Optimisation of quantum Monte Carlo wave function: steepest descent method

TL;DR

This paper demonstrates that the steepest descent method effectively optimizes quantum Monte Carlo wave functions for various atoms, achieving results comparable to diffusion Monte Carlo and exact solutions.

Contribution

It introduces the application of the steepest descent method for wave function optimization in quantum Monte Carlo, with analytical derivatives and successful results for multiple atoms.

Findings

Steepest descent successfully minimizes wave functions.

Ground state energies agree with DMC and exact results.

Method applicable to multiple atomic systems.

Abstract

We have employed the steepest descent method to optimise the variational ground state quantum Monte Carlo wave function for He, Li, Be, B and C atoms. We have used both the direct energy minimisation and the variance minimisation approaches. Our calculations show that in spite of receiving insufficient attention, the steepest descent method can successfully minimise the wave function. All the derivatives of the trial wave function respect to spatial coordinates and variational parameters have been computed analytically. Our ground state energies are in a very good agreement with those obtained with diffusion quantum Monte Carlo method (DMC) and the exact results.