VMC Optimization of Ultra-Compact, Explicitly-Correlated Wave Functions of the Li Isoelectronic Sequence in Its Lowest 1s2s2p Quartet State

TL;DR

This paper demonstrates an efficient VMC method to optimize compact explicitly correlated wave functions for the Li isoelectronic series, achieving high accuracy with minimal parameters.

Contribution

It introduces a VMC optimization approach for explicitly correlated wave functions with ten or fewer parameters, accurately modeling the quartet state.

Findings

Wave functions satisfy cusp conditions

Reproduce at least 99.9% of exact energy

Use ten or fewer parameters for optimization

Abstract

A compact yet accurate approach for representing the wave functions of members of the He and Li isoelectronic series is using explicitly correlated wave functions. These wave functions, however, often have nonlinear forms, which make them challenging to optimize. In this work, we show how Variational Monte Carlo (VMC) can efficiently optimize explicitly correlated wave functions that accurately describe the quartet 1s2s2p state of the Li isoelectronic sequence with ten or fewer parameters. We find that our compact wave functions correctly describe cusp conditions and reproduce at least 99.9% percent of the exact energy.