A major shortcoming of semiempirical (SE) molecular orbital methods is their severe underestimation of molecular polarizability compared with experimental and <i>ab initio</i> (AI) benchmark data. In a combined quantum mechanical and molecular mechanical (QM/MM) treatment of solution-phase reactions, solute described by SE methods therefore tends to generate inadequate electronic polarization response to solvent electric fields, which often leads to large errors in free energy profiles (FEPs). To address this problem, here we present a hybrid framework that improves the response property of SE/MM methods through high-level molecular-polarizability fitting. Specifically, we place on QM atoms a set of corrective polarizabilities (referred to as chaperones), whose magnitudes are determined from machine learning (ML) to reproduce the condensed-phase AI molecular polarizability along the minimum free energy path. These chaperone polarizabilities are then used in a machinery similar to a polarizable force field calculation to compensate for the missing polarization energy in conventional SE/MM simulations. Because QM atoms in this treatment host SE wave functions as well as classical polarizabilities, both polarized by MM electric fields, we name this method doubly polarized QM/MM (dp-QM/MM). We demonstrate the new method on the free energy simulations of the Menshutkin reaction in water. Using AM1/MM as a base method, we show that ML chaperones greatly reduce the error in the solute molecular polarizability from 6.78 to 0.03 Å<sup>3</sup> with respect to the density functional theory benchmark. The chaperone correction leads to ∼10 kcal/mol of additional polarization energy in the product region, bringing the simulated FEPs to closer agreement with the experimental results. Furthermore, the solute-solvent radial distribution functions show that the chaperone polarizabilities modify the FEPs through enhanced solvation corrections when the system evolves from the charge-neutral reactant state to the charge-separated transition and product states. These results suggest that the dp-QM/MM method, enabled by ML chaperone polarizabilities, provides a very physical remedy for the underpolarization problem in SE/MM-based free energy simulations.

Doubly polarized QM/MM with machine learning chaperone polarizability

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