Interatomic forces in hexamethylenetetramine

Abstract

A formalism expressing the intermolecular mode frequencies of rigid molecules explicitly in terms of phenomenological interatomic force constants is developed for a general uni-molecular crystal. The restraints on the force constants necessary for the dynamical matrix to be hermitian for all symmetries and general force fields are given. This ‘interatomic’ lattice dynamical model is used to analyse the intermolecular mode dispersion curves of deuterated hexamethylenetetramine (DHMT), assuming various interatomic force systems. It is found that an unambiguous choice of the best force system cannot be made from this analysis, but the shortest D. . . N bond is found to be the dominant bond. A ‘6-exponential’ form is then assumed for the interatomic pair potentials in DHMT, and the constants of these potentials are determined by fitting to the DHMT dispersion curves. Most of the constants are poorly determined by this analysis, only the long-range part of the D-D interaction showing a significant change from the values independently estimated from hydrocarbons. The ‘rigid molecule’ assumption is then removed, and using the fitted interatomic pair potentials and the known internal force field the effect of the internal vibrations on the intermolecular modes is calculated. Significant shifts, larger than the experimental error in some cases, are found in many external mode frequencies due to the molecular distortions. Small shifts are also found in the internal mode frequencies, some of them being unexpectedly negative. The rigid molecule approximation is indicated to be of doubtful validity for most molecules, but an approximate procedure is suggested for retaining it in analyses of external mode dispersion curves. Certain systematic discrepancies are noted in the fitting and it is suggested that neglect of the octopole moment of the DHMT molecule may be the cause.