A Full Additive QM/MM Scheme for the Computation of Molecular Crystals with Extension to Many-Body Expansions

An additive quantum mechanics/molecular mechanics (QM/MM) model for the theoretical investigation of molecular crystals (AC-QM/MM) is presented. At the one-body level, a single molecule is chosen as the QM region. The MM region around it consists of a finite cluster of explicit MM atoms, represented by point charges and Lennard-Jones potentials, with additional background charges to mimic periodic electrostatics. Cluster charges are QM-derived and calculated self-consistently to ensure a polarizable embedding. We have also considered the extension to many-body QM corrections, calculating the interactions of a central molecule to neighbouring units in the crystal. Full gradient expressions have been derived, also including symmetry information. The scheme allows for the calculation of molecular properties as well as unconstrained optimisations of the molecular geometry and cell parameters with respect to the lattice energy. Benchmarking the approach with the X23 reference set confirms the convergence pattern of the many-body extension, although comparison to plane wave DFT reveals a systematic overestimation of cohesive energies by 6-16 kJ·mol⁻¹ . While the scheme primarily aims to provide an inexpensive and flexible way to model a molecule in a crystal environment, it can also be used to reach highly accurate cohesive energies by the straightforward application of wave function correlated approaches. Calculations with local coupled cluster with singles, doubles, and perturbative triples, albeit limited to numerical gradients, show an impressive agreement with experimental estimates for small molecular crystals.