ISSN:
0192-8651
Keywords:
Computational Chemistry and Molecular Modeling
;
Biochemistry
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Chemistry and Pharmacology
,
Computer Science
Notes:
The determination of the vibration-rotation eigenvalues (for an electronic state of a diatomic molecule) is done using various algorithms, where the differential equation y″ + f(r)y = 0 (with given initial values yo and y′o at an origin ro) is to be integrated, that is, to be replaced by a “convenient” difference equation (DE). The best known are those of: Numerov (N), Runge-Kutta (RK), and the Taylor series expansion (TS). Each algorithm is commonly associated with an “appropriate” DE, and the conventional comparisons of algorithms and/or DE are often misleading. This work compares different DE used in the same algorithm for the same potential and with the same tests. It considers the mentioned conventional DE, and three nonconventional ones: Hajj et al. (HKN) [J. Comp. Phys., 16, 150 (1974)], Cash and Raptis (CR) [Comput. Phys. Commun., 32, 299 (1984)], and Kobeissi “integrals superposition” (IS) [J. Phys. B, 15, 693 (1982)]. A convenient test of these DE is presented and applied. It is shown that: (i) if ∊ is the average error by using Numerov DE, it is of 4∊ for RK, 2∊ for TS, ∊ × 10-3 for HKN, 4∊ × 10-4 for CR and ∊ × 10-6 for IS; (ii) if τ is the average computing time by using Numerov DE, it is of 2.9τ for RK, 3.4τ for TS, 1.5τ for HKN, 2.7τ for CR and 0.9τ for IS.
Additional Material:
4 Tab.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/jcc.540090807
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