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 small organic molecules, e. g. protein 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 28/3/2025.

Date1H MAE (ppm)13C MAE (ppm)17O MAE (ppm)15N MAE (ppm)19F MAE (ppm)195Pt MAE (ppm)Method Training Test Dataset Literature
1/19905.5**----- 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 NMRShiftD[7]
5/2007-2.22---- CSEARCH CSEARCH NMRShiftDB[7]
1/2008 0.28-----CHARGE n/a Wiley 1H NMR database[8]
1/2008 0.28-----Pretsch Increments n/a Wiley 1H NMR database[8]
1/2008 0.28-----Pretsch 3D increments n/a Wiley 1H NMR database[8]
1/2008 0.28-----Combined n/a Wiley 1H NMR database[8]
9/2008 0.154 -----HOSE NMRShiftDB *[9]
9/2008 0.154 -----J48 NMRShiftDB *[9]
9/2008 0.154 -----RF NMRShiftDB *[9]
9/2008 0.154 -----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]
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]
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]
6/2024-0.9***---- GNN 2026 organic molecules 171 benzenic structures[28]
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]
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]
*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). 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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