STEREODIRECTED DISCRETE BASES IN HINDERED ROTOR PROBLEMS - ATOM DIATOM AND PENDULAR STATES

The stereodirected discrete basis method is applied to the solution of hindered rotor problems. The assumptions of the method are presented along with its connections with finite basis representations (FBR), discrete variable representations (DVR), and finite difference (FD) approximations. The convergence of the energy eigenvalues is determined for four model atom-diatom problems and one pendular state problem. The method has an error that decreases as N(b)-2 where N(b) is the size of the discrete basis set. The discrete eigenvectors that result from the method have simple orthogonality relationships and use in matrix element calculations. The discrete (\nuOMEGA]) basis needs more functions for convergence than the helicity (\jOMEGA]) basis, but the discrete basis calculations are easier because the Hamiltonian matrix is banded, no integrals over the potential are required, and only N(b) scalar potential evaluations are needed. For coupled-channel atom-rotor problems the Hamiltonian matrix is heptadiagonal, and for the coupled-states approximation the Hamiltonian matrix is tridiagonal. Angular truncation can also be used to accelerate the discrete basis calculations.