  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.
