The finite basis representation as the primary space in multidimensional pseudospectral schemes

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Abstract
We emphasize the merits and the superiority of the most complete nondirect product representation in non-Cartesian coordinates. Beyond the proper choice of basis set we show how to further optimize the spectral range in multidimensional calculations. The combined use of a fully pseudospectral scheme and the finite basis representation (FBR) as the primary space ensures the smallest prefactor in the semilinear scaling law of the Hamiltonian evaluation with respect to the FBR size. In the context of scattering simulations we present a simplified asymptotic treatment which increases the efficiency of the FBR-based pseudospectral approach. An optimal 6D pseudospectral scheme is proposed to treat the vibrational excitation and/or dissociation of a diatomic molecule scattering from a rigid, corrugated surface, and serves to illustrate our discussion. A 5D numerical demonstration is made for the rotationally inelastic scattering of N2 from a model LiF surface.