{"id":"13153462-0782-4351-a2ac-abdfb9a3f76c","arxiv_id":"2508.18371","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"Rescaling the Eliashberg spectral function by the ratio of tetrahedra to Gaussian Fermi-level DOS yields converged Tc predictions on coarse grids, especially for systems with sharp DOS peaks.","lead":"The paper proposes a cheap post-processing correction that rescales the electron-phonon spectral function by the ratio of an accurate tetrahedra density of states to the Gaussian-smeared value, fixing a common source of Tc error on coarse grids. This could let high-throughput screening find high-Tc hydrides like Mg2IrH6 that standard coarse-grid methods would miss.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Scalar DOS rescaling assumes a multiplicative error that is not generally true; LaH10 shows the failure mode and no criterion identifies when it applies.","rationale":"The reader's weakest_assumption exactly identifies the load-bearing premise: the coarse-grid error in α2F is assumed to be dominated by a multiplicative error in the Fermi-level DOS. My concern is the same. The paper is honest about limitations, including the LaH10 counterexample and the constant-DOS overestimation risk, which strengthens its credibility. However, the abstract's unqualified claim of 'accurate Tc predictions' is broader than the evidence: only six systems are shown, and one contradicts the multiplicative-error assumption. The proposed concrete test—checking the constancy of λ(σ)/NF(σ) across smearing and grid—directly isolates the non-multiplicative error and would establish whether the method is reliable for high-throughput screening. Since the reader already assigned CONDITIONAL with high confidence and the limitation is acknowledged in the paper, no change to the verdict is needed; the conditionality is the correct assessment. The method's cost is negligible and it is reproducible from the description, so the bar for accepting it as a screening tool is mainly demonstrating that the factorization holds broadly, not fixing any internal inconsistency.","tokens_in":14502,"tokens_out":4960,"duration_ms":62007,"concrete_test":"For each of the six systems and a new benchmark set of 20–50 hydride/metallic candidates with sharp DOS features, compute the ratio R(σ,q) = λ(σ,q)/NF(σ,q) using the same Gaussian smearing σ and the same coarse electronic/phonon grids as the default α2F calculation. Under the factorization assumption of Eq. 5, R should be independent of σ and q and equal to the converged value λ_converged/fNF to within the target Tc accuracy (e.g., 10%). Plot R/R_converged versus σ for each system. Any residual σ- or q-dependence of R is precisely the non-multiplicative error that the rescaling cannot correct. If large deviations (>20%) appear for a substantial fraction of candidates, especially those with sharp peaks at the Fermi level, the generic high-throughput claim fails and a system-specific reliability check is necessary before the rescaling is applied.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim rests on Eq. 5 in Sec. III B: multiplying the coarse-grid α2F(ω,σ) by the scalar fNF/NF(σ) corrects the dominant error. This factorization is exact only in the constant-matrix-element, constant-phonon-frequency limit of Eq. 6, where α2F(ω,σ) ∝ NF(σ). In realistic systems, Gaussian smearing changes not only the total DOS normalization but also which k,k′ pairs are sampled, thereby reshaping the distribution of matrix elements and phonon frequencies in α2F. A scalar prefactor can correct the weight but cannot undo a smearing-induced deformation of the spectral function. The paper itself documents the failure mode in LaH10 (Sec. IV), where the default Gaussian method benefits from error cancellation and rescaling slightly worsens the result. Because only six systems are tested and no criterion is given for when the multiplicative assumption holds, a high-throughput user cannot know whether a given candidate is in the regime where rescaling helps, hurts, or strongly distorts Tc. The recommended practice of plotting both curves is a post-hoc diagnostic, not a screening rule. This is the load-bearing soft spot: the method's generality is asserted from a small sample, and the one documented counterexample shows the assumption can fail.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a post-processing rescaling of the Eliashberg spectral function alpha^2 F(omega) computed on coarse Brillouin-zone grids. The rescaling factor is f_NF / N_F(sigma), where f_NF is a high-quality tetrahedra density of states at the Fermi energy and N_F(sigma) is the Gaussian-smearing value used in the Tc calculation. The idea, building on Refs. [50,51], is that the dominant coarse-grid error in alpha^2 F and lambda is a multiplicative error in the Fermi-level DOS, so a scalar prefactor corrects it. The method is tested on Al, Nb, H3S, CaH6, LaH10, and Mg2IrH6. For sharp-DOS systems such as H3S and especially Mg2IrH6, the rescaling reduces the smearing dependence and yields converged Tc values on coarse grids, including ~160 K for Mg2IrH6 on a 2^3 phonon grid. LaH10 is identified as a counterexample where the default Gaussian method benefits from error cancellation and rescaling slightly worsens the result. The authors recommend plotting both default and rescaled curves and discuss limitations of the constant-DOS Eliashberg approximation.","tokens_in":14789,"tokens_out":5128,"duration_ms":61969,"significance":"If the central claim is accepted, the method is a cheap, parameter-free post-processing correction (the only free parameter being the usual mu*) that could be integrated into high-throughput superconducting screening, particularly for systems with sharp DOS features, which are often the most promising high-Tc candidates. The paper is honest about limitations and documents a failure mode, which is a strength. The method is physically motivated and simple to implement, and the benchmark set includes literature-converged systems such as H3S and LaH10. However, the validation is limited to six systems, the strongest success is benchmarked against a prior calculation from the same group, and no quantitative criterion is provided for when the multiplicative rescaling assumption holds. This makes the generality of the abstract claim undersupported. The contribution is incremental relative to Refs. [50,51] but the explicit focus on high-throughput screening and the Mg2IrH6 demonstration give it practical value.","major_comments":[{"comment":"The rescaling is exact only when alpha^2 F(omega,sigma) is proportional to N_F(sigma) with a sigma-independent prefactor, i.e., in the constant-matrix-element, constant-phonon-frequency limit. The paper itself shows this fails for LaH10 (Fig. 3(e), Fig. 6), where rescaling slightly worsens a well-converged default result. The stated condition of 'weak momentum and energy dependence' of |g_nmnu(k,k')|^2 is descriptive, not a screening rule. Because the stated application is high-throughput screening, in which each candidate cannot be individually inspected, the central claim that the rescaled spectral function 'yields accurate Tc predictions' needs either a quantitative diagnostic (e.g., comparing the sigma-dependence of lambda before and after rescaling, or a measure of matrix-element variation) or a clear statement that the rescaling is a heuristic to be used alongside the default curve","section":"Sec. III B, Eq. (5), Sec. IV"},{"comment":"The validation set is only six systems, and the flagship success, Mg2IrH6, is benchmarked against Ref. [27], a prior calculation from the same group. The claim that 'even 2^3 grids reproduce the converged value of 160 K' is demonstrated for a single compound. For a method proposed for high-throughput use, the reader needs at least an indication of false-positive/false-negative behavior over a range of DOS shapes and matrix-element characters. I am not requesting an exhaustive benchmark, but without a broader set or a worst-case bound, the domain of applicability remains underspecified.","section":"Sec. III D/E, Figs. 3-6"}],"minor_comments":[{"comment":"The Gaussian broadening expression is missing a minus sign in the exponent: it should be exp(-epsilon^2/sigma^2).","section":"Eq. (4)"},{"comment":"Typo: 'ESPRC' should be 'EPSRC'.","section":"Acknowledgments"},{"comment":"'an 83 phonon grid' should read 'an 8^3 phonon grid'; similar notation is used inconsistently for other grids.","section":"Sec. III E, Figs. 4-6"},{"comment":"The caption states 'the density of states of the primitive cell' while the text refers to the conventional cell visualized with VESTA; clarify which cell is used for the DOS plot.","section":"Fig. 3 caption"},{"comment":"The sentence 'use this to replace the value obtained by the Gaussian smearing' is imprecise: the rescaling multiplies alpha^2 F by a ratio rather than directly replacing N_F in the calculation. This could be clarified to avoid confusion about the implementation.","section":"Sec. III B"}],"recommendation":"major_revision","confidential_remarks":"The paper is a reasonable incremental methodological contribution that builds directly on Koretsune-Arita and Morice et al. The main reservation is the scope of validation relative to the breadth of the claim. The LaH10 counterexample is acknowledged but not quantified, and no automated decision rule is provided for high-throughput use. If the authors add a practical diagnostic, a small additional benchmark, or temper the abstract's generality claim, the paper could become acceptable. The self-benchmark against the same group's previous Mg2IrH6 calculation should be presented with that context made explicit."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The useful thing here is practical: take the known DOS-rescaling idea from Morice et al. and show it can rescue coarse-grid Tc estimates for systems with sharp Fermi-level DOS features. The core formula is not new, and the authors say so. What is new is the systematic demonstration: six test systems, grid-convergence comparisons, and the striking Mg2IrH6 case where a 2^3 phonon grid plus rescaling gives about 160 K, matching the converged value and representing a large speedup. That is a real result for high-throughput screening.\n\nThe paper does good work in the body. The derivation in Sec. II is clean, and the authors are honest about limitations. They explicitly flag LaH10, where the rescaling slightly worsens an already-converged Tc, and they discuss the constant-DOS overestimation risk for sharp peaks. That level of candor is welcome.\n\nThe soft spot is exactly what the stress-test says: the scalar prefactor corrects a multiplicative DOS error, which is exact only in the constant-matrix-element limit. The paper acknowledges this but gives no criterion for when the assumption holds. Six systems is a small sample, and one of the six is a counterexample. The abstract's claim of \"accurate Tc predictions\" is too strong; the body is more careful. The advice to plot both rescaled and default curves is a sensible diagnostic, but it is not a screening rule. And the Mg2IrH6 benchmark comes from the authors' own prior converged calculation, which is fine but not independent.\n\nNone of this sinks the central claim. For the sharp-DOS systems the method targets, the evidence supports it, and the cost is essentially zero. The paper deserves a serious referee, but the referee should press for a broader benchmark or a clearer statement of applicability. If I worked on high-throughput superconductor screening, I would cite this and probably use the rescaling as a cheap first-pass filter while keeping the default curve for comparison.\n\nRecommendation: send to peer review. It is a modest but solid contribution, and the authors have already done part of the referee's job by stating their own caveats.","headline":"A cheap, physically motivated DOS rescaling that clearly helps sharp-DOS superconductors like Mg2IrH6 and H3S, honestly caveated by the authors, but with no criterion for when it fails.","tokens_in":15331,"tokens_out":1297,"would_cite":true,"duration_ms":18315,"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":"Rescaling the Fermi density of states makes coarse-grid Tc predictions accurate.","keywords":["superconductivity","electron-phonon coupling","density of states","transition temperature","Eliashberg theory","high-throughput screening","coarse grids","hydrides"],"falsifier":"Take a superconductor with a sharp DOS peak at the Fermi energy, compute Tc with the rescaled coarse-grid method, and compare against a fully converged calculation that resolves the DOS shape, for example variable-DOS Eliashberg on fine grids. If the rescaled Tc overshoots by much more than the standard method's underestimate, the multiplicative-DOS assumption is the culprit. Alternatively, compute λ on coarse and fine grids and check whether the ratio λ_coarse / λ_fine tracks N_F(σ) / f_NF.","tokens_in":14395,"feed_emoji":"⚡","tokens_out":5305,"duration_ms":59706,"temperature":0.7,"pith_summary":"The paper argues that the biggest obstacle to cheap, high-throughput predictions of superconducting transition temperatures is not the electron-phonon coupling calculation itself but how the coarse Brillouin-zone grid misestimates the electronic density of states at the Fermi energy. It proposes a post-processing correction: take the electron-phonon spectral function α²F(ω) computed with standard Gaussian smearing on a coarse grid and multiply it by the ratio of an accurate tetrahedra DOS at the Fermi level to the Gaussian-smeared DOS. On systems with sharp density-of-states peaks near the Fermi energy—precisely the systems most likely to be high-Tc—this restores Tc values that otherwise require very dense grids. The paper shows Mg2IrH6, whose Fermi energy sits on a sharp peak, recovering its converged ~160 K Tc even on a 2³ phonon grid, whereas the standard method underestimates it badly. If correct, this gives screening pipelines a nearly free way to avoid discarding promising high-Tc candidates early.","feed_headline":"A DOS rescaling rescues coarse-grid Tc predictions","feed_subtitle":"Cheap screening calculations recover high-Tc candidates like Mg2IrH6 that standard Gaussian smearing would discard.","key_machinery":"The key object is the density-of-states rescaling factor g = f_NF / N_F(σ), applied at the level of the surface-averaged electron-phonon spectral function α²F(ω) and hence to λ. The factor is motivated by the fact that α²F and λ are linearly proportional to the Fermi-level DOS NF; replacing the unreliable Gaussian-smeared value with a tetrahedra value removes the dominant smearing dependence. It does work at almost no additional cost because a converged DOS is typically already computed in screening workflows, and it acts as a post-processing correction rather than requiring new electron-phonon calculations.","core_discovery":"The central claim is that the coarse-grid error in the Eliashberg spectral function is dominated by a multiplicative error in the Fermi-level density of states, so rescaling α²F(ω) by f_NF / N_F(σ) corrects most of the error without refining the grid. Here f_NF is a high-quality DOS from the tetrahedra method and N_F(σ) is the DOS from the Gaussian smearing used in the Tc calculation. In the idealized constant-matrix-element limit this correction is exact, because the coupling λ is then simply proportional to NF. Across six test systems, the rescaling flattens Tc as a function of smearing and accelerates convergence with grid size; the effect is largest when the Fermi energy sits on a sharp","pith_inferences":["Beyond the paper: the same rescaling idea could be applied to other Fermi-surface-weighted quantities, such as transport coefficients or magnetic response, wherever coarse-grid Gaussian weighting is used.","Beyond the paper: a screening heuristic could flag candidates where f_NF / N_F(σ) deviates strongly from unity, since those are the systems whose Tc ranking is most likely wrong under standard methods.","Beyond the paper: the failure mode suggests a practical trust criterion—use rescaling when electron-phonon matrix elements vary smoothly near the Fermi surface, and validate with a small set of fine-grid calculations.","Beyond the paper: the scalar rescaling factor could be generalized to a frequency-dependent or k-dependent correction that also accounts for matrix-element variation, though the paper does not do this."],"forward_implications":["Coarse-grid Tc estimates become reliable enough for early-stage screening, so candidates with sharp DOS peaks survive the first pass.","The method removes the need for very fine electronic k grids, and because k and q grids are often linked, coarser phonon q grids can be used too.","Comparing standard and rescaled curves gives a diagnostic: if rescaling changes Tc strongly, DOS convergence is the bottleneck; if not, matrix-element convergence dominates.","Systems with Fermi energy on a DOS peak may be overestimated by constant-DOS Eliashberg even after rescaling, pushing the workflow toward variable-DOS Eliashberg for final validation.","The correction is general and can be inserted into existing screening pipelines as a post-processing step with negligible cost."],"supporting_citations":[{"why":"Supplies the central correction-factor idea: multiplying the electron-phonon spectral function by a DOS ratio was previously used for BiS2.","marker":"[51]"},{"why":"Establishes that for many superconductors the convergence bottleneck is the Fermi-level DOS, motivating the rescaling approach.","marker":"[50]"},{"why":"Provides the Mg2IrH6 candidate and its converged ~160 K Tc, the benchmark the rescaling reproduces on coarse grids.","marker":"[27]"},{"why":"Formulates the isotropic Eliashberg spectral function and constant-DOS Tc equations that the method corrects.","marker":"[52]"},{"why":"Provides the Gaussian smearing expression and computational implementation used throughout the calculations.","marker":"[55]"},{"why":"Supplies the LaH10 high-Tc reference against which the counterexample case is compared.","marker":"[18]"},{"why":"Supplies the variable-DOS Eliashberg solver used to check overestimation in sharp-peak systems.","marker":"[65]"},{"why":"Shows how van Hove singularities affect Tc in H3S, supporting the discussion of sharp DOS peaks overestimating Tc under constant-DOS equations.","marker":"[71]"}],"fun_headline_variants":["DOS rescaling sharpens coarse-grid Tc accuracy","Correcting Fermi DOS boosts fast Tc predictions","Coarse-grid Tc saved by density-of-states rescale","Rescaled DOS makes high-Tc screening reliable","Tetrahedron DOS rescaling fixes Tc screening"],"cache_read_input_tokens":2688,"weakest_assumption_plain":"The coarse-grid error in the electron-phonon spectral function is mostly a multiplicative error in the Fermi-level density of states, so a single scalar rescaling can fix it; this is exact only when the electron-phonon matrix elements are effectively constant near the Fermi surface.","fun_headline_variants_meta":{"raw":{"variants":["DOS rescaling sharpens coarse-grid Tc accuracy","Correcting Fermi DOS boosts fast Tc predictions","Coarse-grid Tc saved by density-of-states rescale","Rescaled DOS makes high-Tc screening reliable","Tetrahedron DOS rescaling fixes Tc screening"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000157,"raw_usage":{"total_tokens":1030,"prompt_tokens":687,"completion_tokens":343,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":431,"completion_tokens_details":{"reasoning_tokens":270}},"tokens_in":431,"tokens_out":343,"duration_ms":4131,"temperature":1.0,"reasoning_tokens":270,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-05T16:27:02.194518+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take a superconductor with a sharp DOS peak at the Fermi energy, compute Tc with the rescaled coarse-grid method, and compare against a fully converged calculation that resolves the DOS shape, for example variable-DOS Eliashberg on fine grids. If the rescaled Tc overshoots by much more than the standard method's underestimate, the multiplicative-DOS assumption is the culprit. Alternatively, compute λ on coarse and fine grids and check whether the ratio λ_coarse / λ_fine tracks N_F(σ) / f_NF.","supporting_citations":[{"cited_title":"Morice, R","cited_arxiv_id":null,"evidence_quote":"Supplies the central correction-factor idea: multiplying the electron-phonon spectral function by a DOS ratio was previously used for BiS2."},{"cited_title":"Koretsune and R","cited_arxiv_id":null,"evidence_quote":"Establishes that for many superconductors the convergence bottleneck is the Fermi-level DOS, motivating the rescaling approach."},{"cited_title":"Dolui, L","cited_arxiv_id":null,"evidence_quote":"Provides the Mg2IrH6 candidate and its converged ~160 K Tc, the benchmark the rescaling reproduces on coarse grids."},{"cited_title":"Pellegrini and A","cited_arxiv_id":null,"evidence_quote":"Formulates the isotropic Eliashberg spectral function and constant-DOS Tc equations that the method corrects."},{"cited_title":"Giannozzi, S","cited_arxiv_id":null,"evidence_quote":"Provides the Gaussian smearing expression and computational implementation used throughout the calculations."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the LaH10 high-Tc reference against which the counterexample case is compared."},{"cited_title":"Kogler, D","cited_arxiv_id":null,"evidence_quote":"Supplies the variable-DOS Eliashberg solver used to check overestimation in sharp-peak systems."}],"review_version":1}