Quantum Monte Carlo calculations of energy gaps from first principles

TL;DR

This paper reviews quantum Monte Carlo methods for calculating energy gaps from first principles, introduces finite-size correction schemes, and investigates the effects of backflow and multideterminant expansions on excited-state energy accuracy.

Contribution

It presents a comprehensive analysis of finite-size errors, fixed-node errors, and the use of backflow correlations in QMC excited-state calculations, advancing the methodology for accurate energy gap predictions.

Findings

Finite-size effects vary significantly in 2D materials.

Backflow transformations improve fixed-node errors in DMC gaps.

Using larger time steps reduces computational cost without sacrificing accuracy.

Abstract

We review the use of continuum quantum Monte Carlo (QMC) methods for the calculation of energy gaps from first principles, and present a broad set of excited-state calculations carried out with the variational and fixed-node diffusion QMC methods on atoms, molecules, and solids. We propose a finite-size-error correction scheme for bulk energy gaps calculated in finite cells subject to periodic boundary conditions. We show that finite-size effects are qualitatively different in two-dimensional materials, demonstrating the effect in a QMC calculation of the band gap and exciton binding energy of monolayer phosphorene. We investigate the fixed-node errors in diffusion Monte Carlo gaps evaluated with Slater-Jastrow trial wave functions by examining the effects of backflow transformations, and also by considering the formation of restricted multideterminant expansions for excited-state wave functions. For several molecules, we examine the importance of structural relaxation in the excited state in determining excited-state energies. We study the feasibility of using variational Monte Carlo with backflow correlations to obtain accurate excited-state energies at reduced computational cost, finding that this approach can be valid. We find that diffusion Monte Carlo gap calculations can be performed with much larger time steps than are typically required to converge the total energy, at significantly diminished computational expense, but that in order to alleviate fixed-node errors in calculations on solids the inclusion of backflow correlations is sometimes necessary.