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J Chem Theory Comput. 2017 Feb 14;13(2):679-695. doi: 10.1021/acs.jctc.6b01125. Epub 2017 Jan 24.

An Estimation of Hybrid Quantum Mechanical Molecular Mechanical Polarization Energies for Small Molecules Using Polarizable Force-Field Approaches.

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Department of Pharmaceutical Sciences, School of Pharmacy, University of Maryland , 20 Penn Street, Baltimore, Maryland 21201, United States.
Laboratory of Computational Biology, National Institutes of Health, National Heart, Lung and Blood Institute , 5635 Fishers Lane, T-900 Suite, Rockville, Maryland 20852, United States.
State Key Laboratory of Precision Spectroscopy, School of Physics and Materials Science, East China Normal University , Shanghai 200062, China.
NYU-ECNU Center for Computational Chemistry at NYU Shanghai, Shanghai 200062, China.
Max-Planck-Institut für Kohlenforschung , 45470 Mülheim an der Ruhr, NRW Germany, EU.
Center for Functional Nanomaterials, Brookhaven National Laboratory , Upton, New York 11973, United States.
Department of Chemistry, University of California , 1 Shields Avenue, Davis, California 95616, United States.
Q-Chem Inc., 6601 Owens Drive, Suite 105, Pleasanton, California 94588, United States.
Department of Chemistry and Biochemistry, University of Oklahoma , Norman, Oklahoma 73019, United States.


In this work, we report two polarizable molecular mechanics (polMM) force field models for estimating the polarization energy in hybrid quantum mechanical molecular mechanical (QM/MM) calculations. These two models, named the potential of atomic charges (PAC) and potential of atomic dipoles (PAD), are formulated from the ab initio quantum mechanical (QM) response kernels for the prediction of the QM density response to an external molecular mechanical (MM) environment (as described by external point charges). The PAC model is similar to fluctuating charge (FQ) models because the energy depends on external electrostatic potential values at QM atomic sites; the PAD energy depends on external electrostatic field values at QM atomic sites, resembling induced dipole (ID) models. To demonstrate their uses, we apply the PAC and PAD models to 12 small molecules, which are solvated by TIP3P water. The PAC model reproduces the QM/MM polarization energy with a R2 value of 0.71 for aniline (in 10,000 TIP3P water configurations) and 0.87 or higher for other 11 solute molecules, while the PAD model has a much better performance with R2 values of 0.98 or higher. The PAC model reproduces reference QM/MM hydration free energies for 12 solute molecules with a RMSD of 0.59 kcal/mol. The PAD model is even more accurate, with a much smaller RMSD of 0.12 kcal/mol, with respect to the reference. This suggests that polarization effects, including both local charge distortion and intramolecular charge transfer, can be well captured by induced dipole type models with proper parametrization.

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