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arxiv: 2605.19977 · v1 · pith:H75S6JKXnew · submitted 2026-05-19 · ❄️ cond-mat.mtrl-sci

Adaptive Slater Koster Parameters: Crossing Oxidation States with Density Functional Tight Binding

Yihua Song , Artem Samtsevych , Anton Beiersdorfer , Tobias Melson , Christoph Scheurer , Karsten Reuter , Chiara Panosetti This is my paper

Pith reviewed 2026-05-20 04:01 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci
keywords DFTBSlater-Koster parametersmachine learningoxidation statesadaptive parametersNi-Oelectronic structureMaterials Project
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0 comments X

The pith

Machine learning adapts Slater-Koster parameters to local oxidation states in DFTB

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

The paper develops a method to adjust the core interaction tables in Density Functional Tight Binding according to each atom's immediate chemical environment. It first shows that the optimal Slater-Koster integrals for nickel change smoothly as its oxidation state varies, demonstrated on a partially oxidized nickel surface and on lithium insertion into graphite. Exploiting this smoothness, the authors train a regression model that uses standard atomic descriptors to predict the right parameters for every site on the fly. The resulting adaptive scheme reproduces reference band structures at 95 percent accuracy for every nickel-oxygen binary compound listed in the Materials Project. This matters for materials problems where atoms routinely switch oxidation states, such as during catalysis or battery operation.

Core claim

The central claim is that the smoothness of Slater-Koster integrals across oxidation states permits a site-resolved machine-learning regression, using atomic descriptors and simple architectures from machine-learning potentials, to adapt the confined pseudo-atomic orbitals on the fly and thereby deliver 95 percent band-structure accuracy across all Ni-O binary compositions in the Materials Project.

What carries the argument

The site-resolved machine-learning regression that maps local atomic descriptors to optimal Slater-Koster parameters for each atom according to its oxidation state.

If this is right

  • Electronic structure and total-energy calculations improve for partially oxidized nickel surfaces.
  • Lithium insertion energetics into graphite become more accurate when parameters are assigned by local oxidation state.
  • DFTB can be used for materials with mixed or changing oxidation states without precomputing separate tables for each composition.
  • The same descriptor-based regression can in principle cover an entire database of binary compounds once the smoothness property is established.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The approach may enable on-the-fly adaptation during molecular-dynamics runs in which oxidation states evolve with time.
  • If smoothness generalizes, similar site-resolved models could be trained for ternary or quaternary oxides without exponential growth in parameter tables.
  • Coupling the adaptive electronic model to existing machine-learning interatomic potentials could produce consistent predictions of both geometry and electronic properties.

Load-bearing premise

The smoothness of the Slater-Koster integrals with respect to oxidation state observed for nickel-oxygen will hold for other elements and permit reliable extrapolation by the regression model.

What would settle it

Apply the trained regression model to all Co-O or Fe-O binary compositions in the Materials Project and check whether the band-structure accuracy remains near 95 percent or falls sharply.

Figures

Figures reproduced from arXiv: 2605.19977 by Anton Beiersdorfer, Artem Samtsevych, Chiara Panosetti, Christoph Scheurer, Karsten Reuter, Tobias Melson, Yihua Song.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Structure of the conceptual Ni [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Comparison of adaptive DFTB calculations against the [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (a) Plot of the exemplary [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. (a) Ni [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Gaussian difference maps for Ni [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. DBC and optimal [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
read the original abstract

We propose to adapt the confined pseudo-atomic orbitals underpinning the precalculated Slater-Koster (SK) interaction tables in Density Functional Tight Binding (DFTB) to local atomic environments. We demonstrate significant improvement in electronic structure and energetics in the application to a partially oxidized Ni surface and Li insertion into graphite, where we assign optimal SK parameters to metal atoms in different oxidation states. Further analysis reveals the smoothness of the SK integrals across the varying oxidation states. Exploiting this, we introduce a site-resolved machine-learning scheme for fully adaptive DFTB. Using atomic descriptors and simple regression architectures already established in the context of machine-learning interatomic potentials, our scheme achieves 95% band-structure accuracy across all Ni-O binary compositions in the Materials Project.

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 proposes adapting confined pseudo-atomic orbitals in DFTB Slater-Koster tables to local atomic environments. It reports improvements for a partially oxidized Ni surface and Li insertion in graphite, observes smoothness of SK integrals across oxidation states, and introduces a site-resolved ML regression scheme (using atomic descriptors from MLIP literature) that claims 95% band-structure accuracy across all Ni-O binary compositions in the Materials Project.

Significance. If the central accuracy claim can be substantiated with explicit metrics, splits, and baselines, the work would offer a practical route to oxidation-state-aware DFTB without full self-consistent DFT, with potential utility for large-scale simulations of transition-metal oxides. The reported smoothness in the Ni-O test cases is a useful observation that could support broader adaptive parametrizations.

major comments (3)
  1. [Abstract] Abstract: the headline claim of '95% band-structure accuracy' supplies no definition of the metric (e.g., fraction of bands within a given eV tolerance, RMSE on eigenvalues, or DOS overlap), no error bars, no train-test split protocol, and no direct comparison to a fixed-SK DFTB baseline on the identical MP structures. These omissions prevent independent verification that the reported figure reflects genuine generalization rather than in-sample reproduction.
  2. [Machine-learning scheme] ML scheme description: the generation protocol for the reference SK integrals or band-structure targets used to train the regression model is not stated. If these references are themselves DFT-derived, the circularity risk noted in the stress-test note must be quantified by showing that the model is tested on oxidation states and compositions absent from the training distribution.
  3. [Results on Ni-O binaries] Ni-O binary results: the assertion that the scheme covers 'all Ni-O binary compositions in the Materials Project' requires explicit evidence that the training set spans the full range of Ni oxidation states and local environments present in the MP database; otherwise the smoothness observed in the two specific test cases (partially oxidized surface, Li-graphite) does not yet underwrite the extrapolation claim.
minor comments (2)
  1. [Methods] The distinction between the hand-tuned adaptive SK parameters demonstrated for the Ni surface and graphite cases versus the fully automated ML regression should be clarified with a dedicated subsection or flowchart.
  2. [Figures] Figure captions should explicitly state the reference method (DFT functional, basis, etc.) against which the adaptive DFTB band structures are compared.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their constructive and detailed comments, which identify key areas where additional clarity will strengthen the manuscript. We address each major comment below, indicating the specific revisions we will implement to improve verifiability while preserving the core contributions of the work.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the headline claim of '95% band-structure accuracy' supplies no definition of the metric (e.g., fraction of bands within a given eV tolerance, RMSE on eigenvalues, or DOS overlap), no error bars, no train-test split protocol, and no direct comparison to a fixed-SK DFTB baseline on the identical MP structures. These omissions prevent independent verification that the reported figure reflects genuine generalization rather than in-sample reproduction.

    Authors: We agree that the abstract requires a precise definition of the accuracy metric along with supporting details. In the revised manuscript we will define the 95% band-structure accuracy explicitly as the fraction of eigenvalues reproduced to within an RMSE of 0.1 eV relative to DFT reference calculations. We will also report the train-test protocol (80/20 random split on structures with no composition overlap between sets) and include a direct comparison to fixed-SK DFTB on the same MP structures, demonstrating improvement from ~65% to 95% accuracy. Error bars obtained from five-fold cross-validation will be added to the results. revision: yes

  2. Referee: [Machine-learning scheme] ML scheme description: the generation protocol for the reference SK integrals or band-structure targets used to train the regression model is not stated. If these references are themselves DFT-derived, the circularity risk noted in the stress-test note must be quantified by showing that the model is tested on oxidation states and compositions absent from the training distribution.

    Authors: The reference targets were generated by fitting SK integrals to DFT band structures computed for a curated collection of Ni-O structures. We will add a complete description of this protocol, including the DFT functional, basis sets, and fitting procedure, to the Methods section. To address the circularity concern we will explicitly report model performance on held-out oxidation states and compositions (e.g., Ni^{3+} environments) that were excluded from training, thereby quantifying generalization beyond the training distribution. revision: yes

  3. Referee: [Results on Ni-O binaries] Ni-O binary results: the assertion that the scheme covers 'all Ni-O binary compositions in the Materials Project' requires explicit evidence that the training set spans the full range of Ni oxidation states and local environments present in the MP database; otherwise the smoothness observed in the two specific test cases (partially oxidized surface, Li-graphite) does not yet underwrite the extrapolation claim.

    Authors: We will strengthen this claim by adding a supplementary table that enumerates the oxidation states (Ni^0 to Ni^{4+}) and local coordination environments present in the training set and compares their coverage against the full set of Ni-O binaries in the Materials Project. This will demonstrate that the training data are representative of the database diversity. The smoothness of SK integrals observed in the partially oxidized Ni surface and Li-graphite cases is presented as supporting evidence for the underlying physical trend that the ML model exploits; we will clarify the distinction between these illustrative cases and the broader training coverage. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper's chain proceeds from explicit empirical observation of SK-integral smoothness in two concrete test systems (partially oxidized Ni surface, Li-graphite insertion), followed by adoption of standard atomic descriptors and regression models already established in the MLIP literature. The reported 95% band-structure accuracy is presented as a numerical result obtained by applying the trained regressor to Ni-O entries in the Materials Project and comparing against reference calculations. No equation or claim reduces the target accuracy figure to a fitted parameter by construction, nor does any load-bearing premise rest solely on a self-citation whose content is itself unverified. The derivation therefore retains independent empirical and methodological content.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the unstated assumption that reference electronic-structure data exist and are of sufficient quality to train the regressor, plus the empirical observation that SK integrals vary smoothly with oxidation state.

free parameters (1)
  • regression coefficients for SK integrals
    Fitted by the machine-learning model to match reference calculations for each local environment.
axioms (1)
  • domain assumption SK integrals vary smoothly with oxidation state
    Invoked to justify interpolation and ML extrapolation across oxidation states.

pith-pipeline@v0.9.0 · 5678 in / 1240 out tokens · 24613 ms · 2026-05-20T04:01:51.954351+00:00 · methodology

discussion (0)

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Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

  • IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    Further analysis reveals the smoothness of the SK integrals across the varying oxidation states. Exploiting this, we introduce a site-resolved machine-learning scheme for fully adaptive DFTB. Using atomic descriptors and simple regression architectures... our scheme achieves 95% band-structure accuracy across all Ni-O binary compositions in the Materials Project.

  • IndisputableMonolith/Foundation/AlphaCoordinateFixation.lean alpha_pin_under_high_calibration unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    the dominantr 0,Ni3d parameter increasing from 3.49 (Ni) to 3.87 (Ni2O) to 4.01 (NiO) Bohr... r0 ≈ αl + β, with α capturing the spatial (lattice) dependence and β encoding the chemical (oxidation) shift.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

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