ENHANCED METHOD FOR DETERMINING ROVIBRATIONAL EIGENSTATES OF VAN DER WAALS MOLECULES

Abstract

1. S. E. Choi and J. C. Light, J. Chem. Phys. 97, 7031 (1992). 2. D. C. Sorensen, ""The k-step Arnoldi Process,'' in Large-scale Numerical Optimization, T. F. Coleman and Yuying Li, eds. (SIAM Publications, Philadelphia, PA), p 228 (1990); 3. P. Pendergast, Z. Darakjian, E. F. Hayes, and D. C. Sorensen, J. Comp. Phys. 113, 201 (1994) 4. A. C. Peet and W. Yang, J. Chem. Phys. 91, 6598 (1989) 5. (a) B. Chang, J. M. Williamson, D. W. Cullin, J. R. Dunlop and T. A. Miller J. Chem. Phys. /bf 97, 7999 (1992) (b) B. Chang, J. M. Williamson, D. W. Cullin, J. R. Dunlop and T. A. Miller J. Opt. Soc. Am. B 11 198 (1994).Author Institution: The Ohio State University, Columbus, OH 43210The DVR method of Light et al [1] has been modified in four major ways to produce a more efficient scheme for calculating the rotational-vibrational energies of Van der Waals molecules. First, the Sturmian functions are replaced with Lobatto functions. Second, the implicitly restarted Lanczos method (IRLM) of Sorensen [2] is used to determine the eigenpairs of interest. Third, Chebychev polynomial preconditioning is applied to make it easier to project out the unwanted eigenfunctions and thus speed up the convergence of the IRLM [3]. Finally, a very efficient matrix-vector algorithm is introduced that makes maximum use of the underlying sparcity of the DVR Hamiltonian. Calculations for a protype system --- the Ar-HCl molecule --- will be reported. For the Ar-HCl eigensolutions corresponding to zero angular momentum (J = 0), the enhance DVR approach is about three times faster than the original DVR method and about five times faster than the collocation method of Peet and Yang [4]. As the total angular momentum is increased the relative performance of the new DVR approach improves dramatically. For instance with J = 3, the new method is about 20 times faster than the original DVR and 40 times faster than the collocation method. These relative performance comparisons are about the same for the Cray YMP, the SUN Sparc II, the DEC Alpha and the RS 6000-3BT. Applications of this new method to rare gas --- radical species such as Ar-OH and Ne-OH will be reported along with comparisons with the experimental results of Miller et al [5]. Quantitative insights into the interaction potentials for these systems will be discussed