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arxiv: 2604.14470 · v1 · submitted 2026-04-15 · ❄️ cond-mat.mtrl-sci

Environment-dependent tight-binding models from ab initio pseudo-atomic orbital Hamiltonians

Marco Buongiorno Nardelli This is my paper

Pith reviewed 2026-05-10 12:25 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci
keywords environment-dependent tight-bindingpseudo-atomic orbital Hamiltoniansbond screening functionsSlater-Koster parameterstransferable modelsab initio precisiontwisted bilayer graphenesilicon surfaces
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0 comments X p. Extension

The pith

Fitting environment-dependent tight-binding parameters simultaneously to pseudo-atomic orbital spectra from several atomic configurations produces transferable models with ab initio accuracy.

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

This paper develops an environment-dependent tight-binding framework built directly from ab initio pseudo-atomic orbital Hamiltonians. Slater-Koster hopping integrals are augmented by bond-screening functions that depend on local coordination, and all parameters are obtained by fitting the eigenvalue spectrum across multiple atomic configurations at once. The simultaneous fit resolves the usual degeneracy between screening and hopping terms. The resulting models reproduce ab initio electronic structures for systems containing thousands of atoms while remaining computationally efficient. A reader would care because the method supplies fast yet precise Hamiltonians for large-scale calculations of surfaces, superlattices, and twisted bilayers that would otherwise require prohibitive direct ab initio effort.

Core claim

Ab initio pseudo-atomic orbital Hamiltonians already provide an exact representation of the electronic structure in a localized basis equivalent to a Slater-Koster tight-binding model. By augmenting the hopping integrals with bond-screening functions that capture the local environment and determining every parameter through a single fit to the PAO eigenvalue spectrum over several atomic configurations, the degeneracy between screening and hopping is broken. This produces physically meaningful, transferable models that generate Hamiltonians for large systems at ab initio precision, as shown for bulk platinum, silicon surfaces, Si/Ge superlattices, and twisted bilayer graphene containing up to

What carries the argument

bond-screening functions that augment Slater-Koster hopping integrals to encode local coordination environment

If this is right

  • Hamiltonians for systems with thousands of atoms, such as twisted bilayer graphene, can be generated and post-processed for electronic, optical, and transport properties at ab initio accuracy.
  • The same parameter set works across bulk metals, semiconductor surfaces, and heterostructures without re-fitting.
  • The models integrate directly with existing post-processing suites to evaluate a wide range of properties on large-scale structures.
  • All parameters acquire clear physical meaning once the screening-hopping degeneracy is lifted by multi-configuration fitting.

Where Pith is reading between the lines

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

  • The approach could be applied to materials containing defects or interfaces by generating fitting configurations that include those features.
  • Extension to time-dependent or non-equilibrium simulations becomes feasible once the efficient Hamiltonian generation is combined with molecular-dynamics drivers.
  • The same fitting strategy might be used to incorporate additional interactions, such as spin-orbit terms, by including them in the underlying PAO reference calculations.

Load-bearing premise

Parameters obtained from simultaneous fitting to a finite collection of atomic configurations remain accurate and transferable to configurations and system sizes never included in the fit.

What would settle it

Compute the tight-binding eigenvalues or band-derived properties for a new twisted-bilayer geometry or defect configuration outside the fitting set and compare them directly with a full ab initio calculation; large systematic deviations would show the transferability claim fails.

Figures

Figures reproduced from arXiv: 2604.14470 by Marco Buongiorno Nardelli.

Figure 1
Figure 1. Figure 1: FIG. 1. FCC platinum volume-scan results. (a) Band structures at [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. EDTB model for FCC Pt with ad-hoc SOC, processed through the full [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Projected bulk band structure (blue shaded) and surface states (red) for three silicon surfaces: (a) Si(001), (b) Si(110), [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. EDTB (red) vs DFT (black) near the [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Sparse Lanczos band structure of TBG along [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
read the original abstract

\textit{Ab initio} pseudo-atomic orbital (PAO) Hamiltonians express the electronic structure of a solid in a compact, localized basis that spans the same Hilbert space as a conventional Slater--Koster tight-binding model, thereby providing an exact \textit{ab initio} representation without any loss of accuracy. Building on this correspondence, we develop an environment-dependent tight-binding (EDTB) framework in which Slater--Koster hopping integrals are augmented with bond-screening functions that capture the local coordination environment. All parameters are determined by fitting to the PAO eigenvalue spectrum across multiple atomic configurations simultaneously, which breaks the degeneracy between screening and hopping parameters and yields physically meaningful, transferable models capable of generating Hamiltonians for large systems with \textit{ab initio} precision. We demonstrate the efficiency and accuracy of the approach on four prototypical systems: bulk platinum, silicon surfaces, Si/Ge~[001] superlattices, and twisted bilayer graphene with up to $4{,}324$ atoms. The method is implemented in the \paoflow{} code and integrates seamlessly with its full post-processing suite, enabling the evaluation of a broad range of electronic, optical, and transport properties.

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

2 major / 2 minor

Summary. The manuscript develops an environment-dependent tight-binding (EDTB) framework in which Slater-Koster hopping integrals are augmented by bond-screening functions whose parameters are obtained by simultaneous fitting to ab initio PAO eigenvalue spectra from multiple atomic configurations. The resulting models are asserted to be transferable and capable of generating Hamiltonians for large systems at ab initio precision. Demonstrations are provided for bulk platinum, silicon surfaces, Si/Ge [001] superlattices, and twisted bilayer graphene containing up to 4324 atoms; the method is implemented within the paoflow code for subsequent electronic-structure post-processing.

Significance. If the transferability claim is substantiated, the approach would supply a practical route to accurate, environment-dependent tight-binding Hamiltonians for systems whose size precludes direct ab initio treatment, while retaining compatibility with existing PAO-based workflows and post-processing tools. The simultaneous multi-configuration fit is a potentially useful technical step toward resolving screening-hopping ambiguities.

major comments (2)
  1. [Results: twisted bilayer graphene] The central claim that the fitted models achieve 'ab initio precision' for large systems rests on transferability to atomic arrangements outside the training set. In the twisted-bilayer-graphene demonstration, the 4324-atom moiré cell is treated, yet no quantitative comparison of the reconstructed Hamiltonian eigenvalues or matrix elements against direct PAO results (or any independent benchmark) is reported for that configuration or for continuously varying twist angles and registry shifts not included in the fit.
  2. [Methods: fitting strategy] The fitting procedure is described as simultaneously matching PAO eigenvalues across multiple configurations to break the screening/hopping degeneracy. However, the manuscript supplies neither the number and diversity of training configurations, the achieved root-mean-square fitting errors, nor any cross-validation on held-out structures, leaving the uniqueness and physical interpretability of the extracted parameters unquantified.
minor comments (2)
  1. [Methods] Notation for the bond-screening functions and the precise functional form of the environment dependence should be stated explicitly with an equation number in the methods section to allow readers to reproduce the model.
  2. [Figures] Figure captions for the TBG results should indicate the size of the training set relative to the 4324-atom cell and whether any test configurations were used.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments and positive overall assessment of the work. We address each major comment below, providing clarifications and committing to revisions where appropriate.

read point-by-point responses

  1. Referee: [Results: twisted bilayer graphene] The central claim that the fitted models achieve 'ab initio precision' for large systems rests on transferability to atomic arrangements outside the training set. In the twisted-bilayer-graphene demonstration, the 4324-atom moiré cell is treated, yet no quantitative comparison of the reconstructed Hamiltonian eigenvalues or matrix elements against direct PAO results (or any independent benchmark) is reported for that configuration or for continuously varying twist angles and registry shifts not included in the fit.

    Authors: We agree that direct quantitative validation against PAO eigenvalues for the 4324-atom cell would strengthen the transferability claim. However, performing a full PAO calculation for a system of this size is computationally prohibitive, which is precisely the regime the method targets. The manuscript instead demonstrates consistency with expected moiré physics (flat bands, Dirac features) derived from the reconstructed Hamiltonian. To address the concern, we will add in the revision quantitative comparisons of eigenvalues and matrix elements for smaller twist angles and registry shifts (where direct PAO benchmarks are feasible) as well as error metrics on held-out configurations. revision: partial

  2. Referee: [Methods: fitting strategy] The fitting procedure is described as simultaneously matching PAO eigenvalues across multiple configurations to break the screening/hopping degeneracy. However, the manuscript supplies neither the number and diversity of training configurations, the achieved root-mean-square fitting errors, nor any cross-validation on held-out structures, leaving the uniqueness and physical interpretability of the extracted parameters unquantified.

    Authors: We thank the referee for highlighting this omission. The revised manuscript will include a new subsection (or supplementary table) specifying the exact number and diversity of training configurations for each material, the root-mean-square eigenvalue fitting errors achieved, and cross-validation results on held-out atomic configurations. These additions will quantify the robustness, uniqueness, and physical interpretability of the extracted screening and hopping parameters. revision: yes

Circularity Check

0 steps flagged

No circularity: parameters fitted directly to external ab initio PAO spectra

full rationale

The paper's derivation proceeds by establishing a correspondence between ab initio PAO Hamiltonians and Slater-Koster tight-binding models, then augmenting the latter with bond-screening functions whose parameters are obtained via simultaneous fitting to eigenvalue spectra from multiple atomic configurations. This fitting uses independent external data as input and resolves parameter degeneracy through the multi-configuration constraint rather than by internal redefinition or self-reference. Transferability to large systems (e.g., 4324-atom twisted bilayer graphene) is asserted on the basis of explicit demonstrations, not by construction from the training data alone. The sole mention of the paoflow implementation is incidental and does not carry any load-bearing premise. No step reduces to a tautology, fitted input renamed as prediction, or self-citation chain.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that PAO Hamiltonians provide an exact ab initio reference within a localized basis and that multi-configuration fitting yields transferable parameters without overfitting.

free parameters (1)
  • bond-screening function parameters
    Fitted simultaneously to PAO eigenvalue spectra across multiple configurations; specific functional form and number of parameters not stated in abstract.
axioms (1)
  • domain assumption PAO Hamiltonians span the same Hilbert space as conventional Slater-Koster tight-binding models
    Invoked in the first sentence of the abstract as the basis for the exact correspondence.

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Reference graph

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