Communication: Beyond the random phase approximation on the cheap: Improved correlation energies with the efficient radial exchange hole kernel

Abstract

The ACFD-RPA correlation energy functional has been widely applied to a variety of systems to successfully predict energy differences, and less successfully predict absolute correlation energies. Here, we present a parameter-free exchange-correlation kernel that systematically improves absolute correlation energies, while maintaining most of the good numerical properties that make the ACFD-RPA numerically tractable. The radial exchange hole kernel is constructed to approximate the true exchange kernel via a carefully weighted, easily computable radial averaging. Correlation energy errors of atoms with 2-18 electrons show a 13-fold improvement over the RPA and a threefold improvement over the related Petersilka, Gossmann, and Gross kernel, for a mean absolute error of 13 mHa or 5. The average error is small compared to all but the most difficult to evaluate kernels. van der Waals C 6 coefficients are less well predicted, but still show improvements on the RPA, especially for highly polarisable Li and Na. © 2012 American Institute of Physics.