Nitroreductases (NRs) hold promise for converting nitroaromatics to aromatic amines. Nitroaromatic reduction rate increases with Hammett substituent constant for NRs from two different subgroups, confirming substrate identity as a key determinant of reactivity. Amine yields were low, but compounds yielding amines tend to have a large π system and electron withdrawing substituents. Therefore, we also assessed the prospects of varying the enzyme. Several different subgroups of NRs include members able to produce aromatic amines. Comparison of four NR subgroups shows that they provide contrasting substrate binding cavities with distinct constraints on substrate position relative to the flavin. The unique architecture of the NR dimer produces an enormous contact area which we propose provides the stabilization needed to offset the costs of insertion of the active sites between the monomers. Thus, we propose that the functional diversity included in the NR superfamily stems from the chemical versatility of the flavin cofactor in conjunction with a structure that permits tremendous active site variability. These complementary properties make NRs exceptionally promising enzymes for development for biocatalysis in prodrug activation and conversion of nitroaromatics to valuable aromatic amines. We provide a framework for identifying NRs and substrates with the greatest potential to advance. Numerous efforts are underway to develop nitroreductase enzymes to activate prodrugs ,2, remedThe use of enzymes in synthesis applications is gaining prominence ,19,20,21Enterobacter cloacae and close relatives have been shown to reduce nitrated aromatics through a series of two-electron steps via a ping-pong mechanism 0 is the enzyme concentration and [S] is the varied substrate concentration.Data were fit with OriginPro (v 9.0.0) software . Kinetic data for NAD(P)H and nitro substrates were fit according to the Michaelis-Menten equation (Equation (1)) where one substrate was varied while the other was fixed , and whecatk and/or catk/para substituent. To assess the extent to which electron withdrawing substituents stabilize the transition state we analyzed the results according to the Hammett Equation (2) in which Y is the rate  vs. σ [The rate constants obtained, constant  and ρ is0) vs. σ ,74.log Although the plots display considerable scatter, additional constants such as the π constant for hydrophobicity are not considered applicable to nitroaromatics . The dep+ and 10 mM dextrose. Products were extracted with 0.5 mL of ethyl acetate and either analyzed by high-performance liquid chromatography (HPLC) or LC-MS (liquid chromatography- mass spectrometry) after drying under a gentle stream of argon gas and resuspension in water:acetonitrile (50:50). The enzymatic reactions and extractions were carried out in an anaerobic bag. All reactions with ensuing analyses were performed at least twice.The products of reduction of diverse nitroaromatic substrates were screened for amine formation using HPLC (high-performance liquid chromatography) and mass spectrometry (MS). The reactions each contained 100 μM substrate and 1 μM NR in 50 mM Tris-Cl buffer (pH 7.5). A continuous supply of reduced NADH was ensured using 5 U/mL glucose dehydrogenase (GDH), 10 μM NAD® 5 µM C18 100 Å 250 × 4.6 mm , and SPD-M20A prominence diode array detector (PDA). Separation was achieved with an isocratic flow of water:acetonitrile in ratios that were optimized for individual substrates  according to the method of Massey [MsPnbA and dye present, over the course of the reduction. A length of 521 nm was used to evaluate the concentration of oxidized dye (ε521 = 44.7 mM−1·cm−1) and its extinction coefficient at 454 nm (ε454 = 9.85 mM−1·cm−1) was used to correct for a small contribution at that wavelength, which was then used to calculate the % of MsPnbA in the oxidized state. A plot of log(Ered/Eox) vs. log(Dred/Dox) displayed a linear correlation between the two with a slope of 1 confirming applicability of the Nernst equation (Equation. 3) where Eox is the concentration of oxidized MsPnbA and Ered is the concentration of reduced MsPnbA , Dox and Dred are similarly defined for the dye, dn and en are the number of electrons taken up by the dye and the enzyme, respectively (=2). The intercept was used to calculate the midpoint potential of the MsPnbA enzyme The two-electron reduction potential of f Massey . Reducin −252 mV ).log(Erin vacuo [5H8O2C3H6) was truncated by replacement with simple amine (NH2) for the purposes of thermodynamic properties only. All structures were geometry optimized further using ωB97X-D/6-311+G** and then used to calculate vibrational modes, thermodynamic quantities and molecular properties [The method developed employs relatively low level of theory and gas-phase treatment in order to accommodate the relatively large molecules included, without recourse to supercomputers or software that could be inaccessible to general practitioners. All computations were implemented in Spartan’16 (WaveFunction) . All molin vacuo . Only thoperties . The chooperties ,65,66.2). By computing the free energies of the individual oxidized and reduced species we obtained the change in free energy ΔG°rxn for the reaction ArNO2 + BzNO2−• → ArNO2−• + BzNO2 for each aromatic nitro compound ArNO2, ΔG°rxn = G°ArNO2− + G°BzNO2 − G°ArNO2 − GBzNO2−. Then, we used the Nernst equation to convert to reduction potentials: E° = −ΔG°/nF where n is the number of electrons acquired in the reduction (here = 1) and F is Faraday’s constant. Thus −ΔG°rxn/F = E°rxn = E°ArNO2 − E°BzNO2, and the value of E°’BzNO2 = −0.486 V vs. NHE [ArNO2 for each ArNO2 at pH 7 . All potentials were calculated relative to that of nitrobenzene ×4.67. We attribute the very large slope to the importance of water’s high dielectric in stabilizing the charge acquired upon reduction, since our calculations do not implement a polarizable continuum dielectric. Similarly, our use of a smaller basis set than those used by highly-accurate computations is likely a reason for the large offset and slope, as larger basis sets are needed to provide a good description of the anionic free radical state formed upon reduction. However, the scatter about the line is small, and after using the equation of the line to calibrate our gas-phase computational values, Calc = Comp/4.67−0.379 V, our ‘Calc’ calibrated calculated E° estimates (E°c) display a mean absolute variance of 14 mV from experiment. Calculations were calibrated against experimental values to compensate for the use of a small basis set and the complete neglect of solvent effects . DespiteSubstrate volumes were calculated in Spartan based on CPK atomic volumes.A total of 36 structures annotated as members of the NR family were gathered from the Protein Data Bank (PDB ) based oBuried surface area was obtained using the built-in tool in Chimera and is calculated from the solvent accessible surface area (ASA) per monomer A and B as well as the AB dimer as follows: buried ASA = {ASA(A) + ASA(B) − ASA(AB)}/2  with areWe have evaluated the roles of nitroaromatic substrate properties and type of NR enzyme as potential determinants of the rate of nitro reduction as well as the capacity to yield amine products. Both factors participate, providing independent degrees of freedom with which systems can be optimized, although no simple single answer emerged. It is evident that members of the NR superfamily offer very wide diversity in their active sites and thus the nature of the contacts between flavin and substrate. This superfamily combines the chemical virtuosity of a flavin with a fold that provides stability from afar via an intertwined structure. The different active site constraints provided by sequence excursions from different portions of the peptide chain produce very different active sites in different NR subgroups. We provide the first correlation between amine production and substrate properties, indicating that the best choices will have large π systems and electron withdrawing substituents. Thus, our work predicts that the most promising NR subgroups for screening and engineering are likely to be those with capacious or flexible active sites such as NfsA, Frm2 and HUB. Our comparisons lay a foundation for chemically and structurally-informed development of modified NRs, exploiting the tolerant architecture and versatile cofactor of this large and diverse superfamily.


Culicoides biting midges, which transmit several important animal pathogens, including bluetongue virus (BTV) and epizootic hemorrhagic disease virus (EHDV), are small flies that develop in various semi-aquatic habitats. Previous Culicoides dispersal studies have suffered from the limitations of other labeling techniques, and an inability to definitively connect collected adult midges to specific immature development sites.Stable isotope labeling is a promising method for use in insect mark-capture and dispersal studies. C. sonorensis were successfully labeled with 13C and 15N stable isotopes as larvae developing in a semi-aquatic mud substrate in the laboratory. High and low-dose isotope treatments for both elements significantly enriched midges above the background isotope levels of unenriched controls. Enrichment had no effect on C. sonorensis survival, though a slight (~ 5 day) delay in emergence was observed, and there was no significant effect of pool size on 13C or 15N enrichment levels.Adult 13C or 15N shows promise for Culicoides dispersal studies in the field. This method can be used to identify adult dispersal from larval source habitat where a midge developed. It may be possible to detect a single enriched midge in a pool of unenriched individuals, though further testing is needed to confirm the sensitivity of this method.Stable isotope labeling is life-long, and does not interfere with natural insect behaviors. Stable isotope enrichment using  Culicoides dispersal is critical to understand the transmission of pathogens like bluetongue virus (BTV) and epizootic hemorrhagic disease virus (EHDV) between farms. Most studies that have attempted to model Culicoides long-distance movement have relied on air current data, with the assumption that infected vectors move across significant distances by wind [Culicoides biting midges are small (1.0–2.5 mm in length) [Knowledge of  by wind –4. Culic length) , 7. In i length) , 9.Culicoides for such studies in both the field and laboratory, including radioactive isotopes [Culicoides that were originally labeled in that study [2-baited traps in a host-poor desert environment [Culicoides spp. cannot be reared in the laboratory for release, and capturing and labeling the number of insects needed to achieve acceptable recapture rates from the field is unfeasible for most marking technologies. Additionally, the marking technique itself has the potential to impact survival and/or behavior (e.g. fluorescent dust) [In traditional mark-recapture studies, insects  are labeled in a way such that their initial location is known, and can later be identified in collections from other areas to determine a linear estimate of movement from the initial area. Several methods have been used to label isotopes , fluoresisotopes , 11, ingisotopes , ingestiisotopes , and immisotopes . These mat study , althougironment . Typicalironment . Most Cunt dust) . The ident dust) .Culex mosquitoes (Diptera: Culicidae) could be successfully labeled as larvae in both the laboratory and field using 15N-labeled potassium nitrate (KNO3) and 13C-labeled glucose added to the development water, and that enrichment was detectable in emerged adults up to at least 55 days post-emergence [Culicoides vector species is mainly semi-aquatic or terrestrial [Culicoides sonorensis Wirth & Jones is the primary North American BTV vector, and lays its eggs on mud at the shallow edges of organically enriched aquatic habitats (e.g. dairy wastewater ponds) [Culicoides stellifer (Coquillett) and C. insignis Lutz, putative EHDV vectors in the southeastern USA [C. sonorensis in a natural mud substrate under laboratory conditions.Stable isotopes are naturally occurring, non-radioactive forms of elements in the environment. Previous studies have demonstrated that enriching aquatic habitats with stable isotopes resulted in emerged insects with isotope levels above natural background levels, indicating that stable isotope labeling can be a means of marking insects for dispersal studies –20. Markmergence . While mrestrial , and ther ponds) . Culicoitern USA , also detern USA . The objC. sonorensis) at a dairy in San Jacinto, CA, USA, in June 2014, and frozen at − 20 °C to kill any preexisting insects. On 1 August 2014, mud was thawed and homogenized by mixing, and 200 ml of mud was added to each of a series of 450 ml clear plastic deli containers, and the same mud was used for both treatment and control replicates. Mud was formed into a gentle “bank” by tapping the bottom edge of the containers against the lab bench. The development substrate (i.e. mud) was allowed to settle briefly (~ 30 min), and then 50 ml of enriched water containing either a “high” or “low” dose of 15N-labeled potassium nitrate  or 13C-labeled glucose  was added to each container such that approximately 1/3 of the mud “bank” was submerged to replicate field conditions. For the high-dose and low-dose treatments, 6 or 2 mg of KNO3 or U-13C6 respectively, were dissolved in 1 l deionized water. Low doses were similar to those used in previous laboratory mosquito labeling studies [C. sonorensis in mud habitats, a high dose of three-times the low dose was selected. Control replicates received 50 ml of deionized water. Ten replicates of each treatment  were used. No additional marked solution was added to the containers after the initial set-up, but additional deionized water was added as-needed throughout the experiment to maintain constant water levels.Mud was collected from wastewater ponds  maintained at the University of California, Riverside. Culicoides sonorensis eggs were laid on moist filter paper on 24 June 2014, and were stored at 4 °C until the start of the experiment (1 August 2014). A small piece of the filter paper with ~ 150–200 eggs was placed 2 cm above waterline in each container immediately after water (control or enriched) was added to the container. The containers were then covered with plastic lids with holes poked in them for air flow. Containers were randomly distributed on a window shelf where they received natural, but not direct, sunlight, and were rotated periodically to account for differences in light exposure. Fluorescent lights were also positioned on both sides of the shelf on a 12:12 h light:dark photoperiod to provide additional light, and mimic typical colony maintenance conditions. The temperature in the laboratory was approximately 23 °C. Containers were checked every 1–3 days for emerged adults. When adults were observed in the containers, they were aspirated into microcentrifuge tubes through access holes cut in the side of the containers, pooled by treatment, and stored at − 20 °C for processing. Each treatment used a dedicated aspirator to prevent cross-contamination. The number of emerged adults per collection day from each container was recorded. Day of emergence was recorded as the number of days since eggs were added to containers. Emergence was considered complete for a given replicate after 3 days with no emergence. Periodically, the mud was gently disturbed by raking the surface with a treatment-specific glass pipette in order to re-suspend nutrients into the water to ensure that microorganisms were present to serve as food for C. sonorensis larvae.Insects used for the study came from an established southern California colony of Culicoides samples were analyzed for isotope enrichment at the Texas A&M University Stable Isotope Geosciences Facility using a Thermo Fisher Scientific Delta V Advantage with Flash EA Isolink attached to a ThermoFinnigan Conflo IV isotope ratio mass spectrometer (IRMS). Insects were pooled in groups of 2–25 individuals by treatment (isotope and dose) for analysis, and 15–17 pools per treatment were analyzed  and 44 (CO2) of a combusted sample are converted to total mass of nitrogen and carbon, respectively, using an intra-run calibration. This calibration consists of a methionine standard prepared at 5 masses ranging from 0.1 mg to 3 mg. The resulting peak areas from these standard analyses are regressed against the known amount of nitrogen and carbon present in each of the masses of methionine utilized in the calibration, a relationship that is highly linear. This calibration is then applied to the peak areas of unknown samples within the run, allowing calculation of their total nitrogen and carbon content. Raw sample δ15N and δ13C measurements are converted to the Air and Vienna Pee Dee Belemnite (VPDB) isotopic scales, respectively, through an intra-run, two-point calibration of ~ 1 mg of l-glutamic acid standards with known isotopic values. The l-glutamic acid standards utilized are USGS 40  and USGS 41 . Internal laboratory standards, at least one of which is similar to the sample matrix, are utilized as internal checks of the accuracy and precision of the calibrations. Powdered rice was used as the standard in this study  with an internal uncertainty of ± 0.2‰ for both δ15N and δ13C (1 sigma).The peak areas of sample mass-to-charge ratios 28  using ‘Treatment’ and ‘Pool’ as fixed factors and δ13C or δ15N as the response variable. Differences in the mean δ13C or δ15N by treatment were analyzed using a Kruskal-Wallis rank sum test followed by Dunn’s test for means separation (dunn.test package) [C. sonorensis tissues by isotope treatment were determined by calculating the percent change in δ13C and δ15N for each treatment replicate compared to the mean δ13C or δ15N of the unenriched controls. The mean percent change for each treatment was then analyzed by ANOVA, followed by Tukey’s HSD. For mixed pools, a natural isotope abundance baseline for groups of six C. sonorensis was calculated from the mean δ13C and δ15N of the mixed pools spiked with midges enriched with the opposite element (i.e. the δ13C for 15N labeled mixed pools and vice versa). Because the amount of other elements in the sample is not affected by enrichment, this allowed us to generate an estimate of natural 13C and 15N abundance for pools of six midges. The δ13C and δ15N of the 13C- and 15N-spiked mixed pools was then compared to this baseline natural abundance. Labeled Culicoides were considered detectable in the mixed pool if the δ13C /δ15N value for that pool was at least three standard deviations above the mean of the natural abundance baseline [Data were analyzed using R (version 3.4.0). Statistical differences in the mean day of emergence, median day of emergence, and the mean number of emerged adults per treatment were analyzed using analysis of variance (ANOVA) followed by Tukey’s honestly significant difference (HSD) test for means separation. Bonferroni’s correction for multiple comparisons (α = 0.005) was used. The effect of pool size on δpackage) . Differebaseline .13C-low dose replicate. Midges had begun to emerge in all treatments by day 32, though there was variation among replicates. Midges first emerged in each cup on days 28–46 for controls, days 32–42 for 13C-high, days 23–43 for 13C-low, days 29–46 for 15N-high, and days 25–43 for 15N-low. The average day of emergence was significantly later in enriched treatments than in controls  = 49.1, P < 0.0001). Both 15N treatments and the 13C-high dose treatment had the latest average emergence date. Emergence in the 13C-low dose treatment was earlier than the other enriched treatments (P < 0.0001), but still later than controls (P = 0.0004). However, the average median day of emergence across replicates within a treatment did not differ between treatments. Although the number of emerged adults varied among replicates for all treatments (ranging between 19–129), there was no significant difference among treatments  or the δ15N  values, and pools of two midges had similar delta values as pools of 25 midges. All replicates of various sized pools from the same treatment were therefore combined for further analysis. Mean δ13C and δ15N values for 13C and 15N-enriched midge pools were significantly greater than unenriched controls  . The mean δ13C and δ15N for the unenriched, control pools was − 22.9‰ and 19.8‰, respectively. The δ13C and δ15N values for 13C and 15N low-dose treatment pools were an average (± SD) of 24.3 ± 11.2% and 49.8 ± 3.89% higher than controls, respectively. The δ13C and δ15N values for 13C and 15N high-dose treatment pools were an average (± SD) of 68.2 ± 13.7% and 69.7 ± 2.47% higher than controls, respectively. The percent increase in isotope enrichment compared to controls was significantly different across all treatments  = 83.0, P < 0.0001), except for the 13C and 15N high-dose treatments, which did not differ from each other. For mixed pools of six midges, the natural abundance baseline δ15N was 20.5 ± 0.35‰, and the natural abundance baseline δ13C was − 23.4 ± 0.30‰. The δ15N of the 15N-mixed pools ranged from 24.8‰ (1 enriched specimen with 5 unenriched) to 40.0‰ (3 of 6 enriched). The δ13C of the 13C-mixed pools ranged from − 21.6‰ (1 of 6 enriched) to − 15.1‰ (3 of 6 enriched). The 15N-mixed pool with the lowest δ15N was twelve standard deviations above the natural abundance mean, and the 13C-mixed pool with the lowest δ13C was six standard deviations above the natural abundance mean.The number of midges in a pool from the same treatment did not affect the δCulicoides in larval habitat for mark-capture studies of adult dispersal. While previous studies have shown that aquatic habitats can be enriched with stable isotopes to label developing insects, here we show proof of concept that insects developing in semi-aquatic habitats can be labeled in the same way. To the best of our knowledge, this study also represents the first time that Culicoides biting midges have been successfully labeled using stable isotope enrichment. Compared to other insects that have been targeted in previous stable isotope labeling studies, Culicoides are small, and it was unknown whether a single midge would contain enough isotope to fall within the instrument’s detection limits, or whether a single enriched midge could be detected in a pool of unenriched individuals.This study provides support that stable isotope labeling can be an effective means to mark immature 13C and 15N-enriched C. sonorensis ranging between 2–25 individuals. There was no significant effect of pool size on δ13C or δ15N, indicating that accurate readings can be achieved with very small pool sizes  when using the methods and instrumentation described here. Additionally, larger pool sizes did not interfere with isotopic measurement accuracy, as had previously been shown for pools of ten Culex pipiens (Forskål) [13C or δ15N values than used in previous stable isotope labeling studies, and supports the potential to use isotopic labeling as part of a mark-capture study of Culicoides adult dispersal.In order to determine how many midges would need to be pooled in order to get a quantitative isotopic measurement, we analyzed pools of Forskål) . A small15N- and 13C- labeled C. sonorensis were sufficient to uniquely enrich midges above the natural isotope abundance levels of control specimens, though even pools of 20–25 midges from high-dose treatments did not reach the same δ13C or δ15N levels compared to single mosquitoes enriched with the same doses [15N we recorded for a 15N-enriched pool of C. sonorensis was 72.6‰ and the highest δ13C we recorded for a 13C-enriched pool was − 2.23‰. For comparison, a previous study enriching Cx. pipiens resulted in δ15N and δ13C values of 514–824‰ and 73–603‰, respectively [Culicoides. Alternatively, given that bioaccumulation of the stable isotopes through a microbial community which is fed upon by larvae is the most likely mechanism of enrichment, we might not have achieved efficient bioaccumulation in these simulated mud substrate habitats. We used mud from the field which had been frozen to kill any wild insects present. The microbial community of this frozen and thawed mud was unknown, and using fresh mud, with an unaltered microbiome, might have improved delivery to the insects. Alternatively, adding the enriched water to the mud containers several days before adding eggs might also have increased enrichment in the adult Culicoides by allowing more time for the isotopes to be fully incorporated in the substrate prior to larvae hatching.Both high and low dose treatments for me doses , 28. Theectively . It is pCulicoides studies. For proof of concept, we tested a small number of mixed pools of labeled and control midges to determine whether these pools would be detectable as “enriched.” These mixed pools had δ13C and δ15N values well above the natural isotope abundance baseline of unenriched pools, even when only one enriched individual was present, though variation would likely be greater in field collected samples, and single midges may be less detectable in larger pool sizes than tested in this study. Future enrichment studies of Culicoides should consider a higher dose of stable isotopes or deliver a dose repeatedly over time to achieve higher δ15N and δ13C, which would improve the ability to detect a single marked individual in a pool of natural abundance specimens.Because of the low capture rate typical of mark-capture studies, the ability to detect a single enriched individual in a pool of unenriched midges is critical for the successful use of stable isotope labeling for C. sonorensis survival, but did delay the average adult emergence time by approximately five days. Emergence was the least affected in the 13C-low dose treatment. The delayed emergence of enriched midges may not have a significant impact on field collections in Culicoides mark-capture studies for dispersal as long as traps are set for a sufficient amount of time, but should be considered if the study objectives include questions about development. Previous studies comparing 15N and 13C enrichment in mosquitoes showed a trend towards higher levels of nitrogen integration in tissues compared to carbon, potentially due to the use of nitrogen-rich food sources [15N was integrated into C. sonorensis tissues than 13C; a ~ 50% increase compared to a ~ 24% increase. However, when isotope concentrations were increased, there was no difference in the percent increase in δ15N or δ13C, suggesting that at higher doses there is no benefit to using one isotope over the other.Enrichment of the larval habitat did not appear to negatively affect  sources . We founCulicoides immunomarking has thus far only been studied in manure-developing species [C. sonorensis. Stable isotope labeling cannot be transferred between individuals, individuals can only be marked by developing in enriched habitats, and it is compatible with aquatic and semi-aquatic habitats.Stable isotope labeling has the benefit of allowing researchers to positively connect captured, adult midges to specific and known larval development sites. Immunomarking is the only other mark-capture technique that allows for this type of data collection. Both techniques potentially allow for differentiation of multiple marked sites by using either different proteins or different atomic elements. Immunomarking may be more accessible to most entomology laboratories, as samples are analyzed using a protein-specific ELISA, while stable isotope labeling requires access to specialized facilities. Costs for processing stable isotope enriched samples vary by institution, though the cost is higher than processing immunomarked samples by ELISA. Using the commercially available ovalbumin ELISA from Sanders & Carpenter  costs ~  species , 29, andCulicoides developing in small, contained substrates in the laboratory environment. Previous field trials labeling mosquitoes with stable isotopes focused on enrichment of smaller container habitats  [Culicoides habitats are often larger than previously studied mosquito habitats, and not artificially contained, like dairy wastewater ponds. These types of habitats would likely require dramatically more isotopic material in order to enrich the specimens than used in container-breeding mosquito studies. A potential solution to this would be to target smaller, highly productive Culicoides sites, or construct a more concentrated experimental field habitat for enrichment. Although we did not measure isotope retention in older individuals in this study, future work should determine whether enrichment is lifelong in Culicoides spp.In this feasibility study, we labeled ic tubs) , 25, 28.Culicoides sonorensis can be successfully labeled with 15N and 13C stable isotopes when the larval habitat is enriched with either a low or a high dose of the isotope. Elevated levels of stable isotope were detected in pools of 2–25 individuals for both low and high doses. A single enriched midge can potentially be detected in a small pool of unenriched midges, though further work is needed to determine the limit of detection using this method. Stable isotope labeling shows promise for future Culicoides mark-capture adult dispersal studies in the field.Additional file 1: Table S1. Pools and pool sizes of emerged adult C. sonorensis analyzed for stable isotope enrichment. Table S2. Mixed pools of labeled and control C. sonorensis analyzed for stable isotope enrichment to determine whether labeled midges were detectable in groups of unlabeled midges.


Following its synthesis and structural characterization, the structural rigidity is confirmed to stem from a unique corner sharing [B3O7]5– polyanionic backbone. Substituting this material with Eu2+ yields UV excitation bands and a narrow violet emission at 416 nm with a full-width at half-maximum of 34.5 nm. More importantly, NaBaB9O15:Eu2+ possesses a quantum yield of 95% and excellent thermal stability.Rare-earth substituted inorganic phosphors are critical for solid state lighting. New phosphors are traditionally identified through chemical intuition or trial and error synthesis, inhibiting the discovery of potential high-performance materials. Here, we merge a support vector machine regression model to predict a phosphor host crystal structure’s Debye temperature, which is a proxy for photoluminescent quantum yield, with high-throughput density functional theory calculations to evaluate the band gap. This platform allows the identification of phosphors that may have otherwise been overlooked. Among the compounds with the highest Debye temperature and largest band gap, NaBaB Identifying phosphors with good thermal stability and quantum efficiency is a prerequisite to improve the performance of white LED light sources. Here, a combined machine learning and density functional theory method is introduced to identify next generation inorganic phosphors. These materials are composed of a host crystal structure, often an oxide, halide, or nitride, that are substituted with a rare-earth luminescent center, typically Eu2+ or Ce3+7. The rare-earth ion absorbs at least part of the LED emission and then re-emits a photon at a longer wavelength. The combination of these emissive lights cover the entire visible portion of the electromagnetic spectrum and thus appears as white light8. The efficiency, color quality, and compact size make these devices not only useful for general illumination, but they are also essential for modern display applications9. Unfortunately, only a handful of the phosphors currently reported in the literature are able to perform the down-conversion process efficiently, as measured by the photoluminescent quantum yield (Φ)10. Even then, some of the phosphors with a high luminescence quantum efficiency also suffer from thermal quenching, where the optical properties, for example, emission wavelength and intensity, change at elevated temperature limiting their range of potential applications15. Therefore, the continued improvement of LED-based lighting requires the discovery of new efficient and thermally robust rare-earth substituted inorganic phosphors.Inorganic phosphors are among the most significant components in a light-emitting diode (LED)-based white light and greatly influence the device’s overall efficacyΦ is to find structurally rigid host compounds with high atomic connectivity16. These characteristics enhance Φ by inhibiting soft phonon modes that lead to non-radiative relaxation, thereby increasing the propensity for photon emission. However, the complex nature of chemical bonding in inorganic solids makes clearly identifying connectivity and structural rigidity challenging, and the comparison of rigidity between multiple solids problematic. Alternatively, it is possible to use a proxy, which is a quantifiable metric that scales with structural rigidity, to compare different materials. Prior work has already shown that a material’s Debye temperature (ΘD) is the most reliable proxy for structural rigidity, and consequently useful for screening Φ19. Materials with a higher ΘD tend to have higher-energy phonon modes that decrease the probability of non-radiative relaxation increasing Φ, whereas materials with a low ΘD tend to contain softer phonon modes that can promote non-radiative relaxation. More importantly, ΘD can be estimated using density functional theory (DFT), allowing for the potential of high-throughput screening20. Nevertheless, this approach has numerous drawbacks; most notably, calculating ΘD using DFT is computationally arduous. DFT cannot easily account for atomic disorder like site sharing which is common in complex inorganic solids, and it is currently restricted to smaller unit cells, typically a few hundred atoms at most. These limitations have permitted the elastic moduli, which are necessary to estimate ΘD, to be calculated for only a few thousand compounds, or <10% of the reported inorganic solids.In the search for new phosphors, research has shown one viable method for identifying materials with a high 22. For example, it is possible to use a kernel ridge regression model to predict a myriad of electronic properties including dielectric constants, electron affinities, formation energies, and even band gaps24. A more intricate method employing a gradient boosting decision tree and universal fragment descriptors is able to predict the electronic as well as mechanical properties, such as bulk and shear modulus, heat capacity, and Debye temperature25. Machine learning has also allowed researchers to predict glass formation26, study magnetoelectric heterostructures27, and optimize microstructure29. The great advantage of using statistical machine-learning methods is that predictions can be quickly made for any given combination of elements, any stoichiometry, or any size unit cell. We show here that it is also possible to use machine learning to predict ΘD for a majority of compounds in the Pearson’s crystal database (PCD)30 in seconds regardless of unit cell size, atomic mixing, or electron correlation resulting in ~120,000 Debye temperatures that can be used for screening inorganic phosphors.Advances in machine learning provides an avenue to significantly expand the physical and mechanical properties of inorganic solids and can push materials development beyond the current capability of DFT aloneΘD alone is still not sufficient to produce a high photoluminescence quantum efficiency inorganic phosphor. A wide band gap (Eg) in the host crystal structure is also crucial20. The size of the band gap sets the relative position of the rare-earth 5d orbitals with respect to the host crystal’s conduction band, which can influence the optical response. If the band gap of the host is small, the excited-state 5d orbitals may be close enough to the conduction band of the host crystal structure to allow (temperature-induced) photoionization or charge transfer. These non-radiative processes can both greatly diminish Φ32. Therefore, it is essential to ensure that any potential host also has a suitable band gap when screening for new phosphors. These two properties can ultimately be optimized by plotting ΘD as a function of DFT calculated Eg, which serves as a sorting diagram. For example, phosphors hosts that fall in the bottom-left corner of this sorting diagram have a low ΘD and a narrow Eg, suggesting that they are likely not worth immediate exploration, whereas compounds in the top-right corner of this plot are not only structurally rigid but also have a wide enough band gap to support rare-earth luminescence20. The success of this initial sorting diagram has already supported the discovery of numerous inorganic phosphors5.Knowledge of a crystal structure’s ΘD with high-throughput calculations using DFT for approximating band gap . These scalable methods increase the number of potential phosphor hosts contained on the new sorting diagram 50-fold compared to the original approach; therefore, functioning as a more robust guide for phosphor development. Here we use this approach to identify one specific crystal structure that stands out among the 2071 materials on our sorting diagram. NaBaB9O15 has a high predicted Debye temperature of 729 K, surprising given the mostly ionic bonding and low-density crystal structure, as well as a wide Eg,DFT of 5.5 eV, making it worthy of experimental investigation. The subsequent synthesis of NaBaB9O15 substituted with Eu2+ indicates that this compound not only has a Φ near unity but also shows minimal thermal quenching. These results substantiate the effectiveness of using this sorting diagram to direct the discovery of the next-generation rare-earth substituted inorganic phosphors.This work establishes a new approach for phosphor screening methods by constructing a more extensive sorting diagram that merges supervised machine learning to predict BDFT) and shear (GDFT) moduli extracted from the Materials Project database can be converted into an approximate Debye temperature  based on the average sound velocity (νm) following Eq. h is Planck constant, kB is Boltzmann constant, n is the number of atoms per formula unit, NA is Avogadro constant, ρ is the crystal structure’s density, M is the molar mass, and νm is the average sound velocity33:νm can be approximated following Eq. νL and νT are the longitudinal and transverse sound velocity, respectively, which can be obtained from the DFT calculated BDFT and GDFT using Eq. ΘD,DFT was obtained for all 2610 compounds, a machine-learning algorithm was developed to predict the Debye temperature using support vector machine regression (SVR) . The 10-fold cross-validation regression analysis for ΘD,SVR is plotted in Fig. ΘD,DFT and the ΘD,SVR with a root mean-squared error of cross-validation of 59.9 K and a mean absolute error of 37.9 K. The coefficient of determination (r2) is 0.89 indicating that the descriptor set does an excellent job expressing the materials Debye temperatures. Nearly all of the data (97%) falls between 50 and 750 K, as highlighted by the darker regions of the plot. The cross-validated ΘD,SVR tends to be slightly underestimated, particularly for materials with extremely high Debye temperatures (>1500 K), which is potentially due to the lack of data with extremely high Debye temperature. In fact, there are only four compounds, BN, Be2C, B6O, and LiB6C, that fall notably below the expected ΘD,SVR, suggesting that our machine-learning model does not capture the chemistry of these very light compounds. Although there are a few incorrect predictions, Fig. The machine-learning model to predict Debye temperature first requires training using a large, diverse set of data. In this case, the 2610 DFT-based bulk  contain rare-earth elements that cannot be readily calculated using conventional DFT and 19,384 (16%) have either disordered positions or site mixing, which is also generally inaccessible with DFT. From this extended list, the search for potential phosphor hosts can be immediately reduced by adhering to a few simple phosphor design criteria. First, knowledge of the band gap is essential for screening phosphor hosts using the sorting diagram, and each compound was further cross-referenced against the Materials Project to ensure that the -level) Eg,DFT is available. Additionally, a majority of rare-earth substituted phosphor hosts contain at least three elements, that is, are ternary phases or higher; therefore, in this study binary compounds are excluded. These two basic requirements reduced the number of possible compounds by 94% to 7504. The list of potential rare-earth substituted inorganic phosphor hosts could be further honed considering rare-earth substituted phosphor hosts are customarily composed of only the elements highlighted by the blue boxes shown in Fig. 10. Finally, any compound following all of these criteria but still calculated to be a metal, that is, Eg = 0, was also removed from the list narrowing the final number of possible phosphor hosts to 2071. The ΘD,SVR of these 2071 compositions was subsequently predicted with the machine-learning model and associated with the DFT calculated band gap . This entire dataset was used to screen potential inorganic phosphor hosts and is provided as Once the training set has been constructed, the machine-learning algorithm can be used to estimate Eg,DFT as a function of their predicted ΘD,SVR, illustrated in Fig. Eg,DFT ≤ 0.4 eV) PBE-level band gaps, suggesting that these phases are not likely viable options as rare-earth substituted phosphor hosts. There are also a considerable number (22%) with a ΘD,SVR <250 K, indicating that these materials may not have the structural rigidity necessary for a high Φ.Plotting the 2071 compounds’ ΘD,SVR < 500 K and an Eg,DFT only in the range of 0–4 eV, which suggests that any emission will likely have a rather low Φ when substituted with a rare-earth ion. Conversely, nitrides 2SiO4:Eu2+, as well as numerous reports of materials that have low luminescence quantum efficiency reinforcing the range of Debye temperatures and band gaps17. In contrast, fluorides 3:Eu2+ 15, BaRbPO4:Eu2+34, and LiSrPO4:Eu2+35, supporting the sorting diagram’s suggestion.Decomposing the sorting diagram into the compositional information indicates several trends related to the potential of different phosphor hosts. For example, Fig. des Fig.  have modtes Fig.  and alumtes Fig. , which ades Fig.  all showdes Fig.  tend to 3+-substituted Ba2Y5B5O17 has a blue emission with an Φ of 70% at room temperature that can be increased to nearly 90% by substituting the harder cation Lu3+ for the comparatively softer Y3+37. Similarly, NaSrBO3:Ce3+ and NaCaBO3:Ce3+ both have a reported Φ of ≈75%39. Many of the borate phosphors including K2Al2B2O7:Eu2+ are also thermally robust showing minimal loss of luminescence at high temperature40. Although the search for borate phosphors is directed based on the machine-learning algorithm, the discovery of these materials was still achieved through traditional means including isovalent substitution of known materials, rationally searching phase space, or through serendipitous discovery.Analyzing metadata-like composition is clearly indispensable for directing the search for new materials, with the potential to shift the search toward remarkable composition space, such as focusing on borates. Indeed, a few high-efficiency borate phosphors have already been reported. For example, CeΦ phosphors. For example, examining the sorting diagram shows that CaAlB3O7 has a very high ΘD,SVR of 732 K and Eg,DFT of 5.3 eV due to the presence of alternating layers of [AlO6] octahedral and [BO4] tetrahedra connected through edge and corner sharing, with the Ca2+ decorated among the very dense anionic network41. Li5Rb2B7O14 is also a phase of interest given that ΘD,SVR is 703 K and Eg,DFT is 4.5 eV. This phase is a non-centrosymmetric crystal structure that contains a three-dimensional network of polyborate chains producing the expected rigid crystal structure42. Both of these phases are viable phosphor hosts and worth consideration. Additionally, perhaps the most unique crystal structure suggested by the sorting diagram is NaBaB9O15  powder X-ray diffraction. The structure of the unsubstituted, that is, x = 0, sample was analyzed using high-intensity, high-resolution synchrotron X-ray powder diffraction data, shown in Fig. The synthesis of NaBaB9O15 adopts the non-centrosymmetric trigonal space group R3c (no. 161). As illustrated in Fig. 3O7]5– subunits in which two [BO3]3– trigonal planar units and one [BO4]5– tetrahedron are linked by the vertices. The refined B–O bond lengths within the trigonal planes range between 1.33 and 1.38 Å, while the bond lengths within the [BO4]5– tetrahedron are slightly longer (1.45–1.49 Å). The arrangement of the [B3O7]5– units generates large tunnels along the [001] direction that are occupied by Ba2+ and Na+. The Ba2+ ions are coordinated in a nine-vertex distorted tri-capped trigonal prism, whereas six oxygen atoms form a highly distorted trigonal antiprism surrounding the Na+ ions. This combination of corner sharing [B3O7]5– polyhedra is remarkable because it constructs a network that is not especially dense. In fact, the calculated density of NaBaB9O15 is only 2.669 g cm–3 which is half the density of the other reported Na-Ba-B-O phases44. Such a porous anionic network would not be predicted to form a rigid crystal structure. However, the high ΘD likely arises due to the presence of high-frequency vibrational modes from the unique [B3O7] structural unit, which forms an extended and intertwined polyanionic backbone. Moreover, the high concentration of very light boron atoms also gives rise to the presence of high-frequency phonon modes. This combination of composition and crystal structure both contribute to the anomalously high Debye temperature for NaBaB9O15. Because machine learning has minimal bias, the prediction is undiscriminating in which crystal structures are suggested, highlighting the importance of using this approach to identify phases that may otherwise be disregarded.NaBaBΘD based on the Debye–Waller theory as a confirmation of the machine-learning prediction46. Although this is a considerable approximation that assumes a single acoustic branch and ignores the optical modes, it is still valuable for comparing the machine-learning predicted Debye temperature to an experimental value. Using the mean-square atomic displacement parameters, <ΘiD, can be calculated for each crystallographically independent atom, i, following Eq. m is the atomic mass and uieq, is the atomic displacement parameter. The overall Debye temperature (ΘD) can then be approximated by taking the stoichiometrically weighted average of ΘiD, according to the formula NaBaB9O15:ΘD using the refined <ΘD,SVR. This is in an excellent agreement considering that the B and G values used in the training set are derived from DFT using the Voigt–Reuss–Hill approximation and neglects the temperature dependence of the elastic moduli. Moreover, the scattering refinement data are based on synchrotron X-ray diffraction, which is not particularly adept at evaluating atomic displacement parameters. Nevertheless, the small difference indicates that machine learning is indeed a viable technique for quickly estimating ΘD,SVR.Once the crystal structure is refined from high-resolution scattering data, it is possible to experimentally estimate entclass1pt{minimaΘD,SVR and wide PBE-level calculated band gap suggests that NaBaB9O15 has strong potential as an inorganic phosphor host. Considering that the PBE-level calculations significantly underestimate Eg, a HSE06 hybrid functional calculation was conducted using the Vienna ab initio Simulation Package49 to ensure that this compound has a sufficient band gap to tolerate the rare-earth’s electronic transitions. The result confirms NaBaB9O15 indeed has a very wide calculated Eg,HSE of 7.3 eV. The phosphor was then prepared by substituting Eu2+ as the luminescent center for Ba2+ following NaBax1–EuxB9O15 . The compound maintains phase purity across the entire substitution range examined, as plotted in Supplementary Figure 2+ has a broad ultra-violet excitation band ranging from 230 to 385 nm, as shown in Fig. λex = 275 along with two shoulders at λex = 315 and λex = 365 nm. The emission spectra collected by exciting at these three wavelengths produces an identical emission peak with a maximum emission wavelength at 416 nm, indicating that the multiple excitation peaks arise from the electronic transitions between the Eu2+ 4f orbitals to multiple Eu2+ 5d orbital excited states. The emission spectra can be fit by a single Gaussian peak, depicted in Fig. 2+. This is in agreement with the refined crystal structure that only contains one substitution site, Ba(1). The single Eu2+ site was further supported by measuring the photoluminescence lifetime  1931 coordinate of  and has a very narrow full-width at half-maximum (FWHM) of only 1962 cm–1 (34.5 nm). These data show that this material eclipses the industry standard blue-emitting phosphor BaMgAl10O17:Eu2+, which has a FWHM of ≈2200 cm−1 (≈50 nm)50, but NaBaB9O15:Eu2+ is still broader than the recently reported blue-emitting AELi2[Be4N6]:Eu2+  phosphors that have a FWHM of only ≈1200 cm−1 (≈25 nm)51.The high 9O15 host is likely a highly rigid phosphor host based on the predicted ΘD,SVR, the Φ of NaBaB9O15:Eu2+ system was extensively analyzed. First, the rare-earth concentration was optimized by varying the loading of Eu2+. As shown in Fig. 2+ concentration in NaBaB9O15:Eu2+ has the highest Φ = 95(1)%, and increasing the Eu2+ concentration causes an abrupt drop in Φ. Exciting the phosphor at 340 nm shows the same optimized concentration of Eu2+ with a slight decrease in Φ to ≈75% with an increase in the rare-earth content beyond 3 mol% again causing a drop in Φ. The origin of the emission loss stems from an energy transfer process between adjacent luminescence centers. The critical distance between luminescent centers for this concentration quenching process (RC) can be calculated following Eq. V is the volume of the unit cell, xc is the optimized rare-earth concentration, and N is the number of crystallographically independent Eu2+ positions in a unit cell52. In NaBaB9O15:Eu2+, using a volume of 1857.28 Å, an optimized concentration of x = 0.03, and six Eu2+ crystallographic sites, the critical distance is approximately 27 Å. Such a large RC means that self-quenching is not a very prominent mechanism for non-radiative relaxation in this crystal structure, partly explaining the excellent Φ:0.97Eu0.03EuB9O15 possesses an outstanding thermal response. As shown in Fig. –1) at 80 K to FWHM = 40.1 nm (2286.1 cm–1) at 500 K. This change can be attributed to increased electron–phonon line broadening at elevated temperatures associated with the excited state 5d orbitals of Eu2+5. More importantly, the emission spectrum at high temperature does not show any thermal quenching, which is the loss of luminescence with increasing temperature, even as the temperature approaches 500 K  of the excited state nuclear coordinates with respect to the ground state nuclear coordinates. If the Δr separating the potential energy surfaces is large, then the two potential energy surfaces can cross (interact), which supplies a mechanism for non-radiative relaxation via electron–phonon coupling13. Conversely, in systems where Δr is small, the potential energy surfaces do not interact and the relaxation process can proceed uninhibited, ideally by luminescence. Empirically the best approach for preventing a large Δr, as it relates to changes in bond lengths, might be to target rigid crystal structures54. However, recent research has showed that ΘD, as a proxy for rigidity, is not always predictive of thermal quenching56.The second non-radiative relaxation process occurs via electron–phonon coupling of the ground state and excited state potential energy surfacesr in a solid state material is to estimate the electron–phonon coupling by ascertaining a material’s Huang–Rhys factor S58. Experimentally, S can be extracted by measuring the FWHM of the rare-earth substituted phosphor’s emission peak as a function of temperature and fitting these data with Eq. kB is the Boltzmann constant60. A system that has strong electron–phonon coupling (large Δr) tends to have S > 5, whereas weak electron–phonon coupling  occurs when S < 1. Fitting the temperature-dependent luminescence data for NaBaB9O15:Eu2+  light (315 nm) light, while the optimal Eu2+ concentration produces a maximum Φ of 95%. Moreover, the FWHM of the emission is only 34.5 nm, making NaBaB9O15:Eu2+ a narrow violet-emitting phosphor. Temperature-dependent luminescent measurements indicate that this compound is also extremely thermally robust with minimal thermal quenching of up to 500 K due to the lack of non-radiative relaxation pathways. These experimental results support that machine learning is an indispensable tool necessary to direct the search for next generation of rare-earth substituted inorganic phosphors. Although the phosphor discovered in this work is not immediately applicable in current LED-based white lighting devices, it has great potential for use in other applications such as UV-excited laser lighting. Furthermore, the excellent thermal properties of this crystal structure suggest that it is an excellent platform to modify the excitation/emission peaks through chemical substitution. Shifting the optical properties to longer wavelength will make this material viable as a next-generation rare-earth substituted inorganic phosphor.In conclusion, the Debye temperature of 2071 potential phosphor hosts was predicted with the assistance of machine learning and correlated with their (PBE-level) DFT calculated band gaps. The construction of a sorting diagram based on these two intrinsic material properties is suitable to navigate vast phase space to identify classes of the next generation of inorganic phosphors. For example, borates are worth significant investigation due to their outstanding Debye temperatures and wide (PBE-level) band gaps. One specific borate highlighted by the sorting diagram is NaBaBΘD, the bulk modulus B and shear modulus G of 3248 compounds were obtained from the Material Project database as well as from our own calculations61. These values were then cross-referenced with PCD30 to ensure that all the compositions used for machine learning are experimentally reported, that is, not a predicted crystal structure. Additionally, only binary, ternary, and quaternary compositions were considered, and any compound containing group 18 elements, hydrogen, Tc, or Z > 83 (except for U and Th), were omitted. Finally, thin films, foils, or suspensions were excluded. These criteria reduced the number of elastic moduli in our final training dataset to 2610 compounds, including 1343 binary phases, 1229 ternary phases, and 38 quaternary phases. To distinguish between the polymorphs, the materials were labeled as “composition, space group number.”To develop the supervised machine-learning model for predicting ® (R2017a) environment62. The training set employed DFT calculated Debye temperatures obtained as described below. Our SVR applied a radial basis function as the kernel function and was optimized using venetian blinds cross-validation (CV) with 10-fold data splits. The compounds considered by the machine-learning algorithm were evaluated using a descriptor set of 34 distinct compositional variables along with four math expressions including the difference, average, and the largest and smallest values, as well as 14 crystal structure variables such as space group number, crystal system, and electron density, among others. The full descriptor set is provided in Supplementary Table x-vector data) were used to build the machine-learning training model, which was represented in a 2610 × 150 matrix that was normalized, mean-centered, and rescaled to the unit variance. Calculated Debye temperature, ΘD, was used as y-vector data (or dependent variable). This model used an optimized cost parameter (C) and gamma (γ) functions of 32 and 0.0032, respectively, where C regulates the tradeoff between minimization of error and maximization of the margins and γ is the kernel parameter controlling the influence of each support vector. This SVR model was then used to predict the Debye temperature of compounds contained within PCD.The machine-learning model was then constructed based on an SVR analysis using PLS_Toolbox (version 8.2.1) within the MATLAB9O1564. Therefore, NaBax1–EuxB9O15  was prepared via solid-state reactions starting from NaHCO3 , BaCO3 , H3BO3 , and Eu2O3 . The starting materials were loaded in the requisite stoichiometric ratios, thoroughly ground using an agate mortar and pestle, and subsequently sintered at 600 °C for 2 h in air to decompose the reagents and initiate the reaction. The samples were then ground and heated at 700 °C for 15 h, followed by a second grinding and heating at 750 °C for 5 h to obtain a phase pure product. These two heating steps were performed in alumina crucibles using a fused silica tube furnace under a reducing atmosphere (5% H2/95% N2) with heating and cooling ramps of 3 °C min–1. The products were finally ground in an agate mortar and pestle then sieved (<325 mesh) prior to characterization.One phosphor host of particular interest identified in PCD by machine learning is NaBaBλ = 1.54183 Å). Additionally, powder synchrotron X-ray diffraction data was collected on NaBaB9O15 at 295 K with a calibrated wavelength of 0.457667 Å 65. The crystal structure was refined based on the Rietveld method using the GSAS package with a shifted Chebyshev function employed to describe the background and a pseudo-Voigt function for determining peak shape67. The final crystal structure was visualized using VESTA68.The samples were all checked for phase purity using powder X-ray diffraction on a PanAnalytical X’Pert powder diffractometer equipped with Cu Kα radiation (0.97Eu0.03B9O15 and then pressed into a 13 mm pellet. The temperature was controlled using a Janis liquid nitrogen cryostat (VPF-100) and the emission spectra were collected from 80 to 500 K in 20 K increments using a λex = 340 nm. The absolute  photoluminescent quantum yield was determined by placing the samples encapsulated in the silicone resin inside a Spectralon-coated integrating sphere  and exciting at 315 nm69. The luminescence lifetime decay measurements were collected using a Horiba DeltaFlex Lifetime System equipped with a NanoLED N-330 nm LED (λex = 336 nm) and a 400 nm longpass filter. A total measurement length of 3.2 μs was employed using a repetition rate of 250 kHz and a delay of 10 ns.Steady-state photoluminescent spectra were collected at room temperature on a Photon Technology International fluorescence spectrophotometer with a 75 W xenon arc lamp for excitation. The samples were mixed into an optically transparent silicone resin  and deposited on a quartz substrate (Chemglass) for the room temperature measurements. Temperature-dependent measurements required the sample to be mixed with KBr in a 10:1 molar ratio of KBr:NaBaSupplementary InformationDescription of Additional Supplementary FilesSupplementary Data 1


Decades of catalysis research have created vast amounts of experimental data. Within these data, new insights into property-performance correlations are hidden. However, the incomplete nature and undefined structure of the data has so far prevented comprehensive knowledge extraction. We propose a meta-analysis method that identifies correlations between a catalyst’s physico-chemical properties and its performance in a particular reaction. The method unites literature data with textbook knowledge and statistical tools. Starting from a researcher’s chemical intuition, a hypothesis is formulated and tested against the data for statistical significance. Iterative hypothesis refinement yields simple, robust and interpretable chemical models. The derived insights can guide new fundamental research and the discovery of improved catalysts. We demonstrate and validate the method for the oxidative coupling of methane (OCM). The final model indicates that only well-performing catalysts provide under reaction conditions two independent functionalities, i.e. a thermodynamically stable carbonate and a thermally stable oxide support. The incomplete nature and undefined structure of the existing catalysis research data has prevented comprehensive knowledge extraction. Here, the authors report a novel meta-analysis method that identifies correlations between a catalyst’s physico-chemical properties and its performance in a particular reaction. Successful meta-analysis studies were reported in research fields where quantitative analysis of independently conducted experiments is prevalent, e.g., medical research2, genetics4, biology5, and economics6. Particularly in medical research, meta-analysis is used to aggregate individual studies aiming at the same treatment effect and employing the same research design . In this case, the main goal and benefit of meta-analysis is to obtain a more precise and robust effect estimate than any individual study can deliver.Meta-analysis7, CO-oxidation10, transesterification in biodiesel production11, and electro-catalytic oxidation of alcohols in direct alcohol fuel cells12. However, neither did these studies identify new structure–activity relationships nor could they provide simple chemical explanations for the observed statistical effects.Despite the existence of a vast amount of well-documented experiments also in heterogeneous catalysis, hardly any corresponding meta-analyses have been reported. Efforts to collect and analyze sets of literature data have been reported primarily for the water gas shift reaction (WGS)12), (2) statistical learning methods that search exploratively for relationships in the data, and (3) failure to incorporate existing chemical knowledge to inform and direct the statistical work. Another challenge faced in heterogeneous catalysis results (4) from the unsystematic heterogeneity of the available data. Each experimental report typically explores a narrow range of catalyst compositions and reaction conditions. However, the employed reaction conditions vary widely between different publications, which influences the catalytic performance via chemical kinetics, and makes a meta-analysis challenging.The shortcomings of these reports can be attributed, e.g., to (1) rather small datasets being used  information on catalyst composition, reaction conditions and catalyst performance. The study employed formal mathematical approaches  to search for correlations between catalyst composition and catalyst performance. The study concluded that some combinations of key elements contained in a catalyst can contribute to high C2 selectivity or yield, but did not result in a general model that correlates catalyst composition to catalytic performance with proven statistical significance and robustness. Unfortunately, a simple correlation between elemental composition and performance is also not likely to exist, since materials with the same nominal composition can often adopt very different structures and surface terminations that should result in different OCM performances. Hence, descriptors other than just elemental composition are needed.A significant break-through in terms of the dataset quality was reported by Zavyalova et al. in 2011We report a meta-analysis method that can identify statistically significant correlations between the physico-chemical properties assigned to a catalyst material and its performance in a given reaction. The method employs three distinct sources of information to achieve this goal. It incorporates in addition to (i) the experimental data reported in literature also (ii) general textbook knowledge about fundamental material properties and (iii) the experienced intuition of a chemist or material scientist about possible property–performance correlations. The OCM is used here as an example to illustrate the approach and derive property–performance correlations.The method is schematically outlined in Fig. The chemical hypothesis (iii) can now be translated into a set of formal sorting rules (4). These sorting rules express in a formal way, which descriptors are assumed to correlate with high catalytic performance. More precisely, a sorting rule states that a catalyst will be assigned to one specific property group (5) if the catalyst’s descriptors possess values within a defined range. Applying the rules to the extended dataset (3) divides the data into smaller subsets of so-called property groups (5). Then, the measured performance value of each catalyst is used to compute for each property group a density distribution of the performance indicator (6), its averaged value as well as a standard deviation. If the descriptors chosen in step 4 represent properties that are indeed relevant to the catalysts performance, then the performance distributions (6) should differ significantly between the corresponding property groups. However, these performance distributions do not account yet for the fact that each catalyst was measured at different reaction conditions.T) and the ratio of feed gases (here: pCH4/pO2). Moreover, it considers to which of two compared property groups a given catalyst had been assigned. The regression procedure adjusts all regression coefficients βi in order to minimize the deviation between experimental and computed yield values over all entries in the two groups. The computed regression results (8) quantify the influence of temperature (βT), pressure ratio (βCH4/O2), and most importantly, the effect of belonging to either one of the two compared catalyst groups (βgroup) on the catalysts performance (YC2). The results significance is judged via a t-test that calculates for each β-regression coefficient a corresponding p-value. Low p-values (p < 0.05) indicate a high statistical significance, with, e.g., p < 0.05 implying a confidence exceeding 95% that two compared catalyst groups are indeed distinctly different in their performance  is invoked that approximates the influence of, e.g., temperature ( results  quantifyIn step (9), the obtained models are compared to additional spectroscopic, computational and fundamental evidence from literature. An iterative refinement of hypotheses (iii), descriptors (3), sorting rules (4) and if possible also the studied data (2) results in robust and statistically significant property–performance models.2 coupling products  while avoiding total oxidation16. The OCM reaction is catalyzed by numerous materials with very diverse elemental compositions17. Economic viability of the process would require C2 yields well above the best values (ca. 30%) reported so far18. Despite decades of research, the reaction mechanism is not fully understood even for extensively studied catalyst such as Li/MgO and Mn-Na2WO4/SiO220. It is generally presumed that the reaction network involves gas-phase reactions coupled to reactions at the catalyst surface23, where surface defects facilitate C–H bond activation. Unfortunately, the required high reaction temperatures (500 to 1000 °C)20 obstruct many common in situ analytical tools. Hence, definite proof exists so far neither for the relevance of such defects under practical operation conditions nor the critical contribution of gas-phase reactions. Moreover, no generally valid correlation between a catalyst’s composition, its structure and its OCM performance has been established yet.The oxidative coupling of methane aims to convert methane and oxygen selectively into C13 after corrections and outlier removal from the data  and (c) numerical values that describe catalyst performance . Out of these categories, elemental composition, reaction temperature (T), reactant partial pressure  ratio (pCH4/pO2) and C2 yield (YC2) were evaluated. Figure YC2 as a function of (a) reaction temperature, (b) pCH4/pO2, and (c) contact time to illustrate the covered data range and the data heterogeneity. , the physico-chemical criteria related to hypothesis (1) divide the contained catalysts into two subgroups . The subsequently applied hypotheses (2), (3), and (4) divide these subgroups further, resulting in 10 terminal subgroups 1a, 4a…4h, and 2d. For each terminal subgroup, the respective five most frequent catalyst compositions are listed in Fig. 2 yield.Numerous hypotheses were tested. The derived best model employs four different hypotheses to divide the OCM dataset into a total of 18 different property groups as illustrated by the tree-like representation shown in Fig. ses (2), , and (4)2 yield distribution within the group along with the mean C2 yield  and its standard deviation. The horizontal arrows that connect two respective boxes represent the performed statistical tests. Figure C2,corr) for each terminal group. All observed p-values are lower than 0.005, which underlines the extremely high statistical significance of the derived final model.Figure Hypothesis 1—ability to form at least one carbonate compound: An initial assessment of the dataset gave the impression that many OCM catalysts contain components that can form a carbonate. Hypothesis 1 therefore proposes that a good OCM catalyst contains at least one chemical element that is known to form a carbonate compound.n = 38) is not able to form any carbonate, whereas the vast majority of reported catalysts can form at least one carbonate (1b: n = 1764)  than catalysts in group 1a . The difference in C2 yield computed via multiple regression analysis  proves to be statistically highly significant on a >99.5 % confidence level (p < 0.005). Also the regression coefficients obtained for temperature  and pressure ratio pCH4/pO2  show high statistical significance with higher C2 yields corresponding to higher temperatures and higher oxygen partial pressures  show on average a 7.6 % higher yield of C2WO4/SiO2 system  states that among all the oxides that can possibly be formed by a catalyst’s cations, at least one oxide is present that possesses a Tammann temperature higher than the individual temperature at which the catalyst was tested in OCM. An additional criterion (ii) imposes that the mass content of this stable oxide amounts to at least 50 wt% of the catalyst’s constituents, assuming that they are present in the form of their respective most stable oxides. An additional criterion (iii) used for the group assignment is the presence of an element other than the designated support oxide, and its ability to form a carbonate.n = 197) if none of a catalyst’s components fulfilled both support criteria (i) and (ii)  represents all catalysts where one component fulfils both support criteria , and where an additional cation is present that is able to form a carbonate. Catalysts were assigned to group 2c “self supported” (n = 263) when a catalyst contained only one component, and if this component satisfied both support criteria AND could form a carbonate. All remaining catalysts were assigned to group 2d “not assigned” (n = 47) for further noise reduction.A catalyst was assigned to group 2a “unsupported” (ii) Fig. . Group 22 yields  than catalysts in the group 2a “unsupported”  and group 2c “self-supported” . The differences are statistically highly significant.Catalysts in group 2b “supported” showed higher Cn = 1257) and contains most of the classical OCM catalysts . Most group entries consist of a binary combination of La or alkali metals with an alkaline earth element . Typically, the support criteria are satisfied by the thermally stable oxide of the alkaline earth element. Many of the cation combinations that include heavy metals  and alkali elements  are assigned to group 2a “unsupported” because their respective (super)oxides fail the thermal stability criterion (i), or because the stable oxide is not present in sufficiently large amounts (ii). The “self-supported” catalysts 2c contain only a single cation, which is either a lanthanide or an alkaline earth element, and forms a thermally stable oxide. The 47 catalysts placed in group 2d “not assigned” comprise mostly binary combinations that contain a large amount of a stable support oxide, but fail criterion (iii) because the second element (that is not the designated support) cannot form a carbonate.The best-performing group (2b “supported”) features the highest number of catalyst entries , all other catalysts to group 3b “oxide-supported” (n = 322). Most of the “carbonate supported” catalysts consist of La or an alkali element combined with an alkaline earth element where typically the alkaline earth elements provide the support functionality. The “oxide-supported” catalysts (the designated support oxide cannot form a carbonate) comprise mostly alkali and alkaline earth elements or Na2WO4 supported on either alumina, silica or titania  clearly outperform the oxide-supported group 3b (8.6%) by about 2.9% C2 yield (βgroup = -3.30) and with high statistical significance (p = 0.000), providing further evidence for the beneficial and important role of carbonates in OCM catalysis.The carbonate-supported catalysts , 2.36% (4c/4d), and 5.11% (4e/4f) . It divides the groups 2a, 3a, 3b, and 2c into the respective subgroups 4a, c, e, g , and subgroups 4b, d, f, h   were assigned to different groups on level 3 , both end up in the respective subgroups that can form at least one t.d. stable carbonate . In general, the role of the thermodynamically most stable carbonate is typically fulfilled by alkaline, alkaline earth, or lanthanide elements in the subgroups 4b/d/f/h. In absence of these elements no thermodynamically stable carbonate can be formed and lower yields are observed  and with a so-called “robust regression” (see Supplementary Notes 14–18 for details). The model retained the same statistically significant correlations, except for few instances where some correlations on level 4 lost their statistical significance. The final model is therefore highly robust despite the data heterogeneity, potential publication bias within the data and the small size of some of the formed terminal groups.The robustness of the final model Figs.  and 4 wa2 yields. The model predicts the highest C2 yield  when (1b) at least one of the elements contained in the catalyst can form a carbonate, (2b) the catalyst contains an additional element that forms a thermally stable oxide, (3a) this oxide is also able to form a carbonate, and (4d) at least one of the possible carbonates is thermodynamically stable at the applied OCM reaction temperature. Also a comparison of the best-performing terminal group 4d with each other terminal group  in terms of yield difference (βgroup) and p-value shows a very high statistical significance (p < 0.005).The derived model reveals clear property–performance correlations. It establishes for the first time a generalized set of physico-chemical properties that discriminate between high- and low-performing OCM catalysts. Four simple hypotheses suffice to divide 1802 catalysts into 10 groups of distinct properties and OCM performance Fig. . Followi24 is one out of several possible descriptors for basicity . Basicity has been proposed by many authors as an important feature of OCM catalysts31. However, no general quantitative model for the impact of basicity on OCM performance has been established so far.The nature of the hypothesis formulation in terms of chemical conditions facilitates a direct physico-chemical interpretation. Good OCM catalysts comprise at least two elements, with one of the elements being able to form a carbonate at the temperatures of OCM reaction, and a second element that can form a thermally stable (non-sintering) oxide under OCM conditions (hypothesis 2). Good OCM catalysts thus provide two functionalities, i.e., a “support” and an “active phase”. The thermally stable oxide  acts as support and provides a high surface area during OCM (2b). The active phase appears to be related to the ability to form a carbonate. The ability to from a carbonate2 yields (hypothesis 4). Hence, the actual presence of carbonates during OCM is likely. Carbonates could therefore contribute to the reaction, i.e., via ongoing transitions from carbonate into oxide and vice versa, which would continuously produce new defect sites32. However, the presence of carbonate phases can assist also the formation and stabilization of peroxide species36. Such peroxides species could activate methane in a selective fashion to generate methyl radicals37. Otsuka et al.39 reacted CH4 with bulk peroxides  and observed C2 coupling products already at 400 °C.The ability to retain a stable carbonate at the studied OCM temperature results in higher C2 yields benefit also from the ability of the support oxide to form a carbonate (3a “carbonate-supported”). Possibly, carbonate formation suppresses unselective combustion of methane and C2 hydrocarbons, which was reported to occur on oxide-supports .C2. Carbon dioxide was so far typically regarded only as an undesired byproduct. However, the only way that carbonates can form during OCM is a reaction with CO2. Hence, CO2 could be essentially required to stabilize carbonate phases that contribute directly to C2 formation or prevent further oxidation of C2 products. This could provide also a new explanation of the observation that a maximum of ca. 30% C2 yield has not been overcome so far when feeding CH4/O2 mixtures to the reactor17. Methane combustion would be essentially required to form CO2 and the carbonate phase, thus limiting the achievable C2 yield. Supplying the required CO2 to the catalyst via CO2 co-feed instead of methane combustion could provide a simple path to improved C2 yields.The essential role of carbonates in the model provides a clear incentive to rethink the classical OCM reaction mechanism and in particular the role of CO2 was experimentally verified. The stability of a carbonate depends on both temperature and CO2 partial pressure. Increasing the CO2 partial pressure should increase the carbonate’s stability, which, according to the model, should increase the C2 yield. We tested this effect experimentally using nine different catalysts belonging to group 3b  or remain constant. For the alumina support alone, which cannot form a carbonate, CO2 addition does not have a measurable impact. The experimental data further support the model interpretation that carbonates are likely to be formed during OCM and result in higher C2 yields.The influence of CO2 yield. What sets the presented meta-analysis apart from previous work is that chemical knowledge and chemical reasoning become an integral part of the analysis, i.e., a chemical instead of mathematical perspective.The following paragraphs discuss the power of the developed meta-analysis method as well as current limitations. The exemplarily performed evaluation of 1802 observations in OCM catalysis provides a clear picture of physico-chemical properties that have a statistically significant impact on the observed C2 yield distributions becoming narrower with each model level. Yet, a considerable variety of C2 yields remains within each property group. This could be improved by further refined hypotheses, additional property descriptors, or more complicated combinations/interactions of the catalyst constituents.The method yields a robust and meaningful model, with CA substantial contribution to the broadness of the distribution results from the variance in the underlying data , or following schemes suggested by Rothenberg and co-workers64.One major advantage of our approach is the combination of experimental data with sound chemical textbook knowledge. Thus, hypotheses with a high level of abstraction can be formulated. Pioneering work of, e.g., Schueth66, depositing complete sets of original data in open repositories and using data formats designed for facile data sharing67.In general, statistical tools can explore only correlations between variables that are quantitatively accessible. Quantity, quality, and distribution of literature data could be improved by adopting standardized testing and benchmarking procedures for a particular reaction2 formation and/or prevent subsequent unselective oxidation of the C2 products. Future work could assess the specific role of CO2 and carbonates in OCM using, e.g., in-situ spectroscopic experiments or quantum-chemical calculations. In a broader context, the developed meta-analysis method provides a generic and open platform for data science in heterogeneous catalysis. The concept allows the extensions to other reactions, more complex and fundamental descriptors derived, e.g., from quantum chemistry, and ultimately also the incorporation of a catalyst’s structure. Consequently, it could empower all chemists to work as data scientists and explore the full potential of their valuable experimental data.The developed meta-analysis method allows the identification of catalytic property–performance correlations hidden in the vast body of existing experimental research. Applying the method to the OCM, we identify general correlations between a material’s physico-chemical properties and its OCM performance. Good catalysts comprise at least two elements, with one element being able to form a thermodynamically stable carbonate at the temperatures of OCM reaction, and a second element forming a thermally stable (non-sintering) oxide under OCM conditions. Good catalysts apparently require a support that provides a high surface area at OCM temperatures, and carbonate(s) that either contribute directly to C13 was corrected for errors  based on a comparison with the original literature. Some entries were removed that contained highly unusual feed compositions and contact times, lacked essential information  or were not measured in continuous-flow with methane and oxygen co-feed. Moreover, we removed the predefined data categories “promotor” and “support”, to which Zavyalova et al.13 had assigned some elements, and reassigned the respective elements to the more general categories “cation” and “anion” . Moreover, properties of potentially formed oxides were incorporated . From this melting point, the Tammann temperatureTOCM measurement < Tcarbonate decomposition + 100 K). A “true” value is assigned to the respective support descriptors (iii) if the catalyst contains a cation that can form a thermally stable oxide, i.e., an oxide that possesses a Tammann temperature  higher than the actual temperature at which the OCM data were measured for the catalyst, and if the concentration of this oxide amounted to at least 50 wt% of the catalysts constituents, each in the form of its most stable oxide. The descriptor rules take the reaction temperature explicitly into account for each catalyst, hence the same descriptor can adopt different values depending on the actual conditions under which a catalyst was measured. Supplementary Note The physico-chemical descriptors were computed by a set of instructions that combine values extracted from the OCM catalyst table as well as the elemental-property table. The descriptor values were written into new columns  of an extended data file. Important descriptor categories employed in the present study are the ability of each catalyst component  (i) to form a carbonate compound, (ii) the thermal stability of this carbonate, and (iii) the ability to form a sufficiently stable oxide that could act as catalyst support. A value “true” (“1”) is assigned to a carbonate descriptor (i) if the respective catalyst component is able to form a carbonate. Descriptor (ii) describes whether this carbonate is stable under OCM reaction conditions. A value “true” is assigned if the OCM reaction is measured at a temperature that is lower than the actual temperature at which the carbonate starts to decompose, corrected for an offset that accounts for experimental uncertainties  contain at least one element that can form a carbonate (“can form carbonate”), that (2) contain at least one additional element that fulfils the proposed support criterion of a stable and abundant oxide (“supported”), evaluate (3) whether the element that has been assigned the support function is also able to form a carbonate (“carbonate-supported”), and probe 4) whether the carbonate with the highest decomposition temperature is thermodynamically stable under the respective OCM conditions. Thus, very complex and hierarchically nested hypotheses can be formulated. Supplementary Note  whether 2 products. However, it is obvious from chemical kinetics that the measured C2 yield is critically influenced not only by a catalyst’s composition, but also the reaction conditions  employed in a catalytic test. Due to the lack of standardized OCM test protocols, employed operation conditions vary significantly between different literature reports. Unfortunately, the limited amount of catalytic data available in the studied dataset did not allow a complete kinetic description for each catalyst. In order to mitigate this problem to some extent, the regression equation  and computed yield values over all entries in the two groups. The derived β values quantify the influence of temperature (βT), pressure ratio (βCH4/O2), and most importantly, the effect of belonging to either one of the two compared catalyst groups (βgroup) on YC2. Hence, βgroup is the obtained quantitative measure (in terms of corrected C2 yield) for the influence of a set of physico-chemical properties on the catalytic performance in OCM.A multiple regression analysis was employed in order to quantify the performance difference between catalysts assigned to two different property groups while compensating also for the effect of differences in the OCM measurement conditions. OCM catalysts are often compared based on the obtained yield of Cequation  implemenβ regression coefficient was judged via a t-test. The t-test relates the value of a β regression coefficient to its estimated standard error. From this, a probability value p is calculated for each β regression coefficient. It gives the significance of the observed effect by the probability that an estimated β value is decided to be non-zero, whereas the true value is zero. Lower p-values correspond to a lower probability of erroneous assignment of an effect, and thereby a high statistical significance of the observed effect. A p-value < 0.05 corresponding to a confidence of 95% is typically used as indicator of statistical significance. The p-values p = 0.000  obtained for most of the hypotheses of our OCM example corresponds to a confidence exceeding 99.95% that two compared catalyst groups are indeed distinctly different in their C2 yield. Supplementary Note β values, p-values, and property distributions.The statistical significance of information derived from each YC2.The estimation strategy evaluates four different property–performance hypotheses labeled 1, 2, 3, 4) that divide the initial OCM data successively into smaller subgroups . All individual hypotheses are then assembled into one overall property–performance model  as independent variable instead of YC2, , the effective (corrected) difference in C2 yield  between two compared groups along with the p-value corresponding to the regression coefficients (three significant digits). Moreover, the arithmetic mean of uncorrected C2 yield (2) and corrected (corr) are reported along with the corresponding standard deviation. The presented diagrams display for each subgroup the density of yield observations vs. the uncorrected C2 yields , which were ground, sieved to a size fraction of 200–500 µm, and calcined for 12 h at 800 °C in air. The support was then loaded via wet impregnation with aqueous solutions  and dried at 60 and 150 °C under vacuum, i.e., following a procedure adapted from Kusche et al.69 Catalyst loadings amounted to 23.1 wt% of the employed salt in anhydrous state .Catalytic tests were performed to validate the main findings. Alumina-supported catalysts containing similar loadings of the precursor of either one alkali element  or one alkaline earth element  were prepared via impregnation of the corresponding carbonate or acetate onto the same pre-calcined alumina support. The employed γ-Al14. OCM testing was performed with two different feed compositions, i.e., CH4/O2/N2 (26.2:14.8:59.0) and CH4/O2/N2/CO2 (26.2:14.8:3.0:56.0), using fresh catalysts for each run and a flow rate of 14.7 Nml/min per reactor channel.OCM catalytic tests were performed in a parallel fixed bed reactor featuring 48 quartz tube reactors with 4 mm inner diameter. Each tube carried 50 mg catalyst powder 300 mg of pre-calcined SiC granules placed upstream to ensure efficient feed preheating. Catalytic performance was measured in 25 K intervals  up to 850 °C, holding each temperature to analyze product composition via GCSupplementary InformationDescription of Additional Supplementary FilesSupplementary Data 1Supplementary Data 2Supplementary Data 3Supplementary Data 4Supplementary Data 5