Density Functional Theory, Its Gaussian Implementation and Applications to Complex Systems

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Several chapters of this book are devoted to the problem of electronic correlation. There is no doubt that most of the important chemical phenomena, like chemical bonding, bond dissociation and reactivity, require treatment of this correlation at a high level. The approach we are going to discuss in this chapter, the density functional theory (DFT) also deals with correlation. However, while the conventional quantum chemical methods evaluate the correlation energy through the many-electron wave function, in DFT the electron density is the fundamental object. The computational effort involved with the conventional methods, such as configuration interaction (CI) and many-body perturbation theory, scales as N 5 and higher, where N is the number of electrons involved. The methods of DFT can be optimized to scale as N 3 or even better. The final working DFT equations resemble those involved in Hartree-Fock (HF) (or, really, Hartree) theory. At the same time the results are usually better than those at the HF level and often are comparable to CI results. This allows rapid treatment of larger systems involving heavy elements, on which the practical success of DFT is based. CI and related techniques some times meet convergence problems which are not yet fully understood. For example, the description of a “simple” molecule like Cr2 is still a matter of dispute. It has been estimated that in order to obtain a reasonable description it would be necessary to have a CI expansion of several milion terms1. within the framework of DFT with much less effort 1,2.