A theory of the broadening of the infrared absorption spectra of hydrogen-bonded species, II. The coupling of anharmonic v(XH) and v(XH..Y) modes

Abstract
A theory of the coupling between the $\nu $(XH) and $\nu $(XH..Y) modes of a hydrogen-bonded complex is developed, both modes being assumed anharmonic. It is shown that by making very modest assumptions about the nature of the molecular potential energy surface a simple expression can be obtained for the effective potential function which governs the hydrogen-bond stretching vibration in any particular state of the $\nu $(XH) vibration. Owing to a kinematic coupling effect, which must always be present, the depth, curvature, and minimum position of each effective potential depends on the quantum state of the $\nu $(XH) vibration. The Franck-Condon factors governing the excitation of combination bands and the spread in energy of terms within such bands are calculated. It is shown that for models representing the Me$_{2}$O.HF and Me$_{2}$O.HCl systems at room temperature the intensity of absorption at the frequencies $\nu $(XH) $\pm \nu $(XH..Y) will be appreciable, even if the anharmonicity of the $\nu $(XH) vibration is unaffected by hydrogen bond formation. All the parameters used in the model calculations can be derived from experimental data. The theory provides strong qualitative support for the view that broad $\nu $(XH) infrared bands of hydrogen-bonded systems owe much to contributions from combination bands of the type $\nu $(XH) $\pm n\nu $(XH..Y), as suggested originally by Stepanov. However, the experimental phenomena are more pronounced than those calculated, and a discussion is given of other potential energy terms which will need to be taken into account in a more refined subsequent theory.