Quantum-corrected NMR crystallography at scale

Abstract

Structure determination by chemical-shift-driven NMR crystallography relies on comparing chemical shieldings measured in solid-state NMR experiments with simulations. However, computational cost limits the accuracy of shielding predictions, that usually rely on low-level electronic-structure approximations and neglect thermal and quantum mechanical nuclear motion, leading to large errors, especially for highly informative hydrogen-bonded protons. To address these limitations, we introduce a quantum-nuclei-corrected (QNC-NMR) approach. We generate inexpensively quantum ensembles using PET-MOLS, a novel machine-learning learning model of the interatomic potential transferable across molecular crystals. Using them as inputs to a chemical-shift model results in a two-fold improvement of the agreement with experiments for hydrogen-bonded protons, without the need for empirical corrections. The ability to sample structures consistent with the experimental conditions enables further refinement of the shielding model by finetuning it against measured shieldings. The favorable scaling with system size allows similar improvements for amorphous materials that are otherwise inaccessible to explicit DFT simulations.

Figures (27)

• Figure S1: Comparison of experimental and predicted $^{13}$C chemical shifts computed with ShiftML3, using Static-PBE optimized geometries (a), Static-PBE0 optimized geometries (b), and the QNC-NMR protocol (c). The black diagonal line in each panel corresponds to a perfect correlation. The accuracy of the predictions is evaluated with the root-mean square error (RMSE). On the lower panels, $\Delta$ is the difference between the predicted and the experimental chemical shift ($\Delta$ = $\delta_{pred}$ – $\delta_{exp}$).
• Figure S2: Comparison of experimental and predicted $^{15}$N chemical shifts computed with ShiftML3, using Static-PBE optimized geometries (a), Static-PBE0 optimized geometries (b), and the QNC-NMR protocol (c). The black diagonal line in each panel corresponds to a perfect correlation. The accuracy of the predictions is evaluated with the root-mean square error (RMSE) without (in black) and with the ouliers (in grey). On the lower panels, $\Delta$ is the difference between the predicted and the experimental chemical shift ($\Delta$ = $\delta_{pred}$ – $\delta_{exp}$). Outlier local atomic environments not included in the fitting are displayed in color grey. Those correspond to the structures GEHHIL and GEHHEH whose Schiff base motifs have highly uncertain protonation state and are discussed in more detail the main text.
• Figure S3: $^1$H experimental chemical shifts as a function of the ShiftML3 predicted shieldings for the Static-PBE optimized geometries (a), Static-PBE0 optimized geometries (b), and the QNC-NMR protocol (c). In a black solid line ($\delta = a\sigma +b$) is the fitted linear regression keeping the slope fixed ($\delta_{a=-1, b}$, used in the main text); and in black dashed line ($\delta_{a,b}$) is the linear fit optimizing both the slope and intercept.
• Figure S4: $^{13}$C experimental chemical shifts as a function of the ShiftML3 predicted shieldings for the Static-PBE optimized geometries (a), Static-PBE0 optimized geometries (b), and the QNC-NMR protocol (c). In a black solid line ($\delta = a\sigma +b$) is the fitted linear regression keeping the slope fixed ($\delta_{a=-1, b}$, used in the main text); and in black dashed line ($\delta_{a,b}$) is the linear fit optimizing both the slope and intercept.
• Figure S5: $^{15}$N experimental chemical shifts as a function of the ShiftML3 predicted shieldings for the Static-PBE optimized geometries (a), Static-PBE0 optimized geometries (b), and the QNC-NMR protocol (c). n a black solid line ($\delta = a\sigma +b$) is the fitted linear regression keeping the slope fixed ($\delta_{a=-1, b}$, used in the main text); and in black dashed line ($\delta_{a,b}$) is the linear fit optimizing both the slope and intercept. Outlier local atomic environments not included in the fitting are displayed in color grey. Those correspond to the structures GEHHIL and GEHHEH whose Schiff base motifs have highly uncertain protonation state and are discussed in more detail the main text.