Table7.7suggests that for these calculations the 6-311+G basis leads to essential
saturation, with reaction energies becoming almost constant. By comparison with
Table7.6, TPSS seems to be inferior to B3LYP and M06 for barriers but about as
good for reaction energies; using the (recommended) bigger basis sets, M06 seems
to underestimate the H 2 C¼CHOH barrier and to overestimate the cyclopropylidene
barrier by about 20 kJ mol"^1. All things considered for these reactions, B3LYP with
the 6-311þG or (very similar results) 6-311þþG(2df,2p) basis set was best in
comparison with CBS-QB3. This shows that with the 6-311þG** basis these func-
tionals are saturated and give, at least for these simple isomerizations, barriers and
reaction energies comparable to those from the high-accuracy CBS-QB3 method, and
probably in good agreement with experiment. Here are the times required for some
DFT and CBS-QB3 calculations (optimizationþfrequencies), in each case starting
from an AM1 geometry; the jobs were run with Gaussian 03 [ 78 ] on a 2.66 GHZ
personal computer with 4 GB of RAM and the Vista operating system:
Ethenol (vinyl alcohol, H 2 C¼CHOH)
B3LYP/6-31G* 1.2 min, relative time 1
B3LYP/6-311+G** 1.7 min, relative time 1.4
B3LYP/6-311++G(2df, 2p) 3.9 min, relative time 3.3
CBS-QB3 3.0 min, relative time 2.5For these small molecules CBS-QB3 is not disadvantaged with respect to time,
but for larger systems B3LYP with, say, 6-311þG*, could be the more practical
choice.
Another demonstration that the assertion [ 38 , 58 ] that the 6-31G basis is
generally adequate in DFT should be viewed with some skepticism was provided
by del Rio et al., who found for methyl rotation barriers, in several cases DFT
needed much bigger bases than MP2 or MP4 [ 94 ]. This emphasizes the importance
of reality checks: testing the kind of calculation at hand against model systems for
which experimental data are available.
Some references to the calculation of barriers with DFT are:
In a study of alkene epoxidation with peroxy acids, B3LYP/6-31G gave an
activation energy similar to that calculated with MP4/6-31G//MP2/6-31G but
yielded kinetic isotope effects in much better agreement with experiment than did
the ab initio calculation [ 95 ]. Even better activation energies than from B3LYP
(which it is said tends to underestimate barriers [ 96 , 97 ]) have been reported for the
BH&H-LYP functional [ 97 – 100 ]. In a study by Baker et al. [ 101 ] of 12 organic
reactions using seven methods (semiempirical, ab initio and DFT), B3PW91/6-
31G was best (average and maximum errors 15.5 and 54 kJ mol"^1 ) and B3LYP/6-
31G* second best (average and maximum errors 25 and 92 kJ mol"^1 ). Jursic studied
28 reactions and recommended “B3LYP or B3PW91 with an appropriate basis set”,
but warned that highly exothermic reactions with a small barrier (ca. 10–20 kJ
mol"^1 ) involving hydrogen radicals “are particularly difficult to reproduce” [ 102 ].
Barriers “above 10 kcal mol"^1 (ca. 40 kJ mol"^1 ) should be reliable. Lower activa-
tion energies should be underestimated by 3–4 kcal mol"^1 (ca. 13–17 kJ mol"^1 )”
7.3 Applications of Density Functional Theory 483