Making the random phase approximation to electronic correlation accurate

We show that the inclusion of second-order screened exchange to the random phase approximation allows for an accurate description of electronic correlation in atoms and solids clearly surpassing the random phase approximation, but not yet approaching chemical accuracy. From a fundamental point of view, the method is self-correlation free for one-electron systems. From a practical point of view, the approach yields correlation energies for atoms, as well as for the jellium electron gas within a few kcal/mol of exact values, atomization energies within typically 2-3 kcal/mol of experiment, and excellent lattice constants for ionic and covalently bonded solids (0.2% error). The computational complexity is only O(N(5)), comparable to canonical second-order Møller-Plesset perturbation theory, which should allow for routine calculations on many systems.