The unbiased Diffusion Monte Carlo: a versatile tool for two-electron systems confined in different geometries

TL;DR

This paper demonstrates a versatile, unbiased Diffusion Monte Carlo method for accurately modeling two-electron systems in various geometries without complex guess functions, enabling adaptable and efficient simulations.

Contribution

The work introduces a simple, unbiased DMC approach that is easily adaptable to different confinement geometries for two-electron systems, enhancing computational flexibility.

Findings

Accurate results for two-electron hydrogen species in different confinements.

Method's adaptability to various geometries without complex guess functions.

Successful application to nanotube-like and octahedral confinements.

Abstract

Computational codes based on the Diffusion Monte Carlo method can be used to determine the quantum state of two-electron systems confined by external potentials of various nature and geometry. In this work, we show how the application of this technique in its simplest form, that does not employ complex analytic guess functions, allows to obtain satisfactory results and, at the same time, to write programs that are readily adaptable from one type of confinement to another. This adaptability allows an easy exploration of the many possibilities in terms of both geometry and structure of the system. To illustrate these results, we present calculations in the case of two-electron hydrogen-based species (H$_2$ and H$_3^+$) and two different types of confinement, nanotube-like and octahedral crystal-field.