Enhanced Method for Determining Rovibrational Eigenstates of van der Waals Molecules

Abstract

The discrete variable representation (DVR) method has been modified in three major ways to produce a more efficient scheme for calculating the rotational−vibrational energies of van der Waals molecules. First, the implicitly restarted Lanczos method (IRLM) of Sorensen (SIAM J. Matrix Anal. Appl. 1992, 13, 357) is used to determine the eigenpairs of interest. Second, Chebychev polynomial preconditioning is applied to make it easier to project out unwanted eigenfunctions and thus speed up the convergence of the IRLM. Finally, a very efficient matrix−vector algorithm is introduced that makes maximum use of the underlying sparsity of the DVR Hamiltonian. Calculations for a protypical system Ar−HCl are reported. For the 20 lowest Ar−HCl eigensolutions corresponding to angular momentum J = 1 and using only a single processor of a Cray YMP, the modified DVR approach is about 6 times faster than the original DVR method and 14 times faster than the collocation method of Peet and Yang (J. Chem. Phys. 1989, 91, 6598). As the total angular momentum is increased, the relative performance of the modified DVR approach improves dramatically. For instance, with J = 5 the modified method is about 45 times faster than the original DVR and 100 times faster than the collocation method on a single processor of a Cray YMP. This modified DVR approach also runs significantly faster on a range of workstations such as DEC Alpha and the IBM RS/6000. Application of this method is also shown to be effective in obtaining an improved interaction potential for the A 2Σ+ state of Ar−HO.

Regular and irregular vibrational states: Localized anharmonic modes and transition-state spectroscopy of Na3

“…To improve the convergence rate of the IRLM scheme we use the Chebychev polynomial preconditioning scheme described by Korambath, Wu, and Hayes. 24 …”

High resolution electronic spectroscopy and an empirical potential energy surface for Ne⋅SH/D

“…Details of the computational approaches used to generate this PES have been described elsewhere. 14,17 Briefly, the rotation vibration Hamiltonian is expressed in terms of the Jacobi coordinates of an atom/ diatom complex,…”

A theoretical procedure for determining rovibrational eigenstates of van der Waals complexes

“…In the SCF᎐Cl calculations, the integration lim-i ts are taken as R Table I, the calculated vibrational energy levels for Ar-HCl as a function of the total number of the configurations are given in comparison with the values calculated with the collocation method of Hutson w x 16 and with the modified DVR method of Kow x rambath et al 5 . One can see from Table I that the SCF᎐CI procedure described in the second section may converge the levels faster than the MDVR method.…”