A multiple spawning approach to tunneling dynamics

Quantum mechanical tunneling effects are investigated using an extension of the full multiple spawning (FMS) method. The FMS method uses a multiconfig urational frozen Gaussian ansatz for the wave function and it allows for dy namical expansion of the basis set during the simulation. Basis set growth is controlled by allowing this expansion only when the dynamics signals imp ending failure of classical mechanics, e.g., nonadiabatic and/or tunneling effects. Previous applications of the FMS method have emphasized the modeli ng of nonadiabatic effects. Here, a new computational algorithm that accoun ts for tunneling effects is introduced and tested against exact solution of the Schrodinger equation for two multi-dimensional model problems. The alg orithm first identifies the tunneling events and then determines the initia l conditions for the newly spawned basis functions. Quantitative agreement in expectation values, tunneling doublets and tunneling splitting is demons trated for a wide range of conditions. (C) 2000 American Institute of Physi cs. [S0021-9606(00)00614-0].