G3(MP2) theory - again saving some time

G3(MP2) is a cheaper variant of G3 theory, in which the effects of basis set extension
are obtained from calculations at the MP2 level of theory. The G3(MP2) energy at
0 degrees Kelvin E₀(G3MP2) is defined as:

E₀(G3MP2) = E[QCISD(T,FC)/6-31G(d)//MP2(FULL)/6-31G(d)]
        + DE(G3MP2large)
        + DE(HLC)
        + ZPE
        + DE(SO)

The definition of the components being:

DE(G3MP2large) = E[MP2(FULL)/G3MP2large//MP2(FULL)/6-31G(d)] - E[MP2(FC)/6-31G(d)//MP2(FULL)/6-31G(d)]

DE(HLC) = -An(beta) - B(n(alpha) - n(beta))
                     A = 9.279 mHartrees; B = 4.471 mHartrees (for molecules)
                     A = 9.345 mHartrees; B = 2.021 mHartrees (for atoms)
                     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)/6-31G(d)//MP2(FULL)/6-31G(d) single point
• MP2(FC)/G3MP2large//MP2(FULL)/6-31G(d) single point

Comments:

• Open shell systems are treated using unrestricted wavefunctions (UHF, UMP2 . . )
• The higher level correction (HLC) is included to compensate for remaining deficiencies
  of the method. In contrast to G2 theory, separate values for parameters A and B have been
  optimized for atoms and molecules to give the smallest average absolute deviation from
  experiment.
• Spin orbit correction terms E(SO) (mainly of experimental origin) are added only for atoms
• The G3MP2large basis set is almost identical to the G3large basis used in G3 except that
  core polarization functions are not included. A local copy of the G3MP2large basis set can be found here.
• In contrast to G3 theory, the MP2 single point calculation is performed within the
  frozen core approximation (MP2(FC)).
• The mean absolute devitiation for the extended G2 neutral set (148 reaction energies) is
  1.18 kcal/mol.

Literature:

• L. A. Curtiss, K. Raghavachari,
  "G2 Theory"
  The Encyclopedia of Computational Chemistry, P. v. R. Schleyer (editor-in-chief),
  John Wiley & Sons Ltd, Athens, USA, 1998, 2, 1104 - 1114.
• L. A. Curtiss, P. C. Redfern, K. Raghavachari, V. Rassolov, J. A. Pople,
  "Gaussian-3 theory using reduced Møller-Plesset order"
  J. Chem. Phys. 1999, 110, 4703 - 4709.