Phase-corrected surface hopping: Correcting the phase evolution of the electronic wavefunction

In this paper, we show that a remarkably simple correction can be made to the equation of motion which governs the evolution of the electronic wavefunction over some prescribed nuclear trajectory in the fewest-switches surface hopping algorithm. This corrected electronic equation of motion can then be used in conjunction with traditional or modified surface hopping methods to calculate nonadiabatic effects in large systems. Although the correction adds no computational cost to the algorithm, it leads to a dramatic improvement in scattering probabilities for all model problems studied thus far. We show that this correction can be applied to one of Tully's original one-dimensional model problems or to a more sophisticated two-dimensional example and yields substantially greater accuracy than the traditional approach.