Computation of CCSD(T)-Quality NMR Chemical Shifts via Δ-Machine Learning from DFT

Abstract

NMR spectroscopy undoubtedly plays a central role in determining molecular structures across different chemical disciplines, and the accurate computational prediction of NMR parameters is highly desirable. In this work, a new Δ-machine learning approach is presented to correct DFT-computed NMR chemical shifts using input features from the calculation and in addition highly accurate reference data at the CCSD(T)/pcSseg-2 level of theory with a basis set extrapolation scheme. The model is trained on a data set containing 1000 optimized and geometrically distorted structures of small organic molecules comprising most elements of the first three periods and containing data for 7090 1H and 4230 13C NMR chemical shifts. Applied to the PBE0/pcSseg-2 method, the mean absolute deviation (MAD) on the internal NMR shift test set is reduced by 81% for 1H and 92% for 13C at virtually no additional computational cost. For 12 different DFT functional and basis set combinations, the MAD of the ML-corrected NMR shifts ranges from 0.021 to 0.039 ppm (1H) and from 0.38 to 1.07 ppm (13C). Importantly, the new method consistently outperforms the simple and widely used linear regression correction technique. This behavior is reproduced on three different external benchmark sets, confirming the generality and robustness of the correction scheme, which can easily be applied in DFT-based spectral simulations.

Modular Bicyclophane‐Based Molecular Platforms

“…In compound 8, the ring current anisotropy effect on the respective protons vanishes as no close proximity of them to the now-fused m-terphenylene units is observed. Even though, the relative shifts of the strongly shifted protons going from 7 to 8 is explained qualitatively, NMR chemical shift calculations of the Boltzmann averaged conformer ensembles of both compounds indicate a significant overestimation of this effect, specifically for t. To verify the r 2 SCAN0[CPCM [16] ]/def2-TZVPP chemical shifts, a novel machine learning (ML) correction [17] to reproduce CCSD(T) quality NMR chemical shifts was applied. The ML correction yields only small corrections to the original relative r 2 SCAN0 shifts.…”

Machine learning-based correction for spin–orbit coupling effects in NMR chemical shift calculations

“…As in our previous work on the correction of 1 H and 13 C NMR chemical shifts using machine learning, 55 quantum chemical ab initio data serve as target for the model presented herein. The use of experimental data would increase the overall complexity thus making the data set less suitable for applying an ML correction procedure.…”

“…51 ML approaches can exploit their full potential for highly accurate predictions if they are combined with DFT and use features from a converged electronic structure as input (Δ-ML). This has been shown to yield highly accurate electronic energies 52 and NMR chemical shifts 53–56 at costs not significantly higher than for the underlying low-level method.…”

“…We are therefore confident that a combination of separate correlation and spin–orbit corrections will be beneficial for the efficient computation of reasonably accurate NMR chemical shifts. We previously proposed an ML-based correction method that obtains the (beyond DFT) correlation contribution to NMR chemical shifts based on coupled cluster (CCSD(T)) reference data, 55 which we now call Δ corr -ML. In this work, we present an efficient and highly transferable approach called Δ SO -ML to compute the spin–orbit relativistic contribution to 13 C and 1 H NMR chemical shifts.…”

Frontiers of molecular crystal structure prediction for pharmaceuticals and functional organic materials

“…Machine learning models for predicting chemical shifts 268–284 promise to accelerate NMR crystallography even further. The traditional NMR crystallography protocol involves first predicting a set of candidate crystal structures, computing the NMR spectra for each one, and comparing them against experiment, all of which can require substantial computational effort.…”