PARALLEL ALGORITHM FOR VIBRATIONAL EIGENSTATE CALCULATIONS USING THE DISCRETE VARIABLE REPRESENTATION.
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Date
1993
Journal Title
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Publisher
Ohio State University
Abstract
The discrete variable representation (DVR) has emerged as a viable tool in the calculation of the vibrational spectra of triatomic molecules [1]. Light et al. have developed the method of sequential diagonalization/truncation (SDT) as an efficient means for the preparation and diago nalization of the vibrational Hamiltonian. The SDT transforms the relatively large Hamiltonian matrix into one with reduced dimensionality. In doing so, however, the original sparse structure of the matrix is lost and a dense matrix results that must be kept and subsequently diagonalized. This method, though quite accurate and efficient for light triatomic systems, requires significant storage when applied to the study of systems with a high density of states. We have reformulated the DVR/SDT approach using a very efficient diagonalization method namely, Sorensen's Implicitly Restarted Arnoldi Method. [2]. The advantage of this method is that it calculates the desired number of cigenpairs through a scheme that relies solely on matrix-vector multiplications. As a result, it is possible to maintain the sparse structure of the DVR Hamiltonian matrix and carry out the same SDT transformation implicitly as part of the matrix-vector multiplication. Another advantage of this approach is that the computer codes are inherently parallelizable because blocks of the matrix-vector operations can be distributed directly to a large number of processors. This new approach will allow the extension of the range of systems that can be studied to moleules containing heavier atoms as well as to molecular systems containing more than three atoms.
Description
$^{1}$ Choi, S. E. and J. C. Light, J. Chem. Phys. 97, 7031 (1992). $^{2}$ Sorensen, D. C. ""The k-step Arnoldi Process. In Large-scale Numerical Optimization, T. F. Coleman and Yuying Li eds. SIAM Publications, Philadelphia, PA, 228-237.
Author Institution: Department of Chemistry, The Ohio State University
Author Institution: Department of Chemistry, The Ohio State University