Explicit representation of anisotropic force constants for simulating intermolecular vibrations of multiply hydrogen-bonded systems.

We investigated the mechanical nature of multiply hydrogen-bonded systems by means of ab initio quantum chemical calculations, and we derived a set of force constants to reproduce the anisotropic vibration modes of such systems. Twenty multiply hydrogen-bonded molecular dimers were selected for evaluation of the stiffness of their hydrogen bonds. By means of a multivariate analysis, the principal values of the stiffness tensor were divided into the contributions from each hydrogen bond. Force constants in the stretching directions were estimated to be 20.2 and 11.5 N m(-1) for NH...O and NH...N pairs, respectively. The obtained parameter set was used to reconstruct the various intermolecular vibration motions, and reasonable values in the low-frequency (ca. terahertz) region were obtained. Comparison of the multivariate analysis with the normal-mode analysis suggested that the off-diagonal terms for the transverse and rotational motions may appreciably contribute to the coupling of those basic motions.