Total angular momentum conservation in ab initio Born-Oppenheimer molecular dynamics

We prove both analytically and numerically that the total angular momentum of a molecular system undergoing adiabatic Born-Oppenheimer dynamics is conserved only when pseudomagnetic 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 in the adiabatic limit.