Equivalence of Particle-Particle Random Phase Approximation Correlation Energy and Ladder-Coupled-Cluster-Double

TL;DR

This paper proves analytically and demonstrates numerically that the particle-particle RPA correlation energy is equivalent to ladder-CCD energy, linking two important methods in quantum chemistry.

Contribution

It establishes the theoretical equivalence between pp-RPA and ladder-CCD correlation energies, providing a foundation for future research.

Findings

pp-RPA and ladder-CCD reduce to identical algebraic equations

Numerical results show correlation energy differences are largely canceled in reaction energies

The proof assumes the stability of the pp-RPA equation

Abstract

We present an analytical proof and numerical demonstrations of the equivalence of the correlation energy from particle-particle random phase approximation (pp-RPA) and ladder-couple-cluster-doubles (ladder-CCD). These two theories reduce to the identical algebraic matrix equation and correlation energy expressions, under the assumption that the pp-RPA equation is stable. The numerical examples illustrate that the correlation energy missed by pp-RPA in comparison with couple-cluster single and double is largely canceled out when considering reaction energies. This theoretical connection will be beneficial to future pp-RPA studies based on the well established couple cluster theory.