Pith. sign in

REVIEW 2 major objections 4 minor 104 references

Tight-binding vibrational responses can be made to obey all-electron sum rules by adding nuclear-velocity-dependent Peierls phases to the hopping.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · deepseek-v4-flash

2026-08-01 10:43 UTC pith:XVP7QBFB

load-bearing objection Tight-binding vibrational sum rules restored by a velocity phase — a sound derivation, with the exact sum rule conditional on the delta-like orbital assumption. the 2 major comments →

arxiv 2607.20117 v1 pith:XVP7QBFB submitted 2026-07-22 cond-mat.mes-hall

Frequency-dependent electron-phonon coupling and vibrational responses in tight-binding and continuous Dirac models with nuclear velocity correction

Paolo Fachin , Francesco Macheda , Paolo Barone , Francesco Mauri This is my paper
classification cond-mat.mes-hall
keywords tight-bindingelectron-phonon couplingBorn effective chargesnon-adiabatic vibrational responsesum rulesnuclear velocity correctionelectron translation factorHaldane model
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper argues that standard tight-binding and Dirac model Hamiltonians, built from atomic orbitals rigidly attached to nuclei, give qualitatively wrong frequency-dependent vibrational responses: their sums over atoms of Born effective charges and force constants vanish, while all-electron theory requires nonzero values tied to the optical conductivity. The missing ingredient, the paper claims, is the nuclear-velocity-dependent phase that moving nuclei imprint on atomic orbitals, known as the electron-translation factor. When this phase is included, the hopping gains Peierls-like velocity-dependent phases that act as a velocity vertex in the electron-phonon coupling, restoring the all-electron sum rules without fitting. The corrected models reproduce first-principles results for metallic gapped graphene and produce qualitatively different behavior for the Haldane model, including topological-state-dependent corrections.

Core claim

The paper's central claim is that including the nuclear-velocity phase in localized atomic orbitals changes the tight-binding Hamiltonian so that the frequency-dependent Born effective charges and force-constant matrix satisfy the same non-adiabatic sum rules as all-electron calculations. Concretely, the sum over all atoms of the Born effective charges becomes −iω(m/e)σ_{αβ}(ω), exactly the all-electron result, where the entire contribution comes from the velocity derivative of the Hamiltonian. The same mechanism restores the sum rules involving the force-constant matrix and the electronic susceptibility. The authors test this in metallic gapped graphene, where the corrected sum rule agrees

What carries the argument

The central object is the velocity-including atomic orbital, |ϕ^{Ṙ,R}⟩ = e^{iα(ˆr)}|ϕ^R⟩ with α(ˆr) = (m/ℏ) Ṙ·(ˆr−R), an electron-translation factor that makes the orbital follow the moving nucleus. In the tight-binding approximation, this phase produces nuclear-velocity-dependent Peierls-like phases on inter-site hoppings, modifying the electron-phonon coupling vertex as ∂H/∂R → ∂H/∂R − iω ∂H/∂Ṙ. In the Dirac low-energy limit this velocity vertex is simply proportional to the band velocity. The key identity is Eq. (84), which uses these velocity terms plus the delta-like orbital assumption to convert the sum of Born effective charges into the optical conductivity, restoring the all-electron

Load-bearing premise

The load-bearing premise is the diagonal position operator assumption (Eq. 34), that localized orbitals behave as delta-like functions centered at atomic sites; if orbitals have finite width, the exact equality in Eq. (84) between the summed Born effective charges and the optical conductivity is no longer guaranteed.

What would settle it

Construct a tight-binding model with Slater-type or other finite-width orbitals, compute its frequency-dependent summed Born effective charges, and compare them to −iω(m/e)σ_{αβ}(ω) computed from the same model. Any deviation that grows with orbital overlap or width would show the exact sum-rule restoration is an artifact of the delta-orbital assumption.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Tight-binding and Dirac model calculations of frequency-dependent Born effective charges and force constants will no longer have identically vanishing sum rules; they will match all-electron non-adiabatic behavior without additional fitting parameters.
  • The electron-phonon coupling vertex acquires an additional velocity-dependent term, which in low-energy Dirac models is simply proportional to the phonon frequency and band velocity.
  • In metallic gapped graphene, the corrected Born effective charges reproduce ab initio Drude-weight results; corrections can reach roughly 50% at high doping.
  • The Haldane model's off-diagonal Born effective charges acquire velocity corrections proportional to the Hall conductivity, yielding a nonzero value in the topological off-resonant limit.
  • The corrections affect the optical phonon linewidth at resonance, especially when the two sublattice masses are unequal, and are larger for weak electron-phonon coupling.

Where Pith is reading between the lines

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

  • Because the exact sum-rule restoration relies on delta-like orbitals, models with finite-width orbitals will need the full matrix elements of e^{iα(ˆr)}; deviations from Eq. (84) would then diagnose how much physics the tight-binding parametrization misses.
  • The same velocity vertex should appear in other low-energy models beyond the Dirac honeycomb case, such as continuum models of twisted or one-dimensional systems; weakly coupled materials with small electron-phonon coupling are the most sensitive testbeds.
  • A cheap empirical check of any tight-binding model: compare its atomic-summed Born effective charges to measured or first-principles optical conductivity using Eq. (84); disagreement would flag missing nonlocal or velocity-dependent physics.
  • The mechanism that makes the wavefunction complex and enables currents in TB models should also produce nonzero phonon magnetic moments and vibrational circular dichroism in models that previously gave zero, a directly testable prediction.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 4 minor

Summary. This paper derives the effect of nuclear velocity on atomic orbitals (electron-translation factors) in LCAO and tight-binding frameworks. Using an Ehrenfest Lagrangian with velocity-including orbitals, the authors obtain an effective tight-binding Hamiltonian with nuclear-velocity-dependent Peierls-like phases in the hoppings and a velocity-dependent mass correction on the on-site energies. They show that these corrections modify the first- and second-order nuclear-displacement derivatives (electron-phonon couplings) by adding velocity vertices proportional to the band velocity, and that they restore the all-electron frequency-dependent sum rules for Born effective charges (Eq. (84)) and for the force-constant matrix (Eqs. (87)-(88)). The theory is applied to gapped graphene and the Haldane model, with a benchmark against ab initio calculations for metallic gapped graphene.

Significance. If correct, this work resolves a long-standing qualitative failure of tight-binding and low-energy models: the vanishing of the non-adiabatic vibrational sum rules. The central derivation is analytic, and the nuclear-velocity phase is a physical input (an electron-translation factor), not a fudge designed to reproduce the sum rule; Eq. (84) follows algebraically from the derived Hamiltonian under the stated delta-like orbital assumption. The paper provides an explicit, self-contained formalism, including second-order derivatives, and a nontrivial ab initio benchmark for the Born-effective-charge sum rule in metallic gapped graphene (Fig. 1(d)). The low-energy Dirac result—a simple velocity vertex proportional to the band velocity—is elegant and should be directly useful for model studies of chiral phonons, vibrational circular dichroism, and non-adiabatic effects in topological systems. The main caveat is the diagonal-position/delta-like orbital assumption, which limits the generality of the exact sum rule and is not quantitatively controlled.

major comments (2)
  1. [§II C, Eqs. (82)-(84) and Eq. (34)] The exact sum rule (84) is derived under the diagonal position-operator assumption Eq. (34), which the paper itself states is compatible only with delta-like orbitals (text after Eq. (82)). For finite-width orbitals, (i) Eq. (38) becomes a matrix element of exp[i α(r)], so the hopping form Eq. (39) is no longer exact; (ii) the overlap S^{R,dot R} is no longer diagonal, reintroducing the Pulay velocity terms Eqs. (30)-(31); and (iii) the acceleration terms in Eq. (23) do not vanish, so the on-site form Eq. (35) misses m Rddot·(r-R) contributions. These terms enter the same vertices f^JI and σ used in Eq. (84). The authors provide no estimate of their magnitude, and the single ab initio comparison (Fig. 1(d)) is one material and one sum rule. The central claim that tight-binding models restore the all-electron sum rules is therefore established only within the delta-like orbital model; a g
  2. [Sec. III A and III B] The numerical validation is limited to the Born-effective-charge sum rule in metallic gapped graphene (Fig. 1(d)) and to model calculations for the Haldane model and phonon lifetimes. There is no first-principles benchmark for the force-constant sum rules Eqs. (87)-(88) or for the off-diagonal Hall-type charge response Eq. (98). While this does not affect the internal consistency, it leaves the practical accuracy of the delta-like approximation for finite-width orbital bases untested outside the single graphene-derived system. A test on a material with more diffuse orbitals would strengthen the claim.
minor comments (4)
  1. [Sec. III A 1] The text states that 'Both computations are performed with a Gaussian smearing of ∼0.068 eV, corresponding to room temperature in the Fermi statistics', while the caption of Fig. 1 states a temperature of T=27 meV. Room temperature corresponds to k_B T ≈ 26 meV, not 0.068 eV; please reconcile the smearing parameter and the temperature.
  2. [Fig. 1] The vertical axis labels in Fig. 1(c,d) are not defined in the text; please specify the units and the definition of the plotted Born-effective-charge components (e.g., in units of the electron charge) and the sum-rule quantity.
  3. [Sec. I D 5] The electric-field derivative in Eq. (52) is diagonal in the orbital basis, which is a direct consequence of Eq. (34). This should be stated explicitly when introducing Eq. (52), as it is the same assumption that later controls the sum-rule derivation.
  4. [References] Several cited items are arXiv preprints or in press; please update any that have appeared in journals by the time of publication.

Circularity Check

0 steps flagged

No significant circularity: the sum-rule restoration follows from the physical electron-translation factor via an explicit Ward identity, and the ab initio benchmark is independent.

full rationale

The central chain is not circular. The velocity-dependent phase is introduced in Eq. (4) as a physical electron-translation factor, not as a parameter fitted to reproduce the sum rule. The key identity, Eq. (82), is derived from the explicit Hamiltonian derivative in Eq. (42): summing the nuclear-velocity derivative over sites reproduces the vector-potential (Peierls) vertex, -iω Σ_s ∂H_TB/∂ΔR_s = -iω(m/e) ∂H_TB/∂A. Equation (84) then follows from the linear-response definitions of Z* and σ (Eqs. 63 and 81) together with Eq. (83), which states that Σ_s ∂P/∂R = 0 under the stated diagonal-position/delta-orbital hypothesis. This is a Ward identity, not an equality imposed by construction. The paper explicitly flags the limiting assumption: 'the assumption of a diagonal position operator, defined in Eq. (34), is compatible only with the hypothesis that the atomic orbitals are delta-like functions centred at the atomic sites' (Sec. II C, after Eq. (82)). This makes the exact equality conditional, but it is a stated physical limitation, not a hidden circularity. The ab initio comparison (Fig. 1d) is an independent benchmark performed with a modified Quantum Espresso implementation with travelling pseudopotentials, and the tight-binding sum-rule side does not depend on the fitted electron-phonon coupling β_e-ph because Z^{ΔR} is proportional only to the optical conductivity (Eq. 94). Self-citations (e.g., Refs. 30, 57–59) provide background and some of the all-electron sum-rule literature, but the same sum rules are also supported by external references (Refs. 26–28), and the present derivation is self-contained once the physical velocity-including orbital phase is adopted. The finite-width-orbital issue is a correctness/robustness concern, not circularity.

Axiom & Free-Parameter Ledger

4 free parameters · 5 axioms · 0 invented entities

The central sum-rule derivation is parameter-free and rests on standard quantum mechanics plus the stated delta-like orbital idealisation. The parameters listed are model inputs for the application sections, not fitted to the paper's central claim. No new physical entities are introduced.

free parameters (4)
  • β_e-ph (dimensionless electron-phonon coupling) = 2.38
    Taken from ab initio matrix element averaged over the zone-centre optical phonon of graphene; used in applications (Sec. III), not fitted to the sum-rule result.
  • Spring-model force constants for the zero-frequency force-constant matrix = Not given numerically
    Fitted to match ab initio phonon frequencies of graphene (Sec. III B); used as baseline for phonon linewidth corrections.
  • Gaussian smearing temperature = 27 meV (~0.068 eV)
    Used in both tight-binding and ab initio Fermi-Dirac occupations for the metallic gapped graphene comparison (Sec. III A 1); standard numerical broadening.
  • Graphene lattice and hopping parameters (a, t1, ℏvF) = a=2.46 Å, t1=3.4 eV, ℏvF=7.2 eV·Å
    Standard literature values for graphene, used as model inputs in the application sections.
axioms (5)
  • domain assumption Velocity-including atomic orbital e^{i m/ℏ Ṙ_s·(r-R_s)} satisfies the Schrödinger equation for a nucleus moving at constant velocity (neglecting acceleration/Stark mixing)
    Sec. I A; basis of the derivation; the acceleration term is dropped, assuming large energy separation from excluded orbitals.
  • ad hoc to paper Diagonal position operator on the atomic-orbital basis (delta-like orbitals)
    Eq. (34) and Sec. II C; required for Eq. (38) and for vanishing ∂P/∂R sum rule (Eq. (83)); this is the load-bearing assumption of the tight-binding sum-rule restoration.
  • domain assumption Orthogonal tight-binding basis with time-independent overlap
    Sec. I D; standard in orthogonal tight-binding.
  • domain assumption Ehrenfest/semiclassical treatment of nuclei and quantum electrons; linear response with non-self-consistent TB vertices
    Secs. I C and II; standard for TB electron-phonon response; self-consistency is neglected.
  • domain assumption Position operator diagonal in electric-field coupling (Peierls substitution)
    Eqs. (51)-(53); standard TB coupling to electric field; used for optical conductivity and sum rules.

pith-pipeline@v1.3.0-alltime-deepseek · 29866 in / 16218 out tokens · 154694 ms · 2026-08-01T10:43:02.455500+00:00 · methodology

0 comments
read the original abstract

The nuclear motion induces in the electronic atomic orbitals a nuclear-velocity-dependent phase (also known as electron-translation factor), which modifies the effective Hamiltonians constructed from localised atomic orbitals. In this work, using an Ehrenfest Lagrangian approach for the localised atomic orbitals (LCAO) and tight-binding methods, we determine, at any order in the nuclear velocity, the equations of motion and the vibrational responses within a linear response formalism, focusing on the tight-binding assessment of the Born effective charges and the force-constant matrix. The appearance of nuclear-velocity-dependent Peierls-like phases in the non-local part of the interactions restores the all-electron sum rules for frequency-dependent vibrational responses. In tight-binding models these corrections crucially modify the vibrational response from a qualitative point of view, also yielding contributions required to capture phenomena such as vibrational circular dichroism. We test these corrections in the tight-binding model for metallic gapped graphene - finding excellent agreement with \textit{ab initio} calculations - and for the topological time-reversal symmetry breaking Haldane model.

Figures

Figures reproduced from arXiv: 2607.20117 by Francesco Macheda, Francesco Mauri, Paolo Barone, Paolo Fachin.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Gapped graphene lattice model, with alternating sites with either an excess or a deficiency of electric charge, [PITH_FULL_IMAGE:figures/full_fig_p015_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Real (a) and imaginary (b) parts of the Born effective charges and the related sum rules are plotted as a function [PITH_FULL_IMAGE:figures/full_fig_p018_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (a)Lattice representation of the Haldane model. Arrows identify the direction for the 2 [PITH_FULL_IMAGE:figures/full_fig_p020_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Phonon linewidth as a function of the ratio between the electronic band gap and the phonon frequency for gapped [PITH_FULL_IMAGE:figures/full_fig_p021_4.png] view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

104 extracted references · 4 canonical work pages

  1. [1]

    The all-electron wavefunctions are orthonormal⟨ψ J |ψI ⟩=δ JI

    LCAO In the adiabatic LCAO method describing a molecule or a crystal, theI-th eigenstate single-particle all-electron wavefunction|ψ I ⟩is expanded on a set of localised atomic orbitals rigidly centred in the static nuclear positions,Rb, {|ϕRb bi ⟩}as|ψ I ⟩= X b,i cI bi |ϕRb bi ⟩, wherec I bi are the expan- sion coefficients of theI-th state on thei-th at...

  2. [2]

    (9), it follows that the diagonalisation of the tight-binding Hamiltonian matrix yields the energies and the related eigenvectors

    Orthogonal tight-binding Assuming that the orbitals in the basis are orthogonal S R bj,b′i =⟨ϕ Rb bj |ϕRb′ b′i ⟩=δ bb′δij and defining the on-site energy and the hopping, respectively, as ∆bi =⟨ϕ Rb(t) bi |H AE|ϕRb(t) bi ⟩(13) and t0 bj,b′i =⟨ϕ Rb bj | ˆp2 2m +V( ˆr)|ϕ Rb′ b′i ⟩, b̸=b ′,(14) we obtain the tight-binding Hamiltonian HTB bj,b′i =t 0 bj,b′i(1...

  3. [3]

    (23) reduces to HR, ˙R bj,bi =⟨ϕ Rb(t) bj | ˆp2 2m +V( ˆr)− m| ˙Rb(t)|2 2 +m ¨Rb(t)·( ˆr−R b(t))|ϕ Rb(t) bi ⟩

    On-site energy If the two atomic orbitals belong to the same site, the phases cancel and the Hamiltonian of Eq. (23) reduces to HR, ˙R bj,bi =⟨ϕ Rb(t) bj | ˆp2 2m +V( ˆr)− m| ˙Rb(t)|2 2 +m ¨Rb(t)·( ˆr−R b(t))|ϕ Rb(t) bi ⟩. (33) The first two terms give the same on-site energy as for the atomic orbitals at fixed nuclei, ∆ bi = ⟨ϕRb(t) bi |H AE|ϕRb(t) bi ⟩....

  4. [4]

    For atomic orbitals at fixed nuclei, the hopping is defined in Eq

    Hopping Hopping terms connect orbitals located on different sites. For atomic orbitals at fixed nuclei, the hopping is defined in Eq. (14), whereas, in the presence of nu- clear motion, we define the hoppingt bj,b′i, depending on the positions of the moving nuclei, as tbj,b′i =⟨ϕ Rb(t) bj | ˆp2 2m +V( ˆr)|ϕ Rb′ (t) b′i ⟩, b̸=b ′.(36) For moving nuclei, th...

  5. [5]

    Lagrangian and Hamiltonian The complete Ehrenfest Lagrangian for this tight- binding approximation is obtained from the LCAO La- grangian (Eq. (19)) by applying the tight-binding ap- proximation to the effective Hamiltonian and setting the overlap matrix diagonalS R, ˙R bj,b′i =δ b,b′δij LTB = X s (Ms +mN core el )| ˙Rs(t)|2 2 − NelX I=1 " X bj,b′i cI bj(...

  6. [6]

    Linear response to nuclear displacement in the tight-binding approximation Here, we compute the derivative of the tight-binding Hamiltonian in both the real and the reciprocal space that are used to assess the vibrational responses in the Section II. We remind that, in the context of linear re- sponse, the derivatives of the tight-binding Hamiltonian are ...

  7. [7]

    Linear response to an electric field in the tight-binding approximation We consider the coupling to the electric fieldE(t) in the scalar potential gauge, where, assuming that the position operator is diagonal according to Eq. (34), the coupling Hamiltonian in the real space reads HTB em bj,b′i =e(R+τ s)·E(t)δ ss′δij.(51) Therefore, the electric field deri...

  8. [8]

    This originates from the presence of conducting electrons, which con- tribute to the DC conductivity

    Metallic gapped graphene For metallic systems, even in the zero-frequency limit, the sum rule for the frequency-dependent Born effective charges does not vanish [26, 27, 58, 59]. This originates from the presence of conducting electrons, which con- tribute to the DC conductivity. In the infinite electronic lifetime (clean) limit, the intraband (Drude) con...

  9. [9]

    In our calculations, we set a difference in the valence charge of the two atoms of 2δ= 0.2 that produces a di- rect gap at theKpointE gap = 0.43 eV- corresponding to ∆ in the tight-binding approach - as plotted in panel (b) of Fig. 1. In theab initiosimulation, the Drude weight is computed using two velocity vertices to include the nuclear velocity correc...

  10. [10]

    The explicit expressions for the Born effective charges and the optical conductivity for gapped graphene are reported in Ref

    Resonance between electronic and vibrational excitations in gapped graphene and Haldane model In this section, we study the nuclear velocity correction to the Born effective charges when the phonon frequency 17 resonates with electronic interband transitions for the time-reversal invariant (gapped graphene) and breaking (Haldane model) systems, within the...

  11. [11]

    =M C ω2 ph 2 . Although the phonon self-energy Π R sα,s′α could have three different independent values by symme- try (ΠR Aα,Aα,Π R Aα,Bα,Π R Bα,Bα ), because of the electron- phonon coupling of the low-energy model, these three el- ements have the same absolute value and they are equal to [9, 12, 71] ΠR sα,s′α(ω) =l sls′ 9 4 Vc βe−ph a2 2 ℏω iσαα σ0 ,(10...

    2025

  12. [12]

    Grosso and G

    G. Grosso and G. Pastori Parravicini,Solid State Physics, 2nd ed. (Academic Press, New York, USA, 2013)

    2013

  13. [13]

    Vanderbilt,Berry Phases in Electronic Structure Theory: Electric Polarization, Orbital Magnetization and Topological Insulators(Cambridge University Press, Cambridge, UK, 2018)

    D. Vanderbilt,Berry Phases in Electronic Structure Theory: Electric Polarization, Orbital Magnetization and Topological Insulators(Cambridge University Press, Cambridge, UK, 2018)

    2018

  14. [14]

    W. A. Harrison,Electronic Structure and the Properties of Solids: The Physics of the Chemical Bond(Dover Pub- lications, New York, 1989)

    1989

  15. [15]

    Suzuura and T

    H. Suzuura and T. Ando, Phonons and electron-phonon scattering in carbon nanotubes, Phys. Rev. B65, 235412 (2002)

    2002

  16. [16]

    Piscanec, M

    S. Piscanec, M. Lazzeri, F. Mauri, A. C. Ferrari, and J. Robertson, Kohn anomalies and electron-phonon inter- actions in graphite, Phys. Rev. Lett.93, 185503 (2004)

    2004

  17. [17]

    Ishikawa and T

    K. Ishikawa and T. Ando, Optical phonon interact- ing with electrons in carbon nanotubes, Journal of the Physical Society of Japan75, 084713 (2006), 23 https://doi.org/10.1143/JPSJ.75.084713

    work page doi:10.1143/jpsj.75.084713 2006

  18. [18]

    Venezuela, M

    P. Venezuela, M. Lazzeri, and F. Mauri, Theory of double-resonant raman spectra in graphene: Intensity and line shape of defect-induced and two-phonon bands, Phys. Rev. B84, 035433 (2011)

    2011

  19. [19]

    Sohier, M

    T. Sohier, M. Calandra, C.-H. Park, N. Bonini, N. Marzari, and F. Mauri, Phonon-limited resistivity of graphene by first-principles calculations: Electron- phonon interactions, strain-induced gauge field, and boltzmann equation, Phys. Rev. B90, 125414 (2014)

    2014

  20. [20]

    Bistoni, P

    O. Bistoni, P. Barone, E. Cappelluti, L. Benfatto, and F. Mauri, Giant effective charges and piezoelectricity in gapped graphene, 2D Materials6, 045015 (2019)

    2019

  21. [21]

    S. P. Villani, M. Campetella, P. Barone, and F. Mauri, Giant piezoelectricity driven by thouless pump in con- jugated polymers, npj Computational Materials10, 81 (2024)

    2024

  22. [22]

    Fachin, F

    P. Fachin, F. Macheda, P. Barone, and F. Mauri, Nearly quantized born effective charges as probes for the topo- logical phase transition in the haldane and kane-mele models, Phys. Rev. B110, L201405 (2024)

    2024

  23. [23]

    Fachin, F

    P. Fachin, F. Macheda, P. Barone, and F. Mauri, In- frared markers of topological phase transitions in quan- tum spin hall insulators, npj Computational Materials 11, 307 (2025)

    2025

  24. [24]

    Guandalini, F

    A. Guandalini, F. Macheda, G. Caldarelli, and F. Mauri, Excitonic effects in phonons: Reshaping the graphene kohn anomalies and lifetimes, Phys. Rev. Lett.135, 076401 (2025)

    2025

  25. [25]

    Udina and I

    M. Udina and I. Paul, Antisymmetric raman response, Phys. Rev. Lett.136, 126505 (2026)

    2026

  26. [26]

    Y. Chen, W. Qin, S. Zhang, P. Cui, Q. Niu, and Z. Zhang, Emergence of chiral phonons in two-dimensional kagome lattices harboring electronic chirality, Phys. Rev. Lett. 135, 126608 (2025)

    2025

  27. [27]

    Tateishi, A

    T. Tateishi, A. Kato, and J.-i. Kishine, Elec- tron–chiral phonon coupling, crystal angular mo- mentum, and phonon chirality, Journal of the Physical Society of Japan94, 053601 (2025), https://doi.org/10.7566/JPSJ.94.053601

    work page doi:10.7566/jpsj.94.053601 2025

  28. [28]

    Saparov, B

    D. Saparov, B. Xiong, Y. Ren, and Q. Niu, Lattice dy- namics with molecular berry curvature: Chiral optical phonons, Phys. Rev. B105, 064303 (2022)

    2022

  29. [29]

    Yao and S

    D. Yao and S. Murakami, Theory of spin magnetiza- tion driven by chiral phonons, Phys. Rev. B111, 134414 (2025)

    2025

  30. [30]

    Nuomin, F.-F

    H. Nuomin, F.-F. Song, P. Zhang, D. Sun, and D. N. Beratan, The properties of current induced chiral phonons recapitulate the characteristics of the ciss effect, The Journal of Physical Chem- istry Letters17, 5191 (2026), pMID: 42015808, https://doi.org/10.1021/acs.jpclett.6c00793

    work page doi:10.1021/acs.jpclett.6c00793 2026

  31. [31]

    T. Sato, T. Kato, and A. Manchon, Orbital accumula- tion induced by chiral phonons (2025), arXiv:2511.11272 [cond-mat.mes-hall]

    Pith/arXiv arXiv 2025

  32. [32]

    Tateishi, A

    T. Tateishi, A. Kato, A. S. Ovchinnikov, and J.-i. Kishine, Microscopic theory of chiral-phonon- induced orbital selectivity in helical crystals, Journal of the Physical Society of Japan95, 063705 (2026), https://doi.org/10.7566/JPSJ.95.063705

    work page doi:10.7566/jpsj.95.063705 2026

  33. [33]

    Y. Ren, D. Saparov, and Q. Niu, Nonreciprocal phonons inPT-symmetric antiferromagnets, Phys. Rev. Lett. 134, 206701 (2025)

    2025

  34. [34]

    Cappelluti, L

    E. Cappelluti, L. Benfatto, M. Manzardo, and A. B. Kuz- menko, Charged-phonon theory and fano effect in the op- tical spectroscopy of bilayer graphene, Phys. Rev. B86, 115439 (2012)

    2012

  35. [35]

    Sellati, J

    N. Sellati, J. Fiore, and L. Benfatto, Light-induced fara- day effect from dynamical breakdown of kleinman sym- metry (2026), arXiv:2605.27127 [cond-mat.mtrl-sci]

    Pith/arXiv arXiv 2026

  36. [36]

    Guandalini, G

    A. Guandalini, G. Caldarelli, F. Macheda, and F. Mauri, High- and low-energy many-body effects of graphene in a unified approach, Phys. Rev. B111, 075118 (2025)

    2025

  37. [37]

    C. E. Dreyer, S. Coh, and M. Stengel, Nonadiabatic born effective charges in metals and the drude weight, Phys. Rev. Lett.128, 095901 (2022)

    2022

  38. [38]

    Marchese, F

    G. Marchese, F. Macheda, L. Binci, and al, Born effective charges and vibrational spectra in superconducting and bad conducting metals, Nat. Phys.20(2024)

    2024

  39. [39]

    Stengel, M

    M. Stengel, M. Royo, and E. Artacho, Rototranslational sum rules for nuclear dynamics via traveling pseudopo- tentials, Phys. Rev. Lett.136, 196401 (2026)

    2026

  40. [40]

    Santerv´ as-Arranz, M

    N. Santerv´ as-Arranz, M. Stengel, and E. Artacho, Excess energy and countercurrents after a quantum kick, Phys. Rev. Res.7, 033292 (2025)

    2025

  41. [41]

    Fachin, F

    P. Fachin, F. Macheda, P. Barone, and F. Mauri, Non-adiabatic ehrenfest dynamics with norm-conserving and ultra-soft pseudo-potentials with nuclear veloc- ity corrections on the atomic orbitals within the projector augmented wave method framework (2026), arXiv:2606.06185 [cond-mat.mes-hall]

    Pith/arXiv arXiv 2026

  42. [42]

    D. R. Bates and R. McCarroll, Electron capture in slow collisions, Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences245, 175 (1958)

    1958

  43. [43]

    L. F. Errea, C. Harel, H. Jouini, L. Mendez, B. Pons, and A. Riera, Common translation factor method, Journal of Physics B: Atomic, Molecular and Optical Physics27, 3603 (1994)

    1994

  44. [44]

    L. F. Errea, L. M´ endez, A. Riera, C. Harel, H. Jouin, and B. Pons, Common-translation-factor method with an atomic basis, Phys. Rev. A50, 418 (1994)

    1994

  45. [45]

    Kimura and N

    M. Kimura and N. F. Lane, Traveling-molecular-orbital- expansion studies of electron capture in collisions of fully stripped ions (z=6–9) with h and h 2, Phys. Rev. A35, 70 (1987)

    1987

  46. [46]

    P. M. M. Gab´ as, L. F. Errea, L. M´ endez, and I. Rabad´ an, Ab initio treatment of charge transfer in ion-molecule col- lisions based on one-electron wave functions, Phys. Rev. A85, 012702 (2012)

    2012

  47. [47]

    R. J. Allan and J. Hanssen, Quasimolecular treatment of na-na+, li-li+, li-na+ and na-li+ collisions with a com- mon translation factor, Journal of Physics B: Atomic and Molecular Physics18, 1981 (1985)

    1981

  48. [48]

    W. R. Thorson and J. B. Delos, Theory of near-adiabatic collisions. i. electron translation factor method, Phys. Rev. A18, 117 (1978)

    1978

  49. [49]

    A. K. Belyaev, Revised born-oppenheimer approach and a reprojection method for inelastic collisions, Phys. Rev. A82, 060701 (2010)

    2010

  50. [50]

    J. B. Delos, Theory of near-adiabatic collisions. iii. cou- pled equations arising from expansions involving single- center states, Phys. Rev. A23, 2301 (1981)

    1981

  51. [51]

    L. A. Nafie, Velocity-gauge formalism in the theory of vibrational circular dichroism and infrared absorption, The Journal of Chemical Physics96, 5687 (1992)

    1992

  52. [52]

    L. A. Nafie, Adiabatic molecular properties beyond the born–oppenheimer approximation. complete adiabatic 24 wave functions and vibrationally induced electronic cur- rent density, The Journal of Chemical Physics79, 4950 (1983)

    1983

  53. [53]

    Scherrer, F

    A. Scherrer, F. Agostini, D. Sebastiani, E. K. U. Gross, and R. Vuilleumier, Nuclear velocity perturbation theory for vibrational circular dichroism: An approach based on the exact factorization of the electron-nuclear wave function, The Journal of Chemical Physics143, 074106 (2015)

    2015

  54. [54]

    Ditler, J

    E. Ditler, J. Mattiat, and S. Luber, The position opera- tor problem in periodic calculations with an emphasis on theoretical spectroscopy, Phys. Chem. Chem. Phys.25, 14672 (2023)

    2023

  55. [55]

    Scherrer, R

    A. Scherrer, R. Vuilleumier, and D. Sebastiani, Nu- clear velocity perturbation theory of vibrational circular dichroism, Journal of Chemical Theory and Computation9, 5305 (2013), pMID: 26592268, https://doi.org/10.1021/ct400700c

    doi:10.1021/ct400700c 2013

  56. [56]

    Ditler, T

    E. Ditler, T. Zimmermann, C. Kumar, and S. Luber, Im- plementation of nuclear velocity perturbation and mag- netic field perturbation theory in cp2k and their applica- tion to vibrational circular dichroism, Journal of Chem- ical Theory and Computation18, 2448 (2022), pMID: 35363490, https://doi.org/10.1021/acs.jctc.2c00006

    doi:10.1021/acs.jctc.2c00006 2022

  57. [57]

    Kumar and S

    R. Kumar and S. Luber, Calculation of vibrational cir- cular dichroism spectra employing nuclear velocity per- turbation or magnetic field perturbation theory using an atomic-orbital-based linear response approach, The Jour- nal of Physical Chemistry A129, 4325 (2025), pMID: 40310687, https://doi.org/10.1021/acs.jpca.5c01344

    doi:10.1021/acs.jpca.5c01344 2025

  58. [58]

    D. A. Micha, Time-dependent many-electron treatment of electronic energy and charge transfer in atomic colli- sions, The Journal of Physical Chemistry A103, 7562 (1999)

    1999

  59. [59]

    Runge and D

    K. Runge and D. A. Micha, Time-dependent many- electron approach to slow ion-atom collisions for systems with several active electrons, Phys. Rev. A62, 022703 (2000)

    2000

  60. [60]

    Reyes, D

    A. Reyes, D. Micha, and K. Runge, First principles dy- namics of li–he collisional excitation using atomic core potentials, Chemical Physics Letters363, 441 (2002)

    2002

  61. [61]

    E. C. Alguire, Q. Ou, and J. E. Subotnik, Cal- culating derivative couplings between time-dependent hartree–fock excited states with pseudo-wavefunctions, The Journal of Physical Chemistry B119, 7140 (2015), pMID: 25148602, https://doi.org/10.1021/jp505767b

    doi:10.1021/jp505767b 2015

  62. [62]

    Fatehi, E

    S. Fatehi, E. Alguire, Y. Shao, and J. E. Subotnik, Analytic derivative couplings between configuration- interaction-singles states with built-in electron- translation factors for translational invariance, The Journal of Chemical Physics135, 234105 (2011)

    2011

  63. [63]

    Fatehi and J

    S. Fatehi and J. E. Subotnik, Derivative couplings with built-in electron-translation factors: Application to ben- zene, The Journal of Physical Chemistry Letters3, 2039 (2012), https://doi.org/10.1021/jz3006173

    doi:10.1021/jz3006173 2039

  64. [64]

    Athavale, X

    V. Athavale, X. Bian, Z. Tao, Y. Wu, T. Qiu, J. Rawlin- son, R. G. Littlejohn, and J. E. Subotnik, Surface hop- ping, electron translation factors, electron rotation fac- tors, momentum conservation, and size consistency, The Journal of Chemical Physics159, 114120 (2023)

    2023

  65. [65]

    Q. Ou, G. D. Bellchambers, F. Furche, and J. E. Sub- otnik, First-order derivative couplings between excited states from adiabatic tddft response theory, The Journal of Chemical Physics142, 064114 (2015)

    2015

  66. [66]

    Z. Pu, X. Wu, Y. Wang, C. Fan, W. Yan, Z. Zhou, Y. Q. Gao, and Q. Sun, Analytical excited-state gradients and derivative couplings in tddft with minimal auxiliary basis set approximation and gpu acceleration, Journal of Chemical Theory and Computation22, 1793 (2026), pMID: 41615830, https://doi.org/10.1021/acs.jctc.5c01960

    doi:10.1021/acs.jctc.5c01960 2026

  67. [67]

    T. N. Todorov, Time-dependent tight binding, Journal of Physics: Condensed Matter13, 10125 (2001)

    2001

  68. [68]

    Macheda, P

    F. Macheda, P. Barone, and F. Mauri, Electron-phonon interaction and longitudinal-transverse phonon splitting in doped semiconductors, Phys. Rev. Lett.129, 185902 (2022)

    2022

  69. [69]

    Macheda, T

    F. Macheda, T. Sohier, P. Barone, and F. Mauri, Electron-phonon interaction and phonon frequencies in two-dimensional doped semiconductors, Phys. Rev. B 107, 094308 (2023)

    2023

  70. [70]

    Macheda, P

    F. Macheda, P. Barone, and F. Mauri, First-principles calculations of dynamical born effective charges, quadrupoles, and higher order terms from the charge response in large semiconducting and metallic systems, Phys. Rev. B110, 094306 (2024)

    2024

  71. [71]

    Zabalo, C

    A. Zabalo, C. E. Dreyer, and M. Stengel, Static born charges and quantum capacitance in metals and doped semiconductors, Phys. Rev. B111, 094307 (2025)

    2025

  72. [72]

    R. P. Woodard, The theorem of ostrogradsky (2015), arXiv:1506.02210 [hep-th]

    Pith/arXiv arXiv 2015

  73. [73]

    M. Ostrogradsky, M´ emoires sur les ´ equations diff´ erentielles, relatives au probl` eme des isop´ erim` etres, M´ emoires de l’Acad´ emie Imp´ eriale des Sciences de St.-P´ etersbourg, S´ erie 64, 385 (1850)

  74. [74]

    Motohashi and T

    H. Motohashi and T. Suyama, Third order equations of motion and the ostrogradsky instability, Phys. Rev. D 91, 085009 (2015)

    2015

  75. [75]

    Pulay, Ab initio calculation of force constants and equilibrium geometries in polyatomic molecules, Molecu- lar Physics17, 197 (1969)

    P. Pulay, Ab initio calculation of force constants and equilibrium geometries in polyatomic molecules, Molecu- lar Physics17, 197 (1969)

    1969

  76. [76]

    Scherrer, F

    A. Scherrer, F. Agostini, D. Sebastiani, E. K. U. Gross, and R. Vuilleumier, On the mass of atoms in molecules: Beyond the born-oppenheimer approxima- tion, Phys. Rev. X7, 031035 (2017)

    2017

  77. [77]

    Ponc´ e and X

    S. Ponc´ e and X. Gonze, In search of the electron-phonon contribution to total energy (2025), arXiv:2512.04897 [cond-mat.mtrl-sci]

    arXiv 2025

  78. [78]

    C. J. Pickard and F. Mauri, All-electron magnetic re- sponse with pseudopotentials: Nmr chemical shifts, Phys. Rev. B63, 245101 (2001)

    2001

  79. [79]

    C. J. Pickard and F. Mauri, Nonlocal pseudopotentials and magnetic fields, Phys. Rev. Lett.91, 196401 (2003)

    2003

  80. [80]

    Bennetto and D

    J. Bennetto and D. Vanderbilt, Semiconductor effective charges from tight-binding theory, Phys. Rev. B53, 15417 (1996)

    1996

Showing first 80 references.