A QSPR approach for the fast estimation of DFT/NBO partial atomic charges

The prediction of DFT Natural Bond Orbital (NBO) atomic charges was investigated with machine learning techniques and 2D atomic descriptors. Atomic descriptors were based on atom types (defined by the element and number of neighbour atoms) and topological interatomic distances (number of bonds), so that predictions do not require 3D structures and can be calculated very rapidly. Separate models were built for hydrogen atoms (12,541 atoms in the training set) and non-hydrogen atoms (22,764 atoms in the training set). The best results were achieved with feed-forward neural networks comprising 136 or 155 input neurons (for H atoms and non-H atoms, respectively) and 6 hidden neurons. Predictions for 4178 H atoms and 7587 non-H atoms in independent test sets were obtained with Q²=0.987/RMSE=0.0080/MAE=0.0054 and Q²=0.996/RMSE=0.0273/MAE=0.0182, respectively. The results show how QSPR approaches can provide fast access to accurate estimations of DFT-NBO charges. Such high-level theoretical quantum calculations can thus be used in large-scale applications that otherwise would not afford the intrinsic computational cost.