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arxiv: 2606.12621 · v1 · pith:MPD5J42Unew · submitted 2026-06-10 · ❄️ cond-mat.mtrl-sci · physics.chem-ph

Resolving Finite-Size Errors in EOM-CCSD Band Gaps of Solids with Interacting-Bath Dynamical Embedding Theory

Jiachen Li , Christopher Hillenbrand , Christian Venturella , Enzhi Chen , Tianyu Zhu This is my paper

Pith reviewed 2026-06-27 08:49 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci physics.chem-ph
keywords EOM-CCSDband gapsdynamical embeddingfinite-size errorssemiconductorsinsulatorsGreen's function embeddingthermodynamic limit
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The pith

Interacting-bath embedding lets EOM-CCSD reach dense k-grids and 0.27 eV mean error on ten solids' band gaps.

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

The paper shows that finite-size errors in periodic EOM-CCSD band-gap calculations arise mainly from coarse k-point meshes required by computational cost. Interacting-bath dynamical embedding theory removes this limit by permitting meshes up to 10x10x10 at modest expense, producing stable thermodynamic-limit extrapolations. Under identical numerical settings the resulting EOM-CCSD gaps give a mean absolute error of 0.27 eV against experiment for a test set of ten semiconductors and insulators, lower than the error obtained with G0W0@PBE. The same calculations also place the Zn 3d bands in ZnO at the correct binding energy even while overestimating the gap itself.

Core claim

By embedding a small correlated fragment in an interacting bath constructed from the same mean-field reference, ibDET supplies the dense Brillouin-zone sampling that canonical periodic EOM-CCSD cannot afford. Thermodynamic-limit extrapolations performed on these dense grids converge to band gaps whose mean absolute deviation from experiment is 0.27 eV across the ten-material test set, and the same framework reproduces the Zn 3d binding energy in ZnO.

What carries the argument

interacting-bath dynamical embedding theory (ibDET), which constructs a Green's-function bath from a mean-field reference and embeds a correlated fragment to enable dense k-point sampling.

If this is right

  • EOM-CCSD band gaps become systematically improvable with k-mesh density once ibDET is used.
  • Equal-footing comparisons place EOM-CCSD ahead of G0W0@PBE on the ten-material test set.
  • The Zn 3d binding energy in ZnO is correctly described even though the gap is overestimated.
  • Stable extrapolations to the thermodynamic limit are obtained from meshes up to 10x10x10.
  • ibDET supplies a practical route to wave-function-based band structures in periodic systems.

Where Pith is reading between the lines

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

  • The same embedding construction could be reused with other correlated solvers such as EOM-CCSDT or selected CI without changing the k-sampling strategy.
  • Because the bath is built from the same mean-field reference as the fragment, the approach may transfer directly to defect or surface calculations where local correlation is important.
  • If the 0.27 eV error persists on a larger and more diverse test set, EOM-CCSD plus ibDET would become a reference method for validating cheaper approximations in materials databases.

Load-bearing premise

The interacting-bath approximation adds negligible systematic bias to the extrapolated thermodynamic-limit band gaps.

What would settle it

A side-by-side comparison, on any system small enough for both methods, between ibDET-EOM-CCSD gaps and canonical periodic EOM-CCSD gaps at the same k-mesh density would show whether the embedding step itself shifts the extrapolated values.

Figures

Figures reproduced from arXiv: 2606.12621 by Christian Venturella, Christopher Hillenbrand, Enzhi Chen, Jiachen Li, Tianyu Zhu.

Figure 1
Figure 1. Figure 1: FIG. 1. Extrapolations of embedded HF+CC band gaps against [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Thermodynamic-limit extrapolations of EOM-CCSD band gaps for LiF, MgO, C, and Si obtained from ibDET [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Valence band structure of ZnO at the levels of EOM [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
read the original abstract

Periodic equation-of-motion coupled-cluster theory with single and double excitations (EOM-CCSD) has shown promise for quantitative calculations of band structures in solids. However, its steep computational scaling has limited calculations to relatively coarse $k$-point meshes, leading to sizable finite-size errors and discrepant estimates of thermodynamic-limit band gaps in recent benchmarks. In this work, we revisit EOM-CCSD band gaps for ten semiconductors and insulators using interacting-bath dynamical embedding theory (ibDET), a systematically improvable Green's function embedding framework that enables dense Brillouin-zone sampling at modest computational cost. By pushing the $k$-point sampling up to $10\times10\times10$, well beyond the system sizes accessible in canonical periodic EOM-CCSD calculations, we significantly reduce finite-size errors and obtain stable thermodynamic-limit extrapolations. We further compare $G_0W_0$@PBE, $G_0W_0$@HF, and EOM-CCSD on an equal footing using the same numerical settings in PySCF. We find that EOM-CCSD yields a mean absolute error of 0.27 eV relative to experimental band gaps for a test set of ten semiconductors and insulators, lower than that of $G_0W_0$@PBE. For ZnO, EOM-CCSD also accurately describes the Zn $3d$-band binding energy, despite overestimating the band gap. These results demonstrate that ibDET offers a practical route to high-accuracy many-body electronic structure calculations in periodic systems.

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

1 major / 1 minor

Summary. The manuscript applies interacting-bath dynamical embedding theory (ibDET) to enable EOM-CCSD calculations of band gaps on dense k-point meshes (up to 10×10×10) for ten semiconductors and insulators. Finite-size errors are reduced via extrapolation to the thermodynamic limit, yielding a reported MAE of 0.27 eV versus experiment (lower than G0W0@PBE) when all methods are run in the same PySCF settings; ZnO 3d binding energies are also discussed.

Significance. If the embedding bias is demonstrably small, the approach supplies a systematically improvable route to thermodynamic-limit EOM-CCSD gaps at modest cost, addressing the finite-size limitations that have produced discrepant prior benchmarks.

major comments (1)
  1. [Results (thermodynamic-limit extrapolations and MAE comparison)] The headline MAE of 0.27 eV and the claim of stable thermodynamic-limit extrapolations rest on the assumption that ibDET reproduces canonical periodic EOM-CCSD gaps without appreciable bias once the bath is constructed from the same mean-field reference. No direct numerical benchmark of ibDET-EOM-CCSD versus canonical EOM-CCSD is shown on the small meshes (e.g., 2×2×2 or 3×3×3) where both are computationally feasible; without this anchor, any systematic embedding error remains entangled with the extrapolation and could shift the reported MAE by an amount comparable to the claimed improvement over G0W0@PBE.
minor comments (1)
  1. [Abstract] The abstract states that G0W0@PBE, G0W0@HF, and EOM-CCSD are compared on equal footing, yet the MAE value for G0W0@HF is not reported; adding this number would strengthen the equal-footing claim.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful and constructive review. We respond to the single major comment below.

read point-by-point responses

  1. Referee: [Results (thermodynamic-limit extrapolations and MAE comparison)] The headline MAE of 0.27 eV and the claim of stable thermodynamic-limit extrapolations rest on the assumption that ibDET reproduces canonical periodic EOM-CCSD gaps without appreciable bias once the bath is constructed from the same mean-field reference. No direct numerical benchmark of ibDET-EOM-CCSD versus canonical EOM-CCSD is shown on the small meshes (e.g., 2×2×2 or 3×3×3) where both are computationally feasible; without this anchor, any systematic embedding error remains entangled with the extrapolation and could shift the reported MAE by an amount comparable to the claimed improvement over G0W0@PBE.

    Authors: We agree that a direct benchmark on small meshes where canonical EOM-CCSD remains feasible would strengthen the manuscript and help isolate any residual embedding bias from the finite-size extrapolation. The ibDET construction ensures exact reproduction of the underlying mean-field reference, and the interacting bath is systematically improvable, but we acknowledge that this does not substitute for an explicit numerical comparison in the EOM-CCSD context. We will therefore add such a benchmark (e.g., for silicon on a 3×3×3 mesh) to the revised manuscript and SI, reporting the difference between ibDET-EOM-CCSD and canonical EOM-CCSD. This addition will support the stability of the reported thermodynamic-limit extrapolations and the 0.27 eV MAE. revision: yes

Circularity Check

0 steps flagged

No significant circularity; MAE and extrapolation are externally anchored

full rationale

The paper's central result (EOM-CCSD MAE of 0.27 eV vs experiment, lower than G0W0@PBE) is obtained by applying ibDET to reach 10x10x10 k-meshes and performing thermodynamic-limit extrapolation, then comparing directly to external experimental gaps and to G0W0 run in the same code. No equation or procedure is shown to define the target band gaps in terms of themselves, to rename a fit as a prediction, or to rest the uniqueness of the result on a self-citation chain. The embedding approximation is presented as a systematically improvable framework whose bias is assumed small, but that assumption is not enforced by construction inside the reported numbers. This is the normal case of an application paper whose numerical claims remain falsifiable against independent data.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Abstract-only review; ledger entries are inferred from standard quantum-chemistry assumptions rather than explicit statements in the text.

axioms (2)
  • domain assumption EOM-CCSD truncation is sufficient to capture the dominant correlation effects for band gaps in the chosen semiconductors.
    Implicit in the choice of EOM-CCSD as the solver inside the embedding.
  • domain assumption The thermodynamic-limit extrapolation from finite k-grids is valid once finite-size errors are reduced by dense sampling.
    Central to the claim that 10x10x10 grids yield stable extrapolations.

pith-pipeline@v0.9.1-grok · 5836 in / 1400 out tokens · 18378 ms · 2026-06-27T08:49:02.977430+00:00 · methodology

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