arxiv: 2604.24946 · v1 · submitted 2026-04-27 · ⚛️ physics.chem-ph

Recognition: unknown

¹³C and ¹⁹F Nucleus-Electron Correlation and Self-Energies

Janina Vohdin , Christof Holzer

Authors on Pith no claims yet

Pith reviewed 2026-05-07 17:41 UTC · model grok-4.3

classification ⚛️ physics.chem-ph

keywords nucleus-electron correlationrandom phase approximationGW self-energyvertex corrections13C19FGreen's functionself-interaction error

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The pith

Vertex corrections are required to obtain reasonable GW self-energies for the nuclear densities of 13C and 19F.

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

The paper examines electron correlations with the fermionic nuclei in carbon-13 and fluorine-19. It employs the random-phase approximation to compute these correlation energies and notes a direct link to second-order perturbation theory for the interactions between fermions. Green's function GW self-energies are then evaluated using the nuclear densities, revealing that self-interaction errors make the results unusable without vertex corrections. The work also outlines the technical steps needed for a full quantum mechanical description of these nuclei. This matters because it supplies a practical route to include nuclear quantum effects and fermionic character in electronic structure calculations for molecules containing these isotopes.

Core claim

The central finding is that vertex corrections are strictly necessary to obtain reasonable results when Green's function based GW self-energies are evaluated for the nuclear densities of 13C and 19F. Self-interaction errors otherwise dominate. The random-phase approximation serves as a valuable tool for the nucleus-electron correlation energies, with a special connection to second-order perturbation theory for the inter-fermionic interaction. The theoretical and technical requirements for treating these nuclei quantum mechanically are also addressed.

What carries the argument

The random-phase approximation applied to nucleus-electron correlations, together with vertex-corrected GW self-energies evaluated at nuclear densities.

If this is right

RPA yields nucleus-electron correlation energies via its link to second-order perturbation theory.
Self-interaction errors render uncorrected GW self-energies unreasonable for these nuclear densities.
Vertex corrections must be included to produce usable results.
The approach supplies the theoretical and technical basis for quantum mechanical treatment of 13C and 19F nuclei in molecules.

Where Pith is reading between the lines

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

The same vertex correction requirement may appear when applying GW methods to other light fermionic nuclei.
These techniques could be combined with existing quantum chemistry codes to improve isotope-specific predictions for properties such as NMR shielding.
The outlined connection between RPA and perturbation theory might allow simpler computational routes to correlation energies in related fermionic systems.

Load-bearing premise

The random-phase approximation serves as a valuable tool for obtaining nucleus-electron correlation energies with a direct connection to second-order perturbation theory for the inter-fermionic interaction.

What would settle it

Evaluating the GW self-energies for 13C or 19F nuclear densities both with and without vertex corrections, then checking whether the corrected versions produce nuclear density profiles or correlation energies that match higher-level calculations or experimental observables.

Figures

Figures reproduced from arXiv: 2604.24946 by Christof Holzer, Janina Vohdin.

**Figure 1.** Figure 1: FIG. 1. Calculated electron- view at source ↗

read the original abstract

We present a theoretical and numerical study of the correlation between electrons and the fermionic $^{13}$C and $^{19}$F nuclei. We use the random-phase approximation (RPA) as a valuable tool in obtaining these correlation energies. A special connection between the RPA and second-order perturbation theory for the inter-fermionic interaction is outlined. Subsequently, Green's function based $GW$ self-energies are evaluated for the nuclear densities. The strong influence of self-interaction errors is outlined, and vertex corrections are shown to be strictly necessary to obtain reasonable results. The theoretical and technical requirements for a quantum mechanical treatment of $^{13}$C and $^{19}$F nuclei are also addressed in this work, thereby facilitating further research in this area.

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.

Desk Editor's Note private letter to a colleague

Applies RPA to 13C/19F nucleus-electron correlations and GW self-energies on nuclear densities, but the 'strictly necessary' vertex corrections claim sits on an unbenchmarked RPA baseline.

read the letter

The main takeaway is that the authors extend RPA to electron-fermion nucleus correlations for 13C and 19F, sketch a link to second-order perturbation theory, then evaluate GW self-energies on the nuclear densities and state that vertex corrections are required to tame self-interaction errors. They also lay out the basic requirements for treating these nuclei quantum-mechanically. That combination is new as a targeted numerical study in this narrow setting. The framework is set out clearly enough that someone already working with RPA or GW can follow the steps and see where the self-interaction issue appears in the nuclear-density case. The outline of the RPA–perturbation-theory connection is useful as a starting point for readers who want to adapt the method. The soft spot is the strong claim that vertex corrections are strictly necessary. It depends on RPA delivering a trustworthy correlation energy and on the GW results without vertices being demonstrably bad because of self-interaction. The abstract gives no benchmarks against exact results or higher-order calculations on a model electron-nucleus system, and the perturbation-theory link is only outlined, not tested when the nuclei carry their own strong interactions. Without those checks the necessity statement stays conditional. This paper is for quantum chemists or many-body theorists who already use RPA/GW and want to see the method tried on fermionic nuclei. A reader in that group can extract the technical setup and the self-interaction discussion. It is narrow enough that it will not move the wider field, but the concrete application is worth a referee’s time to verify the derivations and ask for the missing validation numbers. I would send it to peer review rather than desk-reject.

Referee Report

2 major / 1 minor

Summary. The manuscript presents a theoretical and numerical study of electron-fermionic nucleus correlations for ^{13}C and ^{19}F. It employs the random-phase approximation (RPA) to compute nucleus-electron correlation energies, outlines a connection between RPA and second-order perturbation theory for the inter-fermionic interaction, evaluates Green's function-based GW self-energies on nuclear densities, highlights the role of self-interaction errors, and concludes that vertex corrections are strictly necessary to obtain reasonable results. The work also discusses theoretical and technical requirements for a quantum mechanical treatment of these nuclei.

Significance. If the central claims hold, the work could contribute to bridging electronic structure theory with nuclear degrees of freedom by applying GW and RPA frameworks to mixed fermion systems. However, the absence of benchmarks validating the RPA baseline against exact or higher-order results for the electron-nucleus Coulomb interaction in the presence of strong nuclear forces limits the potential impact; the necessity of vertex corrections remains conditional on untested assumptions.

major comments (2)

[Abstract] Abstract: The assertion that vertex corrections are 'strictly necessary' to obtain reasonable GW self-energies for nuclear densities rests on an unbenchmarked RPA treatment of nucleus-electron correlation energies. No explicit comparison to exact results, higher-order perturbation theory, or model systems is provided to demonstrate that the RPA baseline is trustworthy or that the self-interaction errors are the dominant source of unreasonableness.
[Abstract] Abstract: The 'special connection' between RPA and second-order perturbation theory for the inter-fermionic interaction is outlined but not shown to survive when the fermions are nuclei (with their own strong interactions) and the interaction is the electron-nucleus Coulomb term. This connection is load-bearing for the claim that RPA furnishes a valuable tool here, yet no validation or derivation for the mixed system is supplied.

minor comments (1)

[Abstract] The abstract and title use 'nucleus-electron correlation' without clarifying whether the nuclei are treated as point particles or with internal structure; this notation should be defined early for clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and the insightful comments provided. We respond to the major comments point by point below, offering clarifications and committing to revisions that address the concerns raised.

read point-by-point responses

Referee: [Abstract] Abstract: The assertion that vertex corrections are 'strictly necessary' to obtain reasonable GW self-energies for nuclear densities rests on an unbenchmarked RPA treatment of nucleus-electron correlation energies. No explicit comparison to exact results, higher-order perturbation theory, or model systems is provided to demonstrate that the RPA baseline is trustworthy or that the self-interaction errors are the dominant source of unreasonableness.

Authors: We recognize that the manuscript does not include direct comparisons to exact results or higher-order methods for the specific nucleus-electron correlations in ^{13}C and ^{19}F. Such benchmarks are currently beyond reach due to the computational demands of treating strong nuclear forces alongside electronic correlations. Nevertheless, the RPA is a standard approximation in many-body physics for capturing correlation effects through ring summations, and our calculations reveal significant self-interaction errors in the GW self-energies that are independent of the RPA baseline to some extent. In the revised version, we will modify the abstract to qualify the statement on vertex corrections and include additional discussion on the validity of RPA and potential future benchmarks with simplified models. revision: partial
Referee: [Abstract] Abstract: The 'special connection' between RPA and second-order perturbation theory for the inter-fermionic interaction is outlined but not shown to survive when the fermions are nuclei (with their own strong interactions) and the interaction is the electron-nucleus Coulomb term. This connection is load-bearing for the claim that RPA furnishes a valuable tool here, yet no validation or derivation for the mixed system is supplied.

Authors: The special connection between RPA and second-order perturbation theory is based on the general diagrammatic structure applicable to any fermionic system with two-body interactions. For the electron-nucleus Coulomb interaction, the RPA sums the same class of diagrams as in the electronic case. The strong nuclear interactions are incorporated into the nuclear Green's function or density, but the correlation with electrons is treated via the Coulomb term. We will expand the manuscript with a dedicated derivation showing that this connection persists in the mixed system, thereby strengthening the justification for using RPA. revision: yes

Circularity Check

0 steps flagged

No circularity: standard RPA/GW methods applied to new nucleus-electron domain with independent numerical demonstration

full rationale

The paper applies the established random-phase approximation to compute nucleus-electron correlation energies and evaluates Green's function GW self-energies on nuclear densities, showing self-interaction errors and the effect of vertex corrections. The claimed 'special connection' between RPA and second-order perturbation theory is outlined within the work rather than presupposed. No step reduces a prediction or necessity claim to a fitted parameter or self-defined quantity by construction. No load-bearing self-citations or imported uniqueness theorems appear in the provided derivation chain. The results rest on external benchmarks (standard RPA/GW implementations) and direct numerical evaluation rather than tautological redefinition of inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 3 axioms · 0 invented entities

Ledger constructed from abstract only; full text not available for exhaustive extraction of parameters or assumptions.

axioms (3)

domain assumption The random-phase approximation is a valuable tool for obtaining nucleus-electron correlation energies.
Explicitly stated in the abstract as the chosen method.
domain assumption A special connection exists between RPA and second-order perturbation theory for the inter-fermionic interaction.
Outlined in the abstract as part of the theoretical contribution.
domain assumption Vertex corrections are strictly necessary to obtain reasonable GW self-energies for nuclear densities.
Claimed as a key finding in the abstract.

pith-pipeline@v0.9.0 · 5426 in / 1488 out tokens · 64348 ms · 2026-05-07T17:41:13.338723+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

3 extracted references · 2 canonical work pages · 1 internal anchor

[1]

$^{13}$C and $^{19}$F Nucleus-Electron Correlation and Self-Energies

We present a theoretical and numerical study of the correlation between electrons and the fermionic 13C and 19F nuclei. We use the random-phase approximation (RPA) as a valuable tool in obtaining these correlation energies. A special connection between the RPA and second-order perturbation theory for the inter-fermionic interaction is outlined. Subsequent...

work page internal anchor Pith review Pith/arXiv arXiv 2026
[2]

effective

Only the dRPA+Γvariant remedies this issue, removing the artificially low correlation energy in this case. MP2@HF, on the other hand, yields results close to diag+Γ@CHYF, being which is to be expected given the relation of these two methods out- lined in section II B. For the chlorinated species CCl 3F and CH2ClF however more pronounced differences can be...

work page doi:10.1002/chem.201802782 1927
[3]

Koopmans’ theorem for acidic protons,

59T. Schrader, J. Khanifaev, and E. Perlt, “Koopmans’ theorem for acidic protons,” Chem. Commun.59, 13839–13842 (2023). 60F. Caruso, M. Dauth, M. J. van Setten, and P. Rinke, “Benchmark of gw approaches for the gw100 test set,” J. Chem. Theory Comput.12, 5076– 5087 (2016). 61M. Kehry, W. Klopper, and C. Holzer, “Robust relativistic many-body Green’s funct...

2023