The ground state correlation energy of the random phase approximation from a ring coupled cluster doubles approach

We present an analytic proof demonstrating the equivalence between the random phase approximation (RPA) to the ground state correlation energy and a ring-diagram simplification of the coupled cluster doubles (CCD) equations. In the CCD framework, the RPA equations can be solved in O(N(4)) computational effort, where N is proportional to the number of basis functions.