J. Phys. Chem. B 2003, 107, 10919-10933
10919
Atomistic Calculations of Phonon Frequencies and Thermodynamic Quantities for Crystals of Rigid Organic Molecules Graeme M. Day,†,§ Sarah L. Price,*,† and Maurice Leslie‡ Centre for Theoretical and Computational Chemistry, Department of Chemistry, UniVersity College London, 20 Gordon Street, London, WC1H 0AJ, United Kingdom, and CCLRC Daresbury Laboratory, Daresbury, Warrington, WA4 4AD, United Kingdom ReceiVed: April 25, 2003; In Final Form: June 20, 2003
Rigid-body, k ) 0 phonon frequencies have been calculated within the crystal structure modeling program DMAREL, enabling the use of anisotropic atom-atom model potentials. Five organic crystals (hexamethylenetetramine, naphthalene, pyrazine, imidazole, and R-glycine) were chosen to sample a range of intermolecular interactions for determining the sensitivity of the calculated frequencies to changes in the empirical repulsion-dispersion parameters and the electrostatic model. A carefully parameterized simple exp-6 model can describe vibrations in simple van der Waals crystals and some hydrogen bonded crystals reasonably well. However, for weaker polar interactions, an accurate model of the electrostatics is needed. Bending of weak polar interactions and shearing of close contacts with delocalized π-systems are particularly sensitive to the description of electrostatic interactions. Point charge models generally underestimate the resistance to deforming hydrogen bonds, and a distributed multipole model stabilizes these interactions. Because of their statistical nature, vibrational contributions to the energy can be estimated more accurately than the frequencies of individual modes, and the best models give good estimates of zero-point energies and the vibrational partition function, which should be useful in predicting the relative stability of polymorphs.
Introduction Pharmaceutical scientists require an understanding of the thermodynamic properties of the different polymorphic forms of crystalline pharmaceuticals,1,2 lest a phase transformation should occur during manufacture or storage. Indeed, the temperature-pressure behavior, and the possibility of a change of polymorphic form, is a major issue in the development of all molecular crystalline materials.3 The vibrational properties of crystals are responsible for much of their thermal behavior, such as expansion, polymorphic phase transitions, and, eventually, melting. Since kinetic factors can hinder the experimental observation of phase transformations, or even the discovery of the most stable polymorph,4 computational studies of the organic solid state have considerable potential for benefiting the development of novel organic materials. Our main motivation for this study of phonon calculations is to examine the vibrational contributions to the crystal energy, which has been included in studies of the relative stability of polymorphs and predicted crystal structures.5-10 Gavezzotti and Filippini5 calculated energy differences in 204 pairs of polymorphs, including the vibrational entropy calculated from rigidbody harmonic frequencies using the UNI model potential,11,12 and showed that the entropy differences were generally small (
