Regularized Perturbation Theory for <i>Ab Initio</i> Solids

Second-order Møller-Plesset perturbation theory (MP2) for <i>ab initio</i> simulations of solids is often limited by divergence or overcorrelation issues, particularly in metallic, narrow-gap, and dispersion-stabilized systems. We develop and assess three regularized second-order perturbation theories: κ-MP2, σ-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 a lower cost. In rare gas solids, where MP2 already underbinds, κ-MP2 does not make the results much worse, while BW-s2 struggles. These results illustrate both the potential and limitations of regularized perturbation theory for efficient and accurate solid-state simulations. While broader testing is warranted, BW-s2(α = 2) appears particularly promising, with possible advantages over modern random-phase approximations and coupled-cluster theory.