available as keywords in the Gaussian series of computational chemistry suites
[ 177 ], and thecomplete basis set methods, which come from Petersson’s group.
The Gaussian Methods
The key to these methods is the use of high correlation levels and big basis sets.
This series began in 1989 with Gaussian 1, G1 [ 176 ], continued with G2 (1991)
[ 178 ] and G3 (1998) [ 179 ], and has seen the publication (2007) of G4 [ 180 ]. G1 and
G2 are obsolete. The most popular Gaussian high-accuracy methods at present are
G3 and the variation G3(MP2) [ 181 ], designed to shorten computational times with
little loss of accuracy. For G3 the average absolute deviation from experiment is
1.13 kcal mol#^1 (4.7 kJ mol#^1 ) and for G3(MP2) 1.2–1.3 kcal mol#^1 (5.0–5.4 kJ
mol#^1 ), and G3(MP2) seems to be seven to eight times as fast as G3 [ 181 ]. Some
other G3-type methods are G3(B3) and G3(MP2B3) [ 182 ]. Curtiss et al. give the
details of the G4 [ 180 ] method and compare it with G3 and to some extent G1 and
G2. They report that “...the average absolute deviation from experiment shows
significant improvement from 1.13 kcal/mol [4.7 kJ mol#^1 ] (G3 theory) to 0.83
kcal/mol [3.5 kJ mol#^1 ] (G4 theory)”. Comparatively little has yet (June 2009) been
published on G4, and it is unclear if its improved accuracy will outweigh its being
two to three times as slow as G3 and lead to its replacing G3, as this latter method
replaced G2. To speed up the G4 method, its MP4 steps were replaced with MP2
and MP3 (Section 5.4.2) giving G4(MP2) and G4(MP3) [ 183 ]. These have respec-
tively average absolute deviations from experiment of 1.04 kcal/mol [4.35 kJ
mol#^1 ] and 1.03 kcal/mol [4.3 kJ mol#^1 ). The G4(MP2) method appears overall
to be the better of the two; it is two to three times as fast as G3 and although about
twice as slow as G3(MP2), Curtiss et al. say [ 183 ] “Overall, the G4(MP2) method
provides an accurate and economical method for thermodynamic predictions”. It
has an overall accuracy for the G3/05 test set of molecules that is significantly better
than G3(MP2) theory (1.04 vs 1.39 kcal/mol) [4.35 vs 5.8 kJ mol#^1 ] and even better
than G3 theory (1.04 vs 1.13 kcal/mol) [4.35 vs 4.7 kJ mol#^1 ]. G4(MP2) was
said to perform “reasonably well” for the thermochemistry of transition metals,
species that present special problems for computational chemistry [ 184 ] (see too
Section 8.3.4). It seems likely that G4(MP2) will replace G3 and replace or be
competitive with G3(MP2). G4 and its modifications build on G3, and the G3
methods are at present (June 2009) more available and represent a much larger user
pool of experience than the G4 methods; for this reason G3 and its popular variant
G3(MP2) will be discussed below, with some examples. G3(MP2) will handle
molecules with up to about 13 heavy atoms. The results from G4(MP2) should be
modestly more accurate than those from G3(MP2), but the calculation times are
likely to be about twice as long.
A G3 calculation [ 179 ] as implemented in the Gaussian programs uses eight steps:
- An HF/6–31G* geometry optimization, to get a structure for a frequency
calculation - An HF/6–31G* frequency calculation, wanted for the ZPE
310 5 Ab initio Calculations