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

## TL;DR

This paper introduces a correlated sampling method for Auxiliary-Field Quantum Monte Carlo that significantly improves efficiency in calculating energy differences, enabling accurate chemical property predictions with reduced computational cost.

## Contribution

The authors develop a correlated sampling approach for AFQMC that enhances efficiency and accuracy in computing energy differences relevant to chemical transformations.

## Key findings

- Correlated sampling accelerates AFQMC calculations by reducing statistical errors.
- The method achieves chemical accuracy in ionization potentials, free energies, and bond dissociation energies.
- Speed-up factors of 24 to 55 times are observed for various chemical properties.

## 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 fixed-geometry 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.