Essentials of Computational Chemistry

8.5 ADVANTAGES AND DISADVANTAGES OF DFT COMPARED TO MO THEORY 271
orbitals. Such dependence re-introduces a self-consistency requirement into the minimization
of the energy from Eq. (8.39), and this approach is called self-consistent charge densityfunctional
tight-binding (SCC-DFTB) theory. Thus, for a realistic representation of charge
redistribution, one must sacrifice the higher efficiency of DFTB for an SCF approach. Nevertheless,
SCC-DFTB is about as fast as a semiempirical NDDO model and many promising
applications have begun to appear. For example, Elstner et al. (2003) found SCC-DFTB to
compare favorably to B3LYP and MP2 calculations with the 6-311+G(d,p) basis set for
structural and energetic properties associated with biological model systems coordinating
zinc. One feature requiring further attention, however, is that in very large molecules like
biopolymers there are likely to be non-bonded interactions, e.g., dispersion, between different
sections of the molecule. Dispersion is not well treated by SCC-DFTB; in a QM MD study
of the protein crambin, Liu et al. found that inclusion of an ad hoc scaled r −6 potential
between non-bonded atoms (i.e., the attractive portion of a Lennard-Jones potential, cf. Eq.
(2.14)) was required to maintain a structure in acceptable agreement with experiment.
8.5 Advantages and Disadvantages of DFT Compared
to MO Theory
Since 1990 there has been an enormous amount of comparison between DFT and alternative
methods based on the molecular wave function. The bottom line from all of this work is
that, as a rule, DFT is the most cost-effective method to achieve a given level of accuracy,
sometimes by a very wide margin. There are, however, significant exceptions to this rule,
deriving either from inadequacies in modern functionals or intrinsic limitations in the KS
approach for determining the density. This section describes some of these cases.
8.5.1 Densities vs. Wave Functions
The most fundamental difference between DFT and MO theory must never be forgotten: DFT
optimizes an electron density while MO theory optimizes a wave function. So, to determine a
particular molecular property using DFT, we need to know how that property depends on the
density, while to determine the same property using a wave function, we need to know the
correct quantum mechanical operator. As there are more well-characterized operators then
there are generic property functionals of the density, wave functions clearly have broader
utility. As a simple example, consider the total energy of interelectronic repulsion. Even if
we had the exact density for some system, we do not know the exact exchange-correlation
energy functional, and thus we cannot compute the exact interelectronic repulsion. However,
with the exact wave function it is a simple matter of evaluating the expectation value for
the interelectronic repulsion operator to determine this energy,
Eee =
1
rij
(8.43)
where i and j run over all electrons.
i