Deep Neural Network Model to Predict the Electrostatic Parameters in the Polarizable Classical Drude Oscillator Force Field

The Drude polarizable force field (FF) captures electronic polarization effects via auxiliary Drude particles that are attached to non-hydrogen atoms, distinguishing it from commonly used additive FFs that rely on fixed charges. The Drude FF currently includes parameters for biomolecules such as proteins, nucleic acids, lipids, and carbohydrates and small-molecule representative of those classes of molecules as well as a range of atomic ions. Extension of the Drude FF to novel small druglike molecules is challenging as it requires the assignment of partial charges, atomic polarizabilities, and Thole scaling factors. In the present article, deep neural network (DNN) models are trained on quantum mechanical (QM)-based partial charges and atomic polarizabilities along with Thole scale factors trained to target QM molecular dipole moments and polarizabilities. Training of the DNN model used a collection of 39 421 molecules with molecular weights up to 200 Da and containing H, C, N, O, P, S, F, Cl, Br, or I atoms. The DNN model utilizes bond connectivity, including 1,2, 1,3, 1,4, and 1,5 terms and distances of Drude FF atom types as the feature vector to build the model, allowing it to capture both local and nonlocal effects in the molecules. Novel methods have been developed to determine restrained electrostatic potential (RESP) charges on atoms and external points representing lone pairs and to determine Thole scale factors, which have no QM analogue. A penalty scheme is devised as a performance predictor of the trained model. Validation studies show that these DNN models can precisely predict molecular dipole and polarizabilities of Food and Drug Administration (FDA)-approved drugs compared to reference MP2 calculations. The availability of the DNN model allowing for the rapid estimation of the Drude electrostatic parameters will facilitate its applicability to a wider range of molecular species.