Electron-pair densities with time-dependent quantum Monte-Carlo

TL;DR

This paper introduces a method using de Broglie-Bohm trajectories to analyze electron correlation effects in helium, demonstrating control over exchange and Coulomb holes through a simple screening parameter, applicable to ground and time-dependent states.

Contribution

It presents a novel, self-interaction-free approach employing quantum Monte Carlo and trajectory methods to study electron correlations in helium.

Findings

Exchange hole shape controlled by screening parameter

Coulomb hole results from Coulomb repulsion and quantum correlations

Method applicable to ground state and time evolution

Abstract

In this paper we use sets of de Broglie-Bohm trajectories to describe the quantum correlation effects which take place between the electrons in helium atom due to exchange and Coulomb interactions. A short-range screening of the Coulomb potential is used to modify the repulsion between the same spin electrons in physical space in order to comply with the Pauli's exclusion principle. By calculating the electron-pair density for ortho-helium we found that the shape of the exchange hole can be controlled uniquely by a simple screening parameter. For para-helium the inter-electronic distance, and hence the Coulomb hole, results from the combined action of the Coulomb repulsion and the non-local quantum correlations. In this way a robust and self-interaction-free approach is presented to find both the ground state and the time evolution of non-relativistic quantum systems.