Conservation of angular momentum in direct nonadiabatic dynamics

Direct\nnonadiabatic dynamics is used to study processes involving\nmultiple electronic states from small molecules to materials. Compared\nwith dynamics with fitted analytical potential energy surfaces, direct\ndynamics is more user-friendly in that it obtains all needed energies,\ngradients, and nonadiabatic couplings (NACs) by electronic structure\ncalculations. However, the NAC that is usually used does not conserve\nangular momentum or the center of mass in widely used mixed quantum-classical\nnonadiabatic dynamics algorithms, in particular, trajectory surface\nhopping, semiclassical Ehrenfest, and coherent switching with decay\nof mixing. We show that by using a projection operator to remove the\ntranslational and rotational components of the originally computed\nNAC, one can restore the conservation.