Chemistry Reference
In-Depth Information
Becke has proposed a novel approach that formulates the dispersion
interaction in terms of the dipole moment that would be created when consid-
ering an electron and its exchange hole.
138-140
Like DFT-D, these methods
appear to be more reliable than MP2 for noncovalent interactions. Alterna-
tively, other workers
141,142
have combined DFT with symmetry-adapted per-
turbation theory (SAPT)
67
(discussed below). These DFT-SAPT approaches
evaluate the dispersion term via the frequency-dependent density susceptibility
functions of time-dependent DFT, an approach that appears to be theoretically
sound.
There have also been attempts to parameterize new functionals within
the current standard framework, up to and including hybrid, meta-generalized
gradient approximation functionals that depend on the local density, its gra-
dient, and the kinetic energy density, and that mix in Hartree-Fock exchange
(see, e.g., Refs. 143-145). Some of these functionals appear to be
improved
129,146
over the most popular currently available functionals for non-
covalent interactions between molecules that are close to each other (what
Zhao and Truhlar have called
medium-range correlation
);
146
however, with-
out truly nonlocal, nonexchange terms in the functional, such approaches are
unlikely to work at larger distances and thus would not appear to be as pro-
mising in the long run as the more generally applicable approaches discussed
above.
Semiempirical Methods and Molecular Mechanics
As discussed earlier, one of the simplest ways to correct the deficiencies
of popular density functionals for noncovalent interactions is to add an empiri-
cal dispersion term proportional to
r
6
, as is done in molecular mechanics
methods. Given that this appears to work well, one may ask about the perfor-
mance of purely empirical, molecular mechanics force-field methods. These
approaches have the advantage that they are much simpler computationally
and can be applied to systems with thousands of atoms. To date, there has
been limited testing of force-field methods against high-quality quantum
data for noncovalent interactions (in part because such benchmark data is
only now becoming available for a reasonable number of systems). AMBER
has been found to provide good results for intercalators in comparison to
MP2 data with a modified 6-31G* basis set, but only after modification of
some of the terms.
147
In tests of the benzene dimer, Macias and MacKerell
148
found binding energies within a few tenths of 1 kcal mol
1
using a refined
CHARMM force field. Similarly good results have been reported using polar-
izable force fields.
149,150
Using data from our recent work,
151
Figure 5 illustrates the performance
of some popular force-field methods (namely, CHARMM,
152
AMBER,
153
MM3,
154
and OPLS
155
) compared to our estimated CCSD(T) complete basis
set results
66
for the sandwich benzene dimer. Overall, CHARMM and OPLS
