Surface hopping with Ehrenfest excited potential

Given the exponentially scaling cost of full quantum calculations, approximations need to be employed for the simulation of the time evolution of chemical systems. We present a modified version of surface hopping that has the potential to treat larger systems. This is accomplished through an Ehrenfest-like treatment of the excited states, thereby reducing the dynamics to transitions between the ground state and a mean-field excited state. A simplified description of the excited states is achieved, while still allowing for an accurate description of disparate reaction channels. We test our mean-field approximation for the excited states on a series of model problems. Results are compared to the standard surface hopping procedure, with its explicit treatment of all excited states, and the traditional Ehrenfest approach, with its averaging together of all states. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3646920]