Abstract
We present an inexpensive and robust theoretical approach based on the fragment molecular orbital methodology and the spinratio scaled secondorder 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 threebody 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.
Original language  English 

Pages (fromto)  248260 
Number of pages  13 
Journal  Journal of Computational Chemistry 
Volume  42 
Issue number  4 
DOIs  
Publication status  Published  5 Feb 2021 
Keywords
 correlation
 crystal structure
 energy
 energy abinitio
 gasphase
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