Distributed approximating function approach to time-dependent wavepacket propagation in 3-dimensions: atom-surface scattering

The theoretical formalism of the distributed approximating functions (DAF) is applied to solve accurately 3D-atom-surface scattering problems. Formulated in coordinate space, the DAF approach starts from an entirely new idea: providing a “uniform” approximation everywhere to a wavepacket, and results naturally in a near-local or banded free propagator. The banded Toeplitz structure of the DAF free propagator matrix on a uniform grid makes possible the application of the most efficient codes in the matrix-vector multiplication in evolving the wavefunction of a quantum system in time, and with extremely small memory requirements. The numerical study conducted in this paper demonstrates that the DAF method outperforms the most powerful available FFT method both in CPU time and storage requirements. The DAF approach gives the same accurate results as the FFT does, and, in some cases, yields more accurate results.