Energy and variance optimization of many body wave functions

TL;DR

This paper introduces a simple, robust method for optimizing many-body wave functions by reducing statistical fluctuations, demonstrated on molecules like NO2 and decapentaene, outperforming traditional variance minimization techniques.

Contribution

A novel optimization approach that improves the efficiency of parameter tuning in many-body wave functions by modifying the Hessian to reduce statistical noise.

Findings

Effective in optimizing complex Jastrow factors

Outperforms variance minimization methods

Applicable to large molecular systems

Abstract

We present a simple, robust and efficient method for varying the parameters in a many-body wave function to optimize the expectation value of the energy. The effectiveness of the method is demonstrated by optimizing the parameters in flexible Jastrow factors, that include 3-body electron-electron-nucleus correlation terms, for the NO$_2$ and decapentaene (C$_{10}$H$_{12}$) molecules. The basic idea is to add terms to the straightforward expression for the Hessian that are zero when the integrals are performed exactly, but that cancel much of the statistical fluctuations for a finite Monte Carlo sample. The method is compared to what is currently the most popular method for optimizing many-body wave functions, namely minimization of the variance of the local energy. The most efficient wave function is obtained by optimizing a linear combination of the energy and the variance.