Explicitly Correlated Gaussian Basis Approach to Periodic Systems

TL;DR

This paper develops a new explicit correlated Gaussian basis method for calculating the electronic structure of periodic solids, providing closed-form matrix elements and validating the approach on a hydrogen chain.

Contribution

It introduces a formalism for periodic ECG basis functions with a generalized unfolding theorem, enabling efficient variational calculations of solid-state electronic structures.

Findings

Derived closed-form matrix element expressions for periodic ECGs.

Validated the method on an infinite hydrogen chain, matching extrapolated many-body results.

Abstract

Closed-form expressions for all matrix elements required for variational calculation of the electronic structure of periodic solids have been derived using a basis of explicitly correlated Gaussians (ECGs). Periodic basis functions are constructed by summing shifted correlated Gaussians over all composite lattice translations, where a generalized unfolding theorem reduces the resulting double lattice sum to a single sum through a unified computational framework for overlap, kinetic energy, and Coulomb potential operators. The formalism has been validated through application to an infinite one-dimensional hydrogen chain, where the ground-state energy per atom computed in the thermodynamic limit is shown to agree with finite-chain results extrapolated by other many-body methods.