 0.00019*N_A, with N_A = number of alpha valence electrons
and N_B = number of beta valence electrons .

S. A. Gronert,
"Theoretical Studies of Proton Transfers. 1. The Potential Energy Surfaces of the Identity Reactions
of the First- and Second-Row Non-Metal Hydrides with Their Conjugate Bases"
J. Am. Chem. Soc. 1993, 115, 10258 - 10266.

2) G2(+) theory for charged species
A second variation of G2 theory optimized for the treatment of anionic species has been developed
by Radom and coworkers. This variant has been termed "G2(+) theory" and is slightly less demanding
than "G2+". Basis sets including diffuse basis functions are again used at various points of the
compound procedure:

(1) geometry optimizations are performed at the MP2(FC)/6-31+G(d) level of theory
(instead of MP2(FULL)/6-31G(d));
(2) zero point vibrational energies and thermochemical corrections to higher temperatures are obtained
from harmonic vibrational frequencies calculated at the HF/6-31+G(d) level and scaled by 0.8929
(instead of HF/6-31G(d)) and scaled by 0.8929);
(3) the highest level single point calculation is performed at the QCISD(T)/6-311G(d,p)//MP2(FC)/6-31+G(d) level;
(4) the "+" correction is calculated as the difference of MP4(SDTQ,FC)/6-311+G(d,p) and
MP4(SDTQ,FC)/6-311G(d,p) energies;
(5) the "2df" correction is calculated as the difference between MP4(SDTQ,FC)/6-311G(2df,p) and
MP4(SDTQ,FC)/6-311G(d,p) energies;
(6) the "+3df,2p" correction is calculated in a very similar manner as in standard G2 theory from four
single point energy values as:
E(MP2(FC)/6-311+G(3df,2p)) - E(MP2(FC)/6-311G(2df,p)) -
E(MP2(FC)/6-311+G(d,p)) + E(MP2(FC)/6-311G(d,p))
(always using MP2(FC)/6-31+G(d) structures).

The higher level correction is kept unchanged with respect to the original G2 scheme
as E(HLC) = - 0.00481*N_B - 0.00019*N_A, with N_A = number of alpha valence electrons
and N_B = number of beta valence electrons .

M. N. Glukhovtsev, A. Pross, L. Radom,
"Gas-Phase Identity S_N2 Reactions of Halide Anions with Methyl Halides: A High-Level Computational Study"
J. Am. Chem. Soc. 1995, 117, 2024 - 2032.
M. N. Glukhovtsev, A. Pross, L. Radom,
"Gas-Phase Identity S_N2 Reactions of Halide Ions at Neutral Nitrogen: A High-Level Computational Study"
J. Am. Chem. Soc. 1995, 117, 9012 - 9018.
M. N. Glukhovtsev, A. Pross, L. Radom,
"Gas-Phase Non-Identity S_N2 Reactions of Halide Anions with Methyl Halides: A High-Level Computational Study"
J. Am. Chem. Soc. 1996, 118, 6273 - 6284.
M. N. Glukhovtsev, A. Pross, H. B. Schlegel, R. D. Bach, L. Radom,
"Gas-Phase Identity S_N2 Reactions of Halide Anions and Methyl Halides with Retention of Configuration"
J. Am. Chem. Soc. 1996, 118, 11258 - 11264.

3) G2(PU) theory for open shell species
As MP2 and MP4 calculations on open shell systems are frequently plagued by
spin contamination of the reference wavefunction, Morokuma and coworkers suggested
to replace the UMP2 and UMP4 energies contained in G2 theory by the corresponding
spin-projected PUMP2 and PUMP4 values. It was also suggested to replace the unprojected
UQCISD(T) by restricted RCCSD(T) energies.

A. M. Mebel, K. Morokuma, M. C. Lin,
"Ab initio molecular orbital study of potential energy surface for the NH+NO₂ reaction"
J. Chem. Phys. 1994, 101, 3916 - 3922.
A. M. Mebel, K. Morokuma, M. C. Lin, C. F. Melius,
"Potential Energy Surface of the HNO + NO Reaction. An Ab Initio Molecular Orbital Study"
J. Phys. Chem. 1995, 99, 1900.
A. M. Mebel, M. C. Lin, K. Morokuma, C. F. Melius,
"Theoretical Study of the Gas Phase Structure, Thermochemistry and
Decomposition Mechanisms of NH₄NO₂ and NH₄N(NO₂)₂"
J. Phys. Chem. 1995, 99, 6842.

4) G2M theory based on B3LYP geometries
A further improvement over G2(PU) was suggested by Morokuma et al. that
is based on the use of B3LYP/6-311G(d,p) geometries and (unscaled) zero point
vibrational energies. The members of the G2M family differ by the specific
choice of coupled cluster single point energies. In a similar spirit a variation of G2(MP2)
theory termed G2M(MP2) has also been described.

A. M. Mebel, K. Morokuma, M. C. Lin,
"Modification of the GAUSSIAN-2 theoretical model: The use of coupled-cluster energies,
density-functional geometries, and frequencies"
J. Chem. Phys. 1995, 103, 7414 - 7421.

5) G2(B3LYP/MP2/CC) theory - also based on B3LYP geometries
Very similar to the G2M approach by Morokuma et al. is the G2(B3LYP/MP2/CC) theory suggested
by Bauschlicher and Partridge. In this case the B3LYP calculations use the smaller 6-31G(d) basis set.

C. W. Bauschlicher, H. Partridge,
"A modification of the Gaussian-2 approach using density functional theory"
J. Chem. Phys. 1995, 103, 1788 - 1791.

6) G2(BD) and G2(CCSD) theory - replacing the QCISD(T) energies
The use of BD(T)/6-311G(d,p) or CCSD(T)/6-311G(d,p) single point calculations instead of the standard
QCISD(T,FC)/6-311G(d,p)//MP2(FULL)/6-31G(d) energies has been found to give better results for a number
of open shell systems by Radom et al.

P. M. Mayer, C. J. Parkinson, D. M. Smith, L. Radom,
"An assessment of theoretical procedures for the calculation of reliable free radical thermochemistry:
A recommended new procedure"
J. Chem. Phys. 1998, 108, 604 - 615.

7) G2(MP2,SVP)-RAD(p) - a variant of G2(MP2,SVP) for open shell systems
Radom et al. have devised several variants of G2 theory that are particularly appropriate for open shell
systems. G2(MP2,SVP)-RAD(p) theory is based on B3LYP/6-31G(d,p) geometries (adding p-type polarization
functions on hydrogen atoms to the 6-31G(d) basis set used in G2 theory) and zero point vibrational energies,
the latter of which are scaled by 0.9806. A reference energy is then obtained from a RCCSD(T)/6-31G(d)
single point calculation, while basis set effects are estimated as the difference in R(O)MP2/6-31G(d) and
R(O)MP2/6-311+G(3df,2p) single point energies.

P. M. Mayer, C. J. Parkinson, D. M. Smith, L. Radom,
"Toward a Consistent Mechanism for Diol Dehydratase Catalyzed Reactions: An Application
of the Partial-Proton-Transfer Concept"
J. Am. Chem. Soc. 1999, 121, 5700 - 5704.
D. M. Smith, B. T. Golding, L. Radom,
"Understanding the Mechanism of B₁₂-Dependent Diol Dehydratase: A Synergistic
Retro-Push-Pull Proposal"
J. Am. Chem. Soc. 2001, 123, 1664 - 1675.

8) G3(MP2)-RAD - a G3(MP2)B3 variant for open shell systems
Very similar in spirit to G3(MP2)B3 this procedure has been designed by Radom et al. for the
treatment of open shell systems. Energies are calculated according to the following recipe:

(1) geometry optimizations are performed at the UBecke3LYP/6-31G(d) level of theory;
(2) thermocehmical corrections are computed at the UBecke3LYP/6-31G(d) level using a scaling factor of 0.9806;
(3) the highest level single point calculation is performed at the URCCSD(T)/6-31G(d) level. This method has been
implemented in the MOLPRO program package and performs a UCCSD(T) single point calculation based on a
ROHF/6-31G(d) reference wavefunction;
(4) the effects of the basis sets extension are estimated through the difference between ROMP2(FC)/6-31G(d)
and ROMP2(FC)/G3MP2large energies;

The form of the higher level correction (HLC) is kept unchanged with respect to the original G3 scheme as
E(HLC) = - An_b - B(n_a - n_b) for molecules
E(HLC) = - Cn_b - D(n_a - n_b) for atoms
with n_a = number of alpha valence electrons and n_b = number of beta valence electrons.
The parameters optimized for 301 energies of the G2/97 data set (Radom et al., JCP 2003) are:
A=9.413, B=3.969, C=9.438, D=1.888 (all in mhartrees).

D. J. Henry, C. J. Parkinson, P. M. Mayer, L. Radom,
"Bond Dissociation Energies and Radical Stabilization Energies Associated with Substituted Methyl Radicals"
J. Phys. Chem. A 2001, 105, 6750 - 6756.
D. J. Henry, M. B. Sullivan, L. Radom,
"G3-RAD and G3X-RAD: Modified Gaussian-3 (G3) and Gaussian-3X (G3X) procedures for radical thermochemistry"
J. Chem. Phys. 2003, 118, 4849 - 4860.

9) G3(MP2)(+)-RAD(p) - a G3(MP2)B3 variant for open shell systems
Very similar in spirit to G2(MP2,SVP)-RAD(p) this is a modified G3(MP2)B3 procedure by Radom et al.
for the treatment of charged, open shell systems. Energies are calculated according to the following recipe:

(1) geometry optimizations are performed at the UBecke3LYP/6-31+G(d,p)
level of theory, adding p-type polarization functions to hydrogen atoms and
diffuse basis functions to non-hydrogen atoms;
(2) zero point vibrational energies are computed at the UBecke3LYP/6-31+G(d,p)
level and scaled by 0.9806;
(3) the highest level single point calculation is performed at the URCCSD(T)/6-31+G(d) level. This method has been
implemented in the MOLPRO program package and performs a UCCSD(T) single point calculation based on a
ROHF/6-31+G(d) reference wavefunction;
(4) the effects of the basis sets extension are estimated through the difference between
ROMP2(FC)/6-31+G(d) and ROMP2(FC)/G3MP2large energies;

Higher level corrections for molecules and atoms are treated in the same way as in the G3(MP2) scheme.

S. D. Wetmore, D. M. Smith, J. T. Bennett, L. Radom,
"Understanding the Mechanism of Action of B₁₂-Dependent Ethanolamine Ammonia-Lyase:
Synergistic Interactions at Play"
J. Am. Chem. Soc. 2002, 124, 14054 - 14065.
S. D. Wetmore, D. M. Smith, B. T. Golding, L. Radom,
"Interconversion of (S)-Glutamate and (2S,3S)-3-Methylaspartate: A Distinctive B₁₂-Dependent
Carbon-Skeleton Rearrangement"
J. Am. Chem. Soc. 2001, 123, 7963 - 7972.

last changes: 01.04.2008, AS
questions & comments to: axel.schulz@uni-rostock.de