DFT works with electron density, which can be measured and is easily intui-
tively grasped [ 4 ], rather than a wavefunction, a mathematical entity whose physi-
cal meaning is still controversial.
7.4.2 Weaknesses.......................................................
The exact exchange-correlation functionalEXC[r 0 ], one of the terms in the DFT
expression for the energy, is unknown, and no one knows how to fully systemati-
cally improve our approximations to it. In contrast, ab initio energies can be
systematically lowered by using bigger basis sets and by expanding the correlation
method: MP2, MP3,..., or more determinants in the CI approach. It is true that for
a particular purpose 6-311G may not be better than 6-31G, and MP3 is certainly
not necessarily better than MP2, but bigger basis sets and higher correlation levels
willeventuallyapproach an exact solution of the Schr€odinger equation. The accu-
racy of DFT is being gradually improved by modifying functionals, not according
to some grand theoretical prescription, but rather with the aid of experience and
intuition, and checking the calculations against experiment. This makes DFT
philosophically somewhat semiempirical. Some functionals contain parameters
which must be fitted to experiment; these methods are even more distinctly empiri-
cal. Since the functionals are not based purely on fundamental theory, one should be
cautious about applying DFT to very novel molecules. Of course the semiempirical
character of current DFT is not a fundamental feature of the basic method, but arises
only from our ignorance of the exact exchange-correlation functional. Because our
functionals are only approximate, DFT as used today is not variational (the calcu-
lated energy could be lower than the actual energy).
DFT is not as accurate as the highest-level ab initio methods, like QCISD(T) and
CCSD(T) (but it can handle much bigger molecules than can these methods). Even
gradient-corrected functionals apparently were unable to handle van der Waals
interactions [ 167 ], although they did give good energies and structures for hydro-
gen-bonded species [ 168 ], but recent progress in treating van der Waals and other
weak interactions is encouraging [ 44 , 45 ].
DFT today is mainly a ground-state theory, although ways of applying it to
excited states are being developed.
7.5 Summary................................................................
Density functional theory is based on the two Hohenberg–Kohn theorems, which
state that the ground-state properties of an atom or molecule are determined by its
electron density function, and that a trial electron density must give an energy
greater than or equal to the true energy. Actually, the latter theorem is true only if
the exact functional (see below) is used; with the approximate functionals in use
510 7 Density Functional Calculations