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Chemical Shifts in Molecular Solids by Machine Learning
Federico M. Paruzzo, Albert Hofstetter, Félix Musil, Sandip De, Michele Ceriotti, Lyndon Emsley
TL;DR
Chemical-shift prediction in molecular solids requires accurate but expensive first-principles calculations, while diverse local environments challenge machine learning. The paper develops a local-environment machine-learning framework trained on CSD structures and demonstrates DFT-level prediction and crystal-structure identification for cocaine and AZD8329.
Problem
High-accuracy first-principles calculations are needed to predict solid-state chemical shifts, but molecular-solid diversity and environmental sensitivity challenge machine-learning methods.
Method
The authors train a Gaussian Process Regression model on diverse CSD structures to predict chemical shifts from local atomic environments, using farthest-point sampling and unusual-environment detection.
Results
The model correctly identifies the crystal structures of cocaine and AZD8329 by matching experimentally measured shifts with ML-predicted shifts.
Takeaways & Limitations
ML-predicted chemical shifts can support chemical-shift-based solid-state NMR crystallography for these molecular-solid structure assignments.
Abstract
from arXiv · showhide
The calculation of chemical shifts in solids has enabled methods to determine crystal structures in powders. The dependence of chemical shifts on local atomic environments sets them among the most powerful tools for structure elucidation of powdered solids or amorphous materials. Unfortunately, this dependency comes with the cost of high accuracy first-principle calculations to qualitatively predict chemical shifts in solids. Machine learning methods have recently emerged as a way to overcome the need for explicit high accuracy first-principle calculations. However, the vast chemical and combinatorial space spanned by molecular solids, together with the strong dependency of chemical shifts of atoms on their environment, poses a huge challenge for any machine learning method. Here we propose a machine learning method based on local environments to accurately predict chemical shifts of different molecular solids and of different polymorphs within DFT accuracy (RMSE of 0.49 ppm ( 1 H), 4.3ppm ( 13 C), 13.3 ppm ( 15 N), and 17.7 ppm ( 17 O) with $R^2$ of 0.97 for 1 H, 0.99 for 13 C, 0.99 for 15 N, and 0.99 for 17 O). We also demonstrate that the trained model is able to correctly determine, based on the match between experimentally-measured and ML-predicted shifts, structures of cocaine and the drug 4-[4-(2-adamantylcarbamoyl)-5-tert-butylpyrazol-1-yl]benzoic acid in an chemical shift based NMR crystallography approach.
Supporting Information
The paper is titled “Chemical Shifts in Molecular Solids by Machine Learning” and lists authors from EPFL institutes in Lausanne, Switzerland.
- The paper is titled “Chemical Shifts in Molecular Solids by Machine Learning.”
- Federico M. Paruzzo, Albert Hofstetter, Félix Musil, Sandip De, Michele Ceriotti, and Lyndon Emsley are listed as authors.
- The authors are affiliated with Institut des Sciences et Ingénierie Chimiques and Institut des Sciences et Génie Matériaux at EPFL in Lausanne, Switzerland.
I. Methods and Theoretical Background
The methods combine DFT-derived training data, local-environment Gaussian Process Regression, SOAP-based similarity, diversity sampling, and unusual-environment filtering before validation on crystal-structure candidates.
- 61,012 CSD structures were obtained after removing ambiguous atom positions and structures with excessively short interatomic distances.
- Gaussian Process Regression predicts isotropic chemical shielding from an atom’s local environment using a kernel that measures environmental similarity.
- SOAP represents local atomic environments through rotationally invariant overlaps between smooth atomic-density representations.
- Farthest-point sampling orders CSD-61k structures by diversity, with CSD-2k comprising the first 2,000 selected configurations.
- The unusual-environment procedure compares predictions from 40 GPR models with reference DFT shieldings and excludes environments whose instability exceeds three standard deviations.
- The validation compares experimental and predicted 1H shifts for CSP candidates, including 30 cocaine polymorphs and 14 AZD8329 structures.
II. DFT Calculation Times
DFT chemical-shift calculations become more expensive with increasing accuracy and system size, motivating the computational advantages of ShiftML for larger solids.
- II. DFT Calculation Times: CPU time for GIPAW calculations varies with DFT accuracy, plane-wave cutoff energy, and k-point sampling for cocaine polymorph 1.The charge-density cutoff was set to 4Ecutoff.
- II. DFT Calculation Times: Figure S4 compares CPU time against accuracy for cocaine polymorph 1 and against system size across 500 CSD-2k structures.The cocaine unit cell contains 86 atoms.
- II. DFT Calculation Times: GIPAW chemical-shift calculations dominate the computational cost relative to DFT structure optimization as molecular crystal size increases.For approximately 100 atoms, GIPAW requires around 10x more CPU time; for approximately 1,000 atoms, around 80x more is required.
III. ShiftML Prediction Times
ShiftML prediction scales linearly with the number of atoms, while preprocessing and kernel setup contribute substantial fixed costs that are largely independent of test-structure size.
- III. ShiftML Prediction Times: ShiftML prediction time scales linearly with the number of atoms per unit cell.This scaling was observed for investigated structures containing 20 to 1,500 atoms per unit cell.
- III. ShiftML Prediction Times: SOAP reference-vector construction takes around one CPU minute for the investigated structures because it is currently dominated by training-set size.The subsequent chemical-shift prediction takes at most 10-20 CPU seconds for the large structures.
- III. ShiftML Prediction Times: Loading single-species kernels and creating the multiscale kernel takes around 45 minutes on one CPU, but this setup is performed only once.The setup cost is independent of the number and size of subsequently calculated test structures.
- III. ShiftML Prediction Times: Figures S5-S8 report RMSE and MAE learning and evaluation curves for 13C, 15N, and 17O, with multi-kernel curves labelled msk.Evaluation curves use the CSD-500 test set, while Table S4 documents 1H parameter optimization by 3-fold cross-validation.
V. Comparison to Experiments
The experimental comparison evaluates ShiftML 1H shifts across six molecular crystal structures, using assigned shifts and structure-specific calibration between calculated and experimental values.
- V. Comparison to Experiments: 68 experimental 1H chemical shifts from six crystal structures were compared with ShiftML predictions.The structures include naproxen, uracil, an imidazole co-crystal, theophylline, cocaine, and AZD8329.
- V. Comparison to Experiments: The comparison covers naproxen, uracil, a 3,5-dimethylimidazole/4,5-dimethylimidazole co-crystal, theophylline, cocaine, and AZD8329.Their chemical structures and atom-labelling scheme are shown in Figure S9.
- V. Comparison to Experiments: The first four crystal structures were obtained after all-atom geometry optimization with fixed lattice parameters, whereas cocaine and AZD8329 came from separate references.The optimization procedure is described in the cited reference.
- V. Comparison to Experiments: Calculated shieldings were converted to chemical shifts using d = sref - bs, with sref and b fitted by linear regression for each structure.Methyl-group proton shifts were averaged over the three rotational positions.
- V. Comparison to Experiments: Table S8 reports experimental and calculated chemical shifts for the six compounds, with averaging when multiple atoms correspond to one experimental shift.The labelling scheme is given in Figure S3.
VI. Structures and Chemical Shifts of the CSD-6 Set
The CSD-6 set was prepared by selecting single conformations, adding missing hydrogens, and optimizing coordinates with DFT before chemical-shift calculations.
- VI. Structures and Chemical Shifts of the CSD-6 Set: Partial-occupation atoms were removed from CSD-6 structures, leaving one conformation in each structure file.Missing hydrogen atoms were added with IQmol.
- VI. Structures and Chemical Shifts of the CSD-6 Set: All CSD-6 coordinates were DFT optimized before chemical-shift calculations using the same parameters as the CSD-2k set.Predicted shieldings were provided as separate XYZ files named by CSD Refcode.
- VI. Structures and Chemical Shifts of the CSD-6 Set: Figure S10 presents predicted 13C, 15N, and 17O spectra for six large molecular crystals containing 768 to 1,584 atoms per unit cell.The structures are identified by CSD Refcodes.
VII. CSD-2k Set
The CSD-2k set comprises structures selected from CSD using farthest point sampling, with the listed Refcodes following the FPS selection order.
- The CSD-2k set contains structures identified by an ordered list of CSD Refcodes.The ordering follows the farthest point sampling selection.
VIII. CSD-500 set
The CSD-500 set comprises structures identified by a listed collection of CSD Refcodes.
- The CSD-500 set contains structures identified by the listed CSD Refcodes.
IX. Environments Eliminated with the Unusual Environment Detection Procedure
The unusual-environment detection procedure identified a listed set of environments eliminated from the CSD-2k data.
- The eliminated environments are identified by their corresponding numerical indices in the FPS ordering.The supplied section lists these indices across multiple passages.