Total Angular Momentum Conservation in Ehrenfest Dynamics with a Truncated Basis of Adiabatic States

TL;DR

This paper demonstrates that standard Ehrenfest dynamics fails to conserve momentum with a truncated adiabatic basis, but modified equations involving the non-Abelian Berry force do ensure conservation, improving the physical accuracy of simulations.

Contribution

The paper shows that modified Ehrenfest equations with the Berry force conserve momentum, addressing limitations of standard Ehrenfest dynamics in truncated basis sets.

Findings

Standard Ehrenfest dynamics does not conserve momentum with truncated adiabatic basis.

Modified Ehrenfest equations with Berry force maintain momentum conservation.

Numerical example confirms angular momentum conservation with proper equations.

Abstract

We show that standard Ehrenfest dynamics does not conserve linear and angular momentum when using a basis of truncated adiabatic states. However, we also show that previously proposed effective Ehrenfest equations of motion[Amano2005,Krishna2007] involving the non-Abelian Berry force do maintain momentum conservation. As a numerical example, we investigate the Kramers' doublet of the methoxy radical using generalized Hartree-Fock with spin-orbit coupling and confirm angular momentum is conserved with the proper equations of motion. Our work makes clear some of the limitations of the Born-Oppenheimer approximation when using ab initio electronic structure theory to treat systems with unpaired electronic spin degrees of freedom and we demonstrate that Ehrenfest dynamics can offer much improved, qualitatively correct results.