Ab initio crystal structure prediction. II. Flexible molecules

An extension of a recently reported algorithm (J. Comput. Chem., 26, 304 (2005)) for the prediction of the crystal structure of organic materials to molecules whose conformation is likely to be significantly affected by the packing forces is presented. The molecule is modelled as a set of rigid fragments connected by flexible torsion angles whose values in the crystalline environment are determined by the balance of intra- and inter-molecular forces. The intramolecular energy is initially computed using quantum mechanics over a grid in the space of flexible torsion angles. This allows the intramolecular energy to be expressed as a continuous and differentiable function of the torsion angles using multidimensional interpolants based on restricted cubic Hermite polynomials. The intermolecular electrostatic interactions are treated with a conformation-dependent atomic charge model, with the charges also being expressed as functions of the flexible torsion angles using restricted Hermite interpolants. Overall, this approach allows the computationally efficient, yet accurate, evaluation of the parts of the lattice enthalpy that depend on the molecular conformation. The proposed algorithm requires only the atomic connectivity of the molecule under consideration and performs an extensive search for local minima of the lattice enthalpy surface by using deterministic low-discrepancy sequences to ensure an optimal coverage of the search space. Candidate structures can be generated in the 59 most common space groups with one or more crystallographically independent entities. These are then used as starting points of local optimization calculations performed with a sequential quadratic programming algorithm, which makes use of analytical partial derivatives with respect to all inter and intra- molecular degrees of freedom. A parallelized implementation of the algorithm allows minimizations from several hundreds of thousands of initial guesses to be carried out in reasonable time. The algorithm is used to predict the crystal structures of the polymorphic system p-chlorobenzamide and to study the relative stability of the crystal structures of the diastereomeric salt pair (R)-1-phenylethylammonium, (R&S)- 2-phenylbutyrate.