Laplace transformed MP2 for three dimensional periodic materials using stochastic orbitals in the plane wave basis and correlated sampling

TL;DR

This paper introduces a stochastic, Laplace transformed MP2 algorithm using plane wave basis and correlated sampling for efficient, high-accuracy correlation energy calculations in three-dimensional periodic materials.

Contribution

It develops a novel stochastic LTMP2 method with correlated sampling that reduces computational cost and improves accuracy for periodic systems.

Findings

Achieves sub-meV accuracy in correlation energy calculations.

Demonstrates favorable scaling behavior of sample variance.

Significantly accelerates convergence with correlated sampling.

Abstract

We present an implementation and analysis of a stochastic high performance algorithm to calculate the correlation energy of three dimensional periodic systems in second-order M{\o}ller-Plesset perturbation theory (MP2). In particular we measure the scaling behavior of the sample variance and probe whether this stochastic approach is competitive if accuracies well below 1 meV per valence orbital are required, as it is necessary for calculations of adsorption, binding, or surface energies. The algorithm is based on the Laplace transformed MP2 (LTMP2) formulation in the plane wave basis. The time-dependent Hartree-Fock orbitals, appearing in the LTMP2 formulation, are stochastically rotated in the occupied and unoccupied Hilbert space. This avoids a full summation over all combinations of occupied and unoccupied orbitals, as inspired by the work of D. Neuhauser, E. Rabani, and R. Baer in J. Chem. Theory Comput. 9, 24 (2013). Additionally, correlated sampling is introduced, accelerating the statistical convergence significantly.