A route to improving RPA excitation energies through its connection to equation-of-motion coupled cluster theory

TL;DR

This paper explores the theoretical connection between RPA and EOM-CC methods, establishing their equivalence under certain conditions and proposing new approximations to enhance excitation energy calculations.

Contribution

It unifies RPA and EOM-CC approaches, introduces novel approximations, and demonstrates how perturbative corrections can improve excitation energy estimates.

Findings

RPA and EOM-CC are equivalent based on ring coupled cluster doubles.

New approximations improve the accuracy of excitation energies.

Perturbative corrections significantly enhance results.

Abstract

We revisit the connection between equation-of-motion coupled cluster (EOM-CC) and random phase approximation (RPA) explored recently by Berkelbach [J. Chem. Phys. 149, 041103 (2018)] and unify various methodological aspects of these diverse treatment of ground and excited states. The identity of RPA and EOM-CC based on the ring coupled cluster doubles is established with numerical results which was proved previously on theoretical grounds. We then introduce new approximations in EOM-CC and RPA family of methods, assess their numerical performance and explore a way to reap the benefits of such a connection to improve on excitation energies. Our results suggest that addition of perturbative corrections to account for double excitations and missing exchange effects could result in significantly improved estimates.