# Fractional charge by fixed-node diffusion Monte Carlo

## TL;DR

This paper investigates how fixed-node diffusion Monte Carlo (FNDMC) can accurately reproduce the linear energy behavior with fractional electron numbers, demonstrating its effectiveness in electronic structure calculations involving fractional charges.

## Contribution

It shows that FNDMC, when combined with mean-field trial wave functions, can restore the piecewise linearity of energy versus fractional electron number, improving charge localization accuracy.

## Key findings

- FNDMC restores piecewise linearity in $E(N)$ for fractional charges.
- FNDMC effectively localizes charge in systems with fractional electrons.
- FNDMC outperforms other methods in charged noncovalent systems.

## Abstract

Fixed-node diffusion Monte Carlo (FNDMC) is a stochastic quantum many-body method that has a great potential in electronic structure theory. We examine how FNDMC satisfies exact constraints, linearity and derivative discontinuity of total energy $E(N)$ vs. fractional electron number $N$, if combined with mean-field trial wave functions that miss such features. H and Cl atoms with fractional charge reveal that FNDMC is well able to restore the piecewise linearity of $E(N)$. The method uses ensemble and projector ingredients to achieve the correct charge localization. Water-solvated Cl$^-$ complex illustrates superior performance of FNDMC for charged noncovalent systems.