Introduction

Exchange-correlation functionals are often tested by systematic comparison of computed total energies with high-quality experimental data. The most common test set used for such studies [155,98,100,106] is the G2 set of atomization energies, ionization potentials, electron affinities and proton affinities [52]. These tests showed a significantly improved agreement with experiment by the introduction of local density gradients into the functionals. Recently, a portion of the Fock exchange has been included with the exchange functional [119]. With adjustment of some of the parameters involved, the mean absolute deviations between calculation and experiment for chemical energetics begin to approach that for G2 theory.

This chapter uses the G2 experimental data to examine some of the common functionals in use today. This is carried out with three main objectives in mind. Firstly, the emphasis on empirical parameterization is increased. Most previous functionals have first been constrained to satisfy certain limiting conditions, for example the correct behaviour for the uniform electron gas and the scaling at large distances, and then use parametization for the middle ranges. By removing these constraints a functional of high practical value may be attainable. The results may also give some indication of the changes to functionals that are implied by the experimental data, and thus point the way for future functional improvements.

Previously it has been implicitly assumed that a functional designed to be optimal for large basis sets will be equally suitable for small basis set calculations. In fact, E. Bright Wilson's argument (see section 2.2) holds for the density from a small basis set, as well as an infinite one. Yet one would expect the ultimate functionals for the differing basis sets to be quite different. A functional designed for smaller basis sets would also have a high practical value as it would allow large systems (which require small basis sets) to be studied more accurately.

The third objective is to examine the necessity of including Fock exchange in order to obtain good agreement with experiment. Becke has alleged that ``a small exact-exchange component is a natural and necessary constituent of any exchange-correlation approximation aiming for accurate molecular energetics'' [119]. However, doing so introduces non-local effects and consequent computational complications [157,158], and should therefore only be included if it is really needed.