Frozen-orbital and downfolding calculations with auxiliary-field quantum Monte Carlo

TL;DR

This paper introduces frozen-orbital and downfolding techniques within auxiliary-field quantum Monte Carlo to improve computational efficiency and accuracy in electronic structure calculations, especially for heavy atoms and extended systems.

Contribution

It presents a novel implementation of frozen-orbital and downfolding approximations in AFQMC, enabling systematic reduction of computational cost and error in electronic structure simulations.

Findings

Efficient elimination of core electrons in AFQMC calculations.

Inclusion of scalar relativistic effects via Douglas-Kroll-Hess theory.

Systematic downfolding of high-energy states to low-energy models.

Abstract

We describe the implementation of the frozen-orbital and downfolding approximations in the auxiliary-field quantum Monte Carlo (AFQMC) method. These approaches can provide significant computational savings compared to fully correlating all the electrons. While the many-body wave function is never explicit in AFQMC, its random walkers are Slater determinants, whose orbitals may be expressed in terms of any one-particle orbital basis. It is therefore straightforward to partition the full N-particle Hilbert space into active and inactive parts to implement the frozen-orbital method. In the frozen-core approximation, for example, the core electrons can be eliminated in the correlated part of the calculations, greatly increasing the computational efficiency, especially for heavy atoms. Scalar relativistic effects are easily included using the Douglas-Kroll-Hess theory. Using this method, we obtain a way to effectively eliminate the error due to single-projector, norm-conserving pseudopotentials in AFQMC. We also illustrate a generalization of the frozen-orbital approach that downfolds high-energy basis states to a physically relevant low-energy sector, which allows a systematic approach to produce realistic model Hamiltonians to further increase efficiency for extended systems.