Normal modes and local modes in H₂ <i>X</i>: beyond the <i>x</i>, <i>K</i> relations

Abstract

The so-called ‘x, K relations’, which interrelate the normal mode and local mode descriptions of the stretching vibrations of polyatomic molecules, demand simple numerical relationships between the normal mode anharmonicity constants xij and the Darling-Dennison resonance constants Kijkl . In this paper, we examine the consequences of relaxing these demands for the case of H2 X molecules (or groups). Extra terms appear in the equivalent local mode representation which is shown to be similar in form to the recently-described approximate anharmonically coupled anharmonic oscillator model. The normal mode model is also extended to include the effects of Fermi resonance between symmetric stretch and bend, and the equivalent local mode model is derived. The effects of relaxing the x, K relations are examined by reference to the available experimental data for H2O and D2O. It is shown that the extra terms introduced into the model allow a more reliable interpretation of the local mode spectroscopic constants for the stretching vibrations.