Anisotropic Repulsion Potentials for Cyanuric Chloride (C3N3Cl3) and Their Application to Modeling the Crystal Structures of Azaaromatic Chlorides

Torque and atomic forces for Cartesian tensor atomic multipoles with an application to crystal unit cell optimization

New equations for torque and atomic force are derived for use in flexible molecule force fields with atomic multipoles. The expressions are based on Cartesian tensors with arbitrary multipole rank. The standard method for rotating Cartesian tensor multipoles and calculating torque is to first represent the tensor with n indexes and 3(n) redundant components. In this work, new expressions for directly rotating the unique (n + 1)(n + 2)/2 Cartesian tensor multipole components Θpqr are given by introducing Cartesian tensor rotation matrix elements X(R). A polynomial expression and a recursion relation for X(R) are derived. For comparison, the analogous rotation matrix for spherical tensor multipoles are the Wigner functions D(R). The expressions for X(R) are used to derive simple equations for torque and atomic force. The torque and atomic force equations are applied to the geometry optimization of small molecule crystal unit cells. In addition, a discussion of computational efficiency as a function of increasing multipole rank is given for Cartesian tensors. © 2016 Wiley Periodicals, Inc.

Modelling organic crystal structures using distributed multipole and polarizability-based model intermolecular potentials

Crystal structure prediction for organic molecules requires both the fast assessment of thousands to millions of crystal structures and the greatest possible accuracy in their relative energies. We describe a crystal lattice simulation program, DMACRYS, emphasizing the features that make it suitable for use in crystal structure prediction for pharmaceutical molecules using accurate anisotropic atom-atom model intermolecular potentials based on the theory of intermolecular forces. DMACRYS can optimize the lattice energy of a crystal, calculate the second derivative properties, and reduce the symmetry of the spacegroup to move away from a transition state. The calculated terahertz frequency k = 0 rigid-body lattice modes and elastic tensor can be used to estimate free energies. The program uses a distributed multipole electrostatic model (Q, t = 00,...,44s) for the electrostatic fields, and can use anisotropic atom-atom repulsion models, damped isotropic dispersion up to R(-10), as well as a range of empirically fitted isotropic exp-6 atom-atom models with different definitions of atomic types. A new feature is that an accurate model for the induction energy contribution to the lattice energy has been implemented that uses atomic anisotropic dipole polarizability models (alpha, t = (10,10)...(11c,11s)) to evaluate the changes in the molecular charge density induced by the electrostatic field within the crystal. It is demonstrated, using the four polymorphs of the pharmaceutical carbamazepine C(15)H(12)N(2)O, that whilst reproducing crystal structures is relatively easy, calculating the polymorphic energy differences to the accuracy of a few kJ mol(-1) required for applications is very demanding of assumptions made in the modelling. Thus DMACRYS enables the comparison of both known and hypothetical crystal structures as an aid to the development of pharmaceuticals and other speciality organic materials, and provides a tool to develop the modelling of the intermolecular forces involved in molecular recognition processes.

The Nature of Interactions in the Ionic Crystal of 3-Pentenenitrile, 2-Nitro-5-oxo, Ion(−1), Sodium

The hybrid variation -- perturbation many-body interaction energy decomposition scheme has been applied to analyze the physical nature of interactions in the ionic 3-pentenenitrile, 2-nitro-5-oxo, ion(-1), sodium crystal, which can be regarded as a model for a large group of aromatic quaternary nitrogen salts. In the crystal structure the sodium ions and water molecules of adjacent unit cells form a positively charged "inorganic layer" with the sodium ions clustered together along the ab faces with the organic (negative) part in between. This puzzling crystal packing is due to a strong favorable interaction between the water molecule and the sodium ions and a substantial charge transfer from the carbanions that balances out the destabilizing sodium-sodium ion repulsion. Although the majority of cohesion energy of the crystal structure comes from the electrostatic interactions of ions, the resulting net stabilization also depends heavily on the nonadditive delocalization components, due to a counterbalance between the two-body delocalization and exchange effects. The estimated nonadditivity of interactions varies between 12% and 22%.

Characterization of Complicated New Polymorphs of Chlorothalonil by X-ray Diffraction and Computer Crystal Structure Prediction

A simultaneous experimental and computational search for polymorphs of chlorothalonil (2,4,5,6-tetrachloro-1,3-benzenedicarbonitrile) has been conducted, leading to the first characterization of forms 2 and 3. The crystal structure prediction study, using a specifically developed anisotropic atom-atom potential for chlorothalonil, gave as the global minimum in the lattice energy a structure that was readily refined against powder diffraction data to the known form 1 (P2(1)/a). The structure of form 2 was solved and refined from powder diffraction data, giving a disordered structure in the Rm (166) space group (Z = 3). It could also be refined against a P1 ordered model, starting from a low-energy hypothetical sheet structure found in the computational search. This shows that the disorder could be associated with the stacking of ordered sheets. The disordered structure for form 2 was later confirmed by single-crystal X-ray diffraction. The structure of form 3, determined from single-crystal diffraction, contains three independent molecules in the asymmetric unit in P2(1) (4) (Z = 6). Powder diffraction showed that this single-herringbone structure was similar to two low-energy structures found in the search. Further analysis confirmed that form 3 has a similar lattice energy and contains elements from both these predicted structures, which can be considered as good approximations to the form 3 structure.

A Nonempirical Anisotropic Atom−Atom Model Potential for Chlorobenzene Crystals

A nearly nonempirical, transferable model potential is developed for the chlorobenzene molecules (C6ClnH6-n, n = 1 to 6) with anisotropy in the atom-atom form of both electrostatic and repulsion interactions. The potential is largely derived from the charge densities of the molecules, using a distributed multipole electrostatic model and a transferable dispersion model derived from the molecular polarizabilities. A nonempirical transferable repulsion model is obtained by analyzing the overlap of the charge densities in dimers as a function of orientation and separation and then calibrating this anisotropic atom-atom model against a limited number of intermolecular perturbation theory calculations of the short-range energies. The resulting model potential is a significant improvement over empirical model potentials in reproducing the twelve chlorobenzene crystal structures. Further validation calculations of the lattice energies and rigid-body k = 0 phonon frequencies provide satisfactory agreement with experiment, with the discrepancies being primarily due to approximations in the theoretical methods rather than the model intermolecular potential. The potential is able to give a good account of the three polymorphs of p-dichlorobenzene in a detailed crystal structure prediction study. Thus, by introducing repulsion anisotropy into a transferable potential scheme, it is possible to produce a set of potentials for the chlorobenzenes that can account for their crystal properties in an unprecedentedly realistic fashion.