G2(MP2) theory - saving some time

G2(MP2) theory is a substantially cheaper variation of G2 with only slightly
reduced predictive power. The G2(MP2) energy at 0 degree Kelvin E₀(G2MP2)
is defined as:

E₀(G2MP2) = E[QCISD(T,FC)/6-311G(d,p)//MP2(FULL)/6-31G(d)]
        + DE(+3df,2p)
        + DE(HLC)
        + ZPE

The definition of the components being:

DE(+3df,2p) = E[MP2(FC)/6-311+G(3df,2p)//MP2(FULL)/6-31G(d)] - E[MP2(FC)/6-311G(d,p)//MP2(FULL)/6-31G(d)]

DE(HLC) = -An(beta) - Bn(alpha)
                     A = 4.81 mHartrees; B = 0.19 mHartrees
                     n(alpha) = No. of alpha valence electrons
                     n(beta) = No. of beta valence electrons

ZPE = 0.8929 * ZPE[HF/6-31G(d)]

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

• Optimization and frequency calculation at the HF/6-31G(d) level of theory
• Optimization at the MP2(FULL)/6-31G(d) level of theory
• QCISD(T,FC)/6-311G(d,p)//MP2(FULL)/6-31G(d) single point
• MP2(FC)/6-311+G(3df,2p)//MP2(FULL)/6-31G(d) single point

The G2MP2 keyword can be used in Gaussian in order to compute all required energy components
in an orderly manner.

Comments:

• Open shell systems are treated using unrestricted wavefunctions (UHF, UMP2 . . )
• The higher level correction (HLC) is identical to the one used in G2 theory and included
  to compensate for remaining deficiencies of the method. The B value has been chosen such that
  the energy of the hydrogen atom is exact. The A value has been chosen such as to minimize the
  error for the predicted heat of formation of 55 known molecules.
• The mean absolute deviation for the original G2 neutral set (125 reaction energies)
  is 1.58 kcal/mol. The mean absolute deviation for the extended G2 neutral set (148 reaction
  energies) is 2.04 kcal/mol.

Literature:

• L. A. Curtiss, K. Raghavachari, G. W. Trucks, J. A. Pople,
  "Gaussian-2 theory for molecular energies of first- and second-row compounds"
  J. Chem. Phys. 1991, 94, 7221 - 7230.
• L. A. Curtiss, J. E. Carpenter, K. Raghavachari, J. A. Pople
  "Validity of additivity approximations used in Gaussian-2 theory"
  J. Chem. Phys. 1992, 96, 9030 - 9034.
• L. A. Curtiss, K. Raghavachari, J. A. Pople,
  "Gaussian-2 theory using reduced Møller-Plesset orders"
  J. Chem. Phys. 1993, 98, 1293 - 1298.
• M. Glukhovtsev, A. Pross, M. McGrath, L. Radom,
  "Extension of Gaussian-2 (G2) theory to bromine- and iodine-containing molecules:
  Use of effective core potentials"
  J. Chem. Phys. 1995, 103, 1878.
• L. A. Curtiss, P. C. Redfern, B. J. Smith, L. Radom,
  "Gaussian-2 (G2) theory: Reduced basis set requirements"
  J. Chem. Phys. 1996, 104, 5148.