Random phase approximation correlation energy using a compact representation for linear response functions: application to solids

A new approach was recently presented to compute correlation energies within the random phase approximation using Lanczos chains and an optimal basis set (Rocca 2014 J. Chem. Phys. 140 18A501). This novel method avoids the explicit calculation of conduction states and represents linear response functions on a compact auxiliary basis set obtained from the diagonalization of an approximate dielectric matrix that contains only the kinetic energy contribution. Here, we extend this formalism, originally implemented for molecular systems, to treat periodic solids. In particular, the approximate dielectric matrix used to build the auxiliary basis set is generalized to avoid unphysical negative gaps, that make the model inefficient. The numerical convergence of the method is discussed and the accuracy is demonstrated considering a set including three covalently bonded (C, Si, and SiC) and three weakly bonded (Ne, Ar, and Kr) solids.