Multi-Determinant Wave-functions in Quantum Monte Carlo

TL;DR

This paper demonstrates that large-scale multi-determinant expansions in Quantum Monte Carlo significantly reduce fixed-node errors, achieving chemical accuracy and outperforming many traditional quantum chemistry methods in large electronic systems.

Contribution

The study systematically applies multi-determinant expansions in QMC, showing their effectiveness in reducing fixed-node errors and improving energy accuracy over standard methods.

Findings

QMC with multi-determinant wave functions achieves chemical accuracy.

QMC results outperform MP2, CCSD(T), and DFT methods.

Explicitly correlated CCSD(T) remains more accurate than QMC.

Abstract

Quantum Monte Carlo (QMC) methods have received considerable attention over the last decades due to their great promise for providing a direct solution to the many-body Schrodinger equation in electronic systems. Thanks to their low scaling with number of particles, QMC methods present a compelling competitive alternative for the accurate study of large molecular systems and solid state calculations. In spite of such promise, the method has not permeated the quantum chemistry community broadly, mainly because of the fixed-node error, which can be large and whose control is difficult. In this Perspective, we present a systematic application of large scale multi-determinant expansions in QMC, and report on its impressive performance with first row dimers and the 55 molecules of the G1 test set. We demonstrate the potential of this strategy for systematically reducing the fixed-node error in the wave function and for achieving chemical accuracy in energy predictions. When compared to traditional quantum chemistry methods like MP2, CCSD(T), and various DFT approximations, the QMC results show a marked improvement over all of them. In fact, only the explicitly-correlated CCSD(T) method with a large basis set produces more accurate results. Further developments in trial wave functions and algorithmic improvements appear promising for rendering QMC as the benchmark standard in large electronic systems.