It is still a great challenge to seek efficient visible light photocatalyst to realize overall water splitting. In this work, the tetragonal zircon BiVO4 is prepared by epitaxial growth on FTO substrate and its overall water splitting reaction is studied. Under the influence of epitaxial strain, the conduction band position shifts negatively and beyond H+/H2 reduction potential (0 V vs NHE), which enables it to possess the photocatalytic hydrogen evolution activity. After loading cocatalysts, the overall water splitting (λ > 400 nm) is realized , and the value of solar hydrogen conversion efficiency is 0.012%. The single‐particle photoluminescence (PL) spectra and PL decay kinetics tests demonstrate the cocatalysts are beneficial to the separation and transfer of carriers. The new strategy of adjusting the band structure by strain is provided.Overall water splitting to generate H 4 grown on FTO substrate can across the H+/H2 reduction potential (0 V vs NHE), achieving overall water splitting under visible light. This work provides a new strategy of adjusting the band structure by strain for performing photocatalytic overall water splitting on BiVO4.Under the influence of epitaxial strain, the conduction band position of tetragonal zircon BiVO Recently, Domen's group used Al‐doped SrTiO3 to achieve a 96% external quantum efficiency of ultraviolet light from 350 to 360 nm, which led the development of photocatalysis, and ignited the hope of light‐driven water splitting. Although recent research on overall water splitting makes great progress, developing the efficient photocatalysts which have suitable band structure, visible light response, and high charge separation efficiency is still a great challenge.In recent years, solar‐driven water splitting to produce clean hydrogen has been considered as a promising approach to solve energy and environmental issues. Since Honda and Fujishima used TiOhotspots.8, 94 as a chemically stable and visible‐light responsive photocatalyst have drawn much attention. It has three main crystal structures containing monoclinic scheelite (s‐m), tetragonal zircon (z‐t), and tetragonal scheelite (s‐t). Although the z‐t BiVO4 shows lower oxygen evolution activity than s‐m BiVO4, it does not prevent scientists from further exploring it. Our group has previously reported that z‐t BiVO4 can be used as photocathode to construct a bias‐free PEC cell. In addition, no matter which crystal phase of BiVO4, as the conduction band minimum (CBM) is more positive than H+/H2 reduction potential, it has basic limitation of releasing H2. The current research on BiVO4 overall water splitting is mainly focused on constructing Z‐scheme systems and phase transition‐induced band edge engineering. However, overall water splitting on pure z‐t BiVO4 still has not come true.BiVOPEC cell.14 In  Zheng et al. have reported the textured substrate accumulating strain locally greatly enhances the light absorption and surface reaction of the BiVO4 photoanode, reducing the total amount of light absorber required. Minseok Choi theoretically reported the tensile strain makes the CBM energy in s‐m BiVO4 very close to H+/H2 level, while the CBM energy in z‐t BiVO4 shifts upward or even higher than this level. However, there is still lack of general understanding of how epitaxial strain experimentally affects photocatalytic property of BiVO4. Here, we take z‐t BiVO4 as the research object, using unstrained BiVO4 powder and epitaxially strained BiVO4 to study the effect of strain on the band structure and overall water splitting.As we all know, the different lattice parameters of substrate and epitaxial layer may cause lattice mismatch, which leads to epitaxial growth with strain accumulation. The mismatch strain at interface will adjust its physical and chemical properties.21 Zhe22.14 grows on another crystalline material, due to the different lattice parameters of two materials, strain will generate during the growth process. Specifically, when epitaxially growing on a substrate with larger lattice parameters, the BiVO4 unit cell (a = b = 0.730 nm) will suffer in‐plane tensile strain. The greater the lattice mismatch is, the larger the in‐plane tensile strain, leading to the change of each BiVO4 unit cell's lattice parameters (a = b). Based on the density functional theory (DFT), the influence of tensile strain on energy band structure of tetragonal BiVO4 is calculated. As shown in Figure4 undergoes a certain degree of negative shift, in which the valence band (VB) moves to a small extent  is chosen as a substrate  and a slightly twisted BiO8 dodecahedron . To make convenience for characterization and testing, the BiVO4 film grown on FTO substrate is scraped for collection, which is denoted as BiVO4‐FTO sample. In contrast, the naturally nucleated BiVO4 is prepared by coprecipitation method, hereinafter referred to BiVO4 powder. As shown in Figure 4 . Due to the same symmetry with the [101] direction of SnO2, the epitaxially grown BiVO4 shows strong crystallinity along the [101] orientation. The Raman and X‐ray photoelectron spectroscopy (XPS) spectra further show the z‐t BiVO4 is synthesized  of BiVO4  spectra , and EVB is more positive than H2O to O2 oxidation potential (1.23 V vs NHE), indicating the BiVO4‐FTO sample has the possibility of photocatalytic overall water splitting. The specific calculation process and band position analysis of BiVO4 powder were depicted in the DRS and UPS spectra in Figure 4‐FTO sample and BiVO4 powder at the edge of energy bands. The band arrangement of BiVO4 explains why the BiVO4‐FTO sample and BiVO4 powder exhibit significantly different photocatalytic activities.When BiVO (a = b).24 Bas4 Figure , the ban According to the material parameters , all the diffraction peaks of BiVO4‐FTO film and BiVO4‐FTO sample as well as BiVO4 powder are consistent with the Bragg position  of tetragonal zircon BiVO4 with space group I41/amd (PDF: 14‐133). It is worth noting that compared with the naturally nucleated BiVO4 powder, the main peak of BiVO4‐FTO sample shifts toward lower angle , the BiVO4‐FTO film and BiVO4‐FTO sample collected from the substrate have the same in‐plane lattice parameters (a = b = 7.3044 ≈ 7.3047 Å), which is larger than that of naturally nucleated BiVO4 powder.X‐ray diffraction method was used to prove the existence of residual strain. The residual stress can be calculated from the strain which is measured by XRD diffraction.30 Acce Figure , which cFigure4‐FTO. As shown in Figure 4 film grows on the surface of FTO, which can completely bridge the gap at the interface. Figure 4 growth layer, and the contact interface is the region where a large number of lattice distortion occur. Therefore, the FIB‐HRTEM image in Figure 4 and (101) plane of SnO2. Due to the incomplete matching of the interplanar spacing between SnO2 and BiVO4 in the [101] direction, BiVO4 bears strain from interface and shows deformation near the contact interface between them. The BiVO4 sample growing on FTO substrate was carefully scraped off and analyzed by HRTEM. After fast Fourier transform, it is found that there are still lattice distortions in the region near the FTO substrate (white square in the inset), which is consistent with the refined XRD results, indicating the interface strain exist between substrate and film during epitaxial growth progress  and (200) planes of tetragonal BiVO4, and the included angle of 48.5° is consistent with the theoretical value of the angle between (101) and (200) planes. In contrast, according to the XRD  to metals. Due to the metal  particles are small in Figure 4‐FTO photocatalyst loaded with Ag or Rh are provided in Figure x, PbO2) are selectively deposited on the (200) planes under light irradiation where photogenerated holes accumulate and oxidize metal ions  to metal oxides. The relative position of energy levels of different crystal planes can be evaluated by the density functional theory (DFT) calculation. According to the results in Figure 4 shows the higher CBM and valence band maximum (VBM) position, and the VBM of (101) crystal plane is closer to the CBM of (200) crystal plane. This relative energy level position has a positive effect on the formation Z‐type arrangement. Reasonably, the SEM results of photodeposition can be further explained by the electron flow pattern in Figure The scanning electron microscope (SEM) image of BiVOM Figure . The cryD Figure  and SEM 2.22 production, the photocatalytic activities of tetragonal BiVO4 with and without epitaxial strain were tested under visible light irradiation (λ > 400 nm). As indicated in Figure 4 powder cannot release H2, while bare BiVO4‐FTO sample releases small amount of H2. Therefore, to ensure the reaction gas release smoothly, the dual cocatalysts Rh/Cr2O3 and MnOx were loaded by photodeposition method. The loading of cocatalysts is proved by SEM, XPS, and EDS analysis  and oxygen evolution (OER) in the presence of sacrificial agents have been operated , the simultaneous release of hydrogen and oxygen is achieved on BiVO4‐FTO sample with cocatalysts, and the solar hydrogen conversion efficiency (STH) is 0.012%. Other single‐step overall water splitting photocatalysts are shown in Table 4‐FTO sample still retains the crystal structure  of BiVO4‐FTO sample is depicted in Figure 16O2 and 18O2. As shown in Figure 16O2 and 16O2 from H216O are earlier than that of 18O2 from H218O. GC‐MS analysis , while the main product with H218O as the oxygen source is 18O2 (m/z = 36). Therefore, it is clear that the photocatalytic reaction product originates from the H2O splitting. To verify the effect of the crystal planes on photocatalytic hydrogen production, strong alkali was used to treat BiVO4‐FTO film. It can be seen from Figure 4‐FTO retain the crystal structure and chemical composition basically but the original smooth crystal planes are corroded  is higher than those of BiVO4‐FTO (pH = 1.6) and BiVO4‐FTO (pH = 3), indicating that the properly exposed redox crystal facets are beneficial to the photocatalytic water splitting reaction. Surface photovoltage (SPV) measurements  + a2·exp(τ/τ2) + a3·exp(τ/τ3)) shown in Figure 4‐FTO sample with cocatalysts (≈4.910 ± 0.022 ns) is shorter than that of BiVO4‐FTO sample (≈5.490 ± 0.069 ns), demonstrating the carriers are separated and transferred more quickly after loading cocatalysts. The schematic diagram of photocatalytic overall water splitting on tetragonal zircon BiVO4 loaded with cocatalysts is shown in Figure 4, which then migrate to the H2‐evolution cocatalyst Rh/Cr2O3 and O2‐evolution cocatalyst MnOx to participate the surface redox reaction, respectively. This spatially separated structure is beneficial to inhibit the recombination of photogenerated carriers and promote photocatalytic overall water splitting reaction.Here, the single‐particle photoluminescence (PL) spectra and PL decay kinetics tests were used to explore the role of cocatalysts in photocatalytic overall water splitting reaction. Compared with the ordinary photoluminescence spectra, the single particle photoluminescence has less noise and interference from other molecules or particles, so the role of cocatalyst can be studied from the perspective of single particle. PL images of single BiVO34 on FTO substrate was prepared and overall water splitting under visible light irradiation was evaluated. The BiVO4 grown on substrate has better catalytic performance than the naturally nucleated BiVO4. By introducing strain, the energy band position could be effectively adjusted, so that conduction band position shifts up and exceeds the hydrogen evolution potential. The common exposure of oxidizing crystal planes and reducing crystal planes increase the separation efficiency of photogenerated carriers and promote photocatalytic reaction. Considering the s‐m BiVO4 has better light absorption and oxygen generation kinetics, the works on monoclinic BiVO4 and other substrate are in procedure. The new initiative is put forward to adjust the band structure of photocatalyst for overall water splitting under visible light irradiation.In summary, tetragonal BiVO44‐FTO film was grown by hydrothermal method. Typically, the precursor Bi (NO3)3·5 H2O (1 mmol) was dissolved in HNO3 solution , and C10H14N2Na2O8 (1 mmol) was added and stirred for 30 min to obtain solution A. At the same time, NH4VO3 (1 mmol) was dissolved in NaOH solution , and then C10H14N2Na2O8 (1 mmol) was added and stirred for 30 min to obtain solution B. Then A solution was slowly poured into the B solution and the solution became a clear yellow solution. After adjusting the pH to 2, continue to stir the solution for another 30 min and transfer to 100 mL Teflon‐lined autoclave. The FTO glass was sonicated sequentially in acetone, ethanol, and isopropanol for 30 min. Then, put the cleaned FTO glass (3 cm × 4 cm) into 100 mL Teflon‐lined autoclave at an angle, with the conductive surface facing down. After sealing the autoclave, the hydrothermal reaction was carried out at 160 °C for 12 h. The autoclave was naturally cooled to room temperature, and then the FTO glass was taken out, rinsed with deionized water several times, and dried at room temperature. The obtained product was called BiVO4‐FTO film. To make the test convenience, the scraped sample was called BiVO4‐FTO sample.All chemicals are of analytical grade and do not require further purification when used. The BiVO4‐FTO film was immersed in an aqueous solution containing 0.2 × 10−3m KIO3 (100 mL), 0.1 × 10−3m Mn (NO3)2 for MnOx deposition, and 0.1 × 10−3m Pb (NO3)2 for PbO2 deposition, respectively. The reaction system was irradiated under a 300 W Xe lamp (full arc) for 10 min. After irradiation, the BiVO4‐FTO film was washed with deionized water and ethanol and dried. For photoreduction deposition, the steps were almost the same, except that the deposition aqueous solution was composed of 10% (volume ratio) methanol, 0.1 × 10−3m AgNO3 for Ag deposition and 2 mg mL–1 RhCl3·3H2O for Rh deposition, respectively.To perform photooxidation deposition, the BiVO4 powder was synthesized by coprecipitation method. Typically, Bi (NO3)3·5H2O (2 mmol) and NH4VO3 (2 mmol) were simultaneously dissolved in 60 mL of deionized water and stirred vigorously for 2 h. The reaction product was filtered, washed with deionized water and ethanol, and dried in an oven at 100 °C for 5 h. The obtained product was called BiVO4 powder.BiVO The ion–electron interactions were described by projector augmented wave (PAW) method. The generalized gradient approximation (GGA) in the Perdew–Burke–Ernzerh (PBE) with a cutoff energy of 500 eV for exchange–correlation interactions were adopted. A Monkhorst–Pack 7 × 7 × 1 k‐point grid was adopted for all the calculations. The convergence criteria for the force and energy were set to be 0.01 eV Å−1 and 10−4 eV with a vacuum space larger than 20 Å in the z‐direction to avoid interactions between periodic units during the structure relaxation. The magnitude of strain is described by a/a0, here a0 and a denote the lattice parameters of the unstrained and strained systems, respectively. As a result, 10% in‐plane tensile strain is applied to (101) plane of BiVO4.All the calculations were performed by using the Vienna Ab Initio Simulation Package (VASP).38 Theα radiation to reveal the crystal structure. Morphologies were investigated by SEM (Hitachi S‐4800) equipped with an EDS. The UV–vis DRS analyses were recorded by Shimadzu UV‐2550 spectrophotometer using BaSO4 as reflectance standard to explore the optical absorption. The TEM and HRTEM tests were performed with a JEOL JEM‐2100F microscope to analyze the nanostructure and composition of the as‐prepared BiVO4 photocatalyst. The cross‐sectional FIB‐HRTEM samples were analyzed by focused ion beam (FIB) technology. UPS measurements of the as‐prepared samples were performed with He I (21.2 eV) as monochromatic light source and a total instrumental energy resolution of 100 meV. XPS measurements were carried out on a Thermo ESCALAB 250XI spectrometer with a monochromatic Al‐Kα source to explore the element composition and valence states on the surface, and the binding energies were calibrated by the C 1s peak (284.8 eV). Raman spectra were measured on LabRAM HR800 with laser excitation of 532 nm. The reaction liquid used for gas measurement was analyzed by ICP‐OES/AES: Varian (720‐ES). The amounts of H2 and O2 evolution were analyzed using gas chromatography (GC‐7920) equipped with a thermal conductivity detector (Ar as carrier gas). Single particle fluorescence and fluorescence decay measurements were carried out on a confocal microscope instrument. A 375 nm continuous wave (CW) laser was used to excite the interband transition of BiVO4 and pulse frequency was 5 MHz. To detect the source of oxygen, GCMS‐QP2010 was used to detect oxygen isotope. The software used for XRD data refinement is TOPAS academic.XRD patterns were conducted on a Bruker AXS D8 diffractometer equipped with Cu K4‐FTO film is 12 cm2, on which the mass is estimated to be ≈5 mg. Generally, 10 mg photocatalyst was immersed in 100 mL of reaction solution. The photocatalytic HER, OER, and overall water splitting reaction were carried out in 0.02 × 10−3m H2O2, 0.02 m AgNO3 and pure water, respectively. The theoretical loading amounts were 2, 2, and 0.5 wt% for Rh, Cr, and MnOx. For the overall water splitting reaction, after the catalyst was ultrasonically dissolved, the cocatalyst precursor was sequentially added to the reaction solution to carry out the photodeposition reaction. First, a specific amount of RhCl3·3H2O solution (2 mg mL−1) was added to the reaction system, and irradiated for 10 min. Subsequently, the K2CrO4 (2 mg mL−1) and Mn(NO3)2 (0.1 × 10−3m) solution were added to the suspension and irradiated for another 5 min, respectively. The system was evacuated for 30 min to ensure complete removal of air, and then illuminated from the top surface with a 300 W Xe lamp  equipped with a 400 nm cut‐off filter (λ > 400 nm). A cooling water stream was used to maintain the reaction suspension at 288 K. The separated gas was analyzed by gas chromatography . The photocatalytic stability test was performed every 4 h as a cycle. After each independent cycle, the photocatalyst was recycled by centrifugation and redispersed in new solution. The wavelength dependence of the AQE was tested under the same photocatalytic reaction conditions, through the 365, 420, 450, 500, 530, or 700 nm bandpass filters and the masked area of 1 cm2. The photon flux of the incident light was determined using a PL‐MW2000 spectrophotometer . The AQE was calculated from the ratio of the number of electrons reacted to the number of incident photons during the water splitting process. The calculation formula isThe photocatalytic reactions were carried out in a Pyrex reaction cell connected to a closed gas circulation and evacuation system. Typically, the area of the BiVO2 irradiation area). The calculation formula isThe STH efficiency was measured under simulated sunlight (AM 1.5G, 1 cmThe authors declare no conflict of interest.Supporting InformationClick here for additional data file.Supporting InformationClick here for additional data file.


EQ‐5D is a 5‐item questionnaire instrument designed to measure health‐related quality of life. It is extremely important, since it is used to measure health benefits in many studies providing evidence for reimbursement decisions by the National Institute for Health and Care Excellence in England and similar policy bodies in other countries. EQ‐5D has been redesigned in a more detailed form (EQ‐5D‐5L), but much existing cost‐effectiveness evidence is based on the older version (EQ‐5D‐3L). Statistical mapping from one version to another is widely used, exploiting data from multi‐instrument surveys incorporating both variants. However, little is known about the robustness of data from such multi‐instrument surveys. We design a randomized experiment to investigate whether inclusion of both versions at different stages in a single interview gives a reliable picture of the relationship between health measures from the two instruments and embed it in individual interviews from the UK Understanding Society household panel. We find that sequencing of the two versions of EQ‐5D within an interview has a significant impact not only on the resulting data but also on the estimated mapping models. We illustrate the non‐negligible effects in two real‐world cost‐effectiveness examples and discuss the implications for future multi‐instrument survey design. The original EQ‐5D, now known as EQ‐5D‐3L (shortened to 3L henceforth), allows individuals to describe their degree of health impairment using three levels of severity (no problems/some problems/extreme problems). Altogether, 243 different health states can be described in this way. Dolan  estimateEQ‐5D has been redesigned —as the vehicle for our experiment.In this study, we investigate the reliability of the MI survey design by developing and analyzing data from a randomized experiment designed to investigate whether inclusion of both versions of EQ‐5D at different stages in a single interview gives a reliable picture of the relationship between health measures based on the two instruments. We used the 22.1Our experiment was carried in wave 11 of the UKHLS Innovation Panel, with fieldwork conducted in June to September 2018.5L3L, 3L5L and 5Lonly. The two variants of EQ‐5D were separated by numerous survey questions, with a wide range of topics and response options. Not all respondents answered exactly the same questions, as some are context specific .Our experimental design randomized the sample of households into three approximately equal‐sized groups, and every individual within a household was allocated the same experimental treatment. The EQ‐5D instrumentsFieldwork used a multimode strategy, with a random two‐thirds of the panel initially offered a web interview (CAWI) and the remainder by computer‐assisted self‐interviewing (CASI) embedded within the main face‐to‐face interview.p = 0.52), age group (p = 0.15) or existence of a limiting illness or disability (p = 0.37). The incidence of CAWI rather than CASI interviewing was also balanced across treatment groups (p = 0.95).The achieved sample of individuals who gave full responses to the 5L (3L) instrument comprised 2635 (1732) individuals, clustered in 1689 (1278) households. We tested the balance of the sample across treatment groups using Fisher's exact test of independence, based on cross‐tabulations, constructed using only the first respondent individual from each household to avoid intra‐household correlation. We found no flaws in the randomization with respect to gender  are 50% and 41% for 3L and 5L, respectively. However, the sample does have coverage of poorer health states. In their responses to a separate question, 36% of the sample reported a long‐standing illness or disability (LSI); among that group, the sample proportions of state (11111) fall to 17% (3L) and 14%. (5L) Appendix Figures The number of distinct health states reported by the 1732 respondents who completed 3L fully was 64 . For the 2635 respondents completing 5L, the number of distinct states reported was 269 (9% of the 3125 possible). These numbers compare with the 123 (51%) and 676 (22%) distinct states found for 3L and 5L in the EuroQol MI dataset and 136 (56%) and 960 (31%) for the Jan 2011 FORWARD dataset analyzed by Hernández and Pudney . The num2.35L3L and 3L5L groups to receiving repeated EQ‐5D instruments, distinguishing between those who appeared not to notice the repetition, those who noticed but appeared unconcerned, and those who expressed dissatisfaction or other concern about the repetition. We use ordinal response models to examine whether awareness is uniform across respondent groups.We analyze the data in five steps. First, we examine the awareness by respondents of the repetition. As part of our design, CASI interviewers were asked to assess the reactions of respondents in the 3L5L, 5L3L and 5Lonly groups, using domain‐specific χ2 tests and a joint test across all domains, applied to each pair of treatment groups. The joint test is useful as it avoids the pitfalls of multiple testing, but the domain‐specific tests are valuable to identify the sources of significant overall difference. Define pg as the vector of sample proportions from group g ∈ {3L5L, 5L3L, 5Lonly} of the first k‐1 response options, where k is the number of levels (3 or 5). The test statistic for comparison of groups g and h is: χ2=pg–ph′(diagpg−pgpg′)/ng+(diagph−phph′)/nh−1pg–ph. Under the assumption of strictly positive population probabilities and the null hypothesis of identical response probabilities, this has a limiting χ2(k‐1) distribution as ng, nh → ∞ with ng/nh → constant. For some domains there were no responses at the bottom of the response scale. In these cases, we apply the test with the bottom two categories merged and the degrees of freedom therefore reduced by 1. Asymptotically, the test remains valid when implemented in this way, whether or not the population probability of the bottom category is strictly positive. We use only one respondent per household (the first one interviewed), to ensure independence.Second, we test the hypothesis of equal response distributions across the 3L5L and 5L3L groups, using binary probit models to identify types of respondent particularly prone to such conflicts.The third step is to examine the prevalence of low‐3L/high‐5L or low‐5L/high‐3L conflicts within the 3L5L and 5L3L experimental groups and test the hypothesis that the resulting mapping functions are identical. The Dolan (U3) in the range −0.594 to 1, where 1 indicates the best possible level of health‐related quality of life and negative values indicate a state perceived as worse than dead. The distribution of 3L utility scores for the 5L3L and 3L5L groups combined and for the subsample of people with a LSI are shown in Figure U3 = 1, and there are large gaps in the distribution—most importantly the absence of any utility scores in the interval . A flexible approach to modeling is required if the distribution of 3L utility scores is to be captured adequately and models based on mixtures of generalized Tobit‐type components have been found to work well.c = 1 … C:xi is a vector of predictor covariates, βc is a coefficient vector and εic∼N0,σc2 a Gaussian random error, specific to component c. The probability of individual i belonging to the c‐th latent sub‐population has multinomial logit form:wi is a vector of covariates and one of the coefficient vectors δ1…δC is normalized to zero. The utility score Ui for the observed 3L outcome is then assumed to be:Although instruments like EQ‐5D are designed for practical policy use, research on health outcome measurement often stops short of examining the impact of measurement differences in practice. In fact, statistically significant differences between the three experimental groups may or may not matter for practical purposes, so our fourth step is to examine the impact of between‐group differences on statistical mapping, which is the main practical use of MI surveys. We estimate separate statistical mapping models using data from the he Dolan  utility e Dolan U3 in the Estimation of this structure is by maximum likelihood, and a combination of the Bayesian Information Criterion, mean absolute error, root mean squared error and graphical methods  by a less detailed one (3L) which could seem less justifiable to respondents than the reverse ordering used in the 3L5L group.Table 3.2χ2 tests of the hypothesis of equal response distributions between pairs of treatment groups, and the overall χ2 test spanning all five EQ‐5D domains. We apply these tests separately to the subsamples of people who do not report a LSI and those who do .Table χ2 test for responses to the simpler 3L instrument finds no significant evidence of a difference between the 5L3L and 3L5L groups for respondents without any LSI. However, among people who do report an LSI, we find a significant difference (at the 5% level) between the 3L response distributions. Domain‐specific tests suggest that the source of the differences are the mobility and pain domains.The overall 5L3L versus 3L5L (LSI and no‐LSI) and for 3L5L vs. 5Lonly (no LSI).5L3L versus 5Lonly (LSI). Only in one other case  is there a significant difference at the 5% level.Comparisons of the 5L response distributions reveal significant differences for The pain dimension of EQ‐5D should clearly be the main focus of concern for consistency between measures, and this tends to confirm the conclusions of consistency analysis of the existing FORWARD and EuroQol Group datasets  than the 3L5L group, and thus paints a more negative picture of pain. A possible behavioral interpretation of this difference relates to two factors, sequencing and timing. It is well‐established in the survey methods literature that response behavior can be influenced by the existence and nature of questions asked earlier, so the different sequencing of questions in the 5L3L and 3L5L groups may generate behavioral differences. For example, the 3L5L group may deliver a relatively positive assessment because 5L is preceded by 3L and the shorter response scale of 3L has the effect of sensitizing respondents particularly to the upper part of the 5‐point scale for 5L.Figures 3L5L group more fatigued or disengaged and thus more likely to check the first box they see in the response scale, which happens to be “no pain.” This explanation is certainly consistent with the evidence of Figures The timing of a question may also be an important influence because respondents learn or become fatigued or disengaged as the interview progresses, so that questions generate different responses if asked late in the interview than they would if asked early. A possible interpretation alternative or complementary to one based on sequencing is that the later timing of 5L finds respondents in the 5L3L and 5Lonly respondents with LSI), shows a worse pain state on average for the former group, while Figure 3L5L and 5Lonly respondents with no LSI) shows a worse pain state in the latter group. Since 5L3L and 5Lonly differ only in terms of timing and 3L5L and 5Lonly differ only in terms of the existence of a preceding 3L instrument, the differences in Figures Figures 5L3L and 3L5L groups for people who reported having an LSI. As was the case for 5L responses, it reveals a lower proportion of “no pain” responses in the 5L3L group than the 3L5L group. However, this implies a different pattern in terms of sequence and timing than the pattern for 5L responses. Within the 3L5L group, 3L is asked early and is not preceded by another variant of EQ‐5D. Consequently, the effect on 3L responses of preceding 3L by 5L is the mirror image of the effect on 5L responses of preceding 5L by 3L.Figure How should we interpret this puzzling finding? It may hinge on the look of the CASI or CAWI screen that shows the response scale to respondents  in web interviews, which may reflect the characteristics of respondents willing to use the web rather than the CAWI mode itself. There is only weak evidence (p = 0.111) of a relationship between conflicting responses and awareness of repetition, although the point estimate is large—an average increase of 2.4 percentage points in the conflict rate for respondents who show no sign of awareness of the repetition. There are no significant differences between the 5L3L and 3L5L groups or between demographic groups.Table 4The comparison of responses between treatment groups suggests that there are significant biases in EQ‐5D measures produced by repetitive MI surveys. These distortions have the potential to induce measurement error bias into the predictive models that are used for mapping between 3L and 5L quality of life measures. But a statistically significant bias is not necessarily large enough to cause important problems for policy work. To give some insight into this, we use two recent cost‐effectiveness studies to illustrate the response differences revealed by the UKHLS experiment using a framework more directly related to practical applications.4.1The original 3L, combined with the utility scores constructed by Dolan , currentxi contained an intercept and the five items of 5L representing mobility, self‐care, usual activities, pain and anxiety/depression, each treated as numerical variables on the scale 1 … 5. The predictor wi for group membership contained an intercept, a binary variable identifying individuals who reported the best possible health state 11111, and the 5L misery index formed from summing the domain indicators, giving a single variable with range 5 … 25.A statistical mapping model predicts the 3L responses that would have been observed, had the 3L version been implemented, using the 5L responses as predictors. In our illustrative application, we use the Hernández‐Wailoo  mixture 5L3L and 3L5L samples, we arrived at a similar three‐component specification for each. Component c = 1 was a degenerate discrete probability mass at Ui=1, with two other regular Tobit‐type components. The parameter estimates are shown in Table Following a standard specification search carried out independently on the 5L3L + 3L5L sample gives a highly significant rejection of the hypothesis of equal parameters (χ2(20) = 84.4, p = 1.4 × 10−9). The 5L3L model has a probability mass of 0.37 at perfect health state U = 1 and two Tobit components with similar mean predictions (0.799 and 0.847) but with error variance differing by a factor of (0.174/0.041)2 = 18.0. The 3L5L model has a slightly larger discrete probability mass at U = 1 and two other components with quite distinct mean predictions (0.806 and 0.366) and error variances that differ by a smaller margin of (0.109/0.052)2 = 4.4. In summary, it is clear that the significant differences we found in the 5L3L and 3L5L data on EQ‐5D have significant and structurally important implications for mapping models estimated from those data.Although the models have the same three‐component structure, the estimates are quite different. A likelihood ratio test comparing the two separate models to the same structure fitted to the combined 4.23L5L and 5L3L treatment groups into policy‐relevant form using two illustrative cost‐effectiveness applications. These cannot claim to be representative of the broad range of such studies considered by NICE, but they serve to illustrate the way that measurement differences may affect the key calculations made in cost effectiveness studies. The two applications meet our requirements in that they are based on individual‐level trial data incorporating the newer 5L version of EQ‐5D, and their authors kindly agreed to re‐run the cost‐effectiveness calculations for us. It is important to note that the results of these recalculations are simplified and not comparable with the authors' own findings—they relate to a small part of the evaluation process and are based on different mapping approaches. It should also be noted that they are both trials of interventions in health conditions that normally affect quality, rather than length, of life.We put the differences in the mapping functions estimated from the The TITRATE randomized control trial (RCT) was concerned with the management of established moderate cases of Rheumatoid Arthritis receiving stable doses with conventional drug therapies. The trial compared the outcomes of intensive case management (monthly assessments and support by trained nurses) in 169 cases with outcomes in a control group of 167 cases receiving standard care. The aim was to test the hypothesis that intensive management increases the rate of remission in such patients. The study was implemented in 39 English rheumatology centers. Health utilities were derived from participant responses to 5L at baseline, 6 and 12 months. Details of the trial and the economic evaluation are reported in Scott et al. .n = 185) or more costly Rubber Band Ligation  and followed for up to 12 months. The 5L measurements were made at baseline, 1 day, 7 days, 21 days, 6 weeks, and 12 months. Full details of the trial are reported by Brown et al. . Patients were randomly assigned to either Haemorrhoidal Artery Ligation j, use 5L to measure the sequence of quality‐of‐life outcomes over time the trial period.For each trial participant (ii)For each 5L measurement, use the mapping model to predict the expected value of the corresponding unobserved 3L utility outcome.(iii)Qj.Convert the resulting sequence of predicted 3L quality‐of‐life measures to the metric of quality‐adjusted life years (QALY), (iv)Tj for each participant as a present value over the trial period.Measure the total cost of treatment, (v)ΔT=T¯2−T¯1 and ΔQ=Q¯2−Q¯1.Calculate the differences in mean cost and QALY outcomes between participants receiving treatments 1 and 2 as (vi)Calculate the Incremental Cost‐Effectiveness Ratio (ICER), giving the cost per additional QALY delivered by treatment 2 beyond the benefit achieved with treatment 1:Let treatment 1 be the basic treatment , and treatment 2 an alternative treatment hypothesized to be clinically superior. In outline, a cost‐effectiveness study involves the following steps:Treatment 2 is then recommended as an alternative to treatment 1 if the ICER is below the level that NICE regards as an affordable cost . If the ICER is above this threshold, then it is regarded as not cost‐effective, even if it offers a significantly better outcome in QALY terms.5L3L and 3L5L experimental data.Table 5L3L mapping rather than the 3L5L mapping gives a 13% higher estimated mean QALY for both the standard and intensive treatments. However, because the impact is fairly uniform across the two treatments, the QALY difference between the two treatments is only 8% higher for the 5L3L mapping than the 3L5L mapping. This in turn means that the estimated ICER is lower by about 7% when the 5L3L mapping is used.In the TITRATE trial, use of the 5L3L mapping again leads to higher QALY outcomes than the 3L5L mapping, although only by 4% for both the RBL and HAL treatments. The HAL‐RBL QALY difference is 5% higher for the 5L3L mapping, giving an estimated ICER lower by 5%: approximately £77,000 rather than £73,000, but still well above the NICE funding threshold.In the HubBLe trial, the Q¯1 and Q¯2, those biases tend to cancel out to some degree, giving a smaller range of error in the QALY difference ΔQ. However, against this, the QALY difference ΔQ is the denominator of the ICER and, in evaluations where a new technology offers only marginal improvements, that denominator may be quite small. In such cases, even small biases in ΔQ may have a large impact on ICERs and thus on cost‐effectiveness decisions.Both TITRATE and HubBLe share a feature that is likely to be found in a wide range of applications. Although error in the mapping procedure may generate large biases in the mean QALY estimates 5L3L and 3L5L group‐specific mappings .The HubBLe example also illustrates a further important point—that the type of mapping model used and the dataset it is based on may have a much bigger impact on the ICER than the response errors induced by repetitive interviewing in a MI survey. The published cost‐effectiveness result for HubBLe uses a simpler mapping model devised by van Hout et al.  than our5There are many survey instruments used to measure health‐related quality of life outcomes as a basis for the evaluation of medical procedures and pharmaceutical products. Statistical mapping often has to be used to translate outcomes measured by one instrument into an evaluation metric developed in relation to a different instrument. This process requires a multi‐instrument survey that allows the statistician to observe responses to both instruments from the same set of survey participants. It also entails a reliability assumption: that participants give essentially the same responses in a multi‐instrument interview as they would in a conventional interview involving only one of the instruments. Despite the importance of statistical mapping for the policy analysis carried out by official bodies like NICE in England, there has so far been little research aiming to test the hypothesis that multi‐instrument surveys are reliable in this sense.In this paper, we have exploited a randomized experiment in the UKHLS Innovation Panel incorporating two variants of the widely used EQ‐5D instrument (3L and 5L) differing primarily in the number of levels in the response scales. The experiment compared three treatment groups: 5L followed later in the interview by 3L; 3L followed by 5L; and 5L alone; to investigate the MI reliability hypothesis and explore its consequences for economic evaluation. There are seven main findings.First, despite a relatively large separation in time between the two instruments in the interview, there was evidence that a majority of respondents were aware of the (near‐)repetition, with older people more likely to notice and express concern. This may be because older people were more engaged with the survey, rather than any inherent age difference in attention span or recall.5L3L and 3L5L, so the ordering of the two instruments has a significant impact. There were also significant differences between the comparisons of the 5L3L and 3L5L groups with the 5Lonly group. The strongest evidence of difference was found in the EQ‐5D domain relating to pain, which is the most highly weighted domain in the most widely used utility scoring systems for the UK.Second, there were statistically significant differences in both the 3L and 5L response distributions between Third, for the 5L instrument, these significant differences at the level of individual components of EQ‐5D also carry over to overall summary measures of health‐related quality of life, specifically the “misery index” defined as the sum over the five health domains of EQ‐5D, and the utility score proposed by Devlin et al. . EvidencFourth, the nature of the ordering effects for questions on pain is quite complex. We have found that, if 5L is preceded by 3L, then it generates a higher proportion of favorable “no pain” responses relative to asking 5L alone or before 3L. Conversely, when 3L is preceded by 5L, use by respondents of the “no pain” option is reduced relative to the responses from people who are asked 3L first. A possible interpretation is that asking 3L  first visually primes respondents to the first few points on a subsequently encountered 5L scale; while asking 5L  primes respondents to use later points on a 3L scale encountered subsequently.Fifth, strongly conflicting responses  occurred for just over 5% of respondents—a conflict rate that could be large enough to cause serious bias in some types of statistical analysis. The occurrence of conflicting responses is significantly higher among those with a long‐standing health problem, and is significantly lower among people completing the interview online.Sixth, we used the 3L and 5L responses to estimate flexible statistical models for mapping from 5L measurements to the 3L utility basis approved by NICE for its cost‐effectiveness work. This was done separately for randomized groups with 5L preceding 3L and 3L preceding 5L, and we found that the fitted models exhibited substantial structural differences, suggesting that question ordering in MI surveys can have major implications for mapping procedures.5L3L and 3L5L mapping models to revisit two real‐life cost‐effectiveness studies, finding that the key ICER differed by 5% in one case and 7% in the other. Although there was no difference in the conclusions in either case , differences of this magnitude could be important for more marginal cost‐effectiveness applications. However, comparison with results obtained by the original study authors suggests that question ordering in the MI survey used to estimate the mapping model has much less effect than the choice of econometric approach used to develop the mapping model.Seventh, we used the alternative There are some important implications from our findings for the design of future multi‐instrument surveys to be used for mapping between health outcome measures. Most important is to be aware of the possibility that sequencing and timing of the 3L and 5L instruments within an interview may affect responses, and this means that there is a strong case for designs that randomize the ordering of the two instruments and possibly also randomize the use of ascending and descending response scales. Such designs would not “solve” the response error problem, but they would allow the analyst to check for the existence of response distortions and carry out robustness checks.Many MI surveys used in health economics are now web‐based because of the lower cost of web interviewing. There is some concern that web surveys introduce bias through differences in the pattern of non‐response or changes in respondents' behavior. It is reassuring that we have found no evidence of significant differences between the CASI and CAWI subsamples, except in the probability of strongly conflicting 3L and 5L responses—where web interviews appear to reduce the frequency of conflict .No.Supplementary Material S1Click here for additional data file.


Here, we present reactive radicals that are generated from sulfonyl azides: sulfonyl nitrene radical anion, sulfonyl nitrene and sulfonyl amidyl radical, and test their gas phase reactivity in C−H activation reactions. The sulfonyl nitrene radical anion is the least reactive and its reactivity is governed by the proton coupled electron transfer mechanism. In contrast, sulfonyl nitrene and sulfonyl amidyl radicals react via hydrogen atom transfer pathways. These reactivities and detailed characterization of the radicals with vibrational spectroscopy and with DFT calculations provide information necessary for taking control over the reactivity of these intermediates.Photocatalytic generation of nitrenes and radicals can be used to tune or even control their reactivity. Photocatalytic activation of sulfonyl azides leads to the elimination of N Photochemical activation of sulfonyl azides leads to generation of reactive radicals that activate aliphatic C−H bonds. This study compares intrinsic reactivities of triplet sulfonyl nitrene, sulfonyl amidyl radicals and sulfonyl nitrene radical anions in the gas phase towards a series of hydrocarbons and correlates it to their structures investigated by ion spectroscopy. The most reactive triplet nitrene abstracts a hydrogen atom from ethane. Sulfonyl nitrenes have been attracting chemists’ attention for more than a half of a century because of their ability to form C−N bonds.1, 2 I3) by photoexcited Ru(bipy)3(PF6)2  leads to nitrene‐based chemistry  by.− generated from the reaction mixture of nonaflyl azide (NfN3) and Ru(bipy)32+ after the irradiation at 445 nm. The NfN.− anions (m/z 297) cannot be directly detected from solution by electrospray ionization mass spectrometry (ESI‐MS) presumably due to their high reactivity.[2CH.− 3(PF6)2 shows the signals of the parent ions (m/z 174) as well as of the nitrene fragment ImH+SO2N.. , acetone, methanol, THF, cyclohexane and ethane. The bond dissociation energy of reactive ethanethiol (88.6±2.− reactivity pattern is consistent with proton‐coupled electron transfer (PCET) mechanism of the detected hydrogen atom transfer (HAT) reactions.Next, we tested the reactivity of the generated intermediates with various substrates in the gas phase Table . NonaflyH+SO2N.. was able to abstract a hydrogen atom from ethanethiol, acetylacetone, acetone, methanol, tetrahydrofuran, cyclohexane and even ethane, which clearly attests to a much larger reactivity of the free nitrene compared to the nitrene radical anion  and also an intense double HAT . As expected, the reactivity of ImH+SO2NH⋅ is dominated by hydrogen atom transfer reactions.The products of the double HAT show more or less statistical distribution of H and D (influenced by the kinetic isotope effect), which clearly indicates that the reaction mechanism does not correspond to the HH+SO2N.. and ImH+SO2NH⋅ was revealed in their reaction with ethane . Hence, we used the fact that we see almost exclusively single HAT and determined the kinetic isotope effect (KIE) in the reaction of ImH+SO2N.. with CH3CD3 .[H+SO2NH(R). This is because the rebound of two radicals is very exothermic. The excess energy cannot be dissipated in the dilute gas phase; therefore, the rebound products usually release their energy by eliminating a small fragment. Here, we observe the formation of protonated imidazole (ImH+) and nitrogen insertion (RNH+) which might be signs of the fragmentation of the rebound product ImH+SO2NH(R) .In solution, the initial HAT between the nitrene reactant R'N R'NH(R).2, 3 W2N.., R=F,3,2Cl, CHCl2,4H3S,3,p‐BrPh, p‐MePh, CH3H+SO2N.. and of ImH+SO2NH⋅.To connect the observed reactivities with the structures of the intermediates, we have characterized the studied ions with IR photodissociation spectroscopy.H+SO2N3. The predicted structure of ImH+SO2N3 has a synperiplanar geometry between the azide function and one of the S=O bonds which agrees with geometries of other sulfonyl azides .[H+SO2N3  corresponds to the SO2 asymmetric vibration. The SO2 symmetric vibration band is in the range 1205–1230 cm−1. This region shows several bands of vibrations coupled with the S=O vibration. Most likely, the symmetric SO2 vibration band is at 1205.5 cm−1 and red‐shifts to 1201 cm−1 upon the isotopic labelling . The experimental band at 1624 cm−1 might correspond to a combination band of the imidazole C−H out‐of‐plane wagging and twisting vibrations which is present in the anharmonic calculations . Overall, the agreement between the experiment and theory demonstrates that the chosen theoretical method provides IR spectra that can serve for the assigning of the correct structure of this type of ions.First, we tested the experimental and theoretical methods by studying the stable precursor Imure S74).36, 37H+SO2N3 as a reference and the benchmark in our hand, we measured the spectrum of ImH+SO2N... The experimental spectrum of ImH+SO2N..  is −20 cm−1  and of the SO2 symmetric vibration band (1195.5 cm−1) −7 cm−1 . We excluded all other possible isomers including pseudo‐Curtius rearranged ImH+NSO2 based on the agreement between the calculation and the experiment .With the experimental spectrum of Im. Figure c matches. Figure d. The coH+SO2NH⋅  and symmetric (1184 cm−1) SO2 vibrations are slightly red‐shifted with respect to those of ImH+SO2N...We also measured the IRPD spectrum of the amidyl radical Im⋅ Figure e. The frH+SO2N.. and ImH+SO2NH⋅ with only a small delocalization towards the oxygen atoms. This delocalization is larger for ImH+SO2NH⋅ which is associated with prolongation of the S−O bonds and thus the red‐shift observed in the IRPD spectrum above.The agreement between the experimental IR spectra and the theoretical prediction shows that the DFT method describes these radicals well. Hence, we analyzed the calculated spin densities and the geometries in detail Figure . The spi2N... The spin density of FSO2N.. is slightly more delocalized towards the oxygen atoms than in ImH+SO2N.., which agrees with the red‐shifted IR characteristics of the S=O bands (the SO2 asymmetric vibration of FSO2N.. is red‐shifted by 26.5 cm−1 with respect to that of ImH+SO2N..). Finally, we also assessed the radical anion CF3SO2N.− representing the other possible reactive species generated in the photochemical reaction , imidazole‐1‐sulfonyl amidyl radical (ImH+SO2NH⋅) and triplet imidazole‐1‐sulfonyl nitrene (ImH+SO2N..). These radicals are models of possible intermediates in photocatalyzed reactions of sulfonyl azides that lead to the activation of aliphatic C−H bonds. The reactivities observed in solution are in clear correlation with the reactivity of the neutral nitrene and the amidyl radical. Both species react as typical radicals in hydrogen‐atom transfer reactions. The nitrene activates even highly unreactive species like ethane with the kinetic isotope effect of ∼2.3. On the other hand, the nitrene radical‐anion reacted only with “acidic” S−H or O−H bonds suggesting a proton‐ coupled electron‐transfer pathway. However, protonation of the nitrene radical anions leads to the amidyl radicals boosting the reactivity and enabling the C−H activation reactions . Hence, tuning the properties of the photocatalyst can steer the reactivity along different paths  and 3‐azidosulfonyl‐3H‐imidazol‐1‐ium Hydrogen Sulfate (ImH+SO2N3*HSO4−) were prepared by a slightly modified published procedures (See Supporting Information).Nonaflyl azide (NfNiN(ν)) vs. without (i0N) IR irradiation of the trapped ions (1‐iN(ν)/i0N). The IR photons were generated by tunable OPO/OPA photon source.Gas‐phase infrared photodissociation spectra were recorded with a custom‐built instrument described in a detail elsewhere.−1 and by factor 0.965 in the range above 2500 cm−1. Scaling factors have been determined based on overlap between experimental and theoretical spectrum of ImH+SO2N3.The calculations were performed with Gaussian G16 using the B3LYP−D3 functional40, 41The authors declare no conflict of interest.1As a service to our authors and readers, this journal provides supporting information supplied by the authors. Such materials are peer reviewed and may be re‐organized for online delivery, but are not copy‐edited or typeset. Technical support issues arising from supporting information (other than missing files) should be addressed to the authors.Supporting InformationClick here for additional data file.