A generalized surface hopping method

We present a method that allows the mixed quantum-classical dynamics of a system containing both bound and continuum quantum states to be simulated using a surface hopping method. In the limit where the quantum wave function is made up of only contributions from the continuum, this method reduces to mean-field (Ehrenfest) dynamics. We demonstrate the new technique by simulating a simple model of a quantum wave packet colliding with an adsorbed particle on a solid surface. By calculating the mixed quantum-classical evolution of this problem with both mean-field dynamics and our generalized surface hopping scheme and comparing these results to fully quantum solutions, we show that the surface hopping approach can avoid some of the inaccuracies that are common features of mean-field calculations.