A pseudospectral algorithm for the computation of transitional-mode eigenfunctions in loose transition states. II. Optimized primary and grid representations

A highly optimized pseudospectral algorithm is presented for effecting the exact action of a transitional-mode Hamiltonian on a state vector within th e context of iterative quantum dynamical calculations (propagation,diagonal ization, etc.). The method is implemented for the benchmark case of singlet dissociation of ketene. Following our earlier work [Chem. Phys. Lett. 243, 359 (1995)] the action of the kinetic energy operator is performed in a ba sis consisting of a direct product of Wigner functions. We show how one can compute an optimized (k, Omega) resolved spectral basis by diagonalizing a reference Hamiltonian (adapted from the potential surface at the given cen ter-of-mass separation) in a basis of Wigner functions. This optimized spec tral basis then forms the working basis for all iterative computations. Two independent transformations from the working basis are implemented: the fi rst to the Wigner representation which facilitates the action of the kineti c energy operator and the second to an angular discrete variable representa tion (DVR) which facilitates the action of the potential energy operator. T he angular DVR is optimized in relation to the reference Hamiltonian by sta ndard procedures. In addition, a scheme which exploits the full sparsity of the kinetic energy operator in the Wigner representation has been devised which avoids having to construct full-length vectors in the Wigner represen tation. As a demonstration of the power and efficiency of this algorithm, a ll transitional mode eigenstates lying between the potential minimum and 10 0 cm(-1) above threshold have been computed for a center-of-mass separation of 3 Angstrom in the ketene system. The performance attributes of the earl ier primitive algorithm and the new optimized algorithm are compared. (C) 1 999 American Institute of Physics. [S0021-9606(99)00502-4].