On the variational computation of a large number of vibrational energylevels and wave functions for medium-sized molecules

摘要

In a recent publication [J. Chem. Phys. 127, 084102 (2007)], the nearly variational DEWE approach(DEWE denotes Discrete variable representation of the Watson Hamiltonian using the Eckart frameand an Exact inclusion of a potential energy surface expressed in arbitrarily chosen coordinates) wasdeveloped to compute a large number of (ro)vibrational eigenpairs for medium-sized semirigidmolecules having a single well-defined minimum. In this publication, memory, CPU, and hard diskusage requirements of DEWE, and thus of any DEWE-type approach, are carefully considered,analyzed, and optimized. Particular attention is paid to the sparse matrix-vector multiplication, themost expensive part of the computation, and to rate-determining steps in the iterative Lanczoseigensolver, including spectral transformation, reorthogonalization, and restart of the iteration.Algorithmic improvements are discussed in considerable detail. Numerical results are presented forthe vibrational band origins of the ~I2CH_4and ~12CH_2D_2isotopologues of the methane molecule. Thelargest matrix handled on a personal computer during these computations is of the size of(4.10~8)X(4.10~8). The best strategy for determining vibrational eigenpairs depends largely on theactual details of the required computation. Nevertheless, for a usual scenario requiring a largenumber of the lowest eigenpairs of the Hamiltonian matrix the combination of the thick-restartLanczos method, shift-fold filtering, and periodic reorthogonalization appears to result in thecomputationally most feasible approach.