ON THE REMOVAL OF THE EXCHANGE SINGULARITY IN EXTENDED SYSTEMS

A serious problem in the ab-initio Hartree-Fock calculation for extend ed systems is a singularity in the exchange contribution to the band e nergies (the ''exchange pathology''). In the homogeneous electron gas this pathology is exactly cancelled by the correlation contribution ar ising from the sum of all time-ordered ring diagrams (RPA approximatio n). In this article we show that this cancellation is more general and does also occur in periodically extended systems. (C) 1993 John Wiley & Sons, Inc.