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 Wi gner functions and an associated three-dimensional grid of Euler angle s. The grid-spectral transformation is not one to one as more grid poi nts are used than Wigner functions, and thus departs from the Fourier method of Kosloff or the discrete variable representation method of Li ght and collaborators, but this extra number of grid points allows one to achieve a numerically exact integration of all the potential matri x elements in the Wigner basis set. As an example, we apply this metho d 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, 600 7 (1993)]. The calculation consists of coupling a Lanczos scheme with a split representation of the Hamiltonian. The iterative scheme is for mulated entirely within the spectral representation in which the kinet ic energy operator terms are analytic, the potential term being evalua ted in the grid representation. Using the rigid rotor approximation fo r H2O all the J=0 bound states are obtained in a few seconds of comput ation time on a workstation.