Random-phase-approximation correlation method including exchange interactions

Two random-phase-approximation correlation methods are introduced that take into account exchange interactions. The first one, termed RPAX, is obtained from a simple modification of the ring coupled-cluster doubles amplitude equation, while the second, termed RPAX2, is based on the first method using a slightly modified update equation for the amplitudes. It is shown that this second RPAX2 method can be implemented with a computational algorithm that scales only with the fifth power of the molecular size with the aid of density fitting or the Cholesky decomposition of two-electron integrals. It is thus not much more costly than standard second-order perturbation theory methods and can be applied to quite large molecular systems. Moreover, numerical tests for chemical reaction energies and intermolecular interaction energies have shown that the RPAX2 method, if based on a Perdew-Burke-Ernzerhof exchange Kohn-Sham reference determinant, yields results which are very close to coupled-cluster with single, double, and perturbative triple excitations reference results.