G4 theory - improving on G3X

G4 is a compound method in spirit of the other Gaussian theories and attempts to take the accuracy achieved with G3X one small step further. This involves the introduction of an extrapolation scheme for obtaining basis set limit Hartree-Fock energies, the use of geometries and thermochemical corrections calculated at B3LYP/6-31G(2df,p) level, a highest-level single point calculation at CCSD(T) instead of QCISD(T) level, and addition of extra polarization functions in the largest-basis set MP2 calculations. The G4 energy at 0 degree Kelvin E0(G4) is defined as:

E0(G4) = E[CCSD(T,FC)/6-31G(d)//B3LYP/6-31G(2df,p)]
        + DE(+)
        + DE(2df,p)
        + DE(G3largeXP)
        + DE(HF)
        + DE(HLC)
        + ZPE
        + DE(SO)

The definition of the components being:

DE(+) = E[MP4(FC)/6-31+G(d)//B3LYP/6-31G(2df,p)] - E[MP4(FC)/6-31G(d)//B3LYP/6-31G(2df,p)]

DE(2df,p) = E[MP4(FC)/6-31G(2df,p)//B3LYP/6-31G(2df,p)] - E[MP4(FC)/6-31G(d)//B3LYP/6-31G(2df,p)]

DE(G3largeXP) = E[MP2(FULL)/G3largeXP//B3LYP/6-31G(2df,p)] - E[MP2(FC)/6-31G(2df,p)//B3LYP/6-31G(2df,p)]
                         - E[MP2(FC)/6-31+G(d)//B3LYP/6-31G(2df,p)] + E[MP2(FC)/6-31G(d)//B3LYP/6-31G(2df,p)]

DE(HF) = E[RHF/limit] - E[RHF/G3largeXP]
The Hartree-Fock energy at basis set limit E[RHF/limit] is obtained from two separate RHF calculations using a two-point extrapolation formula:

E[RHF/limit] = (E[RHF/mod-aug-cc-pV5Z] - E[RHF/mod-aug-cc-pVQZ] exp(-alpha)) / (1 - exp(-alpha))

with alpha = 1.63; the aug-cc-pV5Z and aug-cc-pVQZ basis sets used here have a reduced number of diffuse basis functions on non-hydrogens as well as a modified basis for hydrogen as compared to the original basis sets.

HLC correction for closed-shell molecules:
DE(HLC) = -An(beta)
                     A = 6.947 mHartrees,
                     n(beta) = number of valence electron pairs;

HLC correction for open-shell molecules:
DE(HLC) = -A'n(beta) - B(n(alpha) - n(beta))
                     A' = 7.128 mHartrees; B = 2.441 mHartrees;
                     n(alpha) = no. of alpha valence electrons; n(beta) = no. of beta valence electrons, always assuming n(alpha) > n(beta);

HLC correction for atoms (neutral and charged):
DE(HLC) = -Cn(beta) - D(n(alpha) - n(beta))
                     C = 7.116 mHartrees; D = 1.414 mHartrees;
                     n(alpha) = no. of alpha valence electrons; n(beta) = no. of beta valence electrons, always assuming n(alpha) > n(beta);

HLC correction for molecules with a single valence pair of s electrons:
DE(HLC) = -2.745 mHartrees

ZPE = ZPE[B3LYP/6-31G(2df,p)], scaling frequencies by 0.9854

The necessary energies can be calculated most efficiently in the following sequence:

Comments:

Literature: