AN EXTENDED STRONG-COUPLING MODEL OF THE IR SPECTRAL PROPERTIES OF MOLECULAR-CRYSTALS WITH 4 H-BONDS IN A UNIT-CELL - THE IMIDAZOLE-TYPE CRYSTALS

In this paper we present a theory of the spectral properties of hydrog en bonded imidazole-type monoclinic molecular crystals in the IR, wher e 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 cel l, a vibrational hamiltonian was derived, describing a strong anharmon ic coupling between the two normal modes of the H-bonds with different frequencies: the high-frequency proton stretching vibration nu(X-H) a nd the low-frequency H-bond stretching vibration nu(X...Y) The propose d model emphasizes an extremely strong coupling between these H-bonds in the unit cell, connected by the inversion centre operation. This co upling occurs not only due to the non-totally symmetric vibrations, bu t also via the totally symmetric H-bond vibrations in the two centrosy mmetric dimers which occupy the unit cell. The coupling is mathematica lly expressed, for the vibrationally excited H-bonds in each dimer, by a dependence of the resonance interaction integral upon the H-bond lo w-energy vibration coordinates. Thus a specific coupling between the n ormal vibrations of the H-bonds in the model system occurs and in cons equence a new mathematical treatment of the problem has to be worked o ut. In this paper we present a method for numerical solution of the vi brational eigenvalue problem for the assumed ''strong-coupling'' model of the crystal. The vibrational dipole selection rules for the optica l transitions in the crystal were also derived, along with the formula s for the integral properties of the crystalline spectra. On the basis of this method, numerical simulation of the crystalline spectra for t he nu(X-H) band region was finally proposed.