Chemical Transformations Approaching Chemical Accuracy via Correlated Sampling in Auxiliary-Field Quantum Monte Carlo

Abstract

The exact and phaseless variants of Auxiliary-Field Quantum Monte Carlo (AFQMC) have been shown to be capable of producing accurate ground-state energies for a wide variety of systems including those which exhibit substantial electron correlation effects. The computational cost of performing these calculations has to date been relatively high, impeding many important applications of these approaches. Here we present a correlated sampling methodology for AFQMC which relies on error cancellation to dramatically accelerate the calculation of energy differences of relevance to chemical transformations. In particular, we show that our correlated sampling-based AFQMC approach is capable of calculating redox properties, deprotonation free-energies, and hydrogen abstraction energies in an efficient manner without sacrificing accuracy. We validate the computational protocol by calculating the ionization potentials and electron affinities of the atoms contained in the G2 Test Set, and then proceed to utilize a composite method, which treats fixedgeometry processes with correlated sampling-based AFQMC and relaxation energies via MP2, to compute the ionization potential, deprotonation free-energy, and the O-H bond disocciation energy of methanol, all to within chemical accuracy. We show that the efficiency of correlated sampling relative to uncorrelated calculations increases with system and basis set size, and that correlated sampling greatly reduces the required number of random walkers to achieve a target statistical error. This translates to CPU-time speed-up factors of 55, 25, and 24 for the the ionization potential of the K atom, the deprotonation of methanol, and hydrogen abstraction from the O-H bond of methanol, respectively. We conclude with a discussion of further efficiency improvements that may open the door to the accurate description of chemical processes in complex systems.

On Achieving High Accuracy in Quantum Chemical Calculations of 3d Transition Metal-Containing Systems: A Comparison of Auxiliary-Field Quantum Monte Carlo with Coupled Cluster, Density Functional Theory, and Experiment for Diatomic Molecules

“…For the isolated ligands, we confirmed the convergence of the energy from ph-AFQMC/PC calculations with increasingly large active space sizes, and found that in all cases except for the sulfur and fluorine atoms, CASSCF did not lower the energy by more than a milli-Hartree with respect to unrestricted Hartree Fock (UHF). Hence, we use UHF for these cases, CASSCF(6e,8o) for S, and CASSCF(7e,16o) for F. The latter is consistent with our previous work, 46 in which we found that an active space of this size was necessary to obtain chemically accurate electron affinities for the F atom.…”

“…Recently we have introduced a correlated sampling (CS) approach for quantities involving energy differences which is capable of reducing computational prefactors 46 and in some cases the severity of the phaseless approximation. 43 In this section, we show that significant reductions in statistical errors are obtained not only for hydrogen abstraction reactions, as shown previously, but also for bond breaking events between a transition metal and a heavier ligand atom.…”

“…The first of these is the use of correlated sampling. 46 With correlated sampling, energy differences between two states are computed by sampling both states with the same set of auxiliary fields, leading to significant cancellation of error. This enables energy differences to be computed in a much shorter amount of propagation time and with fewer samples than would normally be required to obtain a given statistical error.…”

“…46 Furthermore, these measurements at short propagation times are often converged before the full accumulation of the errors associated with the phaseless approximation, thus yielding results that are closer to the unbiased, exact value. 46 The second advance is the development of an efficient implementation of ph-AFQMC on graphical processing units (GPUs), including the use of the Sherman-Morrison-Woodbury (SMW) algorithm to accelerate calculations using multideterminental trial wavefunctions. 43 For problems where correlated sampling is applicable, the combination of these two techniques can reduce the computational effort by more than two orders of magnitude, enabling the method to be applied to larger systems, and also to substantially larger data sets.…”

An auxiliary-Field quantum Monte Carlo perspective on the ground state of the dense uniform electron gas: An investigation with Hartree-Fock trial wavefunctions

“…On the other hand, the cost of achieving the same statistical error for larger systems adds an extra O(N ) to the computational cost of ph-AFQMC. This extra cost for sampling may be avoided by the correlated sampling technique 119,120 , but here we instead compare the total energy per electron. This metric is well-suited for ab-initio solids (or extended systems) in general.…”