  We prove both analytically and numerically that the total angular momentum of
a molecular system undergoing adiabatic Born-Oppenheimer dynamics is conserved
only when pseudo-magnetic Berry forces are taken into account. This finding
sheds light on the nature of Berry forces for molecular systems with spin-orbit
coupling and highlights how ab initio Born-Oppenheimer molecular dynamics
simulations can successfully capture the entanglement of spin and nuclear
degrees of freedom as modulated by electronic interactions.
