An extended “strong-coupling” model of the IR spectral properties of molecular crystals with four H-bonds in a unit cell: the imidazole-type crystals

Abstract

In this paper we present a theory of the spectral properties of hydrogen bonded imidazole-type monoclinic molecular crystals in the IR, where Z = 4, the site symmetry is C i, and infinite open chains of H-bonds are considered. For the model crystal restricted to a single unit cell, a vibrational hamiltonian was derived, describing a strong anharmonic coupling between the two normal modes of the H-bonds with different frequencies: the high-frequency proton stretching vibration v XH and the low-frequency H-bond stretching vibration v X…Y. The proposed model emphasizes an extremely strong coupling between these H-bonds in the unit cell, connected by the inversion centre operation. This coupling occurs not only due to the non-totally symmetric vibrations, but also via the totally symmetric H-bond vibrations in the two centrosymmetric dimers which occupy the unit cell. The coupling is mathematically expressed, for the vibrationally excited H-bonds in each dimer, by a dependence of the resonance interaction integral upon the H-bond low-energy vibration coordinates. Thus a specific coupling between the normal vibrations of the H-bonds in the model system occurs and in consequence a new mathematical treatment of the problem has to be worked out. In this paper we present a method for numerical solution of the vibrational eigenvalue problem for the assumed “strong-coupling” model of the crystal. The vibrational dipole selection rules for the optical transitions in the crystal were also derived, along with the formulas for the integral properties of the crystalline spectra. On the basis of this method, numerical simulation of the crystalline spectra for the v XH band region was finally proposed.