Pith. sign in

REVIEW 4 major objections 4 minor 69 references

Memory-dependent electronic friction for nonadiabatic dynamics at metal surfaces

T0 review · 4 major / 4 minor · reviewed 2026-08-16 · deepseek-v4-flash

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

Pith's one-line read Retaining the full frequency dependence of electronic friction changes how energy is partitioned among nuclear modes in hyperthermal molecule–metal scattering, increasing vibrational and reducing translational energy loss for NO on Au(111).

desk verdict A solid formalism paper whose headline quantitative claim is ahead of its evidence; deserves review but needs either a two-time benchmark or a softer abstract. read the letter →

arxiv 2608.12572 v1 pith:6X3JOVYY submitted 2026-08-12 cond-mat.mtrl-sci physics.chem-ph

Xuexun Lu , Connor L. Box , Nils Hertl , Reinhard J. Maurer This is my paper · ORCID
classification cond-mat.mtrl-sciphysics.chem-ph PACS 71.38.-k79.20.Rf
keywords electronicfrictionmemorykernelnon-Markoviandynamicselectron-holepairexcitationsmolecule-metalscatteringgeneralizedLangevinequationKohn-ShamdensityfunctionaltheoryNO/Au(111)
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

Molecular dynamics with electronic friction treats the energy a moving molecule loses to electron–hole pairs in a metal as a drag force, but almost all applications replace the true frequency-dependent drag by a memoryless Markovian coefficient. This paper derives a practical first-principles route to the full memory kernel—the tensor that keeps track of how strongly the electrons respond at each excitation frequency—and evaluates it for model impurities and for NO scattering on Au(111) using density functional theory. For hyperthermal NO/Au(111) scattering, the memory treatment raises the median total frictional energy loss to 0.42 eV versus 0.21 eV for the zero-frequency Markovian limit, and, more importantly, changes which modes pay: the internal N–O stretch loses more energy while centre-of-mass translation loses less, sharpening the anisotropy of friction. The conclusion is that a single effective Markovian friction coefficient cannot reproduce this mode-selective dissipation, which matters for any state-resolved scattering observable.

What carries the argument

The load-bearing object is the frequency-dependent electronic friction memory kernel $K_{\mu\nu}(\omega;x)$, a tensor over nuclear modes $\mu,\nu$ evaluated at nuclear configuration $x$. In the Kohn–Sham implementation it is built from static electron–phonon coupling matrix elements and Fermi-occupation differences as $K^{\rm KS}_{\mu\nu}(\omega;x) = 2\pi\hbar \sum_{mn}\int dk\, \tilde{g}^\mu_{mn}(k;x)[\tilde{g}^\nu_{mn}(k;x)]^* [n_F(\epsilon_{nk})-n_F(\epsilon_{mk})]\delta(\epsilon_{mk}-\epsilon_{nk}-\hbar\omega)/\hbar\omega$, and it is connected to the retarded electron–hole pair self-energy through $K_{\mu\nu}(\omega;x) = -\frac{\pi}{2\omega}\mathrm{Re}\,\Gamma_{\mu\nu}(\omega;x)$. The causal time-domain kernel is reconstructed by a one-sided cosine transform with a smooth cutoff, $K_{\mu\nu}(t-t';x)=\frac{2\Theta(t-t')}{\pi}\int_0^{\omega_{\rm max}} d\omega\, w(\omega)K_{\mu\nu}(\omega;x)\cos[\omega(t-t')]$. The quasi-adiabatic linear-coupling ansatz collapses the two-time kernel $K(t-t';x(t),x(t'))$ to $K(t-t';x(t))$, which is what makes first-principles evaluation numerically feasible, and the analytical threshold $\omega_*$ for positive semidefiniteness delimits the frequency window in which the memory kernel behaves as a strictly dissipative bath.

What would settle it

Compute the exact two-time kernel $K(t-t';x(t),x(t'))$ (without the local collapse) for one of the six NO/Au(111) trajectories and compare the mode-resolved CPA energy losses with the endpoint-collapsed kernel; if the difference rivals the reported Markovian-vs-memory gap, the local ansatz, not the Markov approximation, dominates the error.

Watch

Extended reading notes

Core claim

The central claim is that electronic friction on nuclei is genuinely frequency-dependent and configuration-dependent, and that retaining this memory is necessary for correct mode-resolved energy dissipation in hyperthermal scattering. The paper establishes this in three steps: for Newns–Anderson impurity models it derives closed-form frequency-dependent friction spectra and a threshold frequency $\omega_*$ beyond which the kernel loses strict positive semidefiniteness; for Kohn–Sham DFT it constructs the tensorial dissipation spectrum from electron–phonon coupling matrix elements; and for NO/Au(111) along six Born–Oppenheimer trajectories it compares the full memory kernel with two Markovian reductions. The memory treatment gives median mode-resolved losses of (0.29, 0.069, 0.017) eV for stretch, orientation, and surface-normal motion, versus (0.20, 0.066, 0.039) eV for the frequency-averaged Markovian tensor: memory transfers dissipation from translation into vibration and raises directional anisotropy. The paper also shows that the results are insensitive to whether the local kernel is anchored at the current or arithmetic-mean configuration, and that the memory description removes the arbitrary choice of which Markovian coefficient to extract from the structured spectrum.

Load-bearing premise

The whole quantitative analysis rests on the quasi-adiabatic assumption that the electronic friction kernel at a moment in time can be computed from the molecule's current configuration alone, ignoring the dependence on past configurations that the exact two-time kernel contains.

Editorial extensions

If this is right

  • Markovian MDEF for hyperthermal scattering will systematically misassign energy loss among nuclear modes: for NO/Au(111) it undercounts stretch-mode dissipation and overcounts translation, biasing any state-resolved vibrational prediction.
  • A Markovian tensor that matches the total dissipated energy can still get the per-mode partitioning wrong, so reproducing total stopping power is not a sufficient validation of the Markov approximation.
  • Memory-dependent friction removes the need to pick a single effective Markovian coefficient, eliminating the arbitrary frequency window (here 1–3 eV) that any such reduction requires.
  • The direction of the memory effect is system-dependent: in the one-dimensional impurity model weak molecule-metal coupling makes memory reduce energy loss, whereas for NO/Au(111) it increases vibrational loss, so no universal rescaling of Markovian friction exists.
  • Mode-resolved dissipation becomes more anisotropic when memory is retained because high-frequency stretch motion and low-frequency translation probe different parts of the friction spectrum.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the same frequency-dependent partitioning holds beyond the classical-path approximation, then full non-Markovian GLE propagation with coloured noise will likely shift final vibrational-state distributions further down than either Markovian model; the paper's 2.5-fold stretch dissipation increase is an upper-bound estimate without steering.
  • The negligible difference between endpoint and arithmetic-mean anchoring found here may not survive for slower dynamics such as thermal desorption or diffusion, where trajectories linger in regions where the friction spectrum changes rapidly over the memory window.
  • The positive-semidefiniteness threshold suggests that at excitation energies above $\omega_*$ the local memory kernel is not a passive dissipative bath; full GLE simulations should test whether those frequencies are ever sampled and how to handle the flag.
  • A practical next step would be fitting a surrogate model of the frequency-dependent friction tensor, allowing thousands of full memory-GLE trajectories and a direct experimental test against state-resolved NO/Au(111) measurements.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 4 minor

Summary. The paper develops a formalism for memory-dependent (non-Markovian) electronic friction for nonadiabatic dynamics at metal surfaces. The authors derive a frequency-dependent friction kernel from a local linear-coupling approximation, evaluate it for two Newns–Anderson model Hamiltonians (Erpenbeck–Thoss and Gardner–Habershon–Maurer) and for Kohn–Sham DFT applied to NO/Au(111), and analyze the positive semidefiniteness of the resulting kernels. They use a classical-path approximation on six BOMD trajectories to compare frictional energy losses from the non-Markovian kernel against zero-frequency (ODF) and frequency-averaged Markovian tensors. The central reported result is that memory effects increase vibrational and reduce translational energy loss for NO/Au(111), thereby increasing the mode anisotropy of dissipation.

Significance. If the central claim is validated, the work is significant because it challenges the adequacy of Markovian MDEF for state-resolved observables in hyperthermal scattering and offers a practical route toward non-Markovian friction from first principles. The formal derivation is coherent and recovers known Markovian limits; the analytical positive-semidefiniteness threshold analysis is a useful contribution in its own right. The paper also ships reproducible data and figure scripts, and it explicitly compares three friction treatments for the same trajectories, which strengthens the presentation. However, the quantitative claim rests on an unvalidated single-configuration ansatz and on a classical-path analysis with only six trajectories, so the significance of the mode-partitioning result is currently conditional.

major comments (4)
  1. [II.B, Eq. (14); II.G, Eq. (61)] The collapse of the two-time kernel K(t-t';x(t),x(t')) to K(t-t';x(t)) is the central approximation, but it is never validated against a calculation that retains the x(t') dependence. The endpoint-versus-arithmetic-mean comparison (Eq. (63) and SM Fig. S8) compares two versions of the collapsed kernel; both omit the same physics. Because the DFT friction spectra in Fig. 6 are strongly geometry- and mode-dependent and the trajectories traverse the region where friction changes rapidly, the mode-resolved energy losses in Fig. 7 could be an artifact of this collapse rather than an intrinsic memory effect. A direct test is required, for example by evaluating the full two-time kernel in the Anderson models along representative trajectories, or by estimating the magnitude of the neglected term from the nuclear displacement over the memory window.
  2. [II.G, Eq. (60); IV.C] The classical-path approximation evaluates dissipative work on fixed BOMD trajectories and neglects feedback of the memory force on the nuclear motion, as the authors acknowledge. This is not merely a quantitative detail: friction-induced velocity changes and altered residence times are precisely the mechanisms that would redistribute energy between modes. With only six trajectories and no reported uncertainty on the medians, the difference between the memory treatment and η_Avg (r: 0.29 vs 0.20 eV; z: 0.017 vs 0.039 eV) is not established as statistically robust. The central claim therefore requires either propagation of the non-Markovian GLE or, at minimum, a perturbative estimate of feedback and a larger trajectory ensemble.
  3. [IV.C and SM Fig. S7] The reported mode-partitioning effect is comparable in size to the numerical uncertainty of the memory kernel. SM Fig. S7 shows the mean total memory dissipation varying between roughly 0.26 and 0.40 eV as the broadening width is changed from 0.01 to 0.6 eV, while the mode-resolved memory-versus-η_Avg differences in Fig. 7 are 0.09 eV for r and 0.022 eV for z. The manuscript should show mode-resolved losses as a function of broadening and of the averaging window [ω1,ω2] used for η_Avg, to demonstrate that the partition change is not a consequence of these numerical choices.
  4. [IV.B, Fig. S3; IV.C, Fig. 7] The GHM model results in Fig. S3 show that memory-dependent friction increases both vibrational and translational energy loss relative to Markovian friction, whereas the DFT-based results in Fig. 7 report a reduction of z loss for the same molecule and surface. The abstract presents the vibrational-increase/translational-reduction pattern as the key outcome for NO/Au(111) without limiting it to the DFT treatment. The manuscript should explicitly reconcile these two results and specify the scope of the mode-partitioning claim.
minor comments (4)
  1. [SM captions and Appendix C] There are several typographical errors, including 'Model Hamiltionian' in the SM title, 'demontrates' in the SM Fig. S3 caption, 'FHi-aims' in SM Fig. S7, and 'closd form' in Appendix C; these should be corrected.
  2. [III.C] The description of the basis set as a '2020 light basis' should be clarified, for example as the FHI-aims '20/20 light' basis, to avoid ambiguity for readers unfamiliar with the FHI-aims tier notation.
  3. [Fig. 6 caption] The caption should specify which curves or lines correspond to η_ODF and η_Avg; the text mentioning 'ηODF with small broadenings (black lines)' is not fully clear from the caption alone.
  4. [II.F, Eq. (54)-(55)] The sentence following Eq. (55), 'We use the same window and cutoff at every configuration,' is grammatically incomplete and should be merged with the following sentence.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the frequency-dependent friction kernel is evaluated from first principles and the reported energy losses are not fitted; self-citations are supporting, not load-bearing.

full rationale

The central comparison is between the full non-Markovian friction kernel computed from Kohn–Sham DFT and two Markovian reductions of the same kernel (the zero-frequency limit and a heuristic frequency average). No parameter of the kernel is tuned to reproduce the reported mode-resolved energy losses; the kernel itself is the first-principles linear-response quantity, and the Markovian limits are derived from it rather than imposed as inputs. The local single-configuration ansatz of Eq. (14) is an approximation whose validity the authors explicitly discuss and test through endpoint versus arithmetic-mean anchoring, but this is a limitation of the chosen dynamical treatment, not a circular reduction: the output energy losses are not equivalent to any fitted input by construction. Self-citations appear for background motivation, for the parametrized model Hamiltonians, and for the FHI-aims implementation, but none of these citations is used to force the central NO/Au(111) result, which rests on direct DFT evaluation of the frequency-dependent friction along Born–Oppenheimer trajectories. The comparison against Markovian ODF and ηAvg is internal rather than circular, and the paper itself acknowledges the heuristic nature of the averaging window. Therefore no circular step is present.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

The central DFT-based results depend on numerical convergence parameters (broadening, cutoff, tapering window) whose values are justified by sensitivity analysis in the SM but are not unique. The model-based results depend on parameters inherited from prior fits against DFT data. The heuristic etaAvg averaging window is explicitly arbitrary. No new entities are postulated.

free parameters (5)
  • ET model hybridization amplitude Delta0 = 0.005 to 0.5 eV (varied)
    Tunable impurity-bath coupling in the Erpenbeck-Thoss model; controls the width and magnitude of the friction spectrum and the strength of memory effects.
  • GHM model hybridization amplitude Delta0 = 0.75 eV
    Fixed by parametrisation against DFT data in the Gardner-Habershon-Maurer model for NO/Au(111).
  • Markovian frequency-averaging window [omega1, omega2] = 1 to 3 eV
    Defines the heuristic etaAvg Markovian tensor; the paper calls this an arbitrary and heuristic choice.
  • Gaussian broadening width sigma = 0.01 eV raw, broadened to 0.05 or 0.6 eV
    Used to smooth the FHI-aims friction spectrum; the final memory-kernel results depend on this choice, with sensitivity shown in SM Figures S7 and S8.
  • Memory-kernel cutoff hbar*omega_max = 3.2 eV
    Hard or tapered cutoff for the one-sided cosine transform; sensitivity shown in SM Figure S6.
assumptions (6)
  • domain assumption Quasi-adiabatic (local linear-coupling) limit: friction kernel quantities are evaluated at the instantaneous configuration x(t), collapsing K(t-t';x(t),x(t')) to K(t-t';x(t))
    Introduced in Eq. (14) and Section II.B; this is the key enabler for first-principles memory kernels and is tested only through endpoint vs arithmetic-mean anchoring, not against a full two-time kernel.
  • domain assumption Weak electron-phonon coupling with first-order truncation in nonadiabatic coupling
    Underlies the MDEF/GLE derivation in Section II.A and limits validity to weakly nonadiabatic systems.
  • standard math Non-interacting electrons (Kohn-Sham or independent-electron Hamiltonian)
    Used to reduce the many-body kernel to the orbital-dependent friction expression of Eq. (50).
  • domain assumption Classical nuclear motion
    MDEF treats nuclei classically; the CPA additionally ignores feedback of the memory force on the trajectory, as stated in Section IIG.
  • domain assumption Head-Gordon-Tully approximation for electron-phonon matrix elements (Eq. 49)
    Replaces Kohn-Sham eigenvalues by the Fermi level in the overlap-response term; cited from prior work as having minor effects.
  • standard math Feynman-Vernon / NEGF influence-functional representation of the bath
    Provides the retarded self-energy expression Eq. (19) and the fluctuation-dissipation relation Eq. (3).

how reviews work

0 comments
Cite this review

Pith. "Pith review of Memory-dependent electronic friction for nonadiabatic dynamics at metal surfaces." pith.science (2026). https://pith.science/paper/6X3JOVYY

@misc{pith2026260812572,
  author       = {Pith},
  title        = {Pith review of: Memory-dependent electronic friction for nonadiabatic dynamics at metal surfaces},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6X3JOVYY}},
  note         = {Machine review of arXiv:2608.12572}
}
read the original abstract

Electronic excitation induced by nuclear motion is a key energy dissipation channel in chemical dynamics at metal surfaces. Here, nonadiabatic effects can be treated via molecular dynamics with electronic friction, where they act as frictional drag and fluctuation force contributions. Commonly, the Markov approximation is imposed, so memory effects are ignored. A theoretical formalism is presented to evaluate tensorial and configuration-dependent electronic friction memory kernels from first principles. We evaluate friction kernels for Newns--Anderson Hamiltonian models as well as within Kohn--Sham density functional theory and analyse their mathematical properties and configuration dependence. For hyperthermal atomic and diatomic scattering, memory effects arising from frequency and configuration dependence of electronic friction affect energy exchange between adsorbate and metal electrons. Memory effects lead to an increase of vibrational and a reduction of translational energy loss in the case of nitric oxide scattering on Au(111), leading to an increase of directional anisotropy of friction. Importantly, memory-dependent evaluation of electronic friction removes the need to define a single effective Markovian friction coefficient from the structured frequency-dependent electronic response.

Figures

Figures reproduced from arXiv: 2608.12572 by the authors.

Figure 1
Figure 1. Panel (a): Energy curves of the one-dimensional [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. Frequency-dependent electronic friction K(ω; x) (solid) and its Markovian limit (dashed, ω-independent) for the Erpenbeck–Thoss model [28, 45] at T = 300 K, versus frequency ω (axis ℏω in eV; vertical scale logarithmic, friction in u · ps−1 ). Colors denote nuclear position x = 1.9–2.2 Å; panels (top to bottom) show coupling ∆(x=0) = 0.4, 0.1, 0.01 eV. Vertical dotted lines mark the particle–hole threshold |h(x)|+3k… view at source ↗
Figure 3
Figure 3. Frequency-dependent electronic friction tensor [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Frictional energy loss, ∆E f , of impurity scattering, computed within the classical-path approximation (CPA), for the Erpenbeck–Thoss model [45]. (a) ∆E f versus the impurity–metal coupling strength, ∆0, at fixed incident trans￾lational energy Et = 2 eV. (b) ∆E f vers…
Figure 6
Figure 6. Figure 6: (a) NO/Au(111) configuration and coordinate sys [PITH_FULL_IMAGE:figures/full_fig_p014_6.png]
Figure 7
Figure 7. Figure 7: CPA frictional energy losses, ∆E f , evaluated over six representative NO/Au(111) scattering trajectories for three friction models: the Markovian ODF tensor η ODF , the Markovian frequency-averaged tensor η Avg, and the non￾Markovian local memory kernel. Both η Avg an…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

69 extracted references · 66 canonical work pages

  1. [1]

    Saalfrank, Quantum dynamical approach to ultrafast molecular desorption from surfaces, Chem

    P. Saalfrank, Quantum dynamical approach to ultrafast molecular desorption from surfaces, Chem. Rev.106, 4116 (2006)

    work page 2006

  2. [2]

    D. J. Auerbach, J. C. Tully, and A. M. Wodtke, Chemical dynamics from the gas-phase to surfaces, Nat. Sci.1, e10005 (2021)

    work page 2021

  3. [3]

    Gergen, H

    B. Gergen, H. Nienhaus, W. H. Weinberg, and E. W. McFarland, Chemically induced electronic excitations at metal surfaces, Science294, 2521 (2001)

    work page 2001

  4. [4]

    C. L. A. Lamont, B. N. J. Persson, and G. P. Williams, Dynamics of atomic adsorbates: Hydrogen on Cu(111), Chem. Phys. Lett.243, 429 (1995)

    work page 1995

  5. [5]

    L. J. Lauhon and W. Ho, Direct observation of the quan- tum tunneling of single hydrogen atoms with a scanning tunneling microscope, Phys. Rev. Lett.85, 4566 (2000)

    work page 2000

  6. [6]

    Huang, A

    Y. Huang, A. M. Wodtke, H. Hou, C. T. Rettner, and D.J.Auerbach,Observationofvibrationalexcitationand deexcitation for NO(ν= 2) scattering from Au(111): Ev- idence for electron–hole-pair mediated energy transfer, Phys. Rev. Lett.84, 2985 (2000)

    work page 2000

  7. [7]

    B. C. Krüger, S. Meyer, A. Kandratsenka, A. M. Wodtke, and T. Schäfer, Vibrational inelasticity of highly vibra- tionally excited NO on Ag(111), J. Phys. Chem. Lett.7, 441 (2016)

    work page 2016

  8. [8]

    Schäfer, N

    T. Schäfer, N. Bartels, K. Golibrzuch, C. Bartels, H.Köckert, D.J.Auerbach, T.N.Kitsopoulos,andA.M. Wodtke, Observation of direct vibrational excitation in gas–surface collisions of CO with Au(111): A new model system for surface dynamics, Phys. Chem. Chem. Phys. 15, 1863 (2013)

    work page 2013

Show all 69 references
  1. [9]

    R. J. V. Wagner, N. Henning, B. C. Krüger, G. B. Park, J. Altschäffel, A. Kandratsenka, A. M. Wodtke, and T. Schäfer, Vibrational relaxation of highly vibra- tionally excited CO scattered from Au(111): Evidence for CO− formation, J. Phys. Chem. Lett.8, 4887 (2017)

    2017

  2. [10]

    Bünermann, H

    O. Bünermann, H. Jiang, Y. Dorenkamp, A. Kandrat- senka, S. M. Janke, D. J. Auerbach, and A. M. Wodtke, Electron–hole pair excitation determines the mechanism of hydrogen atom adsorption, Science350, 1346 (2015)

    2015

  3. [11]

    Dorenkamp, H

    Y. Dorenkamp, H. Jiang, H. Köckert, N. Hertl, M. Kammler, S. M. Janke, A. Kandratsenka, A. M. Wodtke, and O. Bünermann, Hydrogen collisions with transition metal surfaces: Universal electronically nona- diabatic adsorption, J. Chem. Phys.148, 034706 (2018)

    2018

  4. [12]

    Hertl, K

    N. Hertl, K. Krüger, and O. Bünermann, Electronically nonadiabatic H atom scattering from low Miller index surfaces of silver, Langmuir38, 14162 (2022)

    2022

  5. [13]

    Head-Gordon and J

    M. Head-Gordon and J. C. Tully, Molecular dynam- ics with electronic frictions, J. Chem. Phys.103, 10137 (1995)

    1995

  6. [14]

    W. Dou, G. Miao, and J. E. Subotnik, Born– Oppenheimer dynamics, electronic friction, and the in- clusion of electron-electron interactions, Phys. Rev. Lett. 119, 046001 (2017)

    2017

  7. [15]

    Dou and J

    W. Dou and J. E. Subotnik, Perspective: How to un- derstand electronic friction, J. Chem. Phys.148, 230901 (2018)

    2018

  8. [16]

    Persson and B

    M. Persson and B. Hellsing, Electronic damping of adsor- bate vibrations on metal surfaces, Phys. Rev. Lett.49, 662 (1982)

    1982

  9. [17]

    Brandbyge, P

    M. Brandbyge, P. Hedegård, T. F. Heinz, J. A. Misewich, and D. M. Newns, Electronically driven adsorbate exci- 21 tation mechanism in femtosecond-pulse laser desorption, Phys. Rev. B52, 6042 (1995)

    1995

  10. [18]

    B. B. Smith and J. T. Hynes, Electronic friction and elec- tron transfer rates at metallic electrodes, J. Chem. Phys. 99, 6517 (1993)

    1993

  11. [19]

    J.-T. Lü, M. Brandbyge, P. Hedegård, T. N. Todorov, and D. Dundas, Current-induced atomic dynamics, in- stabilities, and Raman signals: Quasiclassical Langevin equation approach, Phys. Rev. B85, 245444 (2012)

    2012

  12. [20]

    N. Bode, S. V. Kusminskiy, R. Egger, and F. von Oppen, Scattering theory of current-induced forces in mesoscopic systems, Phys. Rev. Lett.107, 036804 (2011)

    2011

  13. [21]

    V. U. Nazarov, J. M. Pitarke, C. S. Kim, and Y. Takada, Time-dependent density-functional theory for the stop- ping power of an interacting electron gas for slow ions, Phys. Rev. B71, 121106 (2005)

    2005

  14. [22]

    V. U. Nazarov, T. N. Todorov, and E. K. U. Gross, Vis- couscurrent-inducedforces,Phys.Rev.Lett.133,026301 (2024)

    2024

  15. [23]

    V. U. Nazarov and E. K. U. Gross, Stopping power of electron liquid for slow quantum projectiles, Contrib. Plasma Phys. 10.1002/ctpp.70132 (2026), advance arti- cle, e70132

    2026 doi

  16. [24]

    R. J. Preston, S. L. Rudge, D. S. Kosov, and M. Thoss, Negative electronic friction and non-Markovianity in nonequilibrium quantum systems, Nano Lett.26, 8004 (2026)

    2026

  17. [25]

    Martinazzo and I

    R. Martinazzo and I. Burghardt, Quantum dynamics with electronic friction, Phys. Rev. Lett.128, 206002 (2022)

    2022

  18. [26]

    Martinazzo and I

    R. Martinazzo and I. Burghardt, Quantum theory of elec- tronic friction, Phys. Rev. A105, 052215 (2022)

    2022

  19. [27]

    Dou and J

    W. Dou and J. E. Subotnik, A broadened classical master equation approach for nonadiabatic dynamics at metal surfaces: Beyond the weak molecule–metal cou- pling limit, J. Chem. Phys.144, 024116 (2016)

    2016

  20. [28]

    Gardner, D

    J. Gardner, D. Corken, S. M. Janke, S. Habershon, and R. J. Maurer, Efficient implementation and perfor- mance analysis of the independent electron surface hop- ping method for dynamics at metal surfaces, J. Chem. Phys.158, 064101 (2023)

    2023

  21. [29]

    Gardner, S

    J. Gardner, S. Habershon, and R. J. Maurer, Assess- ing mixed quantum-classical molecular dynamics meth- ods for nonadiabatic dynamics of molecules on metal sur- faces, J. Phys. Chem. C127, 15257 (2023)

    2023

  22. [30]

    Zwanzig,Nonequilibrium Statistical Mechanics(Ox- ford University Press, New York, 2001)

    R. Zwanzig,Nonequilibrium Statistical Mechanics(Ox- ford University Press, New York, 2001)

    2001

  23. [31]

    Olsen and J

    T. Olsen and J. Schiøtz, Memory effects in nonadiabatic molecular dynamics at metal surfaces, J. Chem. Phys. 133, 134109 (2010)

    2010

  24. [32]

    Trenins and M

    G. Trenins and M. Rossi, Non-Markovian effects in quan- tum rate calculations of hydrogen diffusion with elec- tronic friction, Phys. Rev. Lett.134, 226201 (2025)

    2025

  25. [33]

    Li and G

    Y. Li and G. Wahnström, Molecular-dynamics simula- tion of hydrogen diffusion in palladium, Phys. Rev. B 46, 14528 (1992)

    1992

  26. [34]

    J. I. Juaristi, M. Alducin, R. Díez Muiño, H. F. Bus- nengo, and S. A, Role of electron–hole pair excitations in the dissociative adsorption of diatomic molecules on metal surfaces, Phys. Rev. Lett.100, 116102 (2008)

    2008

  27. [35]

    Gerrits, J

    N. Gerrits, J. I. n. Juaristi, and J. Meyer, Electronic friction coefficients from the atom-in-jellium model for Z= 1–92, Phys. Rev. B102, 155130 (2020)

    2020

  28. [36]

    B.HellsingandM.Persson,Electronicdampingofatomic andmolecularvibrationsatmetalsurfaces,Phys.Scr.29, 360 (1984)

    1984

  29. [37]

    R. J. Maurer, M. Askerka, V. S. Batista, and J. C. Tully, Ab initio tensorial electronic friction for molecules on metal surfaces: Nonadiabatic vibrational relaxation, Phys. Rev. B94, 115432 (2016)

    2016

  30. [38]

    C. L. Box, W. G. Stark, and R. J. Maurer, Ab initio calculation of electron–phonon linewidths and molecu- lar dynamics with electronic friction at metal surfaces with numeric atom-centred orbitals, Electron. Struct.5, 035005 (2023)

    2023

  31. [39]

    C. L. Box, N. Hertl, W. G. Stark, and R. J. Mau- rer, Room temperature hydrogen atom scattering exper- iments are not a sufficient benchmark to validate elec- tronic friction theory, J. Phys. Chem. Lett.15, 12520 (2024)

    2024

  32. [40]

    Füchsel, T

    G. Füchsel, T. Klamroth, S. Monturet, and P. Saalfrank, Dissipative dynamics within the electronic friction ap- proach: The femtosecond laser desorption of H2/D2 from Ru(0001), Phys. Chem. Chem. Phys.13, 8659 (2011)

    2011

  33. [41]

    Žugec, A

    I. Žugec, A. Tetenoire, A. S. Muzas, Y. Zhang, B. Jiang, M. Alducin, and J. I. Juaristi, Understanding the pho- toinduced desorption and oxidation of CO on Ru(0001) using a neural network potential energy surface, JACS Au4, 1997 (2024)

    2024

  34. [42]

    Spears, W

    A. Spears, W. G. Stark, and R. J. Maurer, Role of anisotropic electronic friction in laser-driven hydro- gen recombination on copper (2026), arXiv:2604.00709 [physics.chem-ph]

    2026

  35. [43]

    Hertl, C

    N. Hertl, C. L. Box, and R.J. Maurer,Mode selectivity in electron-promoted vibrational relaxation of chemisorbed hydrogen on molybdenum and tungsten surfaces, Fara- day Discuss. 10.1039/d5fd00116a (2026)

    2026 doi

  36. [44]

    C. L. Box, Y. Zhang, R. Yin, B. Jiang, and R. J. Mau- rer, Determining the effect of hot electron dissipation on molecular scattering experiments at metal surfaces, JACS Au1, 164 (2021)

    2021

  37. [45]

    Erpenbeck, C

    A. Erpenbeck, C. Schinabeck, U. Peskin, and M. Thoss, Current-induced bond rupture in single-molecule junc- tions, Phys. Rev. B97, 235452 (2018)

    2018

  38. [46]

    G. Meng, J. Gardner, N. Hertl, W. Dou, R. J. Maurer, and B. Jiang, First-principles nonadiabatic dynamics of molecules at metal surfaces with vibrationally coupled electron transfer, Phys. Rev. Lett.133, 036203 (2024)

    2024

  39. [47]

    J. Hong, N. Hertl, R. J. Maurer, G. Meng, and B. Jiang, Vibrational excitation in gas–surface collisions of CO with Au(111): A first-principles nonadiabatic dynamics study, J. Phys. Chem. C129, 2944 (2025)

    2025

  40. [48]

    Bombín, A

    R. Bombín, A. S. Muzas, A. Serrano Jiménez, J. I. Juaristi, and M. Alducin, Asymmetry and coverage de- pendence in two-pulse correlation measurements of CO photodesorption from Pd(111): Insights from theory, J. Chem. Phys.164, 064709 (2026)

    2026

  41. [49]

    R. P. Feynman and F. L. Vernon, The theory of a gen- eral quantum system interacting with a linear dissipative system, Ann. Phys. (N. Y.)24, 118 (1963)

    1963

  42. [50]

    Z. X. Jin and J. E. Subotnik, A practical ansatz for evalu- ating the electronic friction tensor accurately, efficiently, and in a nearly black-box format, J. Chem. Phys.150, 164105 (2019)

    2019

  43. [51]

    Shang, C

    H. Shang, C. Carbogno, P. Rinke, and M. Scheffler, Lat- tice dynamics calculations based on density-functional perturbation theory in real space, Comput. Phys. Com- mun.215, 26 (2017). 22

    2017

  44. [52]

    J. W. Abbott, C. Mera Acosta, A. Akkoush, A. Am- brosetti, V. Atalla, A. Bagrets, J. Behler, D. Berger, H. Bertschi, B. Bieniek, J. Björk, V. Blum, S. Bohloul, C. L. Box, N. J. Boyer, D. S. Brambila, G. A. Bram- ley, K. R. Bryenton, M. Camarasa-Gómez, C. Car- bogno, F. Caruso,...

    2026

  45. [53]

    Spiering and J

    P. Spiering and J. Meyer, Testing electronic friction mod- els: Vibrational de-excitation in scattering of H2 and D2 from Cu(111), J. Phys. Chem. Lett.9, 1803 (2018)

    2018

  46. [54]

    Meng and B

    G. Meng and B. Jiang, A pragmatic protocol for deter- mining charge transfer states of molecules at metal sur- faces by constrained density functional theory, J. Chem. Phys.157, 214103 (2022)

    2022

  47. [55]

    X. Hu, W. L. Hase, and T. Pirraglia, Vectorization of the general Monte Carlo classical trajectory program VENUS, J. Comput. Chem.12, 1014 (1991)

    1991

  48. [56]

    R. Yin, Y. L. Zhang, and B. Jiang, Strong vibrational relaxation of NO scattered from Au(111): Importance of the adiabatic potential energy surface, J. Phys. Chem. Lett.10, 5969 (2019)

    2019

  49. [57]

    V. Blum, R. Gehrke, F. Hanke, P. Havu, V. Havu, X. G. Ren, K. Reuter, and M. Scheffler, Ab initio molecular simulations with numeric atom-centered orbitals, Com- put. Phys. Commun.180, 2175 (2009)

    2009

  50. [58]

    Head-Gordon and J

    M. Head-Gordon and J. C. Tully, Molecular-orbital cal- culations of the lifetimes of the vibrational modes of CO on Cu(100), Phys. Rev. B46, 1853 (1992)

    1992

  51. [59]

    Askerka, R

    M. Askerka, R. J. Maurer, V. S. Batista, and J. C. Tully, Role of tensorial electronic friction in energy transfer at metal surfaces, Phys. Rev. Lett.116, 217601 (2016)

    2016

  52. [60]

    R. J. Preston, Y. Ke, S. L. Rudge, N. Hertl, R. Borrelli, R. J. Maurer, and M. Thoss, Nonadiabatic quantum dy- namics of molecules scattering from metal surfaces, J. Chem. Theory Comput.21, 1054 (2025)

    2025

  53. [61]

    B. C. Krüger, N. Bartels, C. Bartels, A. Kandratsenka, J. C. Tully, A. M. Wodtke, and T. Schäfer, NO vibra- tional energy transfer on a metal surface: Still a chal- lenge to first-principles theory, J. Phys. Chem. C119, 3268 (2015)

    2015

  54. [62]

    Falsig, J

    H. Falsig, J. Shen, T. S. Khan, W. Guo, G. Jones, S. Dahl, and T. Bligaard, On the structure sensitivity of direct NO decomposition over low-index transition metal facets, Top. Catal.57, 80 (2014)

    2014

  55. [63]

    Sachs, W

    M. Sachs, W. G. Stark, R. J. Maurer, and C. Ortner, Machine learning configuration-dependent friction ten- sors in Langevin heatbaths, Mach. Learn.: Sci. Technol. 6, 015016 (2025)

    2025

  56. [64]

    Meng and B

    G. Meng and B. Jiang, First-principles full-dimensional modelling of vibrational energy transfer of molecule scat- tering from metal surfaces, Nat. Commun.16, 10520 (2025)

    2025

  57. [65]

    V. U. Nazarov and E. K. U. Gross, Exact-factorization framework for electron–nuclear dynamics in electromag- netic fields, J. Chem. Theory Comput.22, 3796 (2026)

    2026

  58. [66]

    Memory-dependent electronic friction for nonadiabatic dynamics at metal surfaces

    A. Sommerfeld, Zur Elektronentheorie der Metalle auf Grund der Fermischen Statistik, Z. Phys.47, 1 (1928). Supplemental Material for "Memory-dependent electronic friction for nonadiabatic dynamics at metal surfaces" Xuexun Lu, 1 Connor L. Box, 2 Nils Hertl, 1, 3 and Reinhard J...

    1928

  59. [67]

    Erpenbeck, C

    A. Erpenbeck, C. Schinabeck, U. Peskin, and M. Thoss, Current-induced bond rupture in single- molecule junctions, Phys. Rev. B97, 235452 (2018)

    2018

  60. [68]

    Gardner, D

    J. Gardner, D. Corken, S. M. Janke, S. Habershon, and R. J. Maurer, Efficient implementation and performance analysis of the independent electron surface hopping method for dynamics at metal surfaces, The Journal of Chemical Physics158, 064101 (2023). S11

    2023

  61. [69]

    Gardner, S

    J. Gardner, S. Habershon, and R. J. Maurer, Assessing mixed quantum-classical molecular dynamics methods for nonadiabatic dynamics of molecules on metal surfaces, The Journal of Physical Chemistry C127, 15257 (2023). S12

    2023

Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.