The Ground State Correlation Energy of the Random Phase Approximation from a Ring Coupled Cluster Doubles Approach

TL;DR

This paper proves that the ground state correlation energy calculated by the Random Phase Approximation (RPA) is equivalent to a simplified ring-diagram version of Coupled Cluster Doubles (CCD), with implications for computational efficiency.

Contribution

It provides an analytic proof of the equivalence between RPA and a ring CCD approach, clarifying their relationship and computational complexity.

Findings

RPA and ring CCD are mathematically equivalent for ground state correlation energy.

RPA equations can be solved with $ ext{O}(N^4)$ computational effort.

The proof enhances understanding of many-body electronic structure methods.

Abstract

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.