Communication: Standard surface hopping predicts incorrect scaling for Marcus' golden-rule rate: The decoherence problem cannot be ignored

We evaluate the accuracy of Tully's surface hopping algorithm for the spin-boson model for the case of a small diabatic coupling parameter (V). We calculate the transition rates between diabatic surfaces, and we compare our results to the expected Marcus rates. We show that standard surface hopping yields an incorrect scaling with diabatic coupling (linear in V), which we demonstrate is due to an incorrect treatment of decoherence. By modifying standard surface hopping to include decoherence events, we recover the correct scaling (similar to V-2). (C) 2011 American Institute of Physics. [doi: 10.1063/1.3663870]