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 $\mathcal{O}(N^4)$ computational effort, where $N$ is proportional to the number of basis functions. 
Gustavo E. Scuseria and Thomas M. Henderson and Danny C. Sorensen