overrated” (relevant to the latter statement he points out that “there are many, many,
different ways to tackle the electronic structure problem from a density functional
point of view...”) [ 63 ]. The likening of DFT to molecular mechanics might appear
mischievous: certainly MM does not recognize electronic charge, an objective feature
of chemical reality with measurable consequences like dipole moments and optical
activity. Nevertheless, this paper raises points which seem to be generally unappreci-
ated, particularly with regard to “the enormous flexibility of in principle exact
formulations” of DFT. Readers may wish to console themselves with the possibility
implied by Perdew et al. [ 47 ] that an exact (if not unique?) nonparameterized
functional can be gradually approached. We now consider applications of DFT.
7.3 Applications of Density Functional Theory............................
In examining the literature for applications of DFT one is (or ought to be) struck by
the fact that there is no method (functional/basis set combination) that isgenerally
best. For every property there seems to be one or two functionals that are superior to
the others, but only for that property. This profusion is more exuberant than for
methods and basis sets in the wavefunction realm (Sousa et al. list 52 functionals in
their Table 2 [ 44 ]). One might conclude that the situation almost borders on the
chaotic, to borrow the term used by Dewar to criticise what he saw as the profusion
of basis sets [ 64 ] (Section 5.3.3.8). However, this judgement would be unfair, if
only because the relative infancy of DFT as a general, practical tool for molecular
calculations requires the exploration of “functional space” for good methods.
Furthermore, in the absence of a perfect solution one should be thankful for the
availability of one that is acceptable for the task at hand. Zhao and Truhlar grant
that those concerned about the profusion of functionals have a case, but make
the point that really satisfactory all-purpose functionals are “unlikely to be discov-
ered in the foreseeable future” and that therefore for now we need specialized
functionals [ 65 ]. Apparent exceptions to the claim that a universally applicable
functional is wanting are presented by B3LYP and the recent M06-type, a family of
four functionals, M06, M06-2X, M06-L, and M06-HF [ 45 ]. However, none of these
excels foralltasks, although M06 in particular is said to be [ 45 ] “for general-
purpose applications” and the M06-family member “with broadest applicability”.
As briefly mentioned in Section7.2.3.4e, B3LYP [ 57 , 58 ] is so popular that it has
been singled out for special attention by Sousa et al. [ 44 ] (where striking pie charts
show B3LYP like Pac-Man devouring other functionals) and Zhao and Truhlar
[ 45 ]. The M06-type functionals have been said to provide “better across-the-board
average performance than B3LYP.” [ 45 ]. Although for most specific tasks a better
functional than B3LYP, or even perhaps than one of the M06 family, can probably
be found, a case can be made for still using B3LYP, for the sake of “backwards
compatibility”, where the results are not simply unreasonably inaccurate. However
it seems likely that an M06 or some even newer functional will in the next few years
overcome inertia and largely replace B3LYP.
7.3 Applications of Density Functional Theory 467