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. Author manuscript; available in PMC: 2019 Mar 13.
Published in final edited form as: J Chem Theory Comput. 2018 Feb 26;14(3):1442–1455. doi: 10.1021/acs.jctc.7b01195

Figure 1.

Figure 1.

Schematic structure of QM/MM-NN for a system containing N atoms in the QM subsystem. Here rQM and rMM are respectively the Cartesian coordinates of the atoms in the QM and MM subsystem, {Gik} is the symmetry function that depends on rQM, i denotes the QM atoms, k denotes different radial and angular functions with different hyperparameters, and {viext} is the external electrostatic potential at QM grids close to atom i as a function of rQM and rMM. After semiempirical QM/MM calculations with rQM and rMM, the total potential energy EQM/MML and the corresponding forces FQM/MML on all QM and MM atoms at the low level are known. Then the energy difference between two levels as ΔE is predicted with QM/MM-NN, and the derivative of ΔE with respect to rQM and rMM is calculated analytically. Finally, the total potential energy EQM/MMH and the corresponding forces FQM/MMH on all QM and MM atoms at the high level is obtained. The differences on the input variables of NN compared to our previous work42 are highlighted in red.