Optimal representation for semiclassical surface hopping methods

A semiclassical surface hopping expansion of the propagator is developed for a general representation of the "fast'' variable quantum states. The representation can be the adiabatic or diabatic representation or any representation between these two. A particular representation is defined, which is optimal in the sense that it minimizes the integrated interstate coupling. The coupling is integrated over a suitable classical trajectory in this definition. Calculations for a simple one-dimensional curve crossing model problem show that the use of this optimal representation can significantly reduce the importance of multihop terms in the expansion. An approximation to this optimal representation is proposed, which is much simpler to implement numerically. Calculations for the model curve crossing problem demonstrate that this approximate optimal representation provides integrated couplings that are very close to those obtained for the optimal representation. These results suggest that this approximate optimal representation provides a computationally attractive representation for use with semiclassical surface hopping methods, when studying problems with curve crossings. (C) 1999 American Institute of Physics. [S0021-9606(99)01109-5].