Predicting Density Functional Theory-Quality Nuclear Magnetic Resonance Chemical Shifts via Δ-Machine Learning.

First-principles prediction of nuclear magnetic resonance chemical shifts plays an increasingly important role in the interpretation of experimental spectra, but the required density functional theory (DFT) calculations can be computationally expensive. Promising machine learning models for predicting chemical shieldings in general organic molecules have been developed previously, though the accuracy of those models remains below that of DFT. The present study demonstrates how much higher accuracy chemical shieldings can be obtained via the Δ-machine learning approach, with the result that the errors introduced by the machine learning model are only one-half to one-third the errors expected for DFT chemical shifts relative to experiment. Specifically, an ensemble of neural networks is trained to correct PBE0/6-31G chemical shieldings up to the target level of PBE0/6-311+G(2d,p). It can predict H, C, N, and O chemical shieldings with root-mean-square errors of 0.11, 0.70, 1.69, and 2.47 ppm, respectively. At the same time, the Δ-machine learning approach is 1-2 orders of magnitude faster than the target large-basis calculations. It is also demonstrated that the machine learning model predicts experimental solution-phase NMR chemical shifts in drug molecules with only modestly worse accuracy than the target DFT model. Finally, the ability to estimate the uncertainty in the predicted shieldings based on variations within the ensemble of neural network models is also assessed.