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 1H, 13C, 15N, and 17O 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.