Correlation Energy

Abstract

Until recently the notion “ab initio calculations” was mostly understood as “ab initio SCF calculations”. As a matter of fact, prior to 1970 the calculations of correlated wave functions for polyatomic molecules were rather exclusive. The situation changed dramatically in the early seventies. Effective algorithms were developed that yield highly correlated wave functions, some of them at a cost only moderately higher than that required for the respective SCF run. So it is perhaps not too optimistic to state that also the calculations with the inclusion of (a part of) the correlation energy are becoming routine. In this chapter we attempt to survey the present state of the art. In Section 4.B. a distinction is made between the problems, where the role of the correlation energy is small and those where it is of crucial importance. As regards the calculations beyond the Hartree-Fock limit there is a large variety of computational methods. We selected those that, in our opinion, are the most suitable for practical purposes or that yield perspectives for further development. The theoretical back-round of the methods is intentionally suppressed. Instead, emphasis is laid on the fundamental idea on which the theory is based, the numerical feasibility, cost, the portion of the correlation energy recovered and reliability in chemical applications.

This chapter is based partly on the reviews of I. Hubač with one of the authors^237,238.