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arxiv: 2606.06185 · v1 · pith:XUGSIQJ2new · submitted 2026-06-04 · ❄️ cond-mat.mes-hall

Non-adiabatic Ehrenfest dynamics with norm-conserving and ultra-soft pseudo-potentials with nuclear velocity corrections on the atomic orbitals within the Projector Augmented Wave Method framework

Paolo Fachin , Francesco Macheda , Paolo Barone , Francesco Mauri This is my paper

Pith reviewed 2026-06-28 00:10 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall
keywords Ehrenfest molecular dynamicsnon-adiabatic processesPAW methodpseudo-potentialsnuclear velocity phasesGalilean invarianceelectron-translation factors
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The pith

Including nuclear-velocity phases on atomic orbitals makes Ehrenfest molecular dynamics Galilean invariant within the PAW pseudo-potential framework.

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

The paper derives the first-principles Ehrenfest equations for non-adiabatic molecular dynamics that incorporate the nuclear-velocity-dependent phases on the atomic-orbital basis when the Hamiltonian is built from norm-conserving or ultra-soft pseudo-potentials in the Projector Augmented Wave method. These phases enter the non-local potential operators as Peierls-like factors and, in the ultra-soft case, produce extra velocity- and acceleration-dependent corrections. A sympathetic reader would care because the phases remove artificial non-adiabatic couplings that otherwise appear whenever nuclei move, restoring a description that is invariant under Galilean boosts.

Core claim

By augmenting the atomic-orbital basis with nuclear-velocity-dependent phases inside the PAW construction, the effective Hamiltonian acquires the correct velocity-dependent terms; the resulting Ehrenfest dynamics is Galilean invariant and free of the spurious non-adiabatic couplings generated when those phases are omitted.

What carries the argument

Nuclear-velocity-dependent phases (electron-translation factors) inserted into the non-local pseudo-potential operators of the PAW Hamiltonian.

If this is right

  • Peierls-like phases appear in the non-local part of both norm-conserving and ultra-soft PAW potentials.
  • Ultra-soft pseudo-potentials acquire additional nuclear-acceleration-dependent corrections.
  • The Ehrenfest equations become invariant under Galilean transformations.
  • Spurious non-adiabatic couplings that arise from a static orbital basis are eliminated.

Where Pith is reading between the lines

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

  • The same phase correction may be needed in any localized-basis non-adiabatic dynamics scheme that treats nuclei as classical particles.
  • The acceleration terms in the ultra-soft case could affect the accuracy of forces in high-velocity regimes such as ion irradiation or shock simulations.
  • Implementation in existing PAW codes would allow direct numerical tests of Galilean invariance on small molecules.

Load-bearing premise

The velocity phases can be added directly to the existing PAW operators while preserving norm conservation and the ultra-soft properties without new uncontrolled approximations.

What would settle it

A simulation of a simple molecule in two reference frames related by a constant boost velocity; without the phases the computed non-adiabatic transition rates differ between frames, while with the phases the rates agree.

read the original abstract

We derive the first-principles Ehrenfest molecular dynamics describing non-adiabatic processes with the inclusion of the nuclear-velocity-dependent phases (also known as electron-translation factors) on the atomic-orbital basis. These phases, appearing when nuclei are treated dynamically, affect effective Hamiltonians constructed from localised orbitals. In this work, we focus on the effects in the first-principles pseudo-potential Hamiltonian, both for the norm-conserving and ultra-soft cases, derived within the Projector-Augmented-Wave (PAW) method framework. Peierls-like phases depending on the nuclear velocities appear in the non-local part of the potential, while additional nuclear velocity and acceleration-dependent corrections appear in the ultra-soft pseudo-potential case. The use of velocity-including atomic orbital basis enables a Galilean-invariant description of the non-adiabatic Ehrenfest molecular dynamics, removing spurious non-adiabatic couplings that arise from neglecting the nuclear velocity phases in the atomic orbitals.

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 / 0 minor

Summary. The manuscript derives first-principles non-adiabatic Ehrenfest molecular dynamics within the PAW framework by incorporating nuclear-velocity-dependent phases (electron-translation factors) on atomic orbitals. It treats both norm-conserving and ultra-soft pseudopotentials, introducing Peierls-like phases in the non-local potential and additional velocity- and acceleration-dependent corrections for the ultra-soft case, with the central claim that this yields a Galilean-invariant description that removes spurious non-adiabatic couplings arising from velocity-neglecting bases.

Significance. If the derivation holds and preserves the defining properties of the pseudopotentials, the result would address a known consistency issue in localized-orbital treatments of non-adiabatic dynamics, providing a formally consistent route to Galilean-invariant Ehrenfest simulations in first-principles codes.

major comments (1)
  1. Abstract: the central claim that velocity-including phases remove spurious couplings and yield Galilean invariance rests on a derivation that is not supplied; without the explicit operators, transformation rules, or proof that norm conservation and ultra-soft properties are preserved, the result cannot be assessed.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their review. The manuscript supplies the full derivation in the body text; the abstract is a summary. We address the comment below and are prepared to revise the abstract for clarity if requested.

read point-by-point responses

  1. Referee: [—] Abstract: the central claim that velocity-including phases remove spurious couplings and yield Galilean invariance rests on a derivation that is not supplied; without the explicit operators, transformation rules, or proof that norm conservation and ultra-soft properties are preserved, the result cannot be assessed.

    Authors: The explicit operators (velocity-dependent Peierls phases on the non-local projectors and the additional velocity- and acceleration-dependent terms for ultra-soft pseudopotentials), the transformation rules under Galilean boosts, and the proofs that norm conservation and the ultra-soft augmentation properties remain intact are all derived and presented in the main text (Sections 2–4) together with the appendices. The abstract states the result; the supporting mathematics is contained in the manuscript. We can add a concise sentence to the abstract summarizing the key steps of the derivation if the referee considers that helpful for readers. revision: partial

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The provided abstract and claims describe a formal first-principles derivation of nuclear-velocity phases within the PAW pseudo-potential operators for norm-conserving and ultra-soft cases. No equations, parameters, or results are shown to reduce to fitted inputs, self-definitions, or load-bearing self-citations. The Galilean invariance follows from the explicit inclusion of phases in the basis, which is the stated contribution rather than a renaming or tautology. The derivation is presented as self-contained against the standard PAW framework.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Review performed on abstract only; no explicit free parameters, axioms, or invented entities are stated in the available text.

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Reference graph

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