On the Meaning of Berry Force For Unrestricted Systems Treated With Mean-Field Electronic Structure

Abstract

We show that the Berry force as computed by an approximate, mean-field electronic structure can be meaningful if properly interpreted. In particular, for a model Hamiltonian representing a molecular system with an even number of electrons interacting via a two-body (Hubbard) interaction and a spin-orbit coupling, we show that a meaningful nonzero Berry force emerges whenever there is spin unrestriction--even though the Hamiltonian is real-valued and formally the on-diagonal single-surface Berry force must be zero. Moreover, if properly applied, this mean-field Berry force yields roughly the correct asymptotic motion for scattering through an avoided crossing. That being said, within the context of a ground-state calculation, several nuances do arise as far interpreting the Berry force correctly, and as a practical matter, the Berry force diverges near the Coulson-Fisher point (which can lead to numerical instabilities). We do not address magnetic fields here.

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Cited by in corpus (3)

• Total Angular Momentum Conservation in Ab Initio Born-Oppenheimer Molecular Dynamics
• Time-Dependent Nuclear-Electronic Orbital Hartree-Fock Theory in a Strong Uniform Magnetic Field
• Mind the Gap: From Resolving Theoretical Foundations of Chiral(ity)-Induced Spin Selectivity to Pioneering Implementations in Quantum Sensing