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Internet Electronic Journal of Molecular Design - IEJMD, ISSN 1538-6414, CODEN IEJMAT
| ABSTRACT - Internet Electron. J. Mol. Des. May 2006, Volume 5, Number 5, 296-305 |
A New Formulation for the Herman-Wallis Coefficients for Infrared
Transitions of A Diatomic Molecule
Mahmoud Korek and Claire Deeb
Internet Electron. J. Mol. Des. 2006, 5, 296-305
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Abstract:
The problem of the radial matrix elements in the infrared
transition vJ↔v'J' of a diatomic molecule is considered. By
using a new expansion in the perturbation theory of the
eigenvalue and the eigenfunction of the two considered states in
terms of the running number m we derived analytical expressions
for the Herman-Wallis coefficients of the rotational factor in the
rovibrational matrix elements. The numerical application to the
ground states of the molecule HCl shows that the present
formulation provides a simple and accurate method for the
calculation of the Herman-Wallis coefficients, even for the high
order coefficients, without any restriction on the potential
function, the operator f(r) and the vibrational
levels v and v'. The
most important methods used in this investigation are the
Rayleigh-Schrödinger perturbation theory and the canonical
functions approach. The main results reported in the paper are
the determination of the Herman-Wallis coefficients. The method
used for the determination of the Herman-Wallis coefficients in
this work allows the calculation of these coefficients for any type
of potential function and to any order of correction in the
perturbation theory.
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