connection method [ 57 ]) gave the best reaction energies [ 74 ]. Many energy differ-
ence comparisons have been published comparing B3LYP/6-31G with HF, MP2
and experiment [ 67 ]. These comparisons involve homolytic dissociation, various
reactions, particularly hydrogenations, acid-base reactions, isomerizations, isodes-
mic reactions, and conformational energy differences. This wealth of data shows
that while gradient-corrected DFT and MP2 calculations are vastly superior for
homolytic dissociations, for “ordinary” reactions (involving only closed-shell spe-
cies), their advantage is much less marked; for example, HF/3-21G, HF/6-31G,
SVWN/6-31G (non-gradient-corrected DFT), all usually give energy differences
similar to those from B3LYP/6-31G and in fair agreement with experiment.
Table7.5compares with experiment [ 86 ] errors for hydrogenations, isomerizations,
bond separation reactions (a kind of isodesmic reaction), and proton affinities; the
methods are HF, SVWN, MP2, and B3LYP, all using the 6-31G basis. In two of
the four cases (hydrogenation and isomerization) the HF/6-31G method gave the
best results; in one case MP2 was best and in one case B3LYP.
For the energy comparison of normal (not involving transition states) closed-
shell organic species correlated methods like MP2 and DFT seem to offer little or
no advantage, unless one needs accuracy within ca. 10–20 kJ mol"^1 of experiment,
in which case high-accuracy methods should be used. The strength of gradient-
corrected DFT methods appears to lie largely in their ability to give homolytic
dissociation energies and activation energies with an accuracy comparable to that
from MP2, but at a time cost comparable to that from HF calculations. Bauschlicher
et al. compared various methods and recommended B3LYP over HF and MP2, to a
large extent on the basis of the performance of B3LYP with regard to atomization
energies and transition metal compounds [ 76 ]. Wiberg and Ochterski compared HF,
MP2, MP3, MP4, B3LYP, CBS-4 and CBS-Q with experiment in calculating
energies of isodesmic reactions (hydrogenation and hydrogenolysis, hydrogen
transfer, isomerization, and carbocation reactions) and found that while MP4/6-
31G and CBS-Q were the best, B3LYP/6-31G was also generally satisfactory
[ 87 ]. Rousseau and Mathieu developed an economical way of calculating heats of
formation by performing pBP/DN calculations on molecular mechanics geome-
tries; rms deviations from experiment were about 16 kJ mol"^1 for a variety of
compounds [ 88 ]. The pBP/DN method was removed from Spartan (Section7.3.1);
it is said [ 68 ] to give results similar to those from BP86/6-311G*, which is available
Table 7.5 Energy errors for hydrogenation reactions, isomerizations, bond separation reactions,
and proton affinities, using four different methods; the basis set is 6-31G*. The errors, in kJ mol"^1 ,
in each case the arithmetic mean of the absolute deviations from experiment of ten reactions, were
calculated from the data in Hehre [ 86 ]
Reaction Method
HF SVWN MP2 B3LYP
Hydrogenation 15 20 17 23
Isomerization 15 19 16 17
Bond separation 11 5 4 10
Proton affinity 14 18 11 7
480 7 Density Functional Calculations