Ab initio computations of molecular systems by the auxiliary-field quantum Monte Carlo method

TL;DR

The paper reviews the auxiliary-field quantum Monte Carlo (AFQMC) method, highlighting its accuracy, efficiency, and recent growth in electronic structure calculations for molecules and materials.

Contribution

It provides a comprehensive introduction to AFQMC, including its variants, theoretical foundations, implementation, and applications to molecular electronic structure.

Findings

AFQMC achieves high accuracy in correlated electron systems.

The method scales favorably with system size, enabling large-scale computations.

AFQMC is highly parallelizable and suitable for high-performance computing.

Abstract

The auxiliary-field quantum Monte Carlo (AFQMC) method provides a computational framework for solving the time-independent Schroedinger equation in atoms, molecules, solids, and a variety of model systems. AFQMC has recently witnessed remarkable growth, especially as a tool for electronic structure computations in real materials. The method has demonstrated excellent accuracy across a variety of correlated electron systems. Taking the form of stochastic evolution in a manifold of non-orthogonal Slater determinants, the method resembles an ensemble of density-functional theory (DFT) calculations in the presence of fluctuating external potentials. Its computational cost scales as a low-power of system size, similar to the corresponding independent-electron calculations. Highly efficient and intrinsically parallel, AFQMC is able to take full advantage of contemporary high-performance computing platforms and numerical libraries. In this review, we provide a self-contained introduction to the exact and constrained variants of AFQMC, with emphasis on its applications to the electronic structure in molecular systems. Representative results are presented, and theoretical foundations and implementation details of the method are discussed.