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

Abstract

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 kJÁmol −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 kJÁmol −1 for the benzene crystal structure at 138 K. This estimate is within 1.6 kJÁmol −1 off the best theoretical prediction of −55.9 kJÁmol −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 kJÁmol −1 over phase I. The proposed approach gives a tremendous potential to predict stability of other molecular crystal polymorphs.

Behavior of counterpoise correction in many‐body molecular clusters of organic compounds: Hartree–Fock interaction energy perspective

“…Benzene clusters for both form I and form II demonstrate a smooth behavior in non‐CP corrected HF energies with increasing cluster size. It has been recently shown that three‐body effects are rather negligible in crystal structures of both forms 3 . Therefore, such smooth behavior is expected.…”

“…It has been recently shown that three‐body effects are rather negligible in crystal structures of both forms. 3 Therefore, such smooth behavior is expected. With introduction of non‐additive interactions such as induction forces present in hydrogen‐bonded clusters of ODH and to some extent in aspirin, the non‐CP corrected HF energies behave differently, no longer exhibiting a smooth behavior with increasing cluster size.…”

“…The accurate prediction of lattice energy in molecular crystals has remained a big challenge in quantum chemistry despite the development of ab‐initio‐ and DFT‐based methods, especially when considering ubiquitous London dispersion forces 1,2 . Recently, we have proposed a new cost‐effective and accurate methodology for the prediction of lattice energy of molecular crystals 3 . The methodology is based on the spin‐ratio scaled method modified from the second‐order Møller–Plesset perturbation theory (SRS‐MP2) that was designed to predict correlation interaction energies below 2 kJ mol −1 regardless of the interaction type–hydrogen bonding or π − π stacking 4,5 .…”

“… 1 , 2 Recently, we have proposed a new cost‐effective and accurate methodology for the prediction of lattice energy of molecular crystals. 3 The methodology is based on the spin‐ratio scaled method modified from the second‐order Møller–Plesset perturbation theory (SRS‐MP2) that was designed to predict correlation interaction energies below 2 kJ mol −1 regardless of the interaction type–hydrogen bonding or π − π stacking. 4 , 5 The SRS‐MP2 method was also formulated to eliminate the basis set superposition error (BSSE) that plagues any molecular system consisting of more than one molecule.…”

Quantum-Mechanical Structure Optimization of Protein Crystals and Analysis of Interactions in Periodic Systems

“…The method can be applied to crystals containing other systems such as DNA with the practical limitation that for some chemical elements DFTB parameters may not be available. Using optimized structures, one can estimate properties such as the lattice energy and gain insight into interactions in crystals with the developed partition analysis. This analysis can be used without fragmentation with possible future applications not only to crystals of macromolecules but to molecular crystals in general and to other systems treated with the PBC such as proteins in solution.…”