Density-Dependent Formulation of Dispersion-Repulsion Interactions in Hybrid Multiscale Quantum/Molecular Mechanics (QM/MM) Models

Mixed multiscale quantum/molecular mechanics (QM/MM) models are widely used to explore the structure, reactivity, and electronic properties of complex chemical systems. Whereas such models typically include electrostatics and potentially polarization in so-called electrostatic and polarizable embedding approaches, respectively, nonelectrostatic dispersion and repulsion interactions are instead commonly described through classical potentials despite their quantum mechanical origin. Here we present an extension of the Tkatchenko-Scheffler semiempirical van der Waals (vdW(TS)) scheme aimed at describing dispersion and repulsion interactions between quantum and classical regions within a QM/MM polarizable embedding framework. Starting from the vdW(TS) expression, we define a dispersion and a repulsion term, both of them density-dependent and consistently based on a Lennard-Jones-like potential. We explore transferable atom type-based parametrization strategies for the MM parameters, based on either vdW(TS) calculations performed on isolated fragments or on a direct estimation of the parameters from atomic polarizabilities taken from a polarizable force field. We investigate the performance of the implementation by computing self consistent interaction energies for the S22 benchmark set, designed to represent typical noncovalent interactions in biological systems, in both equilibrium and out-of-equilibrium geometries. Overall, our results suggest that the present implementation is a promising strategy to include dispersion and repulsion in multiscale QM/MM models incorporating their explicit dependence on the electronic density.