Essentials of Computational Chemistry

7.7 PARAMETERIZED METHODS 241
Table 7.6 Steps in G2 and G3 theory for molecules a,b
Step G2 G3
(1) HF/6-31G(d) geometry optimization HF/6-31G(d) geometry optimization
(2) ZPVE from HF/6-31G(d) frequencies ZPVE from HF/6-31G(d) frequencies
(3) MP2(full)/6-31G(d) geometry
MP2(full)/6-31G(d) geometry
optimization (all subsequent
optimization (all subsequent
calculations use this geometry)
calculations use this geometry)
(4) E[MP4/6-311+G(d,p)]
−E[MP4/6-311G(d,p)]
E[MP4/6-31+G(d)] −E[MP4/6-31G(d)]
(5) E[MP4/6-311G(2df,p)]
E[MP4/6-31G(2df,p)]
−E[MP4/6-311G(d,p)]
−E[MP4/6-31G(d)]
(6) E[QCISD(T)/6-311G(d)]
E[QCISD(T)/6-31G(d)]
−E[MP4/6-311G(d)]
−E[MP4/6-31G(d)]
(7) E[MP2/6-311+G(3df,2p)]
E[MP2(full)/G3large
−E[MP2/6-311G(2df,p)]
−E[MP2/6-311+G(d,p)]
+E[MP2/6-311G(d,p)]
c ]
−E[MP2/6-31G(2df,p)]
−E[MP2/6-31+G(d)]
+E[MP2/6-31G(d)]
(8) −0.00481 × (number of valence electron −0.006386 × (number of valence
pairs) −0.00019 × (number of
electron pairs) −0.002977 × (number
unpaired valence electrons)
of unpaired valence electrons)
E0 = 0.8929 × (2) + E[MP4/6-311G(d,p)] + 0.8929 × (2) + E[MP4/6-31G(d)] +
(4) + (5) + (6) + (7) + (8)
(4) + (5) + (6) + (7) + (8)
a For atoms, G3 energies are defined to include a spin-orbit correction taken either from experiment or other highlevel
calculations. In addition, different coefficients are used in step (8).
b In the G2 method, the 6-311G basis set and its derivatives are not defined for second-row atoms; instead, a basis
set optimized by McLean and Chandler (1980) is used.
c Available at http://chemistry.anl.gov/compmat/g3theory.htm. Defined to use canonical 5 d and 7 f functions.
A modification of G2 by Pople and co-workers was deemed sufficiently comprehensive
that it is known simply as G3, and its steps are also outlined in Table 7.6. G3 is more accurate
than G2, with an error for the 148-molecule heat-of-formation test set of 0.9 kcal mol −1 .Itis
also more efficient, typically being about twice as fast. A particular improvement of G3 over
G2 is associated with improved basis sets for the third-row nontransition elements (Curtiss
et al. 2001). As with G2, a number of minor to major variations of G3 have been proposed to
either improve its efficiency or increase its accuracy over a smaller subset of chemical space,
e.g., the G3-RAD method of Henry, Sullivan, and Radom (2003) for particular application
to radical thermochemistry, the G3(MP2) model of Curtiss et al. (1999), which reduces
computational cost by computing basis-set-extension corrections at the MP2 level instead
of the MP4 level, and the G3B3 model of Baboul et al. (1999), which employs B3LYP
structures and frequencies.
It should be noted that G2 and G3 potentially fail to be size extensive because of the
correction term in step 8. If one is studying a homolytic dissociation into two components,
at what point along the reaction coordinate are the formerly paired electrons considered
to be unpaired? There will be a discontinuity in the energy at that point. In addition, G3
theory uses a different correction for atoms than for molecules, and this too fails to be size
extensive.