Reduction of finite-size effects for second-order M{\o}ller-Plesset perturbation theory with singularity subtraction

TL;DR

The paper introduces MP2 singularity subtraction (MP2SS), a method to reduce finite-size errors in periodic MP2 calculations, enabling accurate energies with coarser k-point meshes.

Contribution

A systematic singularity subtraction approach for MP2 that effectively mitigates finite-size errors in periodic systems.

Findings

MP2SS achieves millihartree accuracy with coarser k-point meshes.

Three MP2SS configurations (Gaussian, exponential, tuned) demonstrate effectiveness.

Singularity subtraction enhances the practicality of MP2 for real materials.

Abstract

Second-order Moller-Plesset perturbation theory (MP2) provides accurate correlation energies for periodic systems but suffers from finite-size errors (FSEs) that have inverse volume scaling due to the Coulomb kernel singularity in reciprocal space. This error scaling limits the routine applicability of MP2 to real materials, requiring prohibitively dense k-point meshes for convergence toward the thermodynamic limit (TDL). We introduce MP2 singularity subtraction (MP2SS), a systematic approach that applies the singularity subtraction strategy to reduce MP2 FSEs. The method employs auxiliary functions and fitting procedures that consider both the singularities present at the origin in reciprocal space and also the discontinuities in the MP2 structure factor that arise from finite k-point sampling. We present three possible MP2SS configurations (Gaussian, exponential, and tuned) which use different combinations of decay functions and demonstrate their performance for gapped systems. All MP2SS configurations consistently achieve millihartree accuracy for correlation energies at coarser k-point meshes than with no correction. Our results establish singularity subtraction as a powerful and flexible approach for mitigating finite-size errors in periodic correlation methods and provide a foundation for extending the technique to higher-order perturbation theories and other post-SCF methods.