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

• Published in: Journal of computational chemistry 2021-02, Vol.42 (4), p.248-260
• Main Authors: Nguyen, Anh L. P., Mason, Thomas G., Freeman, Benny D., Izgorodina, Ekaterina I.
• Format: Article
• Language: English
• Subjects: Benzene; correlation; Crystal lattices; Crystal structure; Crystals; energy; energy ab‐initio; gas‐phase; Hydrocarbons; Lattice energy; Madelung constant; Mathematical analysis; Molecular orbitals; Perturbation theory; Robustness; Stability
• ISSN: 0192-8651; 1096-987X
• DOI: 10.1002/jcc.26452

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. The interplay between the fragment molecular orbital methodology and the spin‐ratio scaled second‐order Møller–Plesset perturbation theory permits the prediction of the lattice energy of benzene crystals within the chemical accuracy.