A precise solution of the rotation bending Schrödinger equation for a triatomic molecule with application to the water molecule

• Published in: Journal of molecular spectroscopy 1979, Vol.74 (1), p.1-8
• Main Authors: Hoy, A.R., Bunker, P.R.
• Format: Article
• Language: English
• ISSN: 0022-2852; 1096-083X
• DOI: 10.1016/0022-2852(79)90019-5

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 ( v 1, v 2, v 3) 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.