DLPNO-MP2 with Periodic Boundary Conditions

TL;DR

This paper introduces a periodic boundary condition extension of DLPNO-MP2, enabling efficient and accurate quantum chemical calculations for periodic systems using localized orbitals and Wannier functions.

Contribution

It develops and benchmarks a novel DLPNO-MP2 method with periodic boundary conditions based on Wannier functions, extending molecular approaches to crystalline materials.

Findings

Method is numerically stable and converges with tighter PNO thresholds.

DLPNO approximations are consistent with molecular and other periodic methods.

Provides reference MP2 energies for various 2D and 3D periodic systems.

Abstract

We present domain-based local pair natural orbital M{\o}ller--Plesset second order perturbation theory (DLPNO-MP2) with Born--von K{\'a}rm{\'a}n boundary (BvK) conditions. The approach is based on well-localised Wannier functions in a LCAO formalism and extends the molecular DLPNO-MP2 implementation Tubromole program package to periodic systems. The PNOs are formed through a PAO-OSV-PNO cascade, using BvK projected atomic orbitals and orbital specific virtuals as intermediaries in an analogous manner to the molecular scheme. Our chargeless and surface-dipole corrected local density fitting approach is shown to be numerically stable and to ensure convergent lattice summations over the periodic images for the two- and three-index Coulomb integrals. Through careful benchmarking, we show that the DLPNO approximations in the BvK-DLPNO-MP2 methods are entirely consistent with those of molecular DLPNO-MP2 calculations, and with an alternative periodic approach Megacell-DLPNO-MP2, reported in Paper II of this series. Smooth convergence to the canonical correlation energy with tightening PNO threshold is observed. Reference MP2 correlation energies are provided for a set of 2D and 3D periodic systems using a triple-zeta basis and supercell sizes up to 11$\times$11 and 7$\times$7$\times$7.