Exploiting temporal nonlocality to remove scaling bottlenecks in nonadiabatic quantum dynamics

An extension of the full multiple spawning (FMS) method for quantum non-adi abatic dynamics that capitalizes on the global nature of quantum mechanics and on the deterministic nature of the FMS method is discussed. The FMS met hod uses a classically motivated time-dependent basis set for the wave func tion and here we demonstrate that the choice of a temporally nonlocal basis set can reduce the scaling of the dominant effort in ab initio multiple sp awning from O(N-2) to O(N), where N is the number of basis functions descri bing the nuclear degrees of freedom. The procedure is applied to a two-dime nsional two electronic state model problem and we show that the temporally nonlocal basis set provides accurate expectation values and branching ratio s over a broad range of energies. (C) 1999 American Institute of Physics. [ S0021-9606(99)01409-9].