Chemistry Reference
In-Depth Information
near future explicitly correlated methods may be the preferred electronic struc-
ture approach for problems with large basis set requirements. Theorists have
improved the efficiency of integral evaluation,
107
allowed for the use of a dif-
ferent basis set for the resolution of the identity versus the other components
of the computation,
108,109
and reformulated the resolution of the identity to
make it more stable numerically,
110
among other achievements.
Perhaps more importantly, faster convergence to the complete basis set
limit has been observed by replacing thelinearR12termswithalternative
correlation factors that might be more complex functions of the interelectro-
nic distance.
111,112
These new approaches are called F12 methods, and
although they remain in a development and testing phase as this chapter is
being written, it is anticipated that they are likely to move into mainstream
use in only a few years. Already, MP2-R12 computations can be performed
in a number of program packages, including MOLPRO,
89
MPQC,
113
TUR-
BOMOLE,
114
and PSI.
115
As more experience is gained in benchmarking and
using R12 and F12 methods, they will become more accessible to a wider
array of users.
Density Functional Approaches
Despite its tremendous success in a wide variety of chemical applications,
density functional theory (DFT)
116,117
has not yet had much impact on studies
of weakly bound complexes. In principle, density functional theory with the
exact functional would provide exact results for any chemical system, includ-
ing van der Waals complexes. In practice, however, the Kohn-Sham formula-
tion of DFT with mainstream functionals is not capable of capturing
dispersion effects, even qualitatively.
28,118,119
This deficiency arises from the
fact that these approaches lack the long-range, nonlocal terms required to
model dispersion. This is true even of gradient-corrected functionals (which
are sometimes confusingly referred to as ''nonlocal'' functionals) because
including information about the gradient of the density does not extend the
range of electron correlations very far. Hybrid functionals include some frac-
tion of Hartree-Fock exchange,
40
which is nonlocal. However, dispersion is
related to dynamical electron correlation, not exchange, and hence hybrid den-
sity functionals also fail to include the proper physics to model dispersion
interactions.
Because DFT is so successful in other areas, and because it has become a
familiar tool to many chemists, there is a great desire to use it for studies of
noncovalent interactions, even though currently popular formulations are
really not appropriate for such studies. The reader is urged to avoid giving
in to this temptation, for the simple reason that there would be no reason to
believe the results for properties such as interaction energies or intermolecu-
lar distances. In an eye-opening study, Johnson, Wolkow, and DiLabio
119
found that out of 25 different density functionals,
all
of them were in error
