SCALABLE ALGORITHMS FOR 3-DIMENSIONAL REACTIVE SCATTERING - EVALUATION OF A NEW ALGORITHM FOR OBTAINING SURFACE FUNCTIONS

Implementation of the adiabatically adjusting, principal axis hypersph erical coordinate (APH) approach of Parker and Pack for three-dimensio nal reactive scattering requires solution of a series of two-dimension al (2D) surface eigenproblems. A new algorithm is presented that takes the discrete variable representation (DVR) of the surface Hamiltonian and transforms it implicitly to the sequential diagonalization trunca tion (SDT) representation of Light and coworkers. This implicit transf ormation step, when combined with the implicit restarted Lanczos metho d of Sorensen with Chebyshev preconditioning, can be used to obtain ac curate solutions to the large-dimensionality surface eigenproblems enc ountered in three-dimensional reactive scattering. Timing results are presented and comparisons made with the previously employed SDT-DVR ap proach for these 2D eigenproblems. The new algorithm is faster than th e SDT-DVR algorithm currently in use by about a factor ranging from 2. 6 to 4.5 for both scalar and vector implementations. This algorithm al so requires much less memory for the same order DVR Hamiltonian than p revious approaches. This permits solution of larger eigenproblems with out resorting to external storage. Strategies for implementing this al gorithm on parallel architecture machines are presented. (C) 1994 Acad emic Press, Inc.