G3X theory - aiming for even higher accuracy

G3X is an improvement over G3 theory in several ways and tries to improve on some weak points of
G3 theory. Important changes are the use of B3LYP/6-31G(2df,p) geometries and the use of larger basis
sets for second row elements (beyond Mg). The G3 energy at 0 degree Kelvin E₀(G3X) is defined as:

E₀(G3X) = E[QCISD(T,FC)/6-31G(d)//B3LYP/6-31G(2df,p)]
        + DE(+)
        + DE(2df,p)
        + DE(G3large)
        + DE(G3Xlarge)
        + 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(G3large) = E[MP2(FULL)/G3large//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(G3Xlarge) = E[HF/G3Xlarge//B3LYP/6-31G(2df,p)] - E[HF/G3large//B3LYP/6-31G(2df,p)]

DE(HLC) = -An(beta) - B(n(alpha) - n(beta))
                     A = 6.783 mHartrees; B = 3.083 mHartrees (for molecules)
                     A = 6.877 mHartrees; B = 1.152 mHartrees (for atoms)
                     n(alpha) = No. of alpha valence electrons
                     n(beta) = No. of beta valence electrons

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

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
• QCISD(T,FC)/6-31G(d)//B3LYP/6-31G(2df,p) single point
• MP4(FC)/6-31+G(d)//B3LYP/6-31G(2df,p) single point
• MP4(FC)/6-31G(2df,p)//B3LYP/6-31G(2df,p) single point
• MP2(Full)/G3large//B3LYP/6-31G(2df,p) single point
• HF/G3Xlarge//B3LYP/6-31G(2df,p) single point (for second row elements only)

Comments:

• The G3large basis set is identical to the one used in G3 theory. The G3Xlarge basis set
  used for the Hartree-Fock calculations adds g-type polarization functions to the G3large basis
  set for elements beyond Mg. A local copy of the G3Xlarge basis set can be found here.
• 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. As in G3 theory, different parameters A and B are used 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 mean absolute deviation for the G3/99 test set (376 data points) is
  1.07 kcal/mol for G3 and 0.95 kcal/mol for G3X theory.

Literature:

• L. A. Curtiss, K. Raghavachari, P. C. Redfern, V. Rassolov, J. A. Pople,
  "Gaussian-3 (G3) theory for molecules containing first and second-row atoms"
  J. Chem. Phys. 1998, 109, 7764 - 7776.
• 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.
• A. G. Baboul, L. A. Curtiss, P. C. Redfern, K. Raghavachari,
  "Gaussian-3 theory using density functional geometries and zero-point energies"
  J. Chem. Phys. 1999, 110, 7650 - 7657.
• L. A. Curtiss, P. C. Redfern, K. Raghavachari, J. A. Pople
  "Gaussian-3X (G3X) theory: Use of improved geometries, zero-point energies, and Hartree-Fock basis sets"
  J. Chem. Phys. 2001, 114, 108 - 117.