  We explore a separable resolution-of-the-identity 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 set up 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.
