We show how the dynamically nonlocal formulation of classical nuclear motion in the
presence of quantal electronic transitions presented many years ago by P. Pechukas [Phys.
Rev. 181, 166 (1969); 181, 174 (1969)] can be localized in time using time dependent
perturbation theory to give an impulsive force which acts when trajectories hop between
electronic surfaces. The action of this impulsive force is completely equivalent to adjusting
the nuclear velocities in the direction of the nonadiabatic coupling vector so as to conserve …