Hexamethylenetetramine lattice

According to rules (1) and (2) hexamethylenetetramine C6H12N4 with the space group and one molecule per primitive cell cannot show any optically allowed lattice vibrations. Indeed, the Raman and IR spectra do not show any bands in the low-frequency region. Oxamide with one molecule per primitive cell Cj at sites C, shows three Raman bands, i.e., the three librations. Naphthalene with two molecules per primitive cell C2/, at sites C, shows six librations in the Raman spectrum. Three translational vibrations are allowed in the IR spectrum. 

In all lattice dynamics treatments for librational degrees of freedom discussed in Section IIC, interactions between these coordinates and translations must be considered. As already pointed out, interaction matrix elements vanish only at the zone center and some very special points on the zone boundary and this only for centro-symmetric solids. The first calculation of the dispersion curves for a molecular solid throughout the Brillouin zone was carried out by Cochran and Pawley (1964) for hexamethylenetetramine (hexamine). Once the librational displacement coordinates have been defined and a potential function chosen, the interaction force constants O, can be calculated. The subscripts refer to the displacement coordinate components, where we use i to designate a translational displacement component and a to designate a librational displacement component m,. The corresponding dynamical matrix elements are Mi, analogous to the M,-, defined in (2,9). In general, the matrix elements are complex, and the matrix is hermitian. 

---