Separable resolution-of-the-identity with all-electron Gaussian bases: Application to cubic-scaling RPA

We explore a separable resolution-of-the-identity (RI) formalism built on quadratures over limited sets of real-space points designed for all-electron calculations. Our implementation preserves, in particular, the use of common atomic orbitals and their related auxiliary basis sets. The setup of the present density fitting scheme, i.e., the calculation of the system specific quadrature weights, scales cubically with respect to the system size. Extensive accuracy tests are presented for the Fock exchange and MP2 correlation energies. We finally demonstrate random phase approximation (RPA) correlation energy calculations with a scaling that is cubic in terms of operations, quadratic in memory, with a small crossover with respect to our standard RI-RPA implementation.