Prediction of lattice energy of benzene crystals: a robust theoretical approach

We present an inexpensive and robust theoretical approach based on the fragment molecular orbital methodology and the spin-ratio scaled second-order Møller–Plesset perturbation theory to predict the lattice energy of benzene crystals within 2 kJ⋅mol⁻¹. Inspired by the Harrison method to estimate the Madelung constant, the proposed approach calculates the lattice energy as a sum of two- and three-body interaction energies between a reference molecule and the surrounding molecules arranged in a sphere. The lattice energy converges rapidly at a radius of 13 Å. Adding the corrections to account for a higher correlated level of theory and basis set superposition for the Hartree Fock (HF) level produced a lattice energy of −57.5 kJ⋅mol⁻¹ for the benzene crystal structure at 138 K. This estimate is within 1.6 kJ⋅mol⁻¹ off the best theoretical prediction of −55.9 kJ⋅mol⁻¹. We applied this approach to calculate lattice energies of the crystal structures of phase I and phase II—polymorphs of benzene—observed at a higher temperature of 295 K. The stability of these polymorphs was correctly predicted, with phase II being energetically preferred by 3.7 kJ⋅mol⁻¹ over phase I. The proposed approach gives a tremendous potential to predict stability of other molecular crystal polymorphs.