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 frequency – structure correlations in crystalline hydrates. It was found that within a few reasonable approximations, a satisfactory theoretical background may be found for the νOH(OD) versus RO⋅⋅⋅O, as well as for the –2XOH(OD) versus νOH(OD) correlations (νOH(OD) is the spectroscopically measured wavenumber of the OH(OD) stretching vibration, RO⋅⋅⋅O is the hydrogen bond distance, and X is the anharmonicity of vibration). The OH(OD) oscillators were treated as mixed cubic – quartic anharmonic systems. The influence of hydrogen bonding on these oscillators was introduced through the changes in the harmonic diagonal force constants (as proposed by Sceats and Rice1), the other diagonal terms in the potential energy expression being regarded as practically unchanged in the course of the hydrogen bonding. The parameters obtained by empirical correlations, within the proposed model, describe the dependence of the intramolecular potential of the uncoupled OH(OD) species on the hydrogen bond strength.