G4(MP2) theory - saving some time over G4

G4(MP2) is a more economical version of G4 theory, in which the effects of basis set extension are obtained from calculations at MP2 level. This is closely similar to the difference between G3 and G3(MP2) theory. The G4(MP2) energy at 0 degree Kelvin E₀(G4MP2) is defined as:

E₀(G4MP2) = E[CCSD(T,FC)/6-31G(d)//B3LYP/6-31G(2df,p)]
        + DE(G3MP2largeXP)
        + DE(HF)
        + DE(HLC)
        + ZPE
        + DE(SO)

The definition of the components being:

DE(G3MP2largeXP) = E[MP2(FC)/G3MP2largeXP//B3LYP/6-31G(2df,p)] - E[MP2(FC)/6-31G(d)//B3LYP/6-31G(2df,p)]

DE(HF) = E[RHF/limit] - E[RHF/G3MP2largeXP]
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-pVQZ] - E[RHF/mod-aug-cc-pVTZ] exp(-alpha)) / (1 - exp(-alpha))

with alpha = 1.63; the mod-aug-cc-pVQZ and mod-aug-cc-pVTZ basis sets used here are modified versions of the standard aug-cc-pVQZ and aug-cc-pVTZ basis sets. The type of modification depends on the element at hand.

HLC correction for closed-shell molecules:
DE(HLC) = -An(beta)
                     A = 9.472 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' = 9.769 mHartrees; B = 3.102 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 = 9.741 mHartrees; D = 2.115 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) = -2.379 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:

• Optimization and frequency calculation at the B3LYP/6-31G(2df,p) level of theory
• CCSD(T,FC)/6-31G(d)//B3LYP/6-31G(2df,p) single point
• MP2(FC)/G3MP2largeXP//B3LYP/6-31G(2df,p) single point
• RHF/mod-aug-cc-pVTZ//B3LYP/6-31G(2df,p) single point
• RHF/mod-aug-cc-pVQZ//B3LYP/6-31G(2df,p) single point

Comments:

• Open shell systems are treated using unrestricted wavefunctions (UHF, UMP2 . . )
• The higher level correction (HLC) is supposed to compensate for the remaining deficiencies
  of the method. In contrast to G3 theory, the parameters now differentiate between open- and
  closed-shell systems, atoms, and the special case of single 1s electron valence pairs.
• Spin orbit correction terms E(SO) (mainly of experimental origin) are added only for atoms
• The mean absolute deviation for the full G3/05 data set of 454 data points is 0.83 kcal/mol for
  G4, 1.04 kcal/mol for G4(MP2), 1.13 kcal/mol for G3, and 1.39 for G3(MP2).

Literature:

• L. A. Curtiss, P. C. Redfern, K. Raghavachari,
  "Gaussian-4 theory using reduced order perturbation theory"
  J. Chem. Phys. 2007, 126, 124105.
• L. A. Curtiss, P. C. Redfern, K. Raghavachari,
  "Gaussian-4 theory"
  J. Chem. Phys. 2007, 126, 84108.

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