Staggered mesh method for correlation energy calculations of solids: Second order M{\o}ller-Plesset perturbation theory

TL;DR

This paper introduces a staggered mesh approach for MP2 correlation energy calculations in solids, reducing finite-size errors by addressing integrand discontinuities, especially effective for low-dimensional and symmetric systems.

Contribution

The paper proposes a novel staggered mesh method that improves MP2 energy calculations by mitigating quadrature errors without additional parameters or significant computational cost.

Findings

Reduces finite-size errors in MP2 calculations.

Effective for quasi-1D, 2D, and symmetric 3D systems.

No tunable parameters needed.

Abstract

The calculation of the MP2 correlation energy for extended systems can be viewed as a multi-dimensional integral in the thermodynamic limit, and the standard method for evaluating the MP2 energy can be viewed as a trapezoidal quadrature scheme. We demonstrate that existing analysis neglects certain contributions due to the non-smoothness of the integrand, and may significantly underestimate finite-size errors. We propose a new staggered mesh method, which uses two staggered Monkhorst-Pack meshes for occupied and virtual orbitals, respectively, to compute the MP2 energy. The staggered mesh method circumvents a significant error source in the standard method, in which certain quadrature nodes are always placed on points where the integrand is discontinuous. One significant advantage of the proposed method is that there are no tunable parameters, and the additional numerical effort needed can be negligible compared to the standard MP2 calculation. Numerical results indicate that the staggered mesh method can be particularly advantageous for quasi-1D systems, as well as quasi-2D and 3D systems with certain symmetries.