  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.
