  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, access the method performance for 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 DFT-QM/CG-MM accurately reproduces
DFT-QM/MM radial distribution functions and 3-body correlations between 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.
