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 (ML) 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 a Δ-ML approach. Specifically, an ensemble of neural networks (NN) is trained to correct PBE0/6-31G chemical shieldings up to PBE0/6-311+G(2d,p) which can predict ¹H, ¹³C, ¹⁵N, and ¹⁷O chemical shieldings with root-mean-square errors of 0.12, 0.79, 1.82, and 2.66 ppm. Furthermore, the ability to estimate the uncertainty in the predicted shieldings based on variations within the ensemble of NN models is also assessed. Finally, it is also demonstrated that the ML model predicts experimental solution-phase NMR chemical shifts in drug molecules with only modestly worse accuracy than the target DFT model.