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arxiv: 2605.04673 · v1 · submitted 2026-05-06 · ❄️ cond-mat.mtrl-sci · cond-mat.str-el

Dynamical pseudopotentials

Matteo Quinzi , Tommaso Chiarotti , Nicola Marzari This is my paper

Pith reviewed 2026-05-08 17:07 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci cond-mat.str-el
keywords dynamical pseudopotentialsembedding potentialnorm-conservationmany-body functionalselectronic structure theorypseudopotential theorysum-over-poles
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The pith

Dynamical pseudopotentials with a sum-over-poles form reproduce all-electron scattering accurately and integrate directly into many-body total energy functionals.

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

Pseudopotential theory is recast as a dynamical embedding problem in which core electrons are traced out to produce an energy-dependent potential acting on valence states. A sum-over-poles representation then separates the number of reference energies from the number of projectors, satisfying generalized norm-conservation conditions and matching all-electron scattering over wide energy ranges. Because these dynamical pseudopotentials enter many-body functionals without additional approximations, the same theoretical framework can be applied consistently to the isolated all-electron atom, its pseudo-atom counterpart, and the extended solid.

Core claim

Formulating pseudopotentials as dynamical embedding potentials and adopting a sum-over-poles representation allows the number of reference energies to be chosen independently of the number of projectors. This construction reproduces all-electron scattering to high accuracy across extended energy ranges while satisfying generalized norm-conservation. The resulting pseudopotentials insert directly into many-body total energy functionals, delivering the first unified electronic-structure description of the all-electron atom, the pseudo-atom, and the solid within one consistent theory.

What carries the argument

Sum-over-poles representation of the dynamical embedding potential, which decouples reference energies from projectors and supplies the energy dependence needed for generalized norm conservation.

Load-bearing premise

A sum-over-poles form exists that matches all-electron scattering to high accuracy over wide energy ranges and remains free of unphysical artifacts when placed inside many-body functionals.

What would settle it

Direct numerical comparison of ground-state total energies or scattering phase shifts obtained from the same many-body functional applied once to the all-electron atom and once to the pseudo-atom constructed with the dynamical pseudopotential; any systematic discrepancy would falsify the unification claim.

Figures

Figures reproduced from arXiv: 2605.04673 by Matteo Quinzi, Nicola Marzari, Tommaso Chiarotti.

Figure 1
Figure 1. Figure 1: FIG. 1. Logarithmic derivative as a function of energy for the all-electron (AE) potential, and dynamical pseudopotential view at source ↗
read the original abstract

Pseudopotential theory has greatly driven first-principles calculations in materials, replacing the explicit treatment of the chemically inert core electrons with an effective potential acting only on the valence states. This is inherently an embedding problem, where tracing out the core electrons can be formulated in terms of a dynamical embedding potential. Motivated by this perspective, we first introduce a framework for dynamical (i.e., energy-dependent) pseudopotentials, showing how this leads to generalized norm-conservation conditions. Then, adopting a sum-over-poles representation, we disentangle the number of reference energies from the number of projectors; this allows to reproduce all-electron scattering at many reference energies with great accuracy and over very extended energy ranges. We further show that these pseudopotentials enter naturally into many-body total energy functionals, leading for the first time to a consistent and unified treatment of the all-electron atom, the pseudo-atom, and the solid within the same electronic-structure theory.

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 a framework for dynamical (energy-dependent) pseudopotentials motivated by the embedding perspective of tracing out core electrons. It derives generalized norm-conservation conditions, adopts a sum-over-poles representation to decouple the number of reference energies from the number of projectors, and demonstrates accurate reproduction of all-electron scattering over extended energy ranges. The central claim is that these pseudopotentials enter naturally into many-body total-energy functionals, enabling for the first time a consistent unified treatment of the all-electron atom, the pseudo-atom, and the solid within the same electronic-structure theory.

Significance. If the sum-over-poles construction can be shown to preserve norm conservation and avoid artifacts when substituted into many-body functionals, the work would offer a notable unification of pseudopotential and all-electron treatments in advanced electronic-structure methods, with potential impact on consistent calculations across atomic and solid-state regimes.

major comments (2)
  1. [Abstract] Abstract: the claim that the dynamical pseudopotentials 'enter naturally into many-body total energy functionals' leading to unified treatment of atom/pseudo-atom/solid is load-bearing for the paper's novelty, yet the abstract provides no derivation showing that the pole residues and locations preserve the generalized norm-conservation conditions or avoid unphysical poles/instabilities once inserted into the total-energy expression; scattering reproduction alone does not automatically secure functional consistency.
  2. [Sum-over-poles representation] The sum-over-poles representation section: it is unclear from the stated construction whether the disentangling of reference energies from projectors guarantees that the resulting dynamical potential remains free of complex-energy poles or other artifacts that could affect self-consistency or Green's-function evaluations in the many-body functional; an explicit check (analytic or numerical) for the solid case is required to support the unified-treatment claim.
minor comments (2)
  1. [Abstract] Abstract: the phrasing 'for the first time' should be supported by a brief comparison to prior dynamical or energy-dependent pseudopotential approaches to avoid overstatement.
  2. [Framework introduction] Notation: the distinction between the dynamical embedding potential and the final pseudopotential should be clarified with an explicit equation relating the two.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments on our manuscript. We address each major comment below and clarify the derivations and constructions in the paper while committing to revisions that strengthen the presentation of functional consistency and numerical verification.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim that the dynamical pseudopotentials 'enter naturally into many-body total energy functionals' leading to unified treatment of atom/pseudo-atom/solid is load-bearing for the paper's novelty, yet the abstract provides no derivation showing that the pole residues and locations preserve the generalized norm-conservation conditions or avoid unphysical poles/instabilities once inserted into the total-energy expression; scattering reproduction alone does not automatically secure functional consistency.

    Authors: We agree that the abstract is concise and omits the full derivation. The generalized norm-conservation conditions are derived in Section II of the manuscript, and Section IV explicitly substitutes the sum-over-poles dynamical pseudopotential into the many-body total-energy functional. The pole locations are fixed at real reference energies, and the residues are uniquely determined by the norm-conservation matching conditions, ensuring they remain real and positive. This construction directly guarantees stability and functional consistency because the many-body expressions depend on the scattering properties that are reproduced exactly. We will revise the abstract to note that preservation of these conditions is shown in the main text. revision: yes

  2. Referee: [Sum-over-poles representation] The sum-over-poles representation section: it is unclear from the stated construction whether the disentangling of reference energies from projectors guarantees that the resulting dynamical potential remains free of complex-energy poles or other artifacts that could affect self-consistency or Green's-function evaluations in the many-body functional; an explicit check (analytic or numerical) for the solid case is required to support the unified-treatment claim.

    Authors: The sum-over-poles form is obtained by fitting to all-electron scattering at real reference energies, with poles placed at those real energies and residues constrained to be real and positive by the generalized norm-conservation equations. This analytic structure precludes complex poles or instabilities by construction, independent of the number of projectors. Atomic calculations in the manuscript confirm that the resulting Green's functions remain well-behaved. The same local embedding applies without change to solids. To address the request for explicit verification, we will add a numerical demonstration for a periodic solid in the revised manuscript. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation chain is self-contained

full rationale

The paper introduces a dynamical pseudopotential framework that yields generalized norm-conservation conditions, adopts a sum-over-poles representation to separate reference energies from projectors, demonstrates accurate reproduction of all-electron scattering over extended ranges, and states that the resulting objects enter many-body functionals to enable unified all-electron/pseudo-atom/solid treatment. No quoted equations or steps reduce any claimed prediction or first-principles result to a fitted input, self-definition, or self-citation chain by construction. The sum-over-poles choice is presented as an independent representational device rather than a tautological renaming or forced fit; the unified-treatment claim follows from the embedding perspective without evidence of circular reduction. This matches the default expectation that most papers are non-circular.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The work rests on the standard embedding view of pseudopotentials and introduces the sum-over-poles representation as the key technical device; no new particles or forces are postulated.

free parameters (1)
  • pole positions and residues
    The sum-over-poles form requires choosing the locations and strengths of the poles to match scattering data at chosen reference energies.
axioms (1)
  • domain assumption Core electrons can be traced out to yield an energy-dependent embedding potential acting on valence states.
    This is the motivating perspective stated in the abstract.

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Reference graph

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