Combining the Transcorrelated method with Full Configuration Interaction Quantum Monte Carlo: application to the homogeneous electron gas

TL;DR

This paper introduces an efficient transcorrelated Hamiltonian approach combined with FCIQMC to improve convergence in electronic structure calculations, specifically applied to the homogeneous electron gas, achieving faster basis set limit convergence.

Contribution

The paper develops a simple, low-overhead transcorrelated Hamiltonian method compatible with FCIQMC, enhancing convergence rates for electronic structure calculations.

Findings

Convergence rate improved from O(M^{-1}) to O(M^{-5/3})

Effective Hamiltonian contains only two-body operators for plane wave bases

Non-Hermitian transcorrelated Hamiltonian does not hinder FCIQMC application

Abstract

We suggest an efficient method to resolve electronic cusps in electronic structure calculations by using an effective transcorrelated Hamiltonian. This effective Hamiltonian takes a simple form for plane wave bases, containing up to two-body operators only, and its use incurs almost no additional computational overhead compared to that of the original Hamiltonian. We apply this method in combination with the full configuration interaction quantum Monte Carlo (FCIQMC) method to the homogeneous electron gas. As a projection technique, the non-Hermitian nature of the transcorrelated Hamiltonian does not cause complications or numerical difficulties for FCIQMC. The rate of convergence of the total energy to the complete basis set limit is improved from ${\cal O}(M^{-1})$ to ${\cal O}\left({M^{-5/3}}\right)$, where $M$ is the total number of orbital basis functions.