Elsevier Science Home
Computer Physics Communications Program Library
Full text online from Science Direct
Programs in Physics & Physical Chemistry
CPC Home

[Licence| Download | New Version Template] aaee_v1_0.gz(4 Kbytes)
Manuscript Title: A fast quadrature method for computing diatomic RKR potential curves.
Authors: J. Tellinghuisen
Program title: RKRPOT
Catalogue identifier: AAEE_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 6(1973)221
Programming language: Fortran.
Computer: IBM 360/65.
Operating system: HASP/OS/MVT.
RAM: 9K words
Word size: 32
Keywords: Molecular physics, Diatomic, Potential curves, Rkr method, Gaussian quadrature, Vibration.
Classification: 16.3.

Nature of problem:
The RKR method provides a prescription for computing diatomic potential curves from empirical spectroscopic parameters. The right- and left- hand turning points on the curve are related to the spectroscopic quantities through the Klein f and g integrals. The heart of the problem is the evaluation of these improper integrals.

Solution method:
The f and g integrals are obtained by numerical integration, using a very efficient Gauss-Mehler quadrature with weight function (1-x)**-1/2 on the interval (-1,1). For vibrational levels having energy less than ~80% of the dissociation energy De, a 4-point quadrature typically yields an accuracy of 1 part in 10**7.

As written, the program computes the vibrational energy G(v) and rotational constant B(v) from the conventional polynomial expressions for these quantities, with the expansion parameters provided as input. However, the appropriate function routines could be modified easily to include, for example, a mode for interpolating on the raw spectroscopic quantities.

Running time:
For vibrational levels satisfying the condition, G(v) <= 0.8 De, the integral estimates usually converge in two cycles, in which case the program will compute the turning points for each level in 5-10 ms, depending on the number of vibrational and rotational expansion parameters. As the levels approach the dissociation limit, the convergence rate decreases markedly, taking as much as ~ 1/3 s for levels within ~1 cm**-1 of De.