{"id":"2d5ecee9-d338-458a-a571-7cf61112f260","arxiv_id":"1908.01820","paper_version":2,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":3.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"A review of semilocal exchange-correlation potentials concludes that mBJLDA is the most accurate fast method for band gaps, with known weaknesses for bandwidths and electron densities.","lead":"This paper reviews fast approximate methods for calculating electronic band gaps in solids and concludes that the modified Becke-Johnson potential is the most accurate among the cheap methods. It is written for researchers choosing a method for materials calculations, and it also highlights where the method fails.","discovery_kind":"review","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The 76-solid benchmark may be partly in-sample for mBJLDA's fitted parameters; the independent 472-solid set shows parity with HSE06, so 'most accurate' should be softened to 'competitive' unless the overlap is quantified.","rationale":"The reader's weakest assumption identifies a real formal issue: exact Kohn-Sham eigenvalue gaps are not equal to fundamental gaps because of the derivative discontinuity, and the paper itself concedes this in Sec. II D and again in Sec. V. However, this objection does not by itself overturn the central claim, because the claim is empirical and pragmatic: mBJLDA is presented as a fast estimator of band gaps, not as the exact Kohn-Sham potential. The paper is unusually candid about the formal caveat and about the consequences for other properties. The more actionable concern is that the benchmark supporting the headline ranking is contaminated by fitting: alpha and beta in Eq. (16) were optimized against band gaps, and the 76-solid benchmark used in Table I appears to include many of the same solids. That makes the comparison against unfitted HSE06 and GLLB-SC unfair. The independent 472-solid set is the right corrective, and on that set mBJLDA is statistically tied with HSE06 rather than clearly superior, with AK13 and HLE16 nearby. This means the strongest phrasing in Sec. IV ('on average the most accurate') is not firmly established, while the weaker phrasing ('at least as accurate as HSE06') is. A conditional verdict is therefore appropriate: accept the practical recommendation with the caveat that the ranking be re-evaluated on a strictly out-of-sample basis.","tokens_in":34301,"tokens_out":8019,"duration_ms":91944,"concrete_test":"Compile the list of solids used to fit alpha and beta in Ref. 20 (identifiable from Fig. 4 and the original paper), remove every overlapping solid from the 76-solid test set, and recompute Table I MAE/MARE for mBJLDA, GLLB-SC, and HSE06. If mBJLDA's MAE on the complement rises above HSE06's, the reported superiority on the 76-solid set is an in-sample artifact. As a secondary check, repeat the exclusion on the 472-solid set; if mBJLDA remains best or tied on that independent set, the practical claim survives.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim relies on benchmark rankings of mBJLDA against unfitted methods such as HSE06 and GLLB-SC. The formal objection that a multiplicative Kohn-Sham potential's eigenvalue gap should not be compared directly with the experimental fundamental gap is explicitly acknowledged in Sec. II D and Sec. V, so it is an honest limitation rather than a hidden flaw. The more concrete, load-bearing weakness is the fitting status of mBJLDA: the parameters alpha and beta in Eq. (16) were determined in Ref. 20 by minimizing the band-gap error for a group of solids, and Fig. 4 shows that the 76-solid benchmark overlaps substantially with that original fitting set. Table I then compares an in-sample fitted potential (mBJLDA, MAE 0.47 eV) with methods that were not fitted to band gaps (HSE06, MAE 0.82 eV; GLLB-SC, MAE 0.64 eV). This inflates the apparent superiority of mBJLDA. The larger, more independent 472-solid set in Table II paints a different picture: mBJLDA and HSE06 both have MAE = 0.5 eV and MARE 30-31%, with AK13 and HLE16 close behind. That supports the weaker claim 'at least as accurate as HSE06' but undermines the stronger claim 'on average the most accurate among semilocal methods' as a general statement. The paper should either quantify the overlap between the fitting set and the 76-solid test set or present the out-of-sample comparison as the primary evidence.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript is a review of semilocal exchange-correlation potentials for calculating band structures of solids, with a strong focus on the modified Becke-Johnson (mBJLDA) potential. It reviews the formal distinction between multiplicative and non-multiplicative potentials, discusses the role of the derivative discontinuity, and compiles benchmark results from a 76-solid and a 472-solid test set. The paper also presents new WIEN2k results for rare-earth and actinide oxides (Table III) and an analysis of the role of the density-gradient average g in the mBJLDA potential (Table VI). The central conclusions are that mBJLDA is on average the most accurate semilocal method for the fundamental band gap and that it is at least as accurate as hybrid functionals such as HSE06, while its accuracy for other properties such as bandwidths and electron densities is limited. The paper ends with an outlook discussing possible routes toward improved potentials that incorporate a derivative discontinuity.","tokens_in":34644,"tokens_out":5051,"duration_ms":48446,"significance":"If the headline claim is accepted, the paper would establish that a cheap semilocal potential can replace much more expensive GW or hybrid calculations for band gaps of many solids, which would be practically important. The review is comprehensive and useful as a status report, and it includes original benchmarks: WIEN2k data for EV93PW91, AK13, and GLLB-SC on the 472-solid set, f-electron oxide calculations, and the g-dependence analysis in Table VI. The authors are also candid about formal limitations: Section II D clearly states that comparing multiplicative-potential eigenvalue gaps with experimental gaps is not in principle correct, and Section V concedes that mBJLDA gives poor bandwidths and densities. The main weakness is that the strongest claim about mBJLDA's superiority rests on benchmarks that overlap with its fitting set, while the larger independent benchmark shows parity rather than superiority.","major_comments":[{"comment":"The central claim that mBJLDA is 'on average the most accurate' semilocal method for the fundamental band gap is not supported by the out-of-sample evidence. The headline numbers in Table I (mBJLDA MAE 0.47 eV vs. HSE06 0.82 eV and GLLB-SC 0.64 eV) come from the 76-solid benchmark, which overlaps substantially with the fitting set used to determine alpha and beta in Eq. (16) (Ref. 20; Fig. 4 shows the fit for those solids). The larger, more independent 472-solid benchmark in Table II shows mBJLDA and HSE06 both at MAE = 0.5 eV, with AK13 and HLE16 close behind. The paper should either quantify the overlap between the 76-solid set and the original fitting set, or present the 472-solid result as the primary evidence and state the conclusion as 'competitive with HSE06 and among the most accurate semilocal methods' rather than 'the most accurate'.","section":"Sec. III A 1, Table I; Sec. IV"},{"comment":"The central claim in Sec. IV that 'mBJLDA is at least as accurate as hybrid functionals like HSE06' should be accompanied by the caveat, already acknowledged in Sec. II D, that this is a pragmatic comparison of a multiplicative Kohn-Sham eigenvalue gap with experiment, not a formally justified one. Because the derivative discontinuity is missing, mBJLDA's E_KS^g is not the fundamental gap in the exact KS sense; the paper states this in Sec. II D, but the abstract and the summary bullet points do not carry the caveat. Please add a sentence to the abstract or conclusions clarifying that the claim is empirical and specific to the benchmark sets considered.","section":"Sec. II D and Sec. IV"}],"minor_comments":[{"comment":"The WIEN2k calculations for EV93PW91, AK13, and GLLB-SC on the 472-solid set are new, but the text gives no computational parameters; please provide k-point sampling, muffin-tin radii, and convergence criteria in the supplementary material, since the VASP-WIEN2k agreement is not uniform for large-gap systems.","section":"Sec. III A 2 and Table II"},{"comment":"The definition of g_fixed is not explicit; please state which reference value of g from which metal or oxide was used for each row and report the g_fixed values themselves.","section":"Table VI"},{"comment":"The experimental references are single values with no uncertainty estimates, and several of these systems have a range of reported gaps; please include error bars or multiple references and state the spin-orbit treatment for UO2 explicitly.","section":"Table III"},{"comment":"The caption should explicitly define copt and gopt and state that two solids (FeO and ZnO) are excluded from the fit; currently the reader must infer this from the text in Sec. V.","section":"Fig. 4"},{"comment":"The bullet on LDA/GGA states 'in Ref. 131 it is shown that Δxc = Eg − E_KS^g = 0 in solids'; this should be qualified as referring to the thermodynamic limit for LDA/GGA to avoid a universal reading.","section":"Sec. II D"}],"recommendation":"major_revision","confidential_remarks":"The paper is essentially a review from the group that proposed mBJLDA, and the headline claim is supported mainly by in-sample benchmarks. The independent 472-solid benchmark actually dilutes the claim. I would advise the editor that the revision should require either a quantified overlap analysis or a softened central claim; without that, the paper risks overstating the case for mBJLDA. The formal caveat about derivative discontinuities is handled honestly in the body and should be moved into the abstract or conclusions."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: this is a useful review, not a breakthrough. The authors summarize the evidence for mBJLDA as the best fast semilocal potential for band gaps, add a few new benchmark numbers, and are refreshingly honest about the formal problems with their own method.\n\nWhat's actually new: WIEN2k values for EV93PW91, AK13, and GLLB-SC on the 472-solid set; a small table on CeO2/Ce2O3/UO2; and the analysis of how the unit-cell average g controls the gap in TM oxides vs metals. The review of other properties is well done—bandwidth, magnetism, electron density all get a fair treatment, and the message is balanced: mBJLDA wins for gaps, loses for bandwidths, and is mediocre for densities.\n\nNow the soft spots. The central summary claim—'mBJLDA is on average the most accurate'—rests mainly on the 76-solid benchmark, which substantially overlaps the original fitting set for alpha and beta (Fig. 4). On that set, comparing a fitted potential against unfitted hybrids is not an even playing field. The more independent 472-solid set in Table II shows mBJLDA, HSE06, and AK13 all around MAE 0.5 eV and MARE 30-35%; the paper itself says they are 'equally well.' So the strong version of the claim doesn't hold. The weaker version—mBJLDA is competitive with HSE06 and much cheaper—is well supported and practically useful.\n\nThe formal concern about comparing multiplicative KS gaps with experiment is explicitly acknowledged in Sec. II D, so it is not a hidden flaw. It does mean the fitted parameters are pragmatic rather than theoretically grounded, and the authors say as much. The new numbers in Tables III and VI are plausible but lack error bars and fine computational details; that's a minor issue for a review.\n\nI would send this to review. It deserves referee time. The requested revision should be light: soften the summary to 'competitive with HSE06,' and add a sentence quantifying the overlap between the 76-solid set and the original fitting set. That would make the paper's claims more robust.","headline":"A useful, honest review of semilocal band-gap methods; the strong claim for mBJLDA rests on an in-sample 76-solid set, while the independent 472-solid set only shows parity with HSE06.","tokens_in":35159,"tokens_out":3004,"would_cite":true,"duration_ms":30495,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["71.15.Mb","71.20.-b","71.15.-m"],"model":"deepseek-v4-flash","headline":"A fast DFT potential predicts solid band gaps as well as costly hybrids.","keywords":["semilocal exchange-correlation potentials","mBJLDA","fundamental band gap","Kohn-Sham DFT","derivative discontinuity","hybrid functionals","meta-GGA","solid-state benchmarks"],"falsifier":"Take a set of about 100 solids not used in the original alpha/beta fit, measure their fundamental gaps experimentally, and compare mBJLDA against HSE06 mean absolute errors; if mBJLDA's error is clearly worse than HSE06's, or if the c(g) fit fails on a new family as it already does for lead-halide perovskites, the at-least-as-accurate claim is refuted.","tokens_in":34119,"feed_emoji":"⚛️","tokens_out":8749,"duration_ms":82715,"temperature":0.7,"pith_summary":"This paper surveys the fastest class of density-functional approximations for solids — semilocal exchange-correlation potentials — and asks how accurately they reproduce the fundamental band gap, the energy needed to create a separated electron-hole pair. Drawing on benchmarks of 76 and 472 solids, its central conclusion is that the modified Becke-Johnson potential (mBJLDA) is on average the most accurate semilocal method and is at least as accurate as the much more expensive screened hybrid HSE06. Only dielectric-dependent hybrids and GW methods — many-body perturbation approaches — are consistently more accurate. The paper also shows where mBJLDA fails, namely Cu1+ compounds, ZnO, lead-halide perovskites, and 4f/5f oxides, and it identifies the two ingredients that make the potential work: the kinetic-energy density and a cell-averaged density-gradient measure. It argues that the formally sound next step is a non-multiplicative meta-GGA or GLLB-SC-style potential that carries an explicit derivative discontinuity.","feed_headline":"Fast DFT potential matches expensive hybrids for solid band gaps","feed_subtitle":"Benchmarks on 76 and 472 solids put mBJLDA on par with HSE06, with a few named failures.","key_machinery":"The central object is the mBJLDA exchange potential, defined as $v^{\\mathrm{mBJ}}_{x,\\sigma}(\\mathbf{r}) = c\\,v^{\\mathrm{BR}}_{x,\\sigma}(\\mathbf{r}) + (3c-2)\\,\\frac{1}{\\pi}\\sqrt{\\frac{5}{6}}\\sqrt{t_\\sigma(\\mathbf{r})/\\rho_\\sigma(\\mathbf{r})}$, with $c = \\alpha + \\beta\\sqrt{g}$, $\\alpha = -0.012$, $\\beta = 1.023\\,\\mathrm{bohr}^{1/2}$, and $g$ the cell average of $|\\nabla\\rho_\\sigma|/\\rho_\\sigma$. The Becke-Roussel term $v^{\\mathrm{BR}}$ approximates the Slater exchange potential, while the $\\sqrt{t_\\sigma/\\rho_\\sigma}$ term supplies orbital-angular-momentum sensitivity, and the global factor $c$ is what makes the gap come out near experiment. The GLLB-SC potential plays a supporting role in the argument as the formally preferable multiplicative alternative because its orbital-energy dependence yields a calculable derivative discontinuity.","core_discovery":"The authors claim that among semilocal methods, mBJLDA is the most accurate potential for fundamental band gaps. In their 76-solid benchmark it has the lowest mean absolute error (0.47 eV, 15% mean absolute relative error), slightly better than HSE06; in the 472-solid set it ties with AK13, HLE16, and HSE06 at about 0.5 eV and 30-35% mean absolute relative error. Crucially, it is the only semilocal method that handles antiferromagnetic transition-metal oxides well, reaching hybrid-level accuracy for those gaps and magnetic moments. The success is traced to the potential's dependence on the kinetic-energy density $t_\\sigma$ and on $g$, the cell average of $|\\nabla\\rho_\\sigma|/\\rho_\\sigma$: the former lets the potential act differently on orbitals of different angular character, opening d-d gaps; the latter tunes the overall strength $c = \\alpha + \\beta\\sqrt{g}$ and correlates with the value that would reproduce the experimental gap. The paper is explicit that this accuracy comes at a formal price: because mBJLDA is a multiplicative potential with no derivative discontinuity, comparing its eigenvalue gap to the experimental fundamental gap is not in principle correct, and the fitted parameters $\\alpha$ and $\\beta$ inherit that limitation.","pith_inferences":["If mBJLDA's accuracy is as robust as the benchmarks suggest, then a purely local or semilocal functional that omits a cell-averaged inhomogeneity term is unlikely to reproduce its success on antiferromagnetic oxides; this is a testable constraint for meta-GGA design.","The fitted relation $c(\\sqrt{g})$ means every new materials family is, in effect, a prediction of the original fit; the documented failures on lead-halide perovskites and 4f/5f oxides imply the fitted domain is narrower than all solids, and any large screening using mBJLDA should validate against a few higher-level references per family.","A natural extension that the paper does not pursue is to replace the global cell average $g$ with a position-dependent local average for surfaces, interfaces, and molecules; the correlation visible in the paper's c-versus-g plot suggests such a locality-preserving variant could retain much of the gap accuracy while extending applicability.","Combining mBJLDA's two ingredients with the GLLB-SC derivative-discontinuity framework, as the paper suggests, would yield a potential that is both fast and formally grounded; the test of that program is whether the fitted $c$ retains its clean correlation once the discontinuity term is added."],"forward_implications":["For routine band-gap screening of semiconductors and insulators, mBJLDA offers hybrid-level accuracy at a small fraction of the computational cost, making scans over thousands of candidate materials practical.","In antiferromagnetic transition-metal oxides, mBJLDA is the semilocal method of choice: other semilocal potentials fail badly, while mBJLDA matches hybrid accuracy for gaps and magnetic moments.","Because its eigenvalue gap omits the derivative discontinuity, mBJLDA-based gaps should not be interpreted as fundamental gaps in a formally exact sense; the agreement with experiment is the result of empirical fitting.","mBJLDA's bands are too narrow and its electron density is not particularly accurate, so bandwidths, effective masses, and density-sensitive properties like electric-field gradients should be taken from other methods or treated with caution.","The two mBJLDA ingredients — kinetic-energy density and a cell-averaged inhomogeneity measure — are identified as the key building blocks for future fast potentials that include a derivative discontinuity."],"supporting_citations":[{"why":"Introduces the mBJLDA potential and the fitted alpha and beta values that the entire accuracy claim rests on.","marker":"[20]"},{"why":"Provides the 76-solid benchmark of twelve DFT methods, the source of mBJLDA's best-in-class mean errors.","marker":"[29]"},{"why":"Extends the benchmark to effective masses, magnetism, electric-field gradients, and X-ray structure factors, documenting mBJLDA's failures on bandwidth and density.","marker":"[32]"},{"why":"Supplies the 472-solid benchmark showing mBJLDA, AK13, HLE16, and HSE06 within the same accuracy band.","marker":"[33]"},{"why":"Independent study giving RMSEs of 0.91 eV for mBJLDA and 0.50 eV for G0W0, calibrating mBJLDA against a higher-level method.","marker":"[28]"},{"why":"Defines the screened hybrid HSE06, the explicit accuracy benchmark that mBJLDA is claimed to match.","marker":"[15]"},{"why":"Defines the GLLB-SC potential, the formally preferable multiplicative alternative with a calculable derivative discontinuity.","marker":"[21]"},{"why":"Offers alternative alpha and beta parametrizations, showing the sensitivity of the fitted c(g) relation to the training set.","marker":"[73]"}],"fun_headline_variants":["mBJLDA beats hybrid HSE06 on 76-solid gap test","Semilocal mBJ potential hits hybrid-level gaps","No derivative discontinuity? mBJLDA still nails solid gaps","Best semilocal band-gap potential: mBJLDA, MAE 0.47 eV","Kinetic-energy density unlocks semilocal gap accuracy"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The whole ranking assumes that comparing a Kohn-Sham eigenvalue gap with the experimental fundamental gap is meaningful, even though the paper concedes that for a multiplicative potential like mBJLDA this comparison is in principle invalid because the derivative discontinuity is missing.","fun_headline_variants_meta":{"raw":{"variants":["mBJLDA beats hybrid HSE06 on 76-solid gap test","Semilocal mBJ potential hits hybrid-level gaps","No derivative discontinuity? mBJLDA still nails solid gaps","Best semilocal band-gap potential: mBJLDA, MAE 0.47 eV","Kinetic-energy density unlocks semilocal gap accuracy"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000573,"raw_usage":{"total_tokens":2731,"prompt_tokens":995,"completion_tokens":1736,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":611,"completion_tokens_details":{"reasoning_tokens":1642}},"tokens_in":611,"tokens_out":1736,"duration_ms":13443,"temperature":1.0,"reasoning_tokens":1642,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T15:01:25.756332+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take a set of about 100 solids not used in the original alpha/beta fit, measure their fundamental gaps experimentally, and compare mBJLDA against HSE06 mean absolute errors; if mBJLDA's error is clearly worse than HSE06's, or if the c(g) fit fails on a new family as it already does for lead-halide perovskites, the at-least-as-accurate claim is refuted.","supporting_citations":[],"review_version":1}