DLPNO-MP2 for Periodic Systems using Megacell Embedding

TL;DR

This paper introduces Megacell-DLPNO-MP2, a new efficient method for periodic systems that uses localized Wannier functions and supercell embedding, achieving high accuracy and sub-linear scaling in correlation calculations.

Contribution

The paper develops a novel Megacell-DLPNO-MP2 approach that embeds supercell correlation within a megacell without periodic image summation, validated against existing methods.

Findings

Accurate results comparable to other DLPNO-MP2 methods.

Sub-linear scaling with supercell size demonstrated.

Successful calculations with up to 15,000 basis functions.

Abstract

We present a domain-based local pair natural orbital M{\o}ller--Plesset second order perturbation theory (DLPNO-MP2) for periodic systems, working within an LCAO formalism within the Tubromole program package. This approach, Megacell-DLPNO-MP2, embeds a supercell correlation treatment within a megacell and does not involve periodic image summation for the Coulomb integrals. Working in a basis of well-localised Wannier functions, periodicity is instead imposed through rigorous translational symmetry of Hamiltonian integrals and wavefunction parameters. The accuracy of the method is validated through comparison with a complementary periodic DLPNO-MP2 method that employs Born--von K{\'a}rm{\'a}n boundary conditions, described in paper I of this series. The PNO approximations are shown to be equivalent in the two approaches and entirely consistent with molecular DLPNO-MP2 calculations. The Megacell-DLPNO-MP2 method displays sub-linear scaling with respect to supercell size at the asymptotic limit and example calculations are presented with up to 15000 basis functions in the correlation treatment.