Historical NMR shift predictions and bibliography

This is an overview of errors achieved by various nuclear magnetic resonance (NMR) shift prediction methods over time. This list is restricted to solution NMR of small organic molecules, e. g. protein or solid NMR prediction papers are not considered. Previous versions of this table were published in Prediction of chemical shift in NMR: a review and Nuclear Magnetic Resonance and Artificial Intelligence. The table and the image have been compiled by Stefan Kuhn , with help from Nils Schlörer and others. Any additions (new papers, new nuclei) are welcome. This also serves as a shift prediction bibliography.

As explained in the papers, the figures need to be considered with care. In particular, the issue of training and test sets and their influence on the results needs to be considered. Also note:

The following table shows Historically achieved MAEs for various methods and datasets. It contains publications known to us by 21/9/2025.

Date1H MAE (ppm)13C MAE (ppm)17O MAE (ppm)15N MAE (ppm)19F MAE (ppm)195Pt MAE (ppm)Method Training Test Dataset Literature
1/1990-5.5**---- Pretsch increments C13Shift CSEARCH[1]
4/1992-1.56----Optimized Increments OPSI 3 organic molecules[2]
5/19940.19**-----Pretsch increments Custom 200 molecules[3]
7/1997-1.217****----Pyridine increments-disubst pyridines[35]
7/1997-2.42****----Pyridine increments-trisubst pyridines[35]
7/1997-3.665****----AROSIM with orthocorrection-disubst pyridines[35]
7/1997-2.951****----AROSIM with orthocorrection-trisubst pyridines[35]
12/2000-2.4---- classic neural network 57 sesquiterpene lactones 11 organic molecules[4]
1/2002 0.25 ----- classic neural network 120 organic molecules 259 organic molecules[5]
8/2002 -1.2---- classic neural network SpecInfo Taxol[6]
8/2002 -2.4---- classic neural network SpecInfo Taxol[6]
8/2002 -3.8----Pretsch increments ChemDraw Pro Taxol[6]
8/2002 -3.7----Pretsch increments SpecTool Taxol[6]
8/2002 -1.0----HOSE SpecInfo Taxol[6]
8/2002 -2.7----HOSE PredictIt Taxol[6]
8/2002 -1.7----HOSE CNMR 6.0 Taxol[6]
8/2002 -3.4----Cosmas 4.5n/a Taxol[6]
8/2002 -4.0----Gaussian 98n/a Taxol[6]
8/2002 -1.9---- classic neural network SpecInfo 1547 shifts/100 molecules[6]
8/2002 -2.5---- classic neural network SpecInfo 1547 shifts/100 molecules[6]
8/2002 -1.4----SpecInfo SpecInfo 1547 shifts/100 molecules[6]
5/2007-1.59---- ACD/Labs predictor ACD/Labs NMRShiftDB[7]
5/2007-2.22---- CSEARCH CSEARCH NMRShiftDB[7]
1/2008 0.28-----CHARGE n/a Wiley 1H NMR database[8]
1/2008 0.30-----Pretsch Increments n/a Wiley 1H NMR database[8]
1/2008 0.18-----Pretsch 3D increments n/a Wiley 1H NMR database[8]
1/2008 0.28-----Combined n/a Wiley 1H NMR database[8]
1/20080.181.59----NN13C 207,000, 1H 189,00013C 118,000, 1H 116,000 compounds[45]
1/20080.181.71----PLS13C 207,000, 1H 189,00013C 118,000, 1H 116,000 compounds[45]
9/2008 0.154 -----HOSE NMRShiftDB *[9]
9/2008 0.18 -----J48 NMRShiftDB *[9]
9/2008 0.182 -----RF NMRShiftDB *[9]
9/2008 0.215 -----SVM NMRShiftDB *[9]
5/2009-1.85----custom encoding
partial least squares regression		 190,000 structures 16,000 structures[10]
1/2010-1.58----HOSE ACD/Labs205 molecules/2531 shifts[11]
1/2010-1.91----NN ACD/Labs205 molecules/2531 shifts[11]
1/2010-2.15----increment n/a205 molecules/2531 shifts[11]
1/2010-3.29----DFT-GIAO n/a205 molecules/2531 shifts[11]
1/20100.1081-----improved HOSE in house282[12]
4/20190.25 2.82---- stereo HOSE nmrshitdb2 *[13]
4/20190.29 3.52---- HOSE nmrshitdb2 *[13]
5/2019-1.63---- modgraph (HOSE + NN) modgraph 13 molecules[14]
5/2019-2.2---- ML MestreLab 13 molecules[14]
5/2019-1.7---- ML MestreLab 13 molecules[14]
5/2019-1.3---- Ensemble of previous three as per method 13 molecules[14]
8/2019 0.28 1.43---- CNN subset of nmrshitdb2*[15]
11/2019 0.23 2.45---- ML DFT calculations 410 structures[16]
4/2020 0.224 1.355---- MPNN subset of nmrshitdb2 *[17]
6/2020 0.18***2.1***---- DFT+ML90% of 476 13C and 270 1H10% of 476 13C and 270 1H[51]
7/20200.2431.552----MPNNsubset of nmrshitdb2 subset of nmrshitdb2[42]
2/2021 0.11*** 0.70***1.69***2.47***-- Δ-machine learning 57456 DFT calculations 3780 DFT calculations[18]
8/2021---6.12--kernel ridge regression DFT 623 moleculeDFT 205 molecules[19]
12/20210.101.26----GNNSubset of nmrshitdb2*[32]
3/20220.280.95----DU8ML11 K experimental chemical shifts?[47]
5/20220.141.21----ML-J-DP417,00010,000[48]
6/2022-1.0-1.5****----DU8ML10,890 shift valuesNo systematic evaluation done[46]
8/2022----52.63-CNN19F subset of nmrshitdb2*[20]
8/2022----8.88-improved HOSE19F subset of nmrshitdb2*[20]
8/20220.1911.228----GNNSubset of nmrshitdb2*[31]
2/2023-----170.07Laplacian kernel ridge regressionOwn*[34]
9/2023 0.209 2.18---- FullSSPrUCe (GNN) nmrshiftdb2*[21]
11/2023 0.168 2.938---- ComENet GlycoNMR 80% GlycoNMR 10%[22]
11/20230.145 2.550---- DimeNet++ GlycoNMR 80% GlycoNMR 10%[22]
11/2023 0.140 2.492---- SchNet GlycoNMR 80% GlycoNMR 10%[22]
11/2023 0.146 3.044---- SphereNet GlycoNMR 80% GlycoNMR 10%[22]
12/20230.138 1.79---- fragment-based COLMAR 768 COLMAR Metabolites[23]
3/2024 0.210 2.228---- GNNnmrshiftdb2 subset HMDB and CH-NMR-NP[24]
5/2024 0.10-----GNN PROSPRE 3755 compounds PROSPRE 272 compounds [25]
5/2024-0.7---- DFT -132 shifts[26]
6/20240.1850.944---- DFT+3D GNN nmrshiftdb2 80% nmrshiftdb2 20% [27]
6/2024----3.636-Graph convolutional network1900 fluorinated compounds100 fluorinated compounds[50]
7/2024-0.5****---- GNN 1637 benzenic compounds 114 benzenic structures[43]
8/20240.102.06.42.1--ML with QM-based featuresANI-1 with DFT40 molecules[49]
8/2024 0.035****0.31****----E(3) equivariant graph neural network CASPER Monosaccharides [29]
8/20240.026****0.23****----E(3) equivariant graph neural network CASPER Disaccharides [29]
8/20240.033****0.30****----E(3) equivariant graph neural network CASPER Trisaccharides [29]
9/2024-1.28----transfer learning with GNNsnmrshiftdb2 subsetnmrshiftdb2 subset[39]
11/20240.1581.189----GNNnmrshiftdb2*[30]
12/2024----3.31-Gradient Boosting Regression-501 fluorinated compounds[33]
2/20250.1672.025----Multi-task pre-training and unsupervised learningnmrshiftdb2479 molecules[36]
3/20250.070.76-2.26--IMPRESSION 2IG2, DFT generatedinternal[40]
4/20250.0200.262----SE(3) Transformer with pre-training and fine-tuning (NMRNet)4.8 million structures?[44]
7/2025-0.73----polarizable atom interaction neural network (PAiNN)17,588 molecules from Exp22K2,200 molecules from Exp22K[38]
8/20250.05***0.76***----SpookyNet, transformer network with self-attention≈2.7 million equilibrium geometry and chemical shift calculations for a diverse collection of organic molecules601 marine natural products[41]
8/20250.09***1.02***----SpookyNet, transformer network with self-attention≈2.7 million equilibrium geometry and chemical shift calculations for a diverse collection of organic molecules601 marine natural products, with equilibrium geometries reproducing those in the training set[41]
1/20260.17090.9270----permutation-invariant set supervision problem with NMRNetnmrshiftdb24:1 random split[52]
1/2026 0.05590.5060----permutation-invariant set supervision problem with NMRNetmillions of molecular-spectral entries from the literature and nmrshiftdb24:1 random split[52]
*Employs crossvalidation with identical dataset
**Standard deviation instead of mean absolute error, error excludes atoms which are considered impossible to predict.
***Root mean squared error instead of mean absolute error.
****Not included in graph since a specialized subset for testing only.
Abbreviations: ML=machine learning, HOSE=Hierarchically Ordered Spherical Description of Environment, DFT-GIAO=density functional theory - independent atomic orbitals, CNN=Convolutional Neural Network, MPNN=message passing neural network

This figure uses the data from the above table, showing results for 1H and 13C NMR predictions from 1990 until now, ordered by publication time. The light lines give the least squares linear regression up to 6/2024 (this is the data from Nuclear Magnetic Resonance and Artificial Intelligence). The dashed light lines are the least squares linear regression for data up to 2/2001 (this is the data from Prediction of chemical shift in NMR: a review). Data from those timespans, which have been added later and are not in the respective publications, are not included in the regression. Squares indicate ab initio calculations, triangles deep learning methods, pentagons combined methods. As before, conclusions require careful analysis.

Chart as pdf

Literature

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  26. Ramos, S.A.; Mueller, L.J.; Beran, G.J.O. The interplay of density functional selection and crystal structure for accurate NMR chemical shift predictions. Faraday Discuss. 2024, pp. -. https://doi.org/10.1039/D4FD00072B.
  27. Han, C.; Zhang, D.; Xia, S.; Zhang, Y. Accurate Prediction of NMR Chemical Shifts: Integrating DFT Calculations with Three-Dimensional Graph Neural Networks. Journal of Chemical Theory and Computation 2024. https://doi.org/10.1021/acs.jctc.4c00422.
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  29. Maria Bånkestad; Kevin M. Dorst; Göran Widmalm; Jerk Rönnols. Carbohydrate NMR chemical shift prediction by GeqShift employing E(3) equivariant graph neural networks. RSC Advances, 2024, 14, 26585-26595.
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  34. E. E. Ondar, M. V. Polynski, V. P. Ananikov, Predicting 195Pt NMR Chemical Shifts in Water-Soluble Inorganic/Organometallic Complexes with a Fast and Simple Protocol Combining Semiempirical Modeling and Machine Learning. ChemPhysChem 2023, 24, e202200940.
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  40. Yiu C, Honoré B, Gerrard W, Napolitano-Farina J, Russell D, Trist IML, Dooley R, Butts CP. IMPRESSION generation 2 - accurate, fast and generalised neural network model for predicting NMR parameters in place of DFT. Chem Sci. 2025 Mar 31;16(19):8377-8382. doi: 10.1039/d4sc07858f
  41. Hehre T, Klunzinger PE, Deppmeier BJ, Ohlinger WS, Hehre WJ. Practical Machine Learning Strategies 4: Using Neural Networks to Replicate Proton and 13C NMR Chemical Shifts Obtained from ωB97X-D/6-31G* Density Functional Calculations. J Org Chem. 2025 Aug 15;90(32):11478-11485. doi: 10.1021/acs.joc.5c00927.
  42. Seokho Kang, Youngchun Kwon, Dongseon Lee, Youn-Suk Choi: Predictive Modeling of NMR Chemical Shifts without Using Atomic-Level Annotations, J. Chem. Inf. Model. 2020, 60, 8, 3765-3769.
  43. Duprat, F.; Ploix, J.-L.; Dreyfus, G. Can Graph Machines Accurately Estimate 13C NMR Chemical Shifts of Benzenic Compounds? Molecules 2024, 29, 3137. https://doi.org/10.3390/molecules29133137.
  44. Xu, F., Guo, W., Wang, F. et al. Toward a unified benchmark and framework for deep learning-based prediction of nuclear magnetic resonance chemical shifts. Nat Comput Sci 5, 292-300 (2025). https://doi.org/10.1038/s43588-025-00783-z.
  45. Smurnyy YD, Blinov KA, Churanova TS, Elyashberg ME, Williams AJ. Toward more reliable 13C and 1H chemical shift prediction: a systematic comparison of neural-network and least-squares regression based approaches. J Chem Inf Model. 2008 Jan;48(1):128-34. doi: 10.1021/ci700256n.
  46. Novitskiy IM, Kutateladze AG. Peculiar Reaction Products and Mechanisms Revisited with Machine Learning-Augmented Computational NMR. J Org Chem. 2022 Jul 1;87(13):8589-8598. doi: 10.1021/acs.joc.2c00749.
  47. Novitskiy IM, Kutateladze AG. DU8ML: Machine Learning-Augmented Density Functional Theory Nuclear Magnetic Resonance Computations for High-Throughput In Silico Solution Structure Validation and Revision of Complex Alkaloids. J Org Chem. 2022 Apr 1;87(7):4818-4828. doi: 10.1021/acs.joc.2c00169.
  48. Tsai YH, Amichetti M, Zanardi MM, Grimson R, Daranas AH, Sarotti AM. ML-J-DP4: An Integrated Quantum Mechanics-Machine Learning Approach for Ultrafast NMR Structural Elucidation. Org Lett. 2022 Oct 21;24(41):7487-7491.
  49. Jie Li, Jiashu Liang, Zhe Wang, Aleksandra L. Ptaszek, Xiao Liu, Brad Ganoe, Martin Head-Gordon, Teresa Head-Gordon: Highly Accurate Prediction of NMR Chemical Shifts from Low-Level Quantum Mechanics Calculations Using Machine Learning, J. Chem. Theory Comput. 2024, 20, 5, 2152-2166.
  50. Yao Li, Wen-Shuo Huang, Li Zhang, Dan Su, Haoran Xu, Xiao-Song Xue, Prediction of 19F NMR chemical shift by machine learning, Artificial Intelligence Chemistry, Volume 2, Issue 1, 2024, 100043, ISSN 2949-7477, https://doi.org/10.1016/j.aichem.2024.100043.
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Here follows a list of reviews about either spectrum prediction in particular or about NMR and AI/ML in general:

  1. Yao Luo, Xiaoxu Zheng, Mengjie Qiu, Yaoping Gou, Zhengxian Yang, Xiaobo Qu, Zhong Chen, Yanqin Lin, Deep learning and its applications in nuclear magnetic resonance spectroscopy, Progress in Nuclear Magnetic Resonance Spectroscopy, Volumes 146–147, 2025, 101556, https://doi.org/10.1016/j.pnmrs.2024.101556.
  2. HUANG Ting, WANG Jiaxin, ZHANG Wei, YAO Huan. Research Progress of Artificial Intelligence Assisted Nuclear Magnetic Resonance Spectroscopy[J]. Metrology Science and Technology, 2025, 69(7): 3-9. DOI: 10.12338/j.issn.2096-9015.2025.0045.
  3. Das S, Merz KM Jr. Exploring the Frontiers of Computational NMR: Methods, Applications, and Challenges. Chem Rev. 2025, 10.1021/acs.chemrev.5c00259.
  4. Piotr Klukowski, Roland Riek, Peter Güntert, Machine learning in NMR spectroscopy, Progress in Nuclear Magnetic Resonance Spectroscopy, Volumes 148–149, 2025, 101575, https://doi.org/10.1016/j.pnmrs.2025.101575
  5. Kuhn, S.; de Jesus, R.P.; Borges, R.M. Nuclear Magnetic Resonance and Artificial Intelligence. Encyclopedia 2024, 4, 1568-1580. https://doi.org/10.3390/encyclopedia4040102
  6. Xue X, Sun H, Yang M, Liu X, Hu HY, Deng Y, Wang X. Advances in the Application of Artificial Intelligence-Based Spectral Data Interpretation: A Perspective. Anal Chem. 2023 Sep 19;95(37):13733-13745. 10.1021/acs.analchem.3c02540.
  7. van de Sande DMJ, Merkofer JP, Amirrajab S, et al. A review of machine learning applications for the proton MR spectroscopy workflow. Magn Reson Med. 2023; 90(4): 1253-1270. doi: 10.1002/mrm.29793
  8. Vaibhav Kumar Shukla, Gabriella T. Heller, and D.Flemming Hansen, Biomolecular NMR spectroscopy in the era of artificial intelligence, Structure, 2023, 31, 1360-1374
  9. E. Jonas, S. Kuhn, N. Schlörer, Prediction of chemical shift in NMR: A review, Magn Reson Chem 2022, 60(11), 1021. https://doi.org/10.1002/mrc.5234
  10. Cobas C. NMR signal processing, prediction, and structure verification with machine learning techniques. Magn Reson Chem. 2020; 58: 512–519. https://doi.org/10.1002/mrc.4989
  11. Chen D, Wang Z, Guo D, Orekhov V, Qu X. Review and Prospect: Deep Learning in Nuclear Magnetic Resonance Spectroscopy. Chemistry. 2020 Aug 17;26(46):10391-10401. 10.1002/chem.202000246.
  12. Valli, Marilia, Russo, Helena Mannochio, Pilon, Alan Cesar, Pinto, Meri Emili Ferreira, Dias, Nathalia B., Freire, Rafael Teixeira, Castro-Gamboa, Ian and Bolzani, Vanderlan da Silva. "Computational methods for NMR and MS for structure elucidation I: software for basic NMR" Physical Sciences Reviews, vol. 4, no. 10, 2019, pp. 20180108. https://doi.org/10.1515/psr-2018-0108