Essentials of Computational Chemistry

286 8 DENSITY FUNCTIONAL THEORY
Table 8.2 Mean absolute errors in metal–ligand binding
energies for different methods (kcal mol −1 ) a
Level of theory b Ligand
H CH3 CH2
MO theoretical methods
MCPF 6 9 20
QCISD(T) 6
PCI-80
Density functional methods
2 2 4
SVWN 12
BP86 8
BH&HLYP 16
BH&HLYP/ECP 5 9
B3LYP 5 6 4
B3LYP/ECP 9 7
a Complexes MX + where M = Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu,
and X = ligand.
b Basis sets are for the most part double-ζ polarized in quality. Use
of metal effective core potentials is indicated by ECP.
that the pure DFT functional BLYP badly underestimated the activation enthalpies for the
H-atom transfer reactions. This behavior has since been noted by many other authors, and
is part of the motivation for the MPW1K model discussed in Section 8.4.3.
In a different analysis of hydrogen-atom transfer reaction barriers, Lynch and Truhlar
(2003b) considered the forward and reverse barriers for 22 such reactions, and then demonstrated
that the performance of various models on only six data (the forward and reverse
barrier heights for HO + CH4 → H2O + CH3, H+ OH → O + H2, andH+ H2S → H2 +
HS) was highly predictive of their accuracy for all 44 barrier heights. In this and subsequent
work by Zhao et al. (2004), they assayed the accuracy of a substantial number of different
models for this test set and found that modern functionals, and particularly those including a
dependence on the kinetic energy density, gave the best results (Table 8.3, Reaction Set 2).
However, all of the geometries used in this analysis were obtained at the QCISD/MG3 level
(partly in recognition of the multideterminantal character of many H-atom transition-state
structures). So, the reported errors might be expected to change somewhat were geometries
to be located at the DFT levels of theory. In this regard, it is noteworthy that Kang and
Musgrave (2001) examined 29 different barrier heights for H-atom transfer using geometries
optimized at the same level as used to compute energies, and reported mean unsigned errors
of 0.9, 3.3, 3.2, and 2.9 kcal mol −1 , respectively, for KMLYP, B3LYP, BH&HLYP, and G2.
With respect to chemical reactions not involving H-atom transfer, Guner et al. (2003,
2004) examined a set of 11 pericyclic organic reactions having experimental data available
for nine enthalpies of activation and six enthalpies of forward reaction. They found the
B3LYP and MPW1K functionals to be about as accurate for the activation enthalpies as the
more expensive CBS-QB3 and CASPT2 levels, with other functionals doing somewhat less
well (Table 8.3, Reaction Set 3). Interestingly, they found the performance of the B3LYP