doubles (CCSD) orcoupled cluster singles, doubles and triples (CCSDT)
method:
T^CCD¼eT^^2 CHF
T^CCSD¼eðT^^1 þT^^2 ÞCHF
T^CCSDT¼eðT^^1 þT^^2 þT^^3 ÞCHFInstead of the very demanding CCSDT calculations one often performs CCSD
(T) (note the parentheses), in which the contribution of triple excitations is repre-
sented in an approximate way (not refined iteratively); this could be called coupled
cluster approximate (or perturbative) triples. Thequadratic configurationmethod
(QCI) is very similar to the CC method. The most accurate implementation of this
in common use is QCISD(T) (quadratic CI singles, doubles, triples, with triple
excitations treated in an approximate, non-iterative way). The CC method, which is
usually only moderately slower than QCI (Table5.6), is apparently better [ 102 ].
CCSD(T) calculations are, generally speaking, the current benchmark for practical
molecular calculations on molecules of up to moderate size.
Like MP methods, CI methods require reasonably large basis sets for good
results. The smallest (and perhaps most popular) basis used with these methods
is the 6–31G* basis, but where practical the 6–311G** basis, developed especially
for post-HF calculations, might be preferable (see Table5.6). Higher-correlated
single-point calculations on MP2 geometries tend to give more reliable relative
energies than do single-point MP2 calculations on HF geometries (Section 5.4.2, in
Table 5.6 Energies and times for some calculations involving electron correlation; HF jobs are
shown for comparison
Method/basis Input Energy Time (min)
HF/6–31G opt AM1 geom, Hessian #191.96224 7
HF/6–31G opt + freq AM1 geom, Hessian #191.96224 14
MP2/6–31G sp HF/6–31G geom #192.5216 1
MP2/6–311G sp HF/6–31G geom #192.64662 7
MP2/6–31G opt AM1 geom, Hessian #192.5239 11
MP2/6–31G opt + freq AM1 geom, Hessian #192.5239 91
MP4SDTQ/6–31G sp MP2/6–31G* geom #192.57982 33
MP4SDTQ/6–311G* sp MP2/6–31G geom #192.71075 245
QCISD(T)/6–31G sp MP2/6–31G geom #192.57883 93
QCISD(T)/6–311G sp MP2/6–31G geom #192.70884 490
CCSD(T)/6–31G sp MP2/6–31G* geom #192.57808 132
CCSD(T)/6–311G* sp MP2/6–31G geom #192.70798 725
The calculations were done with Gaussian 94W [ 198 ] on C2vacetone, on a 200 MHZ PentiumPro
(a relatively slow machine). A lower absolute energy does not guarantee that a method/basis will
give a more accurate activation or reaction energy, as these latter two are energydifferences, not
absolute energies. MP2¼MP2(fc), sp¼single point. Methods are given in order of the increasing
thoroughness with which they usually treat electron correlation; CC is generally superior to QCI
[ 102 ]. Note that none of the correlation methods is variational: they can give an energy lower than
the true energy
5.4 Post-Hartree–Fock Calculations: Electron Correlation 275