The Pair Correlation Function and the Dielectric Response in the Homogeneous Electron Gas

Recent developments in the theory of the homogeneous electron gas relate the pair correlation function g(0) at the origin to a) the static limit of the exchange and correlation effects as well as to b) an integral over frequencies of the inverse dielectric function. It is shown that any static local field correction violates at least one of both the conditions, and that from the frequency‐dependent treatment of exchange, only the variational approach satisfies both the requirements.