Ab initio computations of molecular systems by the auxiliary‐field quantum Monte Carlo method - Motta, Mario; Zhang, Shiwei (Wiley interdisciplinary reviews. Computational molecular science, 2018)
The auxiliary‐field quantum Monte Carlo (AFQMC) method provides a computational framework for solving the time‐independent Schrödinger 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 nonorthogonal 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 of molecular systems. Representative results are presented, and theoretical foundations and implementation details of the method are discussed. This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods Structure and Mechanism > Computational Materials Science Computer and Information Science > Computer Algorithms and Programming Pictorial illustration of the auxiliary‐field quantum Monte Carlo (AFQMC) algorithm, and of its beyond‐mean‐field nature. Left: independent‐electron methods provide an approximation of the ground state wave function through a deterministic evolution in a manifold (gray surface) of Slater determinants. Right: AFQMC represents the many‐body ground state as a stochastic linear combination of Slater determinants by mapping the electron–electron interaction onto a fluctuating external potential, and the imaginary‐time evolution onto open‐ended random walks in the non‐orthogonal manifold of Slater determinants.