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REVIEW 3 major objections 5 minor 13 references

IMPRESSION -- Prediction of NMR Parameters for 3-dimensional chemical structures using Machine Learning with near quantum chemical accuracy

T0 review · 3 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read A machine-learning model trained on quantum-chemical NMR data can predict 1H shifts, 13C shifts, and 1JCH couplings at DFT-level accuracy in milliseconds.

desk verdict IMPRESSION is a genuinely fast ML replacement for DFT NMR prediction, but the 'independent' test set overlaps the training set (four identical CSD refcodes), so the headline MAEs need recomputation. read the letter →

arxiv 1908.08501 v2 pith:UL5RYU3F submitted 2019-08-22 physics.chem-ph

Will Gerrard , Lars Andersen Bratholm , Martin Packer , Adrian J. Mulholland , David R. Glowacki , Craig P. Butts This is my paper · ORCID
classification physics.chem-ph
keywords NMRpredictionkernelridgeregressionchemicalshiftsscalarcouplingsdensityfunctionaltheory3Dmolecularstructureadaptivesamplingvariancefiltering
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper establishes that a machine-learning system, IMPRESSION, trained on density-functional-theory (DFT) values rather than on experimental measurements, can predict three solution-state NMR parameters—proton and carbon chemical shifts ($\delta^{1}$H, $\delta^{13}$C) and one-bond carbon–proton couplings ($^{1}J_{\mathrm{CH}}$)—from a three-dimensional molecular structure with accuracy comparable to the DFT calculation it was trained on, but in tens of milliseconds instead of hours or days. On an independent test set the model reaches mean absolute errors of 0.23 ppm, 2.45 ppm, and 0.87 Hz for the three parameters, and a variance-based filter flags environments whose predictions should not be trusted. Because the machine learns from computed data, it does not depend on large, error-free experimental databases and can be used for three-dimensional problems like conformation and stereoisomer selection. The practical claim is that routine NMR-based structure elucidation can obtain near-DFT accuracy without paying DFT's computational cost.

What carries the argument

The machinery is kernel ridge regression over atomic chemical environments, using the FCHL representation, which describes a nucleus by the two- and three-body geometry of the atoms around it. The target value for an environment is a regularized weighted sum of kernel similarities to all training environments; for $^{1}J_{\mathrm{CH}}$, the similarity is the product of the carbon-environment and hydrogen-environment kernels. Training environments were chosen by adaptive sampling: repeatedly predict the full candidate pool with several models, add the structures with the highest cross-validation variance, and recompute the DFT references for them. The same variance calculation, evaluated before a prediction is made, serves as the confidence filter that identifies environments outside the training coverage. All reference values come from DFT at the $\omega$B97X-D/6-311g(d,p) level with gauge-invariant atomic orbitals and uncontracted basis functions, including all four spin–spin coupling contributions.

What would settle it

Take a molecule containing sp-hybridized atoms or a strongly anisotropic pi environment, within the same element set, and check whether its IMPRESSION predictions pass the variance cutoffs while differing from high-level DFT by more than 10 ppm for 13C or more than 5 Hz for 1JCH; one clean low-variance, high-error case would refute the claim that the variance filter identifies all unreliable predictions.

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Extended reading notes

Core claim

The central claim is that a kernel machine trained on DFT-computed NMR parameters is a faithful surrogate for the DFT method itself: given the same three-dimensional structure, IMPRESSION reproduces the reference calculations for $\delta^{1}$H, $\delta^{13}$C, and $^{1}J_{\mathrm{CH}}$ with test-set mean absolute errors of 0.23 ppm, 2.45 ppm, and 0.87 Hz, and root-mean-square errors of 0.35 ppm, 3.88 ppm, and 1.39 Hz. After applying a per-parameter variance filter, the model's agreement with experimental measurements on independent validation sets is essentially the same as the underlying DFT method's for proton shifts and one-bond couplings, and close for carbon shifts. The paper also shows that IMPRESSION reproduces DFT's ability to distinguish the correct diastereomer of a polycyclic alkaloid among 14 candidates from its $^{1}J_{\mathrm{CH}}$ values, and to assign diastereotopic protons, which demonstrates that the three-dimensional sensitivity needed for stereochemical problems survives the machine-learning approximation.

Load-bearing premise

The accuracy claim rests on the 882 training structures—drawn by adaptive sampling from a large database of crystal structures of molecules containing only carbon, hydrogen, nitrogen, oxygen, and fluorine—being representative enough of the chemical environments users will encounter that poorly covered cases are rare and that cross-validation variance flags them; the paper's outlier analysis shows sp-hybridized atoms and atoms near pi systems are where this boundary shows.

Editorial extensions

If this is right

  • Structure elucidation workflows that currently wait hours to days per candidate molecule can screen many conformers, diastereomers, or candidate structures in seconds, because the NMR prediction itself is no longer the bottleneck.
  • The variance filter gives each predicted value a usable confidence tag, so automated pipelines can send only uncertain predictions back to full DFT rather than recomputing everything.
  • Because the machine learns from the underlying DFT, any improvement in that DFT reference—better functionals, basis sets, or solvent models—should transfer directly to the machine's accuracy.
  • The learning curves indicate that increasing the training set roughly tenfold would approximately halve the current error, so the reported accuracy is not a ceiling.
  • Molecular-mechanics geometries, if paired with retrained models, could remove the expensive DFT geometry step as well, at the cost of a 30–50% increase in errors for some parameters.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Although the paper tests only carbon, hydrogen, nitrogen, oxygen, and fluorine chemistry, nothing in the kernel-ridge-regression mechanism is element-specific; training the same pipeline on DFT data for heteronuclei such as 15N, 19F, or 31P should work, provided a similarly diverse training superset can be assembled.
  • The variance-based confidence estimate could be used as a prior in Bayesian structure assignment: instead of simply capping errors, a likelihood could be built from the per-environment variance, a natural extension of the paper's geometric-mean error scoring.
  • The paper's own largest errors—up to 63 ppm for carbon shifts and 24.6 Hz for couplings—cluster around sp-hybridized atoms and atoms near pi systems, so a small deliberately diverse benchmark of such molecules would test whether the variance filter flags coverage failures reliably in practice.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The manuscript presents IMPRESSION, a kernel ridge regression (KRR) model with FCHL representations for predicting 1H and 13C chemical shifts and 1JCH scalar couplings from 3D molecular structures. Training labels are DFT values computed at the omega-b97xd/6-311g(d,p) level for 882 adaptively sampled C,H,N,O,F-containing CSD structures; the test set is 410 structures from the CSD-500 set. The authors report test-set MAEs of 0.23 ppm (delta-1H), 2.45 ppm (delta-13C), and 0.87 Hz (1JCH), and a variance-based pre-prediction filter that further improves these values. They also compare against experimental datasets and demonstrate that IMPRESSION can discriminate strychnine diastereomers nearly as well as the underlying DFT method, in a fraction of the computational time.

Significance. If the held-out accuracy numbers survive a clean train/test split, this is a timely and useful contribution: it shows that a kernel-based ML model can reproduce DFT-quality NMR parameters for a nontrivial portion of organic chemical space at negligible computational cost, and the variance filter is a practical way to flag unreliable predictions. The paper includes genuinely useful elements: adaptive sampling to build the training set, a learning-curve analysis, explicit Gaussian input files, and a stereoisomer discrimination test that goes beyond simple error metrics. The experimental comparisons, while not fully independent because of the fitted offset discussed below, are a strength of the paper. The central claim is clear and, subject to the dataset-integrity issue, well supported by the reported numbers.

major comments (3)
  1. [S1.4, S8, 2.1] The claimed independent test set is contaminated. Section 2.1 states that the 410 CSD-500 structures are an independent test set, but the SI training and test CSD lists in Section S8 both contain the exact refcodes AXADAF, IYASUW, LAFHEH and LILDEP. In addition, Section S1.4 states that the initial 100 training structures were chosen at random from the CSD-500 test set. Although those 100 were discarded after the first active-learning round, they were used to train the models that selected subsequent structures, so the training procedure itself was informed by test-set molecules. Because KRR is a memory-based method, train/test overlap can artificially inflate the reported MAE and RMSE values. The authors must compute the set intersection programmatically, remove every overlapping molecule (including graph-isomorphic duplicates under different refcodes), and recompute all unfiltered and variance-filtered test metrics. If the numbers change materially, the abstract's 'near quantum chemical accuracy' claim must be restated with corrected figures.
  2. [2.2] The variance-filter cutoffs (0.1 ppm, 5 ppm, 1 Hz) were selected using the test set itself: the text says 'We therefore identified variance cut-offs for IMPRESSION predictions that provide a good compromise between accuracy and excluded values for the test set.' This makes the filtered test-set MAE/RMSE values optimistically biased, because the filter thresholds were tuned to minimize error on the same data used for evaluation. The unfiltered test metrics are the primary evidence and should be reported as such; the filter cutoffs should be selected on a held-out portion of the training set or by nested cross-validation, and the filtered test metrics should be presented as exploratory rather than as the headline accuracy.
  3. [S1.3, 2.3] The 1JCH test and training labels are not pure DFT values. Section S1.3 states that a 10.91 Hz offset, derived from a comparison of DFT predictions to the 608 experimental couplings in Section 2.3, was applied to the DFT values in both the training and test datasets. Thus the reported 0.87 Hz MAE for 1JCH measures agreement with offset-corrected DFT, not with the raw quantum-chemical method. Moreover, the subsequent experimental comparison for 1JCH is not an independent test of the ML model, because the same experimental data were used to fit the offset. The authors should report the unfiltered raw-DFT test metrics as well, or clearly label the 1JCH results as 'DFT plus fitted offset' throughout the abstract and conclusions.
minor comments (5)
  1. [S1.1] Several citations in the SI are missing or rendered as question marks, e.g., 'Kernel Ridge Regression?' and 'Coulomb Matrix ?'. These placeholders should be replaced with proper references before resubmission.
  2. [2.2] The terms MAE, RMSE, and MaxE are used throughout but only MAE is defined; please define all three the first time they appear.
  3. [2.2] The typo 'comprimise' appears in the sentence introducing the variance cutoffs; it should be 'compromise'.
  4. [3] The conclusion says 'it's underlying DFT method'; this should be 'its underlying DFT method'.
  5. [S4, S6] The SI tables and figures for diastereotopic proton assignment and outlier structures would benefit from a short sentence in each caption stating which level of theory the 'DFT' column refers to (omega-b97xd/6-311g(d,p) after the linear-scaling/offset correction).

Circularity Check

3 steps flagged · score 6.0 of 10

The claimed independent test set is contaminated: four exact CSD refcodes appear in both the training and testing lists, and the adaptive-sampling seed was drawn from the CSD-500 test set; variance-filter thresholds were also tuned on the test set.

  1. fitted input called prediction [SI S1.4 (Adaptive sampling) and SI S8 (CSD structure lists)]
    "An initial set of 100 structures were chosen at random from the CSD-500 test set already obtained from the work by Emsley et al."

    The paper claims the test set is independent: 'The test set, against which the quality of the IMPRESSION predictions is independently tested, was comprised of a further 410 chemical structures ... harvested from the CSD-500 dataset.' However, the adaptive-sampling seed was drawn from that same CSD-500 test set, and the training and testing name lists in Section S8 contain identical refcodes (AXADAF, IYASUW, LAFHEH, LILDEP). Since KRR/FCHL is an interpolation method, a molecule whose environments were used in fitting will produce near-training-label predictions, so the reported held-out MAE/RMSE values (0.23 ppm, 2.45 ppm, 0.87 Hz) are partly in-sample, not a clean out-of-sample estimate of the central 'near DFT accuracy' claim.

  2. fitted input called prediction [Section 2.2 (Performance relative to DFT)]
    "We therefore identified variance cut-offs for IMPRESSION predictions that provide a good comprimise between accuracy and excluded values for the test set, which were found to be 1Hz for 1JCH, 0.1ppm for δ 1H and 5ppm for δ 13C."

    The variance-filter thresholds are selected by optimizing performance on the same test set that is then used to report the filtered accuracy (MAE = 0.23 ppm / 2.17 ppm / 0.81 Hz). This is a test-set fit: the filtered numbers are not a fixed a-priori filter but an in-sample tuned result. The unfiltered metrics are not affected, so this is a partial circularity that inflates the headline filtered accuracy.

1 more flagged steps
  1. fitted input called prediction [SI S1.3 (Correction of DFT NMR parameter predictions for comparison to experiment) and Section 2.3]
    "As a result, the offset (10.91Hz) was applied to the DFT values in both the training and test datasets."

    The 10.91 Hz offset is the average DFT-minus-experiment error measured on the Venkata experimental set, and the same Venkata set is used in Section 2.3 as the experimental validation for 1JCH. Applying this fitted offset to both training and test DFT labels guarantees that any model trained on those labels inherits the calibration, so the reported near-match between variance-filtered IMPRESSION and DFT on that experimental set (MAE 2.01 Hz vs 1.83 Hz) is partly a consequence of the fitted offset rather than an independent prediction. The core ML-vs-DFT reproduction claim is not affected.

full rationale

The paper's main idea — train a kernel machine on DFT-computed NMR parameters and test whether it reproduces DFT on new structures — is not circular in its design: the training labels are DFT values, the models are standard KRR/FCHL, and a genuinely disjoint held-out set would provide independent evidence. No load-bearing self-citation or uniqueness-import argument appears; citations to the QML toolkit and prior Bratholm papers are supporting software/methods references, not the source of the prediction claim. The circularity that does exist is concrete dataset construction and evaluation leakage. First, the 'independent' test set is not fully disjoint from training: the adaptive-sampling seed was chosen from the CSD-500 test set, and the supplied CSD lists contain four exact overlapping refcodes (AXADAF, IYASUW, LAFHEH, LILDEP). Because KRR/FCHL predictions interpolate from training environments, including these molecules in the test set makes a portion of the reported held-out error in-sample. Second, the variance-filter thresholds are explicitly chosen to optimize accuracy on the test set and then evaluated on that same test set, making the filtered metrics partially tuned rather than predictive. Third, the 1JCH experimental comparison inherits a 10.91 Hz offset fitted to the same experimental dataset later used for validation, so the IMPRESSION-vs-experiment agreement is partly calibrated. These issues do not make the entire derivation equivalent to its inputs — the unfiltered learning curves, external DP4 and Venkata validations, and strychnine discrimination provide independent content — but they do mean the headline quantitative claims need recomputation on a truly disjoint test set with fixed filters and independently derived offsets. A score of 6 reflects this partial circularity: several reported 'held-out' or 'filtered' predictions reduce, at least in part, to training or tuning on the evaluation data.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The central claim rests on two pillars: the ML regressor faithfully interpolates DFT labels, and the DFT labels themselves are a valid surrogate for experimental NMR. The former is well tested on a held-out set; the latter is only approximately true, as shown by the 10.91 Hz systematic offset for 1JCH and the imperfect δ13C agreement with experiment. The method introduces no new physical entities but does rely on a chain of domain assumptions about descriptor completeness and training set coverage.

free parameters (5)
  • Kernel width sigma (Laplacian kernel) = not reported
    Hyperparameter for FCHL kernel similarity; optimized via Bayesian optimization with 5-fold CV (SI S1.5), but the optimal value is not stated in the text.
  • l2 regularization lambda = not reported
    Regularization coefficient in KRR objective (SI S1.1); optimized with sigma and cutoff radius, value not given.
  • Atomic environment cutoff radius = not reported
    Cutoff for FCHL environment representation; optimized, value not reported.
  • 1JCH DFT-to-experiment offset = 10.91 Hz
    Systematic offset applied to DFT 1JCH values in training and test sets to match experiment (SI S1.3). Fitted to the Venkata experimental set; it becomes part of the target labels the model learns.
  • Variance filter cutoffs = 0.1 ppm (1H), 5 ppm (13C), 1 Hz (1JCH)
    Chosen as a compromise between accuracy and excluded values on the test set (Section 2.2); they are then applied to experimental validation sets, so part of the reported accuracy is conditional on test-set-selected thresholds.
assumptions (5)
  • standard math Kernel ridge regression with a Laplacian (or FCHL) kernel provides a valid similarity measure for atomic environments.
    Used throughout; the regression is a standard regularized least-squares method (Eqs. 1-3).
  • domain assumption FCHL representations encode the chemical environment of each nucleus well enough for NMR parameter prediction.
    The paper finds FCHL outperforms aSLATM and Coulomb matrices but does not prove that the representation is complete; it is assumed that the environment similarity correlates with NMR parameter similarity.
  • domain assumption DFT at the omegaB97XD/6-311G(d,p) level with GIAO and the 'mixed' option yields NMR parameters accurate enough to serve as training targets and reference values.
    The paper validates this indirectly against experiment (with an offset for 1JCH) but relies on DFT as the ground truth for the central claim of 'near DFT accuracy'.
  • domain assumption The 882 adaptively sampled CSD structures (C,H,N,O,F only) are representative of the chemical space of target molecules.
    The training set spans the CSD but excludes heteroatoms beyond N,O,F and halogens; outliers like sp-hybridized carbons show coverage limits.
  • domain assumption Using a single conformer per molecule for DFT and IMPRESSION comparisons is sufficient to demonstrate relative accuracy.
    Explicitly stated in Section 2.3; this limits direct agreement with experimental data but allows a clean DFT vs ML comparison.

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Cite this review

Pith. "Pith review of IMPRESSION -- Prediction of NMR Parameters for 3-dimensional chemical structures using Machine Learning with near quantum chemical accuracy." pith.science (2026). https://pith.science/paper/UL5RYU3F

@misc{pith2026190808501,
  author       = {Pith},
  title        = {Pith review of: IMPRESSION -- Prediction of NMR Parameters for 3-dimensional chemical structures using Machine Learning with near quantum chemical accuracy},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UL5RYU3F}},
  note         = {Machine review of arXiv:1908.08501}
}
read the original abstract

The IMPRESSION (Intelligent Machine PREdiction of Shift and Scalar Information Of Nuclei) machine learning system provides an efficient and accurate route to the prediction of NMR parameters from 3-dimensional chemical structures. Here we demonstrate that machine learning predictions, trained on quantum chemical computed values for NMR parameters, are essentially as accurate but computationally much more efficient (tens of milliseconds per molecule) than quantum chemical calculations (hours/days per molecule). Training the machine learning systems on quantum chemical, rather than experimental, data circumvents the need for existence of large, structurally diverse, error-free experimental databases and makes IMPRESSION applicable to solving 3-dimensional problems such as molecular conformation and isomerism

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Reference graph

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Reviewed August 14, 2026 · model on record in the stance chip above.