Electron corrected Lorentz forces in solids and molecules in magnetic field

TL;DR

This paper introduces a new formulation of Lorentz forces on ions in solids and molecules under magnetic fields, incorporating electronic effects via Berry curvature, suitable for first-principles molecular dynamics simulations.

Contribution

It presents a novel approach to include electronic contributions to Lorentz forces in ab-initio molecular dynamics, based on Berry curvature, for the first time.

Findings

Derived effective Lorentz forces including electronic effects.

Formulated the forces in a way suitable for density functional simulations.

Demonstrated the approach with H2 molecule dynamics in a magnetic field.

Abstract

We describe the effective Lorentz forces on the ions of a generic insulating system in an magnetic field, in the context of Born-Oppenheimer ab-initio molecular dynamics. The force on each ion includes an important contribution of electronic origin, which depends explicitly on the velocity of all other ions. It is formulated in terms of a Berry curvature, in a form directly suitable for future first principles classical dynamics simulations based {\it e.g.,} on density functional methods. As a preliminary analytical demonstration we present the dynamics of an H$_2$ molecule in a field of intermediate strength, approximately describing the electrons through Slater's variational wavefunction.