Screened exchange corrections to the random phase approximation from many-body perturbation theory

TL;DR

This paper introduces a computationally efficient exchange correction to the RPA based on many-body perturbation theory, improving correlation energy estimates and pair densities in electron systems.

Contribution

A new exchange correction method for RPA that reduces EPV contributions with low computational complexity, enhancing accuracy in electron correlation calculations.

Findings

Improves correlation energy accuracy comparable to SOSEX variants.

Enhances pair density near electron coalescence in the uniform electron gas.

Maintains low computational complexity and memory requirements.

Abstract

The random phase approximation (RPA) systematically overestimates the magnitude of the correlation energy and generally underestimates cohesive energies. This originates in part from the complete lack of exchange terms, which would otherwise cancel Pauli exclusion principle violating (EPV) contributions. The uncanceled EPV contributions also manifest themselves in form of an unphysical negative pair density of spin-parallel electrons close to electron-electron coalescence. We follow considerations of many-body perturbation theory to propose an exchange correction that corrects the largest set of EPV contributions while having the lowest possible computational complexity. The proposed method exchanges adjacent particle/hole pairs in the RPA diagrams, considerably improving the pair density of spin-parallel electrons close to coalescence in the uniform electron gas (UEG). The accuracy of the correlation energy is comparable to other variants of Second Order Screened Exchange (SOSEX) corrections although it is slightly more accurate for the spin-polarized UEG. Its computational complexity scales as $\mathcal O(N^5)$ or $\mathcal O(N^4)$ in orbital space or real space, respectively. Its memory requirement scales as $\mathcal O(N^2)$.