Explicit Representation of Anisotropic Force Constants for Simulating Intermolecular Vibrations of Multiply Hydrogen-Bonded Systems

Abstract

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.

Intermolecular Vibrations in Hydrophobic Amino Acid Crystals: Experiments and Calculations

“…In what follows, we describe an approach that allows the presentation of detailed vibrational character that is not only quantitatively rich but also concise and intuitive. There are other methods of visualizing various kinds of information about interactions in molecular crystals, , and there also exists an efficient method for coarse-grained characterization of intermolecular vibrations , and force constants . An advantage to our approach is that it allows one to analyze the vibrations that simultaneously involve a large number of inter- and intramolecular degrees of freedom.…”

“…There are other methods of visualizing various kinds of information about interactions in molecular crystals, 71,72 and there also exists an efficient method for coarse-grained characterization of intermolecular vibrations 73,74 and force constants. 75 An advantage to our approach is that it allows one to analyze the vibrations that simultaneously involve a large number of inter-and intramolecular degrees of freedom. Additionally, our approach can be applied regardless of the method or model used to obtain the vibrational eigenvectors.…”

Coarse Graining of Intermolecular Vibrations by a Karhunen-Loève Transformation of Atomic Displacement Vectors

“…For the rigid body mechanical calculation, we used a set of force constants that we developed for NH • • • N hydrogen bonds. 28 Note that for transverse motion (e.g., T x -T x ), the force constants (18.9, 6.5, 2.3 N m -1 ) derived from the T/R based expansion are in good agreement with those (22.9, 9.6, 2.4 N m -1 ) from a rigid body approximation. As for rotational motions, the force constants for antisymmetric combinations (e.g., R x -R x ) show good agreement between the two methods.…”

“…In a previous study, we investigated the mechanical nature of multiply hydrogen-bonded systems by means of ab initio quantum chemical calculations. 28 By a multivariate analysis of the curvature of the potential surface for 20 dimeric molecular systems, we derived a set of force constants for translational shear in the x, y, and z directions. The force constants only roughly reproduced the frequencies of the intermolecular vibration modes of a molecular dimer, which in turn indicated the significance of the off-diagonal terms of the dynamical matrix when evaluating the frequency of intermolecular vibration.…”

“…Previously, we pointed out that the frequencies of the intermolecular vibration modes of 5-halogenated-2-aminopyridine do not follow the pseudodiatomic model. 28 For example, the frequency of the Stretch mode was nearly insensitive to changes in the molecular weight. Here we attempt to clarify the relation between the frequencies and molecular weight of 2-aminopyridines on the basis of our present formulation.…”