A precise solution of the rotation bending Schrödinger equation for a triatomic molecule with application to the water molecule
Abstract
In this paper we report the results of improving the nonrigid bender formulation of the rotationvibration 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 rotationbending 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 _{2}O and D _{2}O. 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 rotationvibration 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 _{2}O molecule is 2.65 cm ^{1}.
 Publication:

Journal of Molecular Spectroscopy
 Pub Date:
 January 1979
 DOI:
 10.1016/00222852(79)900195
 Bibcode:
 1979JMoSp..74....1H