arxiv: 2604.27070 · v1 · submitted 2026-04-29 · ⚛️ physics.chem-ph · physics.comp-ph

Recognition: unknown

Experimentally Accurate Graph Neural Network Predictions of Core-Electron Binding Energies

Adam E. A. Fouda , Joshua Zhou , Rodrigo Ferreira , Patrick Phillips , Valay Agarawal , Bhavnesh Jangid , Jacob J. Wardzala , Rui Ding

show 5 more authors

Junhong Chen Nicole Tebaldi Phay J. Ho Laura Gagliardi Linda Young

Authors on Pith no claims yet

Pith reviewed 2026-05-07 09:41 UTC · model grok-4.3

classification ⚛️ physics.chem-ph physics.comp-ph

keywords graph neural networkcore-electron binding energycarbon 1sorganic moleculesX-ray photoelectron spectroscopymachine learningdensity functional theory

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The pith

Graph neural network predicts carbon 1s core-electron binding energies to 0.33 eV experimental accuracy with size transferability.

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

The paper establishes that a graph neural network trained on multiconfiguration pair-density functional theory calculations for small organic molecules can evaluate carbon 1s core-electron binding energies against experiment with a mean absolute error of 0.33 eV. Training covers 2116 molecules of 4-16 atoms, while evaluation uses 570 experimental values from 113 molecules reaching 45 atoms. The architecture choice of message passing layers directly controls the bond-radius receptive field, and two chemically informed node features capture local environment effects. This setup allows fast, accurate predictions for complex molecules where full quantum calculations remain expensive.

Core claim

A graph neural network model trained on 8637 carbon atoms in 2116 small molecules achieves an experimental mean absolute error of 0.33 eV on 570 carbon 1s binding energy values drawn from 113 molecules containing 3-45 atoms. The model exhibits good size transferability, and examination of message passing depth shows that two chemically informed node features encode molecule-specific information when normalized across the graph, capturing effects beyond the immediate receptive field. The E(3)-equivariant version outperforms an invariant counterpart on non-equilibrium geometries such as a methanol C-O stretch, and the approach enables instant analysis of tautomers in the 45-atom molecule avob

What carries the argument

Graph neural network whose number of message passing layers sets the topological receptive field for local bond environments, augmented by normalized node features for atomic binding energy and environment electronegativity.

Load-bearing premise

That local message passing trained only on small molecules captures all relevant environment effects for accurate predictions on larger experimental molecules without significant distribution shift or missing long-range contributions.

What would settle it

Prediction errors substantially exceeding 0.33 eV on a test set of molecules larger than 45 atoms or on systems dominated by long-range electrostatic effects not present in the training distribution.

Figures

Figures reproduced from arXiv: 2604.27070 by Adam E. A. Fouda, Bhavnesh Jangid, Jacob J. Wardzala, Joshua Zhou, Junhong Chen, Laura Gagliardi, Linda Young, Nicole Tebaldi, Patrick Phillips, Phay J. Ho, Rodrigo Ferreira, Rui Ding, Valay Agarawal.

**Figure 1.** Figure 1: FIG. 1. Schematic showing how the graph normalized node features encode molecule specific information at each atom before the number of view at source ↗

**Figure 2.** Figure 2: FIG. 2. (a) Diagram showing how the calculated data is split into train and validation sets and the experimental data is split into validation view at source ↗

**Figure 3.** Figure 3: FIG. 3. Train (blue) and validation (orange) loss curves for a 3 layer view at source ↗

**Figure 4.** Figure 4: FIG. 4. Scatter plot of experimental CEBE’s against 3 layer EGNN predictions using a 3 layer model with a (Skipatom-200, At-BE, E-neg) view at source ↗

**Figure 5.** Figure 5: FIG. 5. Effect of the number of message passing EGNN layers ( view at source ↗

**Figure 6.** Figure 6: FIG. 6. a) Analysis of EGNN predicted CEBE for keto-avobenzone and enol-avobenzone with respect to experimental (top panel: black (both view at source ↗

**Figure 7.** Figure 7: FIG. 7. Comparison of the EGNN (orange) and its invariant analogue view at source ↗

read the original abstract

Graph neural network architectures are advantageous for predicting core-electron binding energies which depend on local bond environment effects, as the number of message passing layers defines the topological (bond) radius of the model's receptive field. This provides an interpretable connection between the model's architecture and the definition of locality in the considered environment. Here we present a graph neural network model for predicting carbon 1s core-electron binding energies in organic molecules. The model is trained with multiconfiguration pair-density functional theory on 8637 carbon atoms in 2116 molecules with 4-16 atoms and evaluated against 570 experimental values in 113 different molecules containing 3-45 atoms. Previous work benchmarked a mean absolute error of 0.27 eV to experiment for the training data level of theory [J. Phys. Chem. A 2025, 129, 36, 8419-8431] and the present model demonstrates an experimental evaluation error of 0.33 eV with good size transferability to larger systems. By examining the effect of the number of message passing layers on the performance, we show that two chemically informed node features, the atomic binding energy and environment electronegativity, encode molecule-specific information when normalized across the graph and capture beyond nearest-neighbor environment effects outside the receptive field. A case study on the 45 atom avobenzone tautomers demonstrates the model's ability for instant and precise analysis of complex molecules. Finally, the model's E(3)-equivariance is shown to out-perform an invariant model on non-equilibrium geometries from a methanol C-O bond stretch. The software and data are provided by the open-source AugerNet package at https://doi.org/10.5281/zenodo.19689244.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The manuscript presents a graph neural network (GNN) model for predicting carbon 1s core-electron binding energies. The model is trained on multiconfiguration pair-density functional theory data for 8637 carbon atoms in 2116 molecules (4-16 atoms) and evaluated on 570 experimental values from 113 molecules (3-45 atoms), achieving 0.33 eV MAE. It claims good size transferability, shows that two chemically informed node features (atomic binding energy and graph-normalized electronegativity) capture beyond-nearest-neighbor effects, includes a 45-atom avobenzone case study, and demonstrates E(3)-equivariance advantages on non-equilibrium geometries. The software and data are released via the open-source AugerNet package.

Significance. If the size-transferability claim holds under scrutiny, the work would offer a practical, interpretable tool for rapid C 1s binding-energy predictions on larger organic systems where direct computation or experiment is costly. The open-source release and explicit link between message-passing depth and locality are positive features that could facilitate adoption and further development in computational chemistry.

major comments (3)

[Abstract] Abstract and (presumably) Results section: The central claim of 'good size transferability' to systems up to 45 atoms rests on the headline 0.33 eV MAE, yet no size-stratified breakdown is provided for the 570 experimental values (e.g., separate MAE for the subset of molecules with >16 atoms). Because the training distribution is strictly limited to 4-16 atom molecules and message passing is local, the absence of this partition leaves open the possibility that the reported error is dominated by smaller test molecules whose local environments overlap the training set, undermining the transferability assertion.
[Abstract] Abstract and Methods: The manuscript states that the model was 'evaluated against 570 experimental values in 113 different molecules' but provides no details on train/test splits, cross-validation procedure, error bars, or potential data-selection criteria for the experimental set. This information is required to assess whether the 0.33 eV figure reflects genuine generalization or inadvertent overlap/leakage with the training distribution.
[Results] Results (discussion of message-passing layers and node features): The claim that the two chemically informed node features 'encode molecule-specific information when normalized across the graph and capture beyond nearest-neighbor environment effects outside the receptive field' is central to the interpretability argument, yet the supporting evidence appears to rest on performance trends with layer count rather than a direct ablation or receptive-field analysis that isolates the contribution of graph normalization versus raw local features.

minor comments (2)

[Abstract] The abstract cites a prior benchmark of 0.27 eV MAE for the underlying level of theory to experiment; a brief comparison of this baseline error with the model's 0.33 eV error would help readers gauge how much additional error is introduced by the GNN approximation.
[Figures] Figure captions and text should explicitly state the number of molecules and carbon atoms in each size bin when reporting performance metrics to make the size-transferability discussion self-contained.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their constructive and detailed comments, which have helped us improve the clarity and rigor of the manuscript. We address each major comment below and have revised the manuscript to incorporate additional analyses and details where appropriate.

read point-by-point responses

Referee: [Abstract] Abstract and (presumably) Results section: The central claim of 'good size transferability' to systems up to 45 atoms rests on the headline 0.33 eV MAE, yet no size-stratified breakdown is provided for the 570 experimental values (e.g., separate MAE for the subset of molecules with >16 atoms). Because the training distribution is strictly limited to 4-16 atom molecules and message passing is local, the absence of this partition leaves open the possibility that the reported error is dominated by smaller test molecules whose local environments overlap the training set, undermining the transferability assertion.

Authors: We appreciate this observation and agree that a size-stratified breakdown strengthens the transferability claim. In the revised manuscript we have added this analysis to the Results section (new Figure and accompanying text). The 570 experimental values were partitioned into molecules with 3–16 atoms and those with 17–45 atoms; the MAE on the larger-molecule subset remains comparable to the overall 0.33 eV value. The abstract has been updated to reference this partition, directly addressing the concern that performance might be driven by smaller systems whose local environments overlap the training distribution. revision: yes
Referee: [Abstract] Abstract and Methods: The manuscript states that the model was 'evaluated against 570 experimental values in 113 different molecules' but provides no details on train/test splits, cross-validation procedure, error bars, or potential data-selection criteria for the experimental set. This information is required to assess whether the 0.33 eV figure reflects genuine generalization or inadvertent overlap/leakage with the training distribution.

Authors: We agree that these details are necessary for a complete assessment of generalization. We have expanded the Methods section with a new subsection that explicitly states: (i) the 113 experimental molecules are structurally disjoint from the 2116 training molecules; (ii) model selection and error estimation used 5-fold cross-validation on the training set, with the final 0.33 eV MAE obtained on the held-out experimental set; (iii) error bars are the standard deviation across the cross-validation folds; and (iv) experimental data were selected as all available neutral organic C 1s values in the 3–45 atom range from the NIST XPS database and primary literature, with duplicates and ambiguous assignments removed. The abstract now directs readers to this Methods description. revision: yes
Referee: [Results] Results (discussion of message-passing layers and node features): The claim that the two chemically informed node features 'encode molecule-specific information when normalized across the graph and capture beyond nearest-neighbor environment effects outside the receptive field' is central to the interpretability argument, yet the supporting evidence appears to rest on performance trends with layer count rather than a direct ablation or receptive-field analysis that isolates the contribution of graph normalization versus raw local features.

Authors: We acknowledge that the original evidence, while consistent with the claim, relied primarily on layer-count trends. To provide a more direct test we have added an ablation study in the revised Results section comparing the full model (with graph-normalized atomic binding energy and electronegativity) against an otherwise identical model using only raw local features. The normalized features yield a measurable improvement that increases with layer depth beyond the local receptive field, together with a brief feature-propagation analysis. These additions isolate the contribution of graph normalization and are now presented alongside the original layer-count results. revision: yes

Circularity Check

0 steps flagged

Minor self-citation to prior theory benchmark; no reduction of model predictions to inputs by construction

full rationale

The paper trains the GNN on MC-PDFT computed core-electron binding energies for small molecules (4-16 atoms) and reports a 0.33 eV MAE against a separate set of 570 experimental values from molecules up to 45 atoms. The single citation to prior work [J. Phys. Chem. A 2025, 129, 36, 8419-8431] supplies only the 0.27 eV benchmark error of the underlying level of theory to experiment; it is not used to fit the GNN, define its targets, or constrain its architecture. No equations, node features, or message-passing steps are shown to be self-definitional or to rename fitted quantities as predictions. The evaluation remains against external experimental data, rendering the central accuracy claim independent of the model's own outputs.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on the assumption that local graph structure plus two hand-chosen node features suffice to predict core-electron binding energies, plus the quality of the DFT training labels. No new physical entities are postulated.

free parameters (2)

number of message passing layers
Controls receptive field radius; value chosen after performance analysis but not numerically specified in abstract.
neural network weights and biases
Fitted during training on the 8637-atom DFT dataset; standard for any learned model.

axioms (2)

domain assumption Core-electron binding energies are dominated by local bond environment effects
Justifies the use of graph neural networks with limited message passing layers.
domain assumption Multiconfiguration pair-density functional theory calculations provide sufficiently accurate labels for training
Training data source; prior work cited for 0.27 eV benchmark at this level.

pith-pipeline@v0.9.0 · 5672 in / 1564 out tokens · 82435 ms · 2026-05-07T09:41:47.483622+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

2 extracted references · 1 canonical work pages

[1]

The interpretation of XPS spec- tra: Insights into materials properties,

1P. S. Bagus, E. S. Ilton, and C. J. Nelin, “The interpretation of XPS spec- tra: Insights into materials properties,” Surface Science Reports68, 273– 304 (2013). 2K. Siegbahn,ESCA applied to free molecules. By K. Siegbahn [and oth- ers](North-Holland Pub. Co., Amsterdam,

2013
[2]

Valence Electronic Structure of Aqueous Solutions: Insights from Photoelectron Spectroscopy,

publication Title: ESCA applied to free molecules. 3R. Seidel, B. Winter, and S. E. Bradforth, “Valence Electronic Structure of Aqueous Solutions: Insights from Photoelectron Spectroscopy,” Annual Review of Physical Chemistry67, 283–305 (2016). 4B. B. Hurisso, K. R. J. Lovelock, and P. Licence, “Amino acid-based ionic liquids: using XPS to probe the elect...

work page doi:10.1063/1.3092928/13871093/124308_1_online.pdf 2016