Density Functional Theory-based Quantum Mechanics/Coarse-grained Molecular Mechanics: Theory and Implementation

Quantum mechanics/molecular mechanics (QM/MM) is a standard computational tool for describing chemical reactivity in systems with many degrees of freedom, including polymers, enzymes, and reacting molecules in complex solvents. However, QM/MM is less suitable for systems with complex MM dynamics due to associated long relaxation times, the high computational cost of QM energy evaluations, and expensive long-range electrostatics. Recently, a systematic coarse graining of the MM part was proposed to overcome these QM/MM limitations in the form of the quantum mechanics/coarse-grained molecular mechanics (QM/CG-MM) approach. Herein, we recast QM/CG-MM in the density functional theory formalism and, by employing the force-matching variational principle, assess the method performance for the two model systems: QM CCl4 in the MM CCl4 liquid and the reaction of tert-butyl hypochlorite with the benzyl radical in the MM CCl4 solvent. We find that density functional theory (DFT)-QM/CG-MM accurately reproduces DFT-QM/MM radial distribution functions and three-body correlations between the QM and CG-MM subsystems. The free-energy profile of the reaction is also described well, with an error <1-2 kcal/mol. DFT-QM/CG-MM is a general, systematic, and computationally efficient approach to include chemical reactivity in coarse-grained molecular models.