Essentials of Computational Chemistry

294 8 DENSITY FUNCTIONAL THEORY
concluded that the B3LYP functional is particularly robust for predicting geometries in
this area. This is consistent with the good behavior of this functional when applied to
minimum-energy structures composed only of first-row atoms as already noted above. Cramer
and Barrows (1998) have emphasized, however, that overdelocalization problems can arise
in ionic examples of such electrocyclic reactions, and caution may be warranted in these
instances.
8.6.3 Charge Distributions
Over the 108 molecules in Test Set B of Table 8.5, Scheiner, Baker, and Andzelm computed
the mean unsigned errors in predicted dipole moments to be 0.23, 0.20, 0.23, 0.19, and
0.16 D at the HF, MP2, SVWN, BPW91, and B3PW91 levels of theory, respectively, using
the 6-31G(d,p) basis set. These results were improved somewhat for the DFT levels of theory
when more complete basis sets were employed.
Cohen and Tantirungrotechai (1999) compared HF, MP2, BLYP, and B3LYP to one another
with respect to predicting the dipole moments of some very small molecules using a very
large basis set, and their results are summarized in Table 8.6. In general the performances of
MP2, the pure BLYP functional, and the hybrid B3LYP functional are about equal, although
both DFT functionals do very slightly better than MP2 for several cases. HF theory shows
its typical roughly 10–15 percent overestimation of dipole moments, and its historically
well-known reversal of moment for carbon monoxide.
In addition to the moments of the charge distribution, molecular polarizabilities have also
seen a fair degree of study comparing DFT to conventional MO methods. While data on
molecular polarizabilities are less widely available, the consensus appears to be that for this
property DFT methods, pure or hybrid, fail to do as well as the MP2 level of theory, with
conventional functionals typically showing errors only slightly smaller than those predicted
by HF (usually about 1 a.u.), while the MP2 level has errors only 25 percent as large. In
certain instances, ACM functionals have been more competitive with MP2, but still not quite
as good.
Table 8.6 Dipole moments (D) for eight small molecules at four levels of
theory using the very large POL basis set a
Molecule HF MP2 BLYP B3LYP Experiment
NH3 1.62 1.52 1.48 1.52 1.47
H2O 1.98 1.85 1.80 1.86 1.85
HF 1.92 1.80 1.75 1.80 1.83
PH3 0.71 0.62 0.59 0.62 0.57
H2S 1.11 1.03 0.97 1.01 0.97
HCl 1.21 1.14 1.08 1.12 1.11
CO −0.25 0.31 0.19 0.10 0.11
SO2 1.99 1.54 1.57 1.67 1.63
a From Cohen and Tantirungrotechai 1999.