Regularized Perturbation Theory for Ab initio Solids

TL;DR

This paper introduces three regularized second-order perturbation theories to improve the accuracy of ab initio solid simulations, especially addressing divergence issues in metallic and narrow-gap systems.

Contribution

It develops and evaluates three novel regularized perturbation methods, with BW-s2 showing high accuracy and potential advantages over existing approaches.

Findings

BW-s2 achieves high accuracy for cohesive energies, lattice constants, and bulk moduli.

$ appa$-MP2 maintains reasonable results in rare gas solids where MP2 underbinds.

BW-s2($$=2) shows promise over modern RPA and coupled-cluster methods.

Abstract

Second-order Moller-Plesset perturbation theory (MP2) for ab initio simulations of solids is often limited by divergence or over-correlation issues, particularly in metallic, narrow-gap, and dispersion-stabilized systems. We develop and assess three regularized second-order perturbation theories: $\kappa$-MP2, $\sigma$-MP2, and the size-consistent Brillouin-Wigner approach (BW-s2), across metals, semiconductors, molecular crystals, and rare gas solids. BW-s2 achieves high accuracy for cohesive energies, lattice constants, and bulk moduli in metals, semiconductors, and molecular crystals, rivaling or surpassing coupled-cluster with singles and doubles at lower cost. In rare gas solids, where MP2 already underbinds, $\kappa$-MP2 does not make the results much worse while BW-s2 struggles. These results illustrate both the potential and the limitations of regularized perturbation theory for efficient and accurate solid-state simulations. While broader testing is warranted, BW-s2($\alpha$ = 2) appears particularly promising, with possible advantages over modern random-phase approximations and coupled-cluster theory.