{"id":"9d43fe0c-7b8b-4ebb-b556-ec64ea8d4395","arxiv_id":"2608.12572","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"Memory-dependent electronic friction, computed from DFT and model Hamiltonians, redirects energy loss from translation to vibration in NO scattering on Au(111), showing that Markovian friction is insufficient for hyperthermal scattering.","lead":"This paper derives a first-principles way to include memory effects in electronic friction, the drag that metal electrons exert on moving molecules. Applied to NO scattering on Au(111), the memory kernel shifts dissipated energy from translation into vibration, changing predicted final vibrational states.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The local single-configuration ansatz of Eq. (14) is the key unvalidated step; the endpoint-vs-arithmetic robustness check probes the anchor choice, not the ansatz itself.","rationale":"I reviewed the formalism and results in good faith. The derivation of the frequency-dependent kernel from the local linear-coupling approximation is coherent, and the PSD analysis in Sec. II.E and Appendix C is a useful independent result. The model calculations (ET and GHM) support the general statement that memory can either suppress or enhance dissipation depending on geometry, and the DFT spectra are the first of their kind. However, the specific headline claim about mode partitioning for NO/Au(111) rests on the local CPA kernel, and the only test performed is between two versions of the same local ansatz. The two-time dependence is not a minor technicality: Eq. (4) shows the kernel is a product of couplings at x(t) and x(t'), and the model's own crossing-region behavior in Fig. 3 shows strong configuration dependence. A full two-time benchmark is feasible in the analytic GHM model and would determine whether the single-configuration collapse is responsible for the reported effect. This is the same concern the reader identified; my verdict is therefore unchanged: the paper merits conditional acceptance, not rejection, because the formalism is sound and the limitation is explicitly acknowledged, but the central quantitative claim is not yet backed by a test of its key assumption.","tokens_in":32103,"tokens_out":5185,"duration_ms":58912,"concrete_test":"Within the analytic Gardner-Habershon-Maurer model (Sec. III.B), evaluate the CPA dissipative energy loss along representative trajectories using a two-time kernel in which the vertex functions A_mu(epsilon; x(tau)) and A_nu(hbar omega + epsilon; x(tau')) of Eqs. (29)-(30) are evaluated at the two endpoint configurations, rather than both at x(tau). Compare the resulting mode-resolved losses with the local endpoint kernel, Eq. (61), and the arithmetic-mean kernel, Eq. (63). If the r/z loss ratio or the vibrational-translational partitioning changes by more than about 20%, the local ansatz is the limiting approximation and the headline claim needs a full two-time treatment; if the partitioning is unchanged, the current robustness check is sufficient.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The abstract's quantitative claim that memory effects increase vibrational and reduce translational energy loss for NO/Au(111) is derived from the local classical-path kernel of Eq. (61), which invokes the quasi-adiabatic collapse K(t-t'; x(t), x(t')) to K(t-t'; x(t)) of Eq. (14). The paper's robustness check compares endpoint vs arithmetic-mean anchoring (Eq. (63) and SM Fig. S8); both are single-configuration constructions, so the test never probes whether the two-time dependence of the kernel matters. The DFT spectra in Fig. 6 are strongly geometry- and mode-dependent, and the trajectories move through the region where friction changes rapidly, so the collapse could be the controlling approximation. The authors explicitly flag the two-time evaluation as requiring state tracking (Sec. II.B) and record the anchoring inequality in Eq. (62), but no calculation against a two-time reference is presented. Until that comparison is made, the mode-resolved losses (memory r/z: 0.29/0.017 eV vs eta_Avg r/z: 0.20/0.039 eV) are not established as an intrinsic memory effect; they could be an artifact of the single-configuration ansatz.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":32379,"tokens_out":6376,"duration_ms":60442,"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":[{"comment":"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.","section":"II.B, Eq. (14); II.G, Eq. (61)"},{"comment":"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.","section":"II.G, Eq. (60); IV.C"},{"comment":"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.","section":"IV.C and SM Fig. S7"},{"comment":"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.","section":"IV.B, Fig. S3; IV.C, Fig. 7"}],"minor_comments":[{"comment":"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.","section":"SM captions and Appendix C"},{"comment":"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.","section":"III.C"},{"comment":"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.","section":"Fig. 6 caption"},{"comment":"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.","section":"II.F, Eq. (54)-(55)"}],"recommendation":"major_revision","confidential_remarks":"The stress-test concern about the single-configuration ansatz is, on reading the paper, valid and is the main reason for the major-revision recommendation. The paper is otherwise well-executed and within scope, and the authors' own limitation statements in Sec. IV.C support the need for additional validation of the load-bearing approximations."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things to know about this one. First, the genuinely new piece is a practical first-principles route to tensorial, frequency-resolved electronic friction memory kernels, plus a closed-form positive-semidefiniteness threshold for the Anderson model. Both are real contributions. Second, the abstract's quantitative claim — memory increases vibrational and reduces translational energy loss in NO/Au(111) — is not yet backed by evidence at that strength. It rests on a classical-path approximation along six BOMD trajectories, with no feedback of the memory force on the trajectory, and on a local single-configuration ansatz that the paper does not actually validate against a two-time reference.\n\nWhat the paper does well: the derivation is careful and recovers the known Markovian limits. The local linear-coupling reduction, Eq. (14), makes the memory kernel computationally tractable and is clearly explained with honest discussion of what it neglects. The frequency-dependent DFT friction tensors for NO/Au(111) are new and physically sensible, and the analytic PSD threshold for the Anderson model is a nice result that goes beyond earlier Markovian treatments. The authors also flag the main limitations themselves: CPA ignores steering, and the two-time kernel evaluation would require state tracking. The citation pattern is appropriate, connecting to prior memory-effect work in Olsen–Schiøtz and Trenins–Rossi as well as the standard NEGF and ODF references.\n\nThe soft spots are in proportion. The stress-test concern about Eq. (14) is on target: the endpoint-versus-arithmetic-mean comparison probes the anchoring choice within a single-configuration ansatz, not the ansatz itself. If the true kernel's dependence on both endpoint configurations matters, the mode-resolved numbers could shift. The small sample of six trajectories is fine for a proof of principle, but the abstract states a general conclusion. The comparison tensor ηAvg is a heuristic 1–3 eV average, which is fine as a straw man but not a rigorous Markovian competitor. And the code that generates the data is not yet available, only plotting scripts. None of this is fatal. The formalism holds together, and the mode-resolved shift toward the stretch coordinate is plausible. But the paper would be stronger if the abstract were recalibrated to what the evidence supports, or if a two-time benchmark on a model system were added.\n\nWho should read it: anyone working on nonadiabatic dynamics at metal surfaces, electronic friction, or state-resolved scattering of molecules from metals. It deserves a serious referee. I would recommend sending it to review, with a request that the authors either validate the local ansatz against a two-time calculation on a model system or soften the abstract's quantitative claims.","headline":"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.","tokens_in":32901,"tokens_out":2554,"would_cite":true,"duration_ms":26216,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["71.38.-k","79.20.Rf"],"model":"deepseek-v4-flash","headline":"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).","keywords":["electronic friction","memory kernel","non-Markovian dynamics","electron-hole pair excitations","molecule-metal scattering","generalized Langevin equation","Kohn-Sham density functional theory","NO/Au(111)"],"falsifier":"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.","tokens_in":31933,"feed_emoji":"⚡","tokens_out":10873,"duration_ms":95337,"temperature":0.7,"pith_summary":"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.","feed_headline":"Electronic friction memory shifts energy loss into vibration","feed_subtitle":"Full friction kernels predict more stretch and less surface-normal loss than Markovian simulations","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Establishes the molecular dynamics with electronic friction generalized Langevin equation and the memory-kernel form used throughout.","marker":"[13]"},{"why":"Provides the NEGF/quasiclassical Langevin derivation whose zero-frequency limit the memory kernel must recover.","marker":"[17]"},{"why":"Supplies the quasi-adiabatic limit and retarded electron-hole self-energy expressions on which the local kernel construction is based.","marker":"[19]"},{"why":"Introduces the ab initio tensorial electronic friction formalism in DFT and the electron-phonon coupling evaluation used here.","marker":"[37]"},{"why":"Documents the implementation details and numerical evaluation of frequency-dependent friction tensors in an electronic structure code.","marker":"[38]"},{"why":"Supplies the previous Markovian MDEF baseline for NO/Au(111) showing underestimated vibrational loss, which this work revisits.","marker":"[44]"},{"why":"Provides the one-dimensional impurity model used to study memory effects on energy dissipation.","marker":"[45]"},{"why":"Provides the two-dimensional Newns–Anderson model of NO/Au(111) and the mixed quantum-classical benchmark context.","marker":"[29]"},{"why":"Gives the zero-frequency Markovian friction ansatz that the memory kernel reduces to in the static limit.","marker":"[50]"},{"why":"Supplies the full-dimensional potential energy surface used to generate the Born–Oppenheimer scattering trajectories.","marker":"[56]"}],"fun_headline_variants":["Memory in electronic friction redirects energy to vibration","Friction memory boosts vibrational over translational loss","Full friction kernels shift energy to vibration","Memory-dependent friction transfers loss to vibration","Electronic friction memory raises directional anisotropy"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Memory in electronic friction redirects energy to vibration","Friction memory boosts vibrational over translational loss","Full friction kernels shift energy to vibration","Memory-dependent friction transfers loss to vibration","Electronic friction memory raises directional anisotropy"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000519,"raw_usage":{"total_tokens":2523,"prompt_tokens":963,"completion_tokens":1560,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":579,"completion_tokens_details":{"reasoning_tokens":1497}},"tokens_in":579,"tokens_out":1560,"duration_ms":9100,"temperature":1.0,"reasoning_tokens":1497,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T00:05:12.098435+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":"Head-Gordon and J","cited_arxiv_id":null,"evidence_quote":"Establishes the molecular dynamics with electronic friction generalized Langevin equation and the memory-kernel form used throughout."},{"cited_title":"Brandbyge, P","cited_arxiv_id":null,"evidence_quote":"Provides the NEGF/quasiclassical Langevin derivation whose zero-frequency limit the memory kernel must recover."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the quasi-adiabatic limit and retarded electron-hole self-energy expressions on which the local kernel construction is based."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Introduces the ab initio tensorial electronic friction formalism in DFT and the electron-phonon coupling evaluation used here."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Documents the implementation details and numerical evaluation of frequency-dependent friction tensors in an electronic structure code."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the previous Markovian MDEF baseline for NO/Au(111) showing underestimated vibrational loss, which this work revisits."},{"cited_title":"Gardner, S","cited_arxiv_id":null,"evidence_quote":"Provides the two-dimensional Newns–Anderson model of NO/Au(111) and the mixed quantum-classical benchmark context."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Gives the zero-frequency Markovian friction ansatz that the memory kernel reduces to in the static limit."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the full-dimensional potential energy surface used to generate the Born–Oppenheimer scattering trajectories."}],"review_version":1}