Explicitly correlated plane waves: Accelerating convergence in periodic wavefunction expansions

TL;DR

This paper explores the use of explicitly correlated plane wave basis functions, including a novel Yukawa-Coulomb factor, to accelerate convergence in periodic wavefunction expansions at the MP2 level, demonstrated on a homogeneous electron gas model.

Contribution

It introduces a new Yukawa-Coulomb correlation factor and demonstrates its effectiveness in improving convergence over traditional methods.

Findings

Yukawa-Coulomb factor enhances convergence of correlation energies.

Plane waves combined with short-range geminals provide a rapidly converging basis.

Method extends the applicability of wavefunction expansions in periodic systems.

Abstract

We present an investigation into the use of an explicitly correlated plane wave basis for periodic wavefunction expansions at the level of second-order M{\o}ller-Plesset perturbation theory (MP2). The convergence of the electronic correlation energy with respect to the one-electron basis set is investigated and compared to conventional MP2 theory in a finite homogeneous electron gas model. In addition to the widely used Slater-type geminal correlation factor, we also derive and investigate a novel correlation factor that we term Yukawa-Coulomb. The Yukawa-Coulomb correlation factor is motivated by analytic results for two electrons in a box and allows for a further improved convergence of the correlation energies with respect to the employed basis set. We find the combination of the infinitely delocalized plane waves and local short-ranged geminals provides a complementary, and rapidly convergent basis for the description of periodic wavefunctions. We hope that this approach will expand the scope of discrete wavefunction expansions in periodic systems.