Molecular rearrangements in organic crystals. II. The role of intermolecular cooperation and dipole–dipole interactions

Abstract

A model to account for intermolecular cooperation during molecular rearrangements is described. A qualitative approach to electrostatic interactions is tested for some halogen-containing molecules.As a first step towards a better understanding of solidstate rearrangements of organic molecules, some potential-energy barriers to rigid-body rotations have been calculated in paper I (Gavezzotti & Simonetta, 1975), by the pairwise potential method. The qualitative, and in some cases quantitative, success of these simple calculations was considered an encouraging start to the application of the same method to more complex problems.The model that was built to perform these calculations (henceforth Model I) showed however some weak points. They are: (a) the crystal was built up of rigid, motionless molecules surrounding the one that undergoes a certain rearrangement, and (b) no electrostatic contribution was included in the calculations. The first point comes abruptly into play when large molecular displacements, such as those involved in phase transitions or solid-state reactions, are considered. The second, although very important in some cases, has presumably a smaller effect than the first. This paper is devoted to the description of a new model that can account for intermolecular cooperation, and, to a first approximation, for the electrostatic interactions in crystals of polar molecules. The molecular cluster model (Model II)If many molecules move at the same time in a crystal, it is no longer possible to evaluate the potential energy by summing the pairwise interactions of one molecule with the surrounding ones. The simplest way of accounting for energetic changes in this case is to consider a molecular cluster, made up of a finite number of molecules, and to calculate the pairwise interactions of each molecule with all other molecules in the cluster. Obviously, the 'energy' calculated in this way can never converge to a true lattice energy, and has no physical meaning in itself. However, differences in these cluster 'energies' reflect true energy changes in the crystal.A given rearrangement is considered to have a driving force, or main reaction coordinate, visualized as the evolution of one or more internal coordinates of one fundamental molecule. Then one or more other molecules in the cluster are allowed appropriate motions, with respect to which the cluster 'energy' is minimized. In this way a minimum-energy pathway is described from reactant to product through the multidimensional energy surface. In doing this, care must be taken that (a) the cluster is large enough to allow the calculation of a substantial amount of the barrier, and (b) no undue freedom is allowed to the molecules nearest to the fundamental one, as a result of truncation of the cluster. The cluster is therefore to be modelled in two shells, the first including the cooperating molecules, and the second to ensure that they experience much the same field as the fundamental one. The size of the first shell can be established by subdivision of ...

Structure of (η6-C6H6)Mo(CO)3 at room temperature and 120 K: motion about equilibrium and far from equilibrium

“…The same behavior was observed for (C6H6)Cr(CO)3. However, these barriers are much higher than those estimated from Raman frequencies, probably because the calculations do not allow for cooperative reorientations (Gavezzotti & Simonetta, 1976) of the neighboring molecules. The temperature dependence of the reorientational barriers implied in the computational model parallels that implied in the interpretation of the Raman frequencies (Chhor & Lucazeau, 1982), which is based on assumptions of the shape of the potentialenergy surface.…”

Hydrogen Bonding and Dynamic Behaviour in Crystals and Polymorphs of Dicarboxylic–Diamine Adducts: A Comparison between NMR Parameters and X‐ray Diffraction Studies

“…In general the experimental activation energies roughly agree with the potential barriers associated with the reorientation process on the basis of attractive and repulsive electrostatic interactions with atoms or nearby molecules. It is well known, [68] however, that potential barrier calculations within the "static environment" approximation tend to overestimate the barrier height.…”

Dynamical processes in crystalline organometallic complexes

“…The potential energy barrier (PB) to molecular or fragment reorientation can be estimated by calculating the packing potential energy at various rotational steps around a predefined rotation axis (for example, an inertial axis or a ligand-to-metal coordinations axis) and by subtracting the energy corresponding to the observed structure (0°rotation).5,47 Reorientations can be performed either within the "static environment" approximation (thus yielding an upper limit for the barrier) or within a "cooperating" environment in which molecules of the surroundings are allowed small torsional and translational motions in order to "give way" to the reorientating molecule or fragment. 48 The calculation of atom-atom potential energy barriers (AAPEB) does not require a priori assumptions on the shape of the potential energy curve (compare with Raman and IQENS). It should be stressed that, since the height of the barrier is essentially determined by the changes in internuclear separation between the outer ligand atoms during reorientation, the problem of a correct parametrization for the inner metal atoms is less severe in AAPEB calculations than in the estimate of the actual PPE values.…”