Essentials of Computational Chemistry

236 7 INCLUDING ELECTRON CORRELATION IN MO THEORY
However, the generally robust nature of MP2 in the above examples simply reflects the
degree to which most minima are already fairly well described by HF wave functions. When
this is not the case, e.g., in TS structures, there are no hard and fast rules that can be cited
with respect to the expected quality of any level of theory. Instead, one is thrown back on
the twin responsibilities of demonstrating either (a) agreement with known experimental data
of one kind or another in the same or related systems or (b) convergence with respect to
treatment of electron correlation. A rough quality ordering that is often observed is
HF < MP2 ∼ MP3 ∼ CCD < CISD
< MP4SDQ ∼ QCISD ∼ CCSD < MP4
< QCISD(T) ∼ CCSD(T) ∼ BD(T) (7.59)
Table 7.4 provides a more quantitative feel for the performance summary embodied in
Eq. (7.59) using data provided by Bartlett (1995) for the absolute errors in various levels of
theory compared to full CI for HB, H2O, and HF using a polarized double-ζ basis set. In this
case, calculations were carried out both at the equilibrium geometries, and also at geometries
where the X–H bonds were stretched by 50% and 100%; correlation should become
more important in describing these higher energy species (see also Dutta and Sherrill 2003).
The ordering of the levels in the table is approximately that listed in Eq. (7.59), although
CCD seems to do fortuitously well. As expected, the lower levels of correlation treatment
degrade markedly compared to the higher levels when the bonds are stretched. A few levels
not generally available in most electronic structure packages are included in the table for
completeness, including MP5, MP6, and levels having full inclusion of triples, represented
by ‘T’ instead of ‘(T)’. The heroically expensive CCSDTQ, which takes full account of all
Table 7.4 Average errors in correlation energies (kcal mol −1 ) compared to full CI for various methods
applied to HB, H2O, and HF at both equilibrium and bond-stretched geometries
Level of theory Equilibrium geometry Equilibrium and stretched geometries
MP2 10.4 17.4
MP3 5.0 14.4
CISD 5.8 13.8
CCD 2.4 8.0
MP4SDQ 2.7 7.1
CCSD 1.9 4.5
QCISD 1.7 4.0
MP4 1.3 3.7
MP5 0.8 3.2
MP6 0.3 0.9
CCSD(T) 0.3 0.6
QCISD(T) 0.3 0.5
CCSDT 0.2 0.5
CCSDTQ 0.01 0.02