(11.0 kcal/mol)” but “these errors are systematic and their effect may be greatly
reduced by the use of isodesmic bond additivity corrections.” [ 185 ]. More typical
CBS-4M errors are (mean absolute deviation from experiment) 3.26 kcal mol#^1
(13.6 kJ mol#^1 )[ 185 ]. There is a modification of CBS-4M designed to decrease the
accumulation of errors with increasing molecular size [ 187 ]. CBS-QB3 can handle
molecules with up to about ten heavy atoms and has a mean absolute deviation from
experiment of 1.10 kcal mol#^1 (4.6 kJ mol#^1 )[ 185 ]. CBS-APNO can handle
molecules with up to about five heavy atoms and has a mean absolute deviation
from experiment of 0.53 kcal mol#^1 (2.2 kJ mol#^1 )[ 113 ].
Complete basis set methods [ 113 ] involve essentially seven or eight steps:
- A geometry optimization (at the HF/3–21G()or MP2/6–31G level, depending
on the particular CBS method) - A ZPE calculation at the optimization level
- An HF single-point calculation with a very big basis set (6–311þG(3d2f,2df,p)
or 6–311þG(3d2f,2df,2p), depending on the particular CBS method) - An MP2 single-point calculation (basis depending on the particular CBS
method) - Something called apair natural orbital extrapolationto estimate the error due to
using a finite basis set - An MP4 single-point calculation
- For some CBS methods, a QCISD(T) single-point calculation
- One or more empirical corrections
Note, as with Gaussian methods, the semiempirical aspect of CBS methods.Comparison of High-Accuracy Multistep Methods
We will concentrate on Gaussian-type and CBS methods, because these have been
the most widely-used and have thus accumulated an archive of results, are the most
accessible, and because several versions of them are available. However, there are
other high-accuracy multistep methods, such as the Weizmann procedures of
Martin and de Oliveira, W1 and W2 [ 188 ], and of Boese et al., W3 and W4
[ 189 ], which like the CBS methods are based on basis set extrapolation. W1 and
W2 have a mean absolute deviation of about 1 kJ mol#^1 (not 1 kcal mol#^1 ), and
incorporate relativistic effects, and W2 has no empirical parameters, unlike the
Gaussian and CBS methods. W3 and W4 methods have similar errors to W1 and
W2, and the authors speculate on the reasons for the obstinate “0.1 kcal/mol
barrier”. These very accurate methods are still limited molecules of about or less
than the reach of CBS-APNO.
Of the Gaussian-type and CBS methods, for high accuracy on very small
molecules CBS-APNO is the appropriate choice, and for “large” molecules the
choice falls on CBS-4M with the acceptance of the possibility of moderately large
errors. For intermediate size molecules the best choice is probably between G3
(MP2) and CBS-QB3. Recall that G3(MP2) is much faster than G3, with little loss of
accuracy in most cases; note too that G4(MP2) will compete with and when widely
312 5 Ab initio Calculations