GRID METHOD FOR THE WIGNER FUNCTIONS - APPLICATION TO THE VAN-DER-WAALS SYSTEM AR-H2O

We present a method to switch back and forth between a basis set of Wigner functions and an associated three-dimensional grid of Euler angles. The grid-spectral transformation is not one to one as more grid points are used than Wigner functions, and thus departs from the Fourier method of Kosloff or the discrete variable representation method of Light and collaborators, but this extra number of grid points allows one to achieve a numerically exact integration of all the potential matrix elements in the Wigner basis set. As an example, we apply this method to the determination of the bound states of the H2O-Ar van der Waals system, already studied by Cohen and Saykally [J. Chem. Phys. 98, 6007 (1993)]. The calculation consists of coupling a Lanczos scheme with a split representation of the Hamiltonian. The iterative scheme is formulated entirely within the spectral representation in which the kinetic energy operator terms are analytic, the potential term being evaluated in the grid representation. Using the rigid rotor approximation for H2O all the J=0 bound states are obtained in a few seconds of computation time on a workstation.