Multi-Determinant Wave-functions in Quantum Monte Carlo

Abstract

Quantum Monte Carlo methods have received considerable attention over the last decades due to the great promise they have for the direct solution to the many-body Schrodinger equation for electronic systems. Thanks to a low scaling with number of particles, they present one of the best alternatives in the accurate study of large systems and solid state calculations. In spite of such promise, the method has not become popular in the quantum chemistry community, mainly due to the lack of control over the fixed-node error which can be large in many cases. In this article we present the application of large multi-determinant expansions in quantum Monte Carlo, studying its performance with first row dimers and the 55 molecules of the G1 test set. We demonstrate the potential of the wave-function to systematically reduce the fixed-node error in the calculations, achieving chemical accuracy in almost all cases studied. When compared to traditional methods in quantum chemistry, the results show a marked improvement over most methods including MP2, CCSD(T) and DFT with various functionals; in fact the only method able to produce better results is the explicitly-correlated CCSD(T) method with a large basis set. With recent developments in trial wave functions and algorithmic improvements in Quantum Monte Carlo, we are quickly approaching a time where the method can become the standard in the study of large molecular systems and solids.