On the potentially transformative role of auxiliary-field quantum Monte Carlo in quantum chemistry: A highly accurate method for transition metals and beyond

Approximate solutions to the ab initio electronic structure problem have been a focus of theoretical and computational chemistry research for much of the past century, with the goal of predicting relevant energy differences to within “chemical accuracy” (1 kcal/mol). For small organic molecules, or in general for weakly correlated main group chemistry, a hierarchy of single-reference wavefunction methods have been rigorously established spanning perturbation theory and the coupled cluster (CC) formalism. For these systems, CC with singles, doubles, and perturbative triples (CCSD(T)) is known to achieve chemical accuracy, albeit at O(N^7) computational cost. In addition, a hierarchy of density functional approximations of increasing formal sophistication, known as Jacob's ladder, has been shown to systematically reduce average errors over large data sets representing weakly-correlated chemistry. However, the accuracy of such computational models is less clear in the increasingly important frontiers of chemical space including transition metals and f-block compounds, in which strong correlation can play an important role in reactivity. A stochastic method, phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC), has been shown capable of producing chemically accurate predictions even for challenging molecular systems beyond the main-group, with relatively low O(N^3-N^4) cost and near-perfect parallel efficiency. Herein we present our perspectives on the past, present, and future of the ph-AFQMC method. We focus on its potential in transition metal quantum chemistry to be a highly accurate, systematically-improvable method which can reliably probe strongly correlated systems in biology and chemical catalysis, and provide reference thermochemical values (for future development of density functionals or interatomic potentials) when experiments are either noisy or absent. Finally, we discuss the present limitations of the method, and where we expect near term development to be most fruitful.