{"id":"8a8d5afb-d453-49ed-85fb-4279af3985d8","arxiv_id":"2412.05062","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"Including wave-like phonon tunneling via the Wigner transport equation quantitatively reproduces measured thermal conductivities of naphthalene and pentacene and explains their weak temperature dependence.","lead":"This paper computes the thermal conductivity of acene crystals (naphthalene to pentacene) using machine-learned potentials and the Wigner transport equation, showing that phonon tunneling between overlapping vibrational bands is essential to match experiments. A generalist should read it because it explains why heat transport in organic semiconductors behaves so differently from conventional crystals, and why it is nearly constant with temperature in pentacene.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The final WTE conductivities rely on one stochastic MTP per acene; for pentacene the retained potential has force RMSD 7.69 meV/Å, above the 5 meV/Å threshold, and third-order IFCs are not directly benchmarked, so an MTP-to-MTP WTE sensitivity test is needed.","rationale":"The reader's CONDITIONAL verdict is well calibrated. My stress-test pass converges on the same load-bearing point but sharpens it: the quantitative claim for the two materials compared with experiment, especially pentacene, rests on a single stochastic MTP whose force RMSD (7.69 meV/Å) exceeds the 5 meV/Å threshold used by Póta et al., and the third-order IFCs derived from it are never checked against DFT. The manuscript does provide real independent support: convergence in q-mesh and supercell size (Supp. Section 2.4), the small BTE/LBTE difference for naphthalene, the two experimental comparisons that bracket the polycrystalline average, and the ±25% linewidth rescaling in Supp. Fig. 24. Those checks make the central conclusion plausible, but they do not bound MTP-instance error. The missing experiment is to run the same WTE pipeline with the other MTPs already trained and reported in Table 1. This is inexpensive relative to DFT and would settle whether the quantitative agreement is robust. I therefore recommend no change to the reader's verdict: conditional until the MTP-spread test is performed. Agreement is partial because the reader flagged anthracene and tetracene RMSDs; in my view the more decisive number is pentacene's 7.69 meV/Å, since pentacene is one of the two experimental systems anchoring the central claim.","tokens_in":38125,"tokens_out":6730,"duration_ms":75442,"concrete_test":"Compute third-order force constants and solve the WTE for naphthalene and pentacene using the second and third independently trained MTPs in Table 1 (same q-mesh, supercells, and 0.03 Å displacement), reporting kappa_tot, kappa_P, and kappa_C at 300 K and over the temperature range of Fig. 3. If the MTP-to-MTP spread is larger than ~10% of kappa_tot or materially degrades the pentacene match to Epstein et al., the retained-MTP choice is load-bearing; if the spread is small and tunneling remains required to match experiment, the concern is resolved. As a secondary check, compute Gamma linewidths from each MTP and compare to the Raman data in Supplementary Fig. 18 to see whether systematic underestimation persists across MTPs.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central quantitative claim is that WTE with phonon tunneling matches the measured naphthalene and pentacene conductivities while BTE underestimates them. This claim is load-bearing on the anharmonic linewidths entering both kappa_P and kappa_C, and those linewidths are determined by MTP third-order IFCs that are not benchmarked against DFT. Table 1 reports force RMSDs of 4.93 meV/Å (naphthalene) and 7.69 meV/Å (pentacene) for the retained MTPs, i.e., pentacene exceeds the 5 meV/Å level that Póta et al. associate with ~2% conductivity accuracy; anthracene (9.23) and tetracene (8.83) are higher. The Raman linewidth comparison in Supplementary Fig. 18 shows systematically narrower simulated than measured linewidths, consistent with overestimated lifetimes. Supp. Fig. 24 rescaling linewidths by ±25% does not fully address this, because it is a global scaling rather than the mode- and MTP-specific error pattern. Since only one of three trained MTPs per acene is used for the final WTE, the sensitivity of kappa_tot, kappa_P, and kappa_C to the stochastic MTP choice is unquantified; if kappa_C changes substantially between MTPs, the quantitative match and the inferred coexistence of propagation and tunneling would not yet be established.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper computes the lattice thermal conductivities of naphthalene, anthracene, tetracene, and pentacene using the Wigner transport equation, with harmonic and third-order force constants obtained from system-specific Moment Tensor Potentials trained on dispersion-corrected DFT data. The central claim is that the Peierls-Boltzmann picture, retaining only particle-like phonon propagation, systematically underestimates measured conductivities, whereas the full WTE including wave-like phonon tunneling quantitatively reproduces experiments for naphthalene and pentacene over the measured temperature ranges. The authors further analyze mode-resolved and directional contributions, finding that acoustic modes conduct mainly by propagation, dense optical bands contribute significantly by tunneling, and the tunneling conductivity along the molecular backbone increases with molecular length, leading to predicted nonmonotonic temperature dependence in tetracene and pentacene.","tokens_in":38325,"tokens_out":4437,"duration_ms":44827,"significance":"If the quantitative agreement holds, the paper is significant: it extends the Wigner transport formulation to crystalline organic semiconductors, gives a reciprocal-space decomposition of heat transport into propagation and tunneling channels for the acene family, and provides falsifiable predictions such as the [001] conductivity minimum in pentacene and the crossover to tunneling-dominated transport along the molecular axis. The manuscript has notable strengths: systematic convergence tests for q-meshes, supercells, and displacement amplitudes; validation of the relaxation-time approximation against a direct LBTE solution for naphthalene; inclusion of measured grain-size boundary scattering for pentacene; and a clear data-availability statement. The principal caveats concern the lack of direct benchmarking of MTP third-order force constants against DFT and the use of a single stochastic MTP per acene for all final WTE numbers.","major_comments":[{"comment":"The WTE conductivities used for the central comparison are computed with a single retained MTP per acene, and the anharmonic linewidths entering both κP and κC are never benchmarked directly against DFT third-order force constants. The retained pentacene MTP has a force RMSD of 7.69 meV/Å (Table 1), above the 5 meV/Å threshold that the authors themselves cite from Póta et al. as sufficient for about 2% thermal-conductivity accuracy. Because the MTP training is stochastic and only the best of three potentials is retained, I ask the authors to report κtot, κP, and κC for all three independently trained MTPs, or at least for the non-retained naphthalene and pentacene MTPs, and to quantify how much of the experimental agreement is a consequence of the particular potential draw.","section":"Validating the parametrized MTPs (Table 1; Supplementary Section 2.2.1)"},{"comment":"The comparison with measured Raman linewidths shows systematically narrower simulated linewidths for anthracene and pentacene, which is consistent with overestimated phonon lifetimes. The ±25% global rescaling in Supplementary Fig. 24 does not bound the resulting error in the central comparison, because it multiplies all linewidths by a single factor and cannot capture mode-specific or MTP-specific inaccuracies; indeed, the Raman comparison shows that some modes are reproduced and others are not. Please provide a mode-resolved sensitivity estimate, or justify why the systematic underestimate of linewidths cannot change the conclusion that tunneling is required to rationalize the experiments.","section":"Supplementary Section 3 and Supplementary Fig. 18"},{"comment":"The anthracene [010] propagation and total conductivities are omitted because the tetrahedron and Gaussian-smearing Brillouin-zone integrations do not converge with respect to the broadening parameter. Since the claim that the in-plane [100]/[010] conductivities are essentially material-independent is one of the main structure-property conclusions, the missing [010] data for anthracene leaves that claim incomplete. Please either provide a converged [010] result using an independent method, such as the adaptive smearing already used in the ShengBTE comparison or the collisional-broadening treatment cited in the text, or explicitly restrict the material-independence claim to the directions that are actually converged.","section":"Fig. 6b and Supplementary Section 2.6"}],"minor_comments":[{"comment":"There are several typos: 'napthalene' should be 'naphthalene', 'comparion' should be 'comparison', and 'provided in in Fig. 3' contains a duplicated 'in'.","section":"Results, 'Heat transport in polycrystalline acenes'"},{"comment":"The quantities V and N_c in Eq. (1) are used without definition; please define them explicitly in the text or in the equation caption.","section":"Eq. (1)"},{"comment":"The caption states that κtot and κP of anthracene are omitted in panel b, while the main text specifically refers to κP[010] and κtot[010]; please harmonize the wording and make the omission visible in the legend itself.","section":"Fig. 6 caption and main text"},{"comment":"The spelling of the naphthalene experimental reference is inconsistent: 'Ueberreiter' in the main text and 'Überreiter' in the Supplementary Information; please standardize the spelling.","section":"References and Supplementary text"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is within the scope of the journal and shows no circularity: the WTE calculation is a first-principles prediction, with the only externally set parameter being the pentacene grain size taken from the experiment. The main risk is the MTP uniqueness and the absence of a direct benchmark of third-order force constants; an MTP-to-MTP WTE sensitivity test is inexpensive and would substantially strengthen the claim. The anthracene [010] omission should be handled in the revision, either by supplying a converged value or by restricting the in-plane material-independence statement. I see no citation or novelty-disclosure issue."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The core result is the first application of the Wigner transport equation to organic semiconductor crystals, and it does what the abstract promises: for naphthalene and pentacene, the total WTE conductivity lands on the experimental values, while the Peierls-Boltzmann result sits clearly below. The temperature independence in pentacene is explained by a growing tunneling contribution that offsets the drop in propagation, and that mechanism is made concrete with mode-resolved cumulative plots and linewidth analysis. The convergence work is genuinely careful: q-mesh tests per material, supercell tests, displacement-amplitude checks, RTA validated against LBTE for naphthalene, and boundary scattering included using the measured pentacene grain size. They also openly flag the anthracene [010] non-convergence and omit that curve, which is the right call even if it weakens the series-wide claim.\n\nThe soft spots are real but not fatal. The third-order force constants are never directly benchmarked against DFT; the validation is force RMSDs on a separate active-learning set. The retained pentacene MTP sits at 7.69 meV/Å, above the 5 meV/Å threshold Póta et al. associate with ~2% conductivity accuracy, and anthracene/tetracene are worse. Since only one of three stochastic MTPs per acene is used, we don't know how much kappa_C moves between MTPs. The Raman linewidth comparison in Supp. Fig. 18 is also systematically narrower in theory than experiment, which is consistent with overestimated lifetimes and hence an inflated kappa_P. The ±25% linewidth rescaling in Supp. Fig. 24 addresses global sensitivity, not mode- or MTP-specific errors. These concerns cut the strength of the quantitative match for pentacene somewhat, but the naphthalene comparison is robust, and even a 10-20% error in kappa_total would not erase the qualitative conclusion that tunneling matters.\n\nI disagree with the stress-test note if it implies the central claim is unestablished; the mechanism is supported by the two materials with data, and the experimental agreement is good enough to take seriously. The paper deserves a serious referee. The referee should ask for an MTP-to-MTP sensitivity test (at least for kappa_C in pentacene), a direct DFT-vs-MTP third-order IFC comparison on a reduced set of q-points or a few phonon modes, and an explicit statement about how the Raman linewidth underestimate would affect the propagation/tunneling split.\n\nWho benefits: anyone working on thermal transport in molecular crystals or on machine-learned potentials for anharmonic lattice dynamics. I'd cite the naphthalene/pentacene WTE result, and I'd send this to review rather than desk-reject.","headline":"First WTE treatment of organic semiconductors that plausibly resolves the BTE underestimate for naphthalene and pentacene, though the full acene-series claims are shakier than the paper's tone suggests.","tokens_in":38952,"tokens_out":1509,"would_cite":true,"duration_ms":17650,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Phonon tunneling carries heat in organic crystals.","keywords":["thermal conductivity","phonon tunneling","Wigner transport equation","organic semiconductors","acenes","machine-learned interatomic potentials","anharmonic lattice dynamics","population and coherence contributions"],"falsifier":"Measure the thermal conductivity of a pentacene single crystal along the molecular long axis between 100 K and 500 K. The paper predicts a minimum near 300 K followed by a rise at higher temperatures, while a particle-only theory predicts monotonic decrease; a monotonic decrease would falsify the large tunneling contribution. A complementary test is to recompute the third-order force constants of anthracene with a more accurate method and check whether the resulting linewidths match measured Raman linewidths; if they broaden substantially, the reported conductivities would change.","tokens_in":37820,"feed_emoji":"🔥","tokens_out":7675,"duration_ms":68916,"temperature":0.7,"pith_summary":"The paper argues that the ultra-low thermal conductivity of crystalline acenes cannot be captured by the standard picture of heat carried by particle-like phonons. It shows that adding a second, wave-like channel, phonon tunneling between overlapping vibration bands as formulated in the Wigner transport equation, makes computed conductivities match measured values for naphthalene and pentacene. This matters because the tunneling contribution grows with temperature and with molecular length, explaining the weak temperature dependence of naphthalene, the almost temperature-independent conductivity of pentacene, and a predicted minimum in pentacene's conductivity along the molecular axis near 300 K.","feed_headline":"Phonon tunneling carries heat in organic crystals","feed_subtitle":"Adding tunneling to phonon propagation matches measured conductivity of naphthalene and pentacene.","key_machinery":"The machinery is the Wigner transport equation (WTE), which splits the lattice thermal conductivity into the population (propagation) contribution, identical to the Boltzmann term, and the coherence (tunneling) contribution, driven by inter-mode coupling between phonon bands whose linewidths overlap. The coherence term is expressed through mode frequencies, heat capacities, generalized velocity operators, and Lorentzian functions of frequency differences and linewidths. To supply the required second- and third-order force constants for crystals with up to 216 modes per cell, the authors train system-specific Moment Tensor Potentials on dispersion-corrected DFT data and evaluate the WTE with these potentials, using the tetrahedron method for Brillouin-zone integration and the relaxation-time approximation after validating it against the linearized Boltzmann solution.","core_discovery":"The central claim is that in all four acenes studied, heat is carried by two coexisting mechanisms: particle-like phonon propagation and wave-like phonon tunneling. The Peierls-Boltzmann equation describes only the first and systematically underestimates the measured thermal conductivity; the Wigner transport equation, whose coherence term couples modes whose broadened bands overlap, accounts for both. With the propagation and tunneling channels combined, the calculated isotropic conductivities of naphthalene and pentacene agree quantitatively with experiment across wide temperature ranges, and the tunneling channel is responsible for the observed weak or vanishing temperature dependence, the growth of conductivity with molecular length along the backbone direction, and the appearance of a conductivity minimum near 300 K for pentacene.","pith_inferences":["The compensation mechanism is likely generic to molecular crystals with many closely spaced optical bands; one testable extension is to apply the same WTE workflow to rubrene or functionalized acenes and look for the same flattening of conductivity with temperature.","Because the simulated Raman linewidths are systematically narrower than measured ones, the third-order force constants likely overestimate phonon lifetimes; if so, the absolute tunneling values may shift with temperature, although the paper's linewidth-rescaling test suggests the qualitative trends would survive.","A direct experimental test would be direction-resolved thermal conductivity of a pentacene single crystal: the predicted minimum near 300 K along the molecular backbone direction and the subsequent increase are specific, falsifiable signatures of the tunneling channel.","If correct, this picture implies that thermal management in organic devices can be engineered by choosing molecular length to control optical-band overlap, rather than only by reducing disorder or grain-boundary scattering."],"forward_implications":["Predictions for naphthalene and pentacene match measured conductivities only when the tunneling channel is included, so organic-semiconductor heat transport calculations that use the Boltzmann equation alone will systematically underestimate thermal conductivity.","The same compensation mechanism explains why naphthalene's conductivity falls only weakly with temperature and pentacene's is nearly temperature-invariant near 300 K.","Along the molecular backbone direction, the tunneling channel grows with molecular length, so tetracene and pentacene should show a minimum and then a rise in conductivity with temperature above roughly 350 K and 300 K, respectively.","The predicted thermal-conductivity anisotropy is opposite to the electrical-conductivity anisotropy: heat prefers the molecular backbone direction, while charge transport prefers the herringbone plane.","The machine-learned potential workflow makes anharmonic lattice dynamics feasible for molecular crystals with large unit cells, extending first-principles-quality heat transport calculations well beyond the acenes."],"supporting_citations":[{"why":"Defines the Peierls-Boltzmann phonon transport equation that the paper shows is insufficient for acenes.","marker":"[17]"},{"why":"Supplies the Wigner transport equation and the population/coherence decomposition used for all thermal conductivity calculations.","marker":"[27]"},{"why":"Gives the unified theory of thermal transport in crystals and glasses that motivates the wave-like tunneling term.","marker":"[28]"},{"why":"Provides the DFT phonon band structures and low-frequency mode analysis used to validate the machine-learned potentials.","marker":"[18]"},{"why":"Establishes the machine-learned force-field workflow adapted here for parametrizing moment tensor potentials.","marker":"[47]"},{"why":"Introduces moment tensor potentials, the surrogate model used to compute force constants.","marker":"[48]"},{"why":"Provides the phono3py implementation used to compute third-order force constants and solve the WTE.","marker":"[57]"},{"why":"Defines the force-error threshold against which the accuracy of the trained potentials is assessed.","marker":"[60]"},{"why":"Reports the experimental naphthalene thermal conductivities that the WTE results are compared to.","marker":"[67]"},{"why":"Reports the experimental pentacene thin-film thermal conductivities and grain size used in the comparison.","marker":"[68]"}],"fun_headline_variants":["Phonon tunneling and propagation carry heat in acenes","Tunneling heat flow explains acene conductivity and dip","Two heat channels unite via Wigner equation for organics","Molecular-length tunneling shapes organic heat conduction","Coherent phonon tunneling drives organic crystal thermal response"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The argument depends on the machine-learned potentials reproducing the true third-order force constants closely enough that the calculated phonon linewidths, and therefore the size of the tunneling term, are trustworthy; for anthracene and tetracene the force errors lie above a threshold previously associated with 2% conductivity accuracy, and the computed Raman linewidths are systematically narrower than measured ones.","fun_headline_variants_meta":{"raw":{"variants":["Phonon tunneling and propagation carry heat in acenes","Tunneling heat flow explains acene conductivity and dip","Two heat channels unite via Wigner equation for organics","Molecular-length tunneling shapes organic heat conduction","Coherent phonon tunneling drives organic crystal thermal response"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000236,"raw_usage":{"total_tokens":1463,"prompt_tokens":867,"completion_tokens":596,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":483,"completion_tokens_details":{"reasoning_tokens":534}},"tokens_in":483,"tokens_out":596,"duration_ms":7693,"temperature":1.0,"reasoning_tokens":534,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T20:55:43.405270+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the thermal conductivity of a pentacene single crystal along the molecular long axis between 100 K and 500 K. The paper predicts a minimum near 300 K followed by a rise at higher temperatures, while a particle-only theory predicts monotonic decrease; a monotonic decrease would falsify the large tunneling contribution. A complementary test is to recompute the third-order force constants of anthracene with a more accurate method and check whether the resulting linewidths match measured Raman linewidths; if they broaden substantially, the reported conductivities would change.","supporting_citations":[{"cited_title":"& Orthmann, H.-J","cited_arxiv_id":null,"evidence_quote":"Reports the experimental naphthalene thermal conductivities that the WTE results are compared to."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Reports the experimental pentacene thin-film thermal conductivities and grain size used in the comparison."}],"review_version":1}