Are high-Z′ polymorphs metastable? Insight from pharmaceutical polymorphs

Abstract

High-Z′ polymorphs are hypothesized to be kinetically trapped products and hence less stable than their low-Z′ counterparts (Z′ = number of symmetry-independent molecules in a crystal structure). Although the existence of such a symmetry–stability relationship would be of fundamental importance to the structural chemistry of molecular crystals, it has yet to be supported by experimental or computational evidence. A major challenge in analyzing high-Z′ crystal structures is the large number of atoms, which makes accurate quantum chemical evaluation of their lattice cohesive energies (LCEs) computationally intensive. A systematic test of this hypothesis in drug polymorphs is made feasible by the CE-B3LYP method, which uses pairwise summation of interaction energies for LCE estimation. Here, we have analyzed 15 drugs (49 polymorphs) of low- and high-Z′ crystal forms in terms of lattice cohesive energies, Kitaigorodskii packing indices (KPI), in-crystal molecular volumes, and crystal densities. Our results show no direct relation between Z′ and the stability of drug polymorphs.