ISSN:
0192-8651
Keywords:
inverse iteration
;
2-dimensional master equations
;
rate coefficient
;
spatial operator
;
Chemistry
;
Theoretical, Physical and Computational Chemistry
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Chemistry and Pharmacology
,
Computer Science
Notes:
Recent developments in unimolecular theory have placed great emphasis on the role played by angular momentum in determining the details of the dependence of the rate coefficient on pressure and temperature. The natural way to investigate these dependencies is through the master equation formulation, where the rate coefficient is recovered as the eigenvalue of the smallest magnitude of the spatial operator. Except for very simple cases, the master equation must be solved with numerical methods. For the 2-dimensional master equation this leads to large sparse matrices and correspondingly lengthy computational times in order to determine the eigenvalue of the least magnitude. A reformulation of the problem in terms of a diffusion equation approximates the final matrix with a narrow banded matrix that can easily be factored using a variation of Gaussian elimination. The 2-dimensional master equation can then be solved with inverse iteration, which rapidly converges to the desired eigenpair. This method can be up to 10 times faster than conventional iterative algorithms for finding the desired eigenpair. © 1997 John Wiley & Sons, Inc. J Comput Chem 18:1004-1010, 1997
Additional Material:
1 Ill.
Type of Medium:
Electronic Resource
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