A quantum theoretical basis for some spectra - Structure correlations in crystalline hydrates

Starting with the perturbation theory and the Hellmann-Feynmann theorem, an attempt was made to derive a fundamental theoretical basis for some freque ncy - structure correlations in crystalline hydrates. It was found that wit hin a few reasonable approximations, a satisfactory theoretical background may be found for the <(nu)over tilde>(OH(OD)), versus R-O ... O, as well as for the -2X(OH(OD)) versus <(nu)over tilde>(OH(OD)) correlations (<(nu)ove r tilde>(OH(OD)), is the spectroscopically measured wavenumber of the OH(OD ) stretching vibration, R-O ... O is the hydrogen bond distance, and X is t he anharmonicity of vibration). The OH(OD) oscillators were treated as mixe d cubic - quartic anharmonic systems. The influence of hydrogen bonding on these oscillators was introduced through the changes in the harmonic diagon al force constants (as proposed by Sceats and Rice(1)), the other diagonal terms in the potential energy expression being regarded as practically unch anged in the course of the hydrogen bonding. The parameters obtained by emp irical correlations, within the proposed model, describe the dependence of the intramolecular potential of the uncoupled OH(OD) species on the hydroge n bond strength.