Page 236 - Strategies and Applications in Quantum Chemistry From Molecular Astrophysics to Molecular Engineer

How Much Correlation Can We Expect to Account for in Density Functional
Calculations ? Case Studies of Electrostatic Properties of Small Molecules

J. WEBER, P. JABER, P. GULBINAT and P.-Y. MORGANTINI
Université de Genève, Département of Chimie Physique, 30 quai Ernest-Ansermet,
1211 Genève 4, Switzerland

1. Introduction
It is well known that the traditional ab initio techniques of quantum chemistry are able to
incorporate many-electron effects through expansions of the many-particle wavefunction,
which leads in principle to systematic procedures to take correlation effects into account.
However, the computational challenge issued by these post-Hartree-Fock calculations is
generally a formidable task, as for both variational configuration interaction (CI) and size-
consistent many-body perturbation theory (MBPT) techniques, the amount of computations
required to reach chemical accuracy is enormous. In addition, these methods, and in
particular those of multiconfiguration self-consistent field (MCSCF) and CI type, are
sophisticated and in virtually no case they can be used as black boxes. Indeed, the problem
is that, unless the system investigated is small enough so as to allow for a full CI treatment,
truncated CI expansions have to be used and, according to the qualified statement of
Berthier et al. [1], "the choice of an appropriate molecular orbital (MO) basis set in then a
considerable concern".

On the other hand, it is indispensable for most molecular properties to account for
correlation effects so as to achieve quantitative, or even sometimes qualitative, predictions
as the neglect of instantaneous repulsions introduces an error which may be significant [2].
Fortunately, substantial efforts have been made in the last twenty years in order to develop
correlated quantum chemical methods and there is ample choice among them today for a
given problem. For example, most of the popular semiempirical models offer the possibility
to include some CI using, e.g., the Pople-Pariser-Parr formalism, as implemented in the
AMPAC series of programs [3]. As far as they are concerned, the techniques based on
density functional theory (DFT) are able to incorporate some treatment of correlation
through the energy functional used to solve the Kohn-Sham equations [4,5]. However, the
degree of correlation introduced in these methods depends on the form of the so-called
exchange-correlation potential and it is difficult to estimate how much correlation is present
in the results unless performing comparative ab initio calculations. As to the latter ones,
they have the advantage to allow in principle for a progressively increasing treatment of
correlation through enlarging the N-electron basis set in CI calculations or through the
introduction of higher orders of perturbation in MBPT studies. It is thus possible to rather
accurately quantify (generally in percent) how much correlation is introduced in, e.g., a CI
study, by comparing the calculated correlation energy with the difference between Hartree-
Fock and "experimental" (when available), or full CI with a very large one-electron basis
219
Y. Ellinger and M. Defranceschi (eds.), Strategies and Applications in Quantum Chemistry, 219–228.
© 1996 Kluwer Academic Publishers. Printed in the Netherlands.