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REVIEW 4 major objections 6 minor 45 references

Universal band center model for the HER activity of non-metal site

T0 review · 4 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read A pz band center corrected by bandgap and ionization energy predicts hydrogen adsorption on non-metal sites across 144 MX2 compounds and beyond.

desk verdict A useful in-sample descriptor for HER on non-metal sites, but the "universal" claim is unverified because the descriptor and its linear fit were selected and evaluated on the same 144 MX2 data points. read the letter →

arxiv 2506.02567 v1 pith:2BPYGRDL submitted 2025-06-03 cond-mat.mtrl-sci

Ruixin Xu , Shiqian Cao , Tingting Bo , Yanyu Liu , Wei Zhou This is my paper
classification cond-mat.mtrl-sci
keywords hydrogenevolutionreactionpzbandcenterdescriptortransitionmetaldichalcogenidesnon-metalactivesitesdensityfunctionaltheoryrandomforestregressionmodifiedmodel
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 argues that hydrogen adsorption on the non-metal site of transition metal dichalcogenides is controlled by a single orbital descriptor: the X-pz band center, corrected by the material's bandgap and the chalcogen's first ionization energy. The authors compute 144 MX2 compounds with density functional theory, use a random forest model to identify the controlling features, and derive a modified band center from a rigid shift of the pre-adsorption density of states. The corrected descriptor reproduces the computed hydrogen adsorption free energy across the whole library with $R^2 = 0.90$, and the same linear trend extends to other 2D layered metal chalcogenides. If correct, the model gives a physical explanation for why the bare pz band center fails for semiconductors and a cheap screening rule for hydrogen evolution catalysts.

What carries the argument

The key object is the modified pz band center $\varepsilon_{p_z}^{re} = \varepsilon_{p_z} - \varepsilon_{\mathrm{gap}} + E_{I-X}$, where $\varepsilon_{p_z}$ is the projected X-pz band center of the clean surface, $\varepsilon_{\mathrm{gap}}$ is the calculated bandgap, and $E_{I-X}$ is the first ionization energy of the chalcogen. It is built in two steps: shifting the pre-adsorption pz density of states by $\varepsilon_{\mathrm{gap}}$ to mimic the bandgap-induced downshift of the bonding and antibonding states, and adding $E_{I-X}$ to remove the periodic offset among S, Se, and Te. This turns the bare pz band center, which fits each chalcogen family separately with $R^2$ between 0.40 and 0.71, into a single linear descriptor for the full MX2 library.

What would settle it

For a wide-gap MX2 such as 1H-MoS2, compare the energy shift of the H-s and X-pz bonding and antibonding peaks in the adsorbed projected density of states with the bandgap: if the shift is not uniformly equal to the bandgap, the rigid-shift derivation fails. Alternatively, apply the proposed linear relation to layered phosphides or nitrides and check whether their computed hydrogen adsorption free energies fall on the same line; a systematic deviation would falsify the claimed universality.

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Extended reading notes

Core claim

The central discovery is that the scatter in the standard pz band center for hydrogen adsorption on MX2 compounds is not noise but a bandgap effect. In semiconductor-like materials, hydrogen adsorption shifts the hybridized H-s and X-pz bonding and antibonding states downward by roughly the bandgap, so materials with nearly equal pz band centers can bind hydrogen very differently. Defining $\varepsilon_{p_z}^{re} = \varepsilon_{p_z} - \varepsilon_{\mathrm{gap}} + E_{I-X}$ collapses the data onto one line, $\Delta G_{H^*} = -0.77\,\varepsilon_{p_z}^{re} + 6.10$, with $R^2 = 0.90$ for all 144 MX2 compounds. The same descriptor places other 2D layered metal chalcogenides such as InS, GeS, SnS, and Bi2Se3 on the same trend, which the paper presents as a universal band center model for non-metal HER sites.

Load-bearing premise

The model assumes that the bandgap shifts the pre-adsorption pz density of states rigidly downward by exactly the bandgap upon hydrogen adsorption, and that adding the isolated atom's first ionization energy with coefficient 1 removes the periodic offset between chalcogens.

Editorial extensions

If this is right

  • The same linear relation $\Delta G_{H^*} = -0.77\,\varepsilon_{p_z}^{re} + 6.10$ predicts HER activity for other 2D layered metal chalcogenides such as InS, GeS, SnS, Bi2Se3, and Bi2Te3, not just the 144 MX2 library.
  • Because the descriptor needs only a clean-surface pz band center, a bandgap, and a tabulated ionization energy, screening for HER catalysts could skip the hydrogen-adsorption relaxation step.
  • The model explains the non-scaling law between pz band center and activity: the bandgap downshifts the antibonding state in semiconductors, weakening hydrogen adsorption relative to the bare band center expectation.
  • The periodic dependence of HER activity on the chalcogen element is attributed to the intrinsic p-orbital energy level of the X atom rather than primarily to bond length or charge transfer.

Reading between the lines

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

  • A direct out-of-family test would apply the same descriptor to layered phosphides, nitrides, or oxides, where the pz orbital and bandgap correction should play the same role; the paper does not include such data.
  • The rigid-shift assumption could be checked by computing the actual relaxation of occupied and unoccupied X-pz states upon hydrogen adsorption; a nonuniform shift would appear as a systematic residual for wide-gap compounds.
  • The coefficient +1 on the ionization energy is the least derived part of the model; fitting it or replacing it with a computed on-site p-orbital energy would test whether the descriptor transfers beyond S, Se, and Te.
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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

4 major / 6 minor

Summary. The paper reports DFT calculations of the hydrogen adsorption free energy ΔG_H* on 144 MX2 monolayers (24 metals, S/Se/Te, 1H/1T phases). A random forest regression identifies the X-pz band center, bandgap, and first ionization energy as key features. The authors propose a modified pz band center descriptor ε_pz^re = ε_pz - ε_gap + E_I-X, and report a linear relation ΔG_H* = -0.77 ε_pz^re + 6.10 with R²=0.90 (Eq. 7, Fig. 5i). They claim this descriptor is universal, extending to other 2D layered metal chalcogenides such as InS, GeS, SnS, and Bi2Se3 (Fig. S4b).

Significance. The paper assembles a substantial first-principles dataset of 144 MX2 monolayers and uses machine learning to identify physically plausible features influencing HER activity. If the proposed descriptor were validated by genuine out-of-sample tests, it would offer a simple and useful extension of band-center concepts to non-metal active sites. The improvement in R² from 0.40–0.71 (raw ε_pz) to 0.90 (modified descriptor) on the same dataset is encouraging. However, the headline 'universal predictor' claim is currently supported only by an in-sample fit and a qualitative supplementary figure, and the mechanistic corrections are introduced ad hoc. The predictive power of Eq. (7) therefore remains unestablished.

major comments (4)
  1. [III, 'The modified band center model', Eq. (7) and Fig. 5(i)] The reported R²=0.90 for Eq. (7) is an in-sample fit: the descriptor form was selected after inspecting random-forest feature importance on the same 144 DFT ΔG_H* values, and the slope and intercept of Eq. (7) are least-squares fits to those same points. The paper does not report any cross-validation or held-out test for the linear model. Because ε_gap and E_I-X take only a few distinct values across S, Se, and Te, the descriptor could absorb chalcogen-specific offsets. Please provide a genuine out-of-sample evaluation, such as training on two chalcogens and testing on the third, or training on one phase and testing on the other, and report the resulting R² and RMSE.
  2. [III, 'The modified band center model', Fig. S4b] The universality claim is supported only by a qualitative statement that the extension materials are 'well integrated' into the MX2 data points. No quantitative error metric, such as R², RMSE, or per-point deviations from Eq. (7), is given for the extension set, which shares the same chalcogen elements as the training set. Please quantify the agreement of the InS/GeS/SnS/Bi2Se3 etc. points with Eq. (7), including error bars on ΔG_H*, or temper the universality claim accordingly.
  3. [III, Eqs. (2)-(5)] The derivation of ε_pz^pre = ε_pz - ε_gap assumes that the post-adsorption electronic structure is obtained by rigidly shifting the pre-adsorption X-pz DOS by exactly ε_gap. The text states 'for the sake of model simplicity, the value of the specific deviation is not considered,' so this shift is not verified. Since this is the central mechanistic step, please test the assumption directly by comparing the pre- and post-adsorption PDOS for representative semiconducting systems, such as 1H-MoS2, and reporting the actual shift of the bonding and antibonding states relative to the PBE bandgap.
  4. [III, Eq. (6)] The first ionization energy E_I-X is added as a correction with a fixed coefficient of 1, motivated by the random-forest feature ranking on the same dataset. This is an ad hoc element rather than a derived term. Please treat the coefficient as a free parameter, report its fitted value with uncertainty, and validate the resulting four-parameter model (slope, intercept, bandgap coefficient, and E_I coefficient) on a held-out subset. A derivation or independent test for the role of E_I-X would strengthen the physical claim.
minor comments (6)
  1. [III, Eqs. (3)-(4)] The derivation around Eqs. (3)–(4) is difficult to follow because Eq. (4) appears garbled in the text; please rewrite the coordinate transformation cleanly and ensure the final expression Eq. (5) follows unambiguously.
  2. [III, Fig. 3(d)] In Fig. 3(d) and the text, the R² values 0.40, 0.56, and 0.71 are reported without the number of data points per subgroup; please state the counts and consider giving confidence intervals for R².
  3. [Abstract and Section III] The abstract refers to '144-transition metal dichalcogenides' while the text says '144 MX2 models'; please unify the terminology.
  4. [III, 'Training ML models for HER of MX2'] The sentence 'the first ionization energy and covalent radius of the same X atom are identical, meaning that there are just three pairs of identical features out of the 144 data points' is unclear; all compounds with the same X share identical values, so the statement should be rephrased.
  5. [References] Reference [42] for scikit-learn should cite Pedregosa et al., JMLR 12, 2825 (2011); Reference [43] for random forests should cite Breiman, Machine Learning 45, 5 (2001).
  6. [Fig. 4(b)] Please clarify in the caption or text whether the reported R²=0.98 and RMSE=0.087 for the random forest model are from cross-validation or from training predictions.

Circularity Check

2 steps flagged · score 6.0 of 10

The headline R2 = 0.90 is an in-sample fit: the descriptor terms and the linear coefficients of Eq. (7) were both determined from the same 144 DFT Delta G_H* values, so the MX2 prediction reduces to regression, and Eq. (5) is definitional under an assumed rigid DOS shift.

  1. fitted input called prediction [Section III, 'The modified band center model', Eqs. (6)-(7) and Fig. 5(i)]
    "Hence, the final modified band center model and predicted equation for ∆GH* would be written as, ... ε_pz^re = ε_pz − ε_gap + E_I-X (6) ... ∆G_H* = −0.77 ε_pz^re + 6.10 (7) It is astonishing that the HER activity of all MX2 could be well depicted by ε_pz^re with R2 of 0.90, as shown in Fig. 5(i)."

    Equation (7) is a least-squares line fitted to the same 144 DFT ∆G_H* values that were used to select the descriptor: the feature-importance ranking of Fig. 4(c) identifies ε_pz, ε_gap, and E_I-X on this dataset, and Eq. (6) is then assembled from those terms before Eq. (7) is fit to the same points. The reported R2 = 0.90 therefore measures in-sample correlation, not predictive accuracy; calling Eq. (7) a 'predicted equation' for MX2 is circular because the prediction is forced by the fit. No held-out MX2 split or external quantitative validation is reported for the R2; the other-2D-chalcogenide check (Fig. S4b) is described only qualitatively as 'well integrated.'

  2. self definitional [Section III, 'The modified band center model', Eqs. (3)-(5)]
    "Here, for the sake of model simplicity, the value of the specific deviation is not considered. Considering pz band center to calculate the weights for the new DOS (ε + εgap), and after the coordinate transformation, the original band center would be written as ... ε_pz^pre = ε_pz − ε_gap."

    The 'derivation' of the bandgap correction is definitional: the new DOS is defined as ρ'_pz(ε) = ρ_pz(ε + ε_gap), so the weighted-average formula (2) transforms identically into ε_pz − ε_gap. The result is thus true by construction and contains no independent information about how adsorption actually shifts bonding and antibonding states; the assumed rigid shift is the entire physical content. The text acknowledges this ('the value of the specific deviation is not considered'), but the paper still presents Eq. (5) as the origin of the bandgap-induced divergence.

full rationale

The central quantitative claim of the paper is Eq. (7), which is called a 'predicted equation,' but its coefficients are least-squares fitted to the same 144 DFT ∆G_H* values used to select ε_pz, ε_gap, and E_I-X via random-forest feature importance. Consequently R2 = 0.90 in Fig. 5(i) is an in-sample correlation, not an out-of-sample prediction; this is the strongest circular step. The bandgap correction in Eq. (5) is also definitional: once the DOS is assumed to shift rigidly as ρ'(ε) = ρ(ε + ε_gap), the identity ε_pz^pre = ε_pz − ε_gap follows algebraically, so the model's 'origin' is an ansatz rather than an independently derived mechanism. The universality claim is not wholly circular because the paper does add external 2D layered chalcogenides (InS, GeS, SnS, Bi2Se3, etc.) in Fig. S4b; however, that check is only qualitative ('well integrated') with no R2/RMSE, so it cannot be judged statistically. Self-citations ([20], [22]) merely document the known non-scaling-law problem and are not load-bearing for the new descriptor. Overall, the central MX2 R2 claim reduces to a fit, giving a score of 6.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The model rests on standard DFT approximations, a qualitative molecular-orbital picture, a rigid-shift bandgap correction, and an atomic ionization-energy term selected via feature importance on the same dataset. The main free parameters are the coefficients of the final linear fit and the hand-set unit coefficients in the descriptor. No new physical entities are introduced. The number of ad hoc choices is moderate for a descriptor paper, but the lack of independent validation is the main epistemic weakness.

free parameters (4)
  • slope and intercept of Eq. 7 = -0.77 eV^-1, 6.10 eV
    Linear regression coefficients tuned to the 144 DFT-calculated Delta G_H* values. The paper calls Eq. 7 a predicted equation, but it is a fit to the training data.
  • bandgap shift coefficient = 1 (fixed by assumption)
    Eq. 5 sets the DOS shift exactly equal to the PBE bandgap rather than fitting or deriving the coefficient. The text says the specific deviation is not considered for simplicity.
  • first ionization energy coefficient = 1 (fixed by assumption)
    Eq. 6 adds E_I-X with coefficient 1, selected after the random-forest model identified E_I-X as important. The coefficient is not fitted and not derived.
  • feature-selection threshold = |PCC| > 0.70
    The Pearson correlation threshold used to reduce 21 input features to 11 is chosen by hand and no ablation is reported.
assumptions (5)
  • domain assumption DFT with the PBE functional and DFT-D2 gives accurate Delta G_H* and bandgaps for HER on these TMDs.
    All adsorption free energies and bandgaps are computed at the GGA-PBE level without hybrid functionals or explicit treatment of PBE bandgap underestimation. This matters because the descriptor subtracts the bandgap. Invoked throughout the Methods section.
  • domain assumption Molecular orbital theory: the filling of the antibonding state formed by H-s and X-pz hybridization determines adsorption strength.
    Invoked in the section 'Origin of HER activity' with support from Refs. [39-41]. This is the standard d-band-style reasoning transferred to non-metal pz states, and its validity for gapped semiconductors is assumed.
  • ad hoc to paper The pre-adsorption pz DOS can be rigidly shifted by the bandgap to represent the post-adsorption electronic structure.
    Eq. 5 uses rho'(epsilon) = rho(epsilon + epsilon_gap). The text admits the specific deviation is not considered. This is the core modeling assumption and is not derived from first principles.
  • ad hoc to paper The NIST first ionization energy of the isolated chalcogen atom represents the periodic offset of the pz band center in the condensed phase.
    Added in Eq. 6 with coefficient 1 based on random-forest feature importance and NIST values. No derivation connects isolated-atom ionization energy to the condensed-phase band center offset.
  • domain assumption The selected 24 transition metals plus S, Se, Te in 1H and 1T phases constitute a representative and stable set of MX2 materials.
    IB and IIB metals are excluded as unstable layered structures based on Refs. [23,36]; no phase-stability or dynamic-stability check is reported for the 144 models.

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Cite this review

Pith. "Pith review of Universal band center model for the HER activity of non-metal site." pith.science (2026). https://pith.science/paper/2BPYGRDL

@misc{pith2026250602567,
  author       = {Pith},
  title        = {Pith review of: Universal band center model for the HER activity of non-metal site},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2BPYGRDL}},
  note         = {Machine review of arXiv:2506.02567}
}
read the original abstract

In this work, the hydrogen evolution reaction activities of non-metal sites in the transition metal dichalcogenides with the stoichiometry of MX2 are investigated using the first principles calculations. The trained machine learning model demonstrates that the pz band center, bandgap, and period effect are the key factors influencing the HER activity of MX2. Furthermore, it also reveals that the observed non-scaling law between the pz band center and HER activity in the semiconductor-like materials originates from the bandgap-induced downshift of bonding and antibonding states. In addition to the bandgap, the intrinsic p orbital energy level of the non-metal atoms also contributes to the periodic variation of pz band center. Extended calculations indicate that the descriptor is equally applicable to the other catalysts, suggesting its universality in predicting the HER activity of non-metal sites.

Figures

Figures reproduced from arXiv: 2506.02567 by the authors.

Figure 2
Figure 2. FIG 2. (a) Gibbs free energy diagram for HER on 1H [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. FIG 3. (a) PDOS of [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗

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