G3 theory - improving on G2

G3 is an improvement over G2 theory in several ways and tries to reproduce effectively QCISD(T)/G3large
energies through a series of calculations at lower level. The G3large basis set is a slightly modified
version of the 6-311+G(3df,2p) basis set used in the G2 procedure. The G3 energy at 0 degree Kelvin
E₀(G3) is defined as:

E₀(G3) = E[QCISD(T,FC)/6-31G(d)//MP2(FULL)/6-31G(d)]
        + DE(+)
        + DE(2df,p)
        + DE(G3large)
        + DE(HLC)
        + ZPE
        + DE(SO)

The definition of the components being:

DE(+) = E[MP4(FC)/6-31+G(d)//MP2(FULL)/6-31G(d)] - E[MP4(FC)/6-31G(d)//MP2(FULL)/6-31G(d)]

DE(2df,p) = E[MP4(FC)/6-31G(2df,p)//MP2(FULL)(6-31G(d)] - E[MP4(FC)/6-31G(d)//MP2(FULL)/6-31G(d)]

DE(G3large) = E[MP2(FULL)/G3large//MP2(FULL)/6-31G(d)] - E[MP2(FC)/6-31G(2df,p)//MP2(FULL)/6-31G(d)]
                         - E[MP2(FC)/6-31+G(d)//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 = 6.386 mHartrees; B = 2.977 mHartrees (for molecules)
                     A = 6.219 mHartrees; B = 1.185 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
• MP4(FC)/6-31+G(d)//MP2(FULL)/6-31G(d) single point
• MP4(FC)/6-31G(2df,p)//MP2(FULL)/6-31G(d) single point
• MP2(Full)/G3large//MP2(FULL)/6-31G(d) single point

Comments:

• While a 6-311+G(3df) basis set has been used in G2 theory for all first and second row
  elements, a different strategy has been pursued in G3 theory. First, a slightly smaller
  6-311+G(2df) basis has been chosen for the first row elements, while a larger 6-311+G(3d2f)
  basis has been chosen for the second row elements. In both cases core polarization functions
  (e.g. p- and d-type for carbon) have also been added. Hydrogen is still treated with a 311+G(2p)
  basis. A local copy of the G3large basis set can be found here.
• 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 G2 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 original G2 neutral set (125 reaction energies) is
  1.00 kcal/mol. The mean absolute deviation for the extended G2 neutral set (148 reaction
  energies) is 0.9 kcal/mol.

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.