VIBRATIONAL EIGENSTATE DETERMINATIONS: IMPROVEMENTS TO THE COLLOCATION METHOD
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Date
1994
Journal Title
Journal ISSN
Volume Title
Publisher
Ohio State University
Abstract
The collocation method [1] is often used to obtain accurate cigenvalues for polyatomic bound-state problems. The basis of this method is a fitting scheme wherein the wave function is taken to be exact at a preselected set of points, namely the collocation points. The imposition of this condition ultimately leads to a generalized eigenvalue problem. The purpose of this paper is to report recent progress in enhancing the accuracy and speed of the diagonalization phase of the collocation method through the use of the Implicitly Restarted Lanezos Method (IRLM) of Sorensen [2]. For the generalized eigenvalue problem, the shift-and-invert version of the IRLM is used in conjunction with various local-support basis sets designed to achieve optimal sparsity of the Hamiltonian. This allows one to use sparse matrix technology to obtain the eigenvalues and eignvectors of interest. Applications of the method of vao der Waals such as $Ar-C_{2}H_{2}$ will be reported.
Description
1. Peet, A. C. and Yang, W., J. Chem. Phys. 90, 1745 (1989). 2. Sorensen, D.C. ""The k-step Arnoldi Process"". In Large-scale Numerical Optimization, T. F. Colcman and Yuying Lieds. SIAM Publications, Philadelphia, PA, 228-237
Author Institution: Department of Chemistry, The Ohio State University
Author Institution: Department of Chemistry, The Ohio State University