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Title:
A precise solution of the rotation bending Schrödinger equation for a triatomic molecule with application to the water molecule
Authors:
Hoy, A. R.; Bunker, P. R.
Affiliation:
AA(Chemistry Department, University of Western Ontario, London, Ontario, Canada), AB(Herzberg Institute of Astrophysics, National Research Council of Canada, Ottawa, Ontario, Canada)
Publication:
Journal of Molecular Spectroscopy, Volume 74, Issue 1, p. 1-8.
Publication Date:
01/1979
Origin:
ELSEVIER
Abstract Copyright:
(c) 1979 Elsevier Science B.V. All rights reserved.
DOI:
10.1016/0022-2852(79)90019-5
Bibliographic Code:
1979JMoSp..74....1H

Abstract

In this paper we report the results of improving the non-rigid bender formulation of the rotation-vibration Hamiltonian of a triatomic molecule [see A. R. Hoy and P. R. Bunker, J. Mol. Spectrosc., 52, 439 (1974)]. This improved Hamiltonian can be diagonalized as before by a combination of numerical integration and matrix diagonalization and it yields rotation-bending energies to high values of the rotational quantum numbers. We have calculated all the rotational energy levels up to J = 10 for the ( v1, v2, v3) states (0, 0, 0) and (0, 1, 0) for both H 2O and D 2O. By least squares fitting to the observations varying seven parameters we have refined the equilibrium structure and force field of the water molecule and have obtained a fit to the 375 experimental energies used with a root mean square deviation of 0.05 cm -1. The equilibrium bond angle and bond length are determined to be 104.48° and 0.9578 Å respectively. We have also calculated these energy levels using the ab initio equilibrium geometry and force constants of Rosenberg, Ermler and Shavitt [ J. Chem. Phys., 65, 4072 (1976)] and this is then the first complete ab initio calculation of rotation-vibration energy levels of high J in a polyatomic molecule to this precision. the rms fit of these ab initio energies to the experimental energies for the H 2O molecule is 2.65 cm -1.
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