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# Carbon-doped SnS2 nanostructure as a high-efficiency solar fuel catalyst under visible light

## Abstract

Photocatalytic formation of hydrocarbons using solar energy via artificial photosynthesis is a highly desirable renewable-energy source for replacing conventional fossil fuels. Using an l-cysteine-based hydrothermal process, here we synthesize a carbon-doped SnS2 (SnS2-C) metal dichalcogenide nanostructure, which exhibits a highly active and selective photocatalytic conversion of CO2 to hydrocarbons under visible-light. The interstitial carbon doping induced microstrain in the SnS2 lattice, resulting in different photophysical properties as compared with undoped SnS2. This SnS2-C photocatalyst significantly enhances the CO2 reduction activity under visible light, attaining a photochemical quantum efficiency of above 0.7%. The SnS2-C photocatalyst represents an important contribution towards high quantum efficiency artificial photosynthesis based on gas phase photocatalytic CO2 reduction under visible light, where the in situ carbon-doped SnS2 nanostructure improves the stability and the light harvesting and charge separation efficiency, and significantly enhances the photocatalytic activity.

## Introduction

Artificial photosynthesis is one of the future energy sources that promises an environmentally friendly alternative to fossil fuels1,2,3,4. In this process, photocatalysts can directly harvest energy from solar light and simultaneously convert CO2 to hydrocarbons, tackling both energy and global environmental problems. Photocatalytic CO2 reduction to hydrocarbon fuels is a solar energy based process that requires highly efficient and stable catalytic materials5, 6. In the past decades, following the pioneering discovery by Inoue et al.7 of photoelectrochemical CO2 reduction in aqueous semiconductor suspensions, various semiconductor materials, in particular TiO2, ZnO, NiO, WO3, and Bi2WO3 have been tested as catalysts for the photocatalytic CO2 reduction reaction8, 9. However, most of these semiconductor materials have a bandgap with energy in the ultraviolet range, resulting in low conversion efficiencies owing to their large band gaps and high charge-carrier recombination rates. To overcome these limitations and to improve photocatalytic CO2 reduction efficiency, semiconductors have been modified by several strategies: nanostructuring, band gap engineering by doping and modification with metal nanoparticles, and hybridization with carbonaceous materials such as Pt/TiO2, GO, g-C3N4, g-C3N4/Bi2WO6, Cu/GO10,11,12,13,14,15,16. Although these hybrid heterogeneous photocatalysts improved the catalytic performance significantly, the overall catalytic selectivity and quantum efficiency are far from the commercial requirements. Recently, an enzyme and semiconductor-hybrid system has been demonstrated to have a high photocatalytic CO2 reduction efficiency of ~ 3–4%17. However, this photocatalyst system suffered from poor enzyme stability. Moreover, the most used narrow band gap semiconductor, CdS, poses another challenge due to its toxicity problem18. As far as photocatalytic CO2 reduction is concerned, we need to develop an environmentally friendly nanostructured hybrid semiconductor, which can take us one step forward from CdS. Apart from the critical narrow band gap and high absorption coefficient to utilize maximum solar energy, efficient charge separation is the other important factor for high activity of a photocatalyst system. Therefore, controlling the carrier diffusion pathway and controlling the defects in the bulk or at the interfaces and surface of a nanostructure semiconductor are the key factors for designing a highly efficient photocatalyst system19.

Since the discovery of graphene, two-dimensional (2D) layered transition metal dichalcogenides and metal sulfide nanostructures are playing an important role in catalysis owing to their wide range of optical and electronic properties20, 21. Moreover, the high surface area and low charge recombination characteristics of 2D materials can potentially enhance the photocatalyst activity22. Among various metal sulfides, SnS2 is a naturally occurring bronze-colored n-type narrow band gap (2.2–2.4 eV) semiconductor known as mosaic gold. During the last few years, it has been demonstrated to be a promising photocatalyst for dye degradation processes23, 24. Recently, it has proven attractive for its potential applications as a light absorber layer for dye-sensitized solar cells25, optoelectronics26, gas sensing27, and energy storage and conversion28. The narrow band gap with around 0.19 µm average photocarriers diffusion length29 and the high quantum yield of SnS2 thus give two advantages for a good photocatalyst under visible light. Sun et al.30 first explored the freestanding single layer SnS2 as an efficient visible-light photocatalyst for water-splitting. Recently, Sun et al.31 have reported the photocatalytic CO2 reduction to CO using SnS2. However, the overall photocatalytic performance is far lower than the practical requirement due to fast recombination of the photogenerated charge carriers. To overcome this problem, it is necessary to synthesize this semiconductor nanostructure doped with metals or non-metals to control the carrier diffusion pathway and charge-carrier recombination. Semiconductor doping with non-metal carbonaceous materials is very popular in photocatalyst systems due to their wide range of light absorption and low photo corrosion as compared with metals. These doped carbon sites act as excellent electron acceptor centers and suppress the charge recombination in the electron transfer process due to electronic interaction between doped carbon and semiconductor. Huang and co-workers32 introduced novel carbon-doped h-BN nanosheets as a sustainable and stable visible photocatalyst system with high efficiency . In 2012, Lin et al.33 reported enhanced photocatalytic water-splitting based on carbon-doped porous ZnO nanoarchitecture. Moreover, the most commonly reported carbon-doped photocatalysts are based on wide band gap semiconductors. Interestingly, doping can create microstrain in the crystal, which affects the electronic and optical properties. Recently, a simulation study has shown a strain-induced indirect-to direct band gap transition in bulk SnS234. This strain induction and non-metal doping studied in semiconductor material promises that there are possibilities of improving the photocatalytic CO2 reduction activity with tuning the optoelectronic property and enhancing separation of photo induced electron-hole pairs by introducing carbon as a doping element into the semiconductor. In this work, we propose a carbon-doped SnS2 nanostructure system with limited average lifetime of photogenerated electrons and holes by shortening the diffusion time so that they can reach the reaction sites before losing their energy. In the hybrid system the conductive carbon incorporated into SnS2 provides the opportunities for fast charge transport in the nanostructure with an interconnected planar structure, thus shortening the diffusion time from semiconductor interior to surface reaction sites. Here, we performed the photocatalytic CO2 reduction using this carbon-doped SnS2 nanostructure (hereafter, referred as SnS2-C) and demonstrated enhanced photocatalytic performance compared with the undoped SnS2 nanoplate (hereafter referred as SnS2). A theoretical study of the CO2 adsorption and dissociation activity for C doped SnS2 has been performed to support the experimental observation. Our results indicate that the carbon-doped nanostructure of SnS2 has a key role in enhancing the visible light photocatalytic activity of the CO2 reduction to solar fuels.

## Results

### Photocatalyst synthesis

The SnS2-C and SnS2 photocatalyst materials were synthesized by a simple hydrothermal method, using a 1:5 stoichiometric mixture of SnCl4.5H2O and an S source (l-cysteine or thiourea) at 180 oC. The two different sulfur sources were chosen to obtain different nanostructures resulting from their different nucleation processes and pH values during the hydrothermal synthesis. Apparently, both l-cysteine and thiourea provide a controlled condition for anisotropic growth of SnS2 nanostructures and nanoplates respectively as schematically shown in Supplementary Figure 1. The detailed synthesis process is described in the Methods.

### Crystal structure analysis

The crystal structure of the as-prepared SnS2-C and SnS2 were characterized by powder X-ray diffraction (PXRD) as shown in Fig. 1a. The PXRD patterns of SnS2-C and SnS2 match well with that of polycrystalline hexagonal SnS2 berndtite (JCPDS no. 01–075–0367) and berndtite-2T (JCPDS no. 00–023–0677), respectively. The facets of SnS2 show quite sharp strong intensities, which demonstrates that thiourea helps for large and thick crystal growth. The PXRD peaks of SnS2-C are broader than the peaks of the SnS2. The peak broadening of SnS2-C implies the nanocrystal and amorphous nature of hexagonal SnS2 after carbon doping. Compared with SnS2, the diffraction peaks of SnS2-C are slightly shifted towards lower angle. The characteristic (001) peak is quite broad and shifts from 15.12 ° to 14.66°, indicating that (001) plane growth of the SnS2-C crystals is greatly inhibited and only few-layered SnS2 is formed, along with lattice expansion, resulting in an enlarged d-spacing owing to the carbon doping during the hydrothermal synthesis in presence of l-cysteine. It is interesting to note that carbon doping occurred in the l-cysteine-assisted hydrothermal process, but not in the thiourea-assisted counterpart. The d-spacing of the (001) plane of SnS2-C is calculated to be 0.604 nm, which is slightly larger than that of SnS2 (0.585 nm). The decreased number of layers and the enlarged inter-layer spacing of SnS2-C could be attributed to the structural strain generated by the expansion of the crystal lattice after interstitial incorporation of carbon. The crystallite size, microstrain and lattice d-spacing of SnS2-C and SnS2 are summarized in Supplementary Table 1. Interestingly, we observed that the crystallite size in SnS2-C is smaller than that in SnS2 and the corresponding microstrain significantly enhanced around 3.6, 3.3 and 1.8 times based on (001), (101), and (110) planes after interstitial C doping into SnS2. Elemental analysis is adopted to identify the elemental compositions of the SnS2-C and SnS2 samples as depicted in Fig. 1b, which shows that the SnS2-C sample contains around 20.78 atomic % C. Although SnS2 shows ~ 2.79 atomic % of C, however, this low C level is very close to the error limit. The calculated atomic ratio of S to Sn is ~ 1.92 and 1.86 for SnS2-C and SnS2, respectively.

### Optical properties

The optical absorption measurement was performed, followed by a tauc plot to estimate the band gap for the as-prepared SnS2-C and SnS2 (Fig. 1c). The observed direct band gaps of SnS2-C and SnS2 are 2.54 and 2.43 eV, respectively. In addition, SnS2-C shows an absorption band edge towards longer wavelength ~ 2.34 eV, indicating a decreased band gap in SnS2-C as compared with undoped SnS2. It is also worth noting that the SnS2-C exhibits a significantly higher absorption ranging from a visible-light wavelength of 530 nm, which is the most intense region in the solar spectrum, towards longer wavelength. In addition, SnS2-C exhibits an indirect band gap 1.75 eV that is smaller than its direct band gap. For SnS2, on other hand its indirect band gap (2.05 eV) is nearly close to its direct band gap. Presumably, the interstitial C doping creating microstrain on SnS2-C, as compared with SnS2, affects the electronic character of the valance band and conduction band edges. This is closely similar with the recently strain-induced band gap transition on bulk SnS2 simulation study34. Thus, we expect that the indirect band gap and additional band edge in SnS2-C, whereas maximize photon absorption, will also affect the electron-hole pair’s lifetime, which is beneficial for charge carrier to participate in the surface photocatalytic application.

To further quantify the doped carbon content in SnS2-C, we have performed solid-state NMR spectroscopic characterizations as shown in Supplementary Figure 2 and 3. The 13C Cross-Polarization Magic Angle Spinning (CPMAS) NMR spectra of SnS2-C shows two broad resonances at 23.8 ppm and at 133.3 ppm, respectively. The observed chemical shifts do not match those of pristine l-cysteine or the related decomposition compound (pyruvic acid) as shown in Supplementary Table 2. The observed resonance in the 13C CPMAS NMR spectrum of SnS2-C remains unchanged after the light activated CO2 reduction reaction. Thus, we believe that the observed chemical shifts in the 13C CPMAS NMR spectra of SnS2-C should be related to the carbon containing molecules doped inside the SnS2 layer during hydrothermal synthesis.

The samples were further investigated by Raman spectral analysis as shown in Fig. 1d. The spectra of both samples illustrate the strong characteristic peaks at 312 and 314.2 cm−1, respectively, of the SnS2-C and SnS2 sample, which are assigned to the A1g mode of SnS2. This observed Raman in plane mode of the atomic vibration shift around 2 cm−1 is strongly related to the significant changes to the inter-layer covalent interaction of SnS in SnS2-C after interstitial carbon doping and is well supported with the reported simulation study34. SnS2 shows another weak peak ~ 206.1 cm−1, resulting from Eg symmetry transition owing to out of plane atomic vibration in the 2H polytype of SnS2. However, for SnS2-C, instead of a single Eg peak in the 2H, we observed a broad peak from 190 to 225 cm−1 corresponding to the 4H and 18R polytypes of the SnS2 phase. Overall, the broadening and softening of A1g peak observed in the SnS2-C, in comparison with SnS2, can be attributed to the interstitial doping into the SnS2-C layer structure and formation of different SnS2 polytypes35. It is also worth noting that excessive incorporation of carbon may lead to formation of carbonaceous matters. As shown in Supplementary Figure 4 the Raman spectra of SnS2-C reveal additional peaks ~ 1186.9, 1336.6, and 1470.1 cm−1, which match the characteristic vibrational modes of 7A1, 6A1g, and 6E2g, respectively, in doped amorphous carbon with pentatomic and heptatomic rings36. The presence of the carbonaceous matters in the SnS2-C may introduce heterogeneous interfaces favorable for carrier separation, as will be discussed later.

### Morphology and microstructure analysis

The morphology of the as-prepared SnS2 samples was characterized by field emission scanning electron microscopy (FESEM). Figure 2(a, b) shows the typical SEM images of SnS2-C and SnS2, respectively, and their insets are the corresponding high-resolution transmission electron microscopy (HRTEM) images. The SnS2-C samples exhibit flower type morphology composed of a number of nanosheets having uniform sheet dimension ~ 300–400 nm; however, these aggregated nanosheets have rough surface. Typical thickness of the SnS2-C nanosheets is ~ 30–60 nm, well underneath the photogenerated carriers diffusion length of SnS2 crystal, which is more favorable for the carrier diffusion process during photocatalytic reaction. For the SnS2 samples, we observed plate-like nanostructures, where the nanoplates are thicker and bigger than those nanosheets in SnS2-C. The nanoplates are ~ 0.5–1 micron in size and 150–250 nm in thickness, whilst showing a smooth surface morphology. Figure 2(c, d) shows the HRTEM lattice fringes of the SnS2-C and SnS2, respectively, and their insets are the corresponding selective area electron diffraction (SAED) patterns. The SAED of SnS2-C reveals the polycrystalline nature and dominant 001, 100, 101, and 110 diffraction planes with other planes, whereas SnS2 shows single-crystal diffraction along the [001] axis. It shall be noted that the HRTEM image analysis indicates the interplaner spacing of SnS2-C is larger than that of SnS2. This result is in good agreement with the XRD analysis results. Figure 2e shows the high-angle annular dark field (HAADF) image and energy dispersive x-ray spectroscopy (EDX) elemental maps of the SnS2-C samples, signifying that the Sn, S and C are evenly distributed within the SnS2-C nanostructure. In Fig. 2f the HAADF-EDX elemental mapping of SnS2 clearly shows Sn and S are well distributed without any elemental carbons. This is consistent with the previous elemental analysis data.

### Chemical composition and photoluminescence study

Figure 3(a, b) presents the comparison of high-resolution XPS spectra of Sn 3d and S 2p of the as-prepared SnS2-C and SnS2 samples. In Fig. 3a, the measured binding energies of SnS2-C as compared with SnS2, corresponding to Sn 3d5/2 and Sn 3d3/2, are higher binding energy shifted and ~ 486.7 and 495.2 eV, respectively; these binding energies indicate Sn4+ ions in the SnS2 samples. This shift is induced by the distortion of the SnS2 lattice after carbon doping. A difference of around 8.4 eV between the two strong Sn 3d peaks is characteristic of tetravalent Sn 3d states. Furthermore, in Fig. 3b, the high-resolution S 2p core level analysis of SnS2-C at binding energies of ~ 161.6 and 162.8 eV corresponds to S 2p3/2 and S 2p1/2, which are good typical values for a metal sulfide with a doublet separation of around 1.2 eV. The observed S 2p3/2 and S 2p1/2 values of SnS2-C are higher binding energy shifted as compared with SnS2. The observed XPS-binding energies of Sn 3d and S 2p spectra confirmed the Sn4+ and S2+ characters of the as-prepared SnS2 samples. Interestingly, in SnS2-C, we observed two extra resolvable peaks around 163.4 and 164.6 eV, which revealed the corresponding S 2p3/2 and S 2p1/2 states of polysulfide. The XPS results are well consistent with the reported value37, 38. To study the transfer and exciton separation behavior of the photogenerated electrons and holes of the as-prepared SnS2 we carried out the photoluminescence (PL) and time-resolved photoluminescence (TRPL) measurements as shown in Fig. 3c (see Supplementary Fig. 5). Two PL peaks around 493 and 548 nm were observed for SnS2; in contrast, these peaks become weak in case of SnS2-C, revealing that the recombination of photo-induced charge carriers is reduced greatly, presumably by the enhanced interfacial charge transfer between the carbonaceous matters and SnS2. The normalized PL spectrum of SnS2-C shows a nearly threefold lower PL intensity as compared with that of SnS2, revealing that carbon doping lowers the recombination rate. To understand the exciton separation behavior, we measured TRPL spectroscopy at 493 and 548 nm emissions to estimate the lifetime of the electron-hole pair. The emission decay data of SnS2 and SnS2-C were fitted biexponentially (see Supplementary Fig. 5) and the calculated slow decay time τ1, fast decay time τ2 and average lifetime τavg are summarized in Fig. 3c. The observed average lifetimes for SnS2-C are 4.88 and 0.33 ns, which are much less than the 12.98 and 24.53 ns for SnS2 at 493 and 548 nm, respectively. This shortening of the lifetime in SnS2-C indicates the emergence of a nonradiative pathway, that is, the delocalization of electrons from SnS2 to C and hence effective carrier separation. Therefore, the lower recombination of photogenerated electrons in the SnS2-C allows them to reach the surface and consequently enhance the photoreduction process. Supplementary Figure 6 shows the impedance spectroscopy data for the SnS2-C and SnS2 on FTO electrodes at an applied potential of 1.2 V (vs NHE) with amplitude of 10 mV and a frequency ranging from 0.01 to 105 Hz in 0.1 M Na2SO4. The Nyquist plot reveals ideal semiconductor behavior of both SnS2-C and SnS2. However, the Nyquist plot for the SnS2-C in the high-frequency domain shows a smaller semicircle with a low RC (270.9 Ω/cm2) compared with that of the SnS2 (398.7 Ω/cm2), suggesting that the presence of carbon in the SnS2-C not only improves the charge transfer behavior but also offers more conducting pathway.

Nitrogen adsorption–desorption isotherm measurements were carried out to determine the surface area of the as-prepared SnS2 samples. Supplementary Figure 7 shows the corresponding N2 adsorption–desorption isotherms for both SnS2 and SnS2-C architectures. The shape of the curve is typical for a type II isotherm, indicating the presence of a macroporous structure for both samples. In addition, the hysteresis loops of type H3 are observed, reflecting the presence of non-rigid aggregates of plate-like particles with macropores network. Using the Brunauer–Emmett–Teller (BET) method, the specific surface area of the SnS2-C was measured as about 26.56 m2/g, which was larger than that of the SnS2 (10.73 m2/g). The two times higher surface area of SnS2-C could offer more active sites exposed for CO2 adsorption, thus more favorable for the photocatalytic CO2 reduction to solar fuels products.

### CO2 reduction mechanism

It is well accepted that the photocatalytic CO2 reduction is a multi-electron reduction. In the initial step, direct photon absorption by SnS2 generates electron-hole pairs. Specifically, carbon-doped SnS2-C significantly extends the absorption band of the materials into longer wavelength range (near 530 nm and above) as compared with undoped SnS2. The carbon doping also promotes the CO2 molecule adsorption on the surface with a relatively small dissociation barrier, as shown in simulation studies. Moreover, carbon-doped SnS2-C containing smaller nanosheets with only a few atomic layers can shorten the charge diffusion time as compared with SnS2. The band edge positions of the photocatalysts directly influence the photocatalytic reduction and oxidation reactions at the catalyst surface. To understand the details of the electronic state and band energy alignment of SnS2-C and SnS2, we performed the ultraviolet photoemission spectroscopy (UPS) study shown in Supplementary Figure 15. The work functions of SnS2-C and SnS2 were calculated to be 4.4 and 4.16 eV (vs vacuum level) (see Supplementary Table 7), from which the corresponding Fermi levels can be deduced. Based on the calculated Fermi levels, conduction band and valence band maxima of SnS2-C and SnS2, we have drawn the electronic band diagram as shown in Fig. 6. A corresponding hypothetical photoreduction mechanism has been proposed. The electronic band diagram clearly shows that the position of the frontier orbitals of CO2 with respect to the conduction band position in both SnS2 and SnS2-C would make multi-electron reduction process feasible. However, in SnS2-C, interstitially doped carbon introduced somewhat longer band tail owing to the microstrain induced new electronic state penetration into the bulk. The doped carbon helps the electrons to migrate faster to the surface of SnS2-C for the reduction reaction. Besides electrons, the photogenerated holes may react with the water molecules to generate oxygen, hydrogen peroxide or hydroxide radicals. The conduction band position of SnS2-C with respect to the onset reduction potential energy of CO2 favors ten-electron reduction on the surface of the photocatalyst. The ten-electron reduction processes are involved in the production of acetaldehyde in our experiment. The overall reactions can be described in the following equations.

$${\mathrm{SnS}}_2 + {{h\nu }} \to {\mathrm{SnS}}_2\left( {{\mathrm{e}}^ - + {\mathrm{h}}^ + } \right)$$
(1)
$${\mathrm{H}}_2{\mathrm{O + }}2{\mathrm{h}}^ + \to 2{\mathrm{H}}^ + {\mathrm{ + 1/2O}}_2$$
(2)
$${\mathrm{H}}_2{\mathrm{O}} + {\mathrm{h}}^ + \to {\mathrm{1/2H}}_2{\mathrm{O}}_2 + {\mathrm{H}}^ +$$
(3)
$${\mathrm{H}}_2{\mathrm{O}} + {\mathrm{h}}^ + \to {}^ \cdot {\mathrm{OH}} + {\mathrm{H}}^ +$$
(4)
$${\mathrm{S}}^{2 - } + 2{\mathrm{h}}^ + \to {\mathrm{S}}$$
(5)
$$2{\mathrm{CO}}_2 + 10{\mathrm{H}}^ + {\mathrm{ + }}10{\mathrm{e}}^ - \to {\mathrm{CH}}_3{\mathrm{CHO}} + 3{\mathrm{H}}_2{\mathrm{O}}$$
(6)

## Discussion

The overall photocatalytic multi-electron CO2 reduction mechanism is more complex than the single electron water-splitting reaction. However, in the photocatalytic CO2 reduction process, the photogenerated holes move around to the surface and cannot be excluded. The S 2p XPS analysis of SnS2-C reveals that the two extra deconvoluted peaks are owing to polysulfides, which may act as scavenging agents to eliminate the photogenerated holes, resulting in more efficient separation of the photogenerated electrons and holes. Moreover, the generation of O2 is suppressed, whereas the yield of acetaldehyde is enhanced. On the other hand, the excess polysulfide oxidizes to elemental sulfur via redox process and suppresses the corrosion of SnS2 during the photocatalytic reaction. Overall, the enhanced photocatalytic reaction may result from combined favorable situations, including band edges tuning by induced microstrain together with high surface area, reduced photocarriers diffusion length and improved charge separation process in carbon-doped SnS2. It is worth to mention that carbon-doped SnS2-C can be synthesized by a simple l-cysteine assisted hydrothermal method and is an effective way to improve the photocatalytic CO2 reduction activity under visible light. Nevertheless, more studies are needed to better understand the mechanism and to further enhance the photocatalytic activity and selectivity of hydrocarbon formation.

In conclusion, carbon-doped SnS2-C was successfully synthesized by an l-cysteine assisted hydrothermal process and was demonstrated to be a highly efficient photocatalyst for CO2 reduction under visible light. The synthesized SnS2-C photocatalyst shows selective photocatalytic CO2 reduction to acetaldehyde with moderately high PCQE above 0.7%. Based on various structural analyses, the C doping is mainly incorporated as interstitials, which introduce micro strains and affect electronic band structures as well as the optical properties. Moreover, DFT calculations suggest that carbon doping also promotes the CO2 molecule adsorption on the surface with a relatively small dissociation barrier in C doped SnS2-C. All these factors lead to significantly enhanced photocatalytic reduction of CO2. We believe that carbon doping in the narrow-band gap of dichalcogenides and other metal sulfides is a promising approach to develop high quantum efficiency photocatalysts for CO2 reduction to solar fuels.

## Methods

### Synthesis

The carbon-doped SnS2 nanoflower (SnS2-C) and SnS2 nanoplate (SnS2) were prepared by hydrothermal process. All the reagents used in the experiment were of analytical grade and used without further purification. In a typical procedure, 1 mM of tin (IV) chloride pentahydrate (SnCl4, 5H2O) and 5 mM l-cysteine (C3H7NO2S) were added to a 60 ml of distilled water and gradually dispersed to form a homogeneous solution by vigorous magnetic stirring for 1 h at room temperature. Finally, the resulting solution was transferred into a Teflon-lined stainless autoclave. The autoclave was sealed and heated at 180 °C for 24 h. After hydrothermal reaction, the sample was cooled to room temperature naturally. The resulting product was collected by centrifugation at 8000 rpm for 10 min and washed several times with distilled water. Finally, the collected yellow SnS2-C powder was vacuum-dried at 80 °C overnight. In a similar procedure using 5 mM thiourea (CH4N2S) as an S source, SnS2 nanoplate (SnS2) was synthesized at 180 °C for 12 h and vacuum-dried at 80 °C. The overall SnS2-C and SnS2 synthesis process is schematically presented in the Supplementary Figure 1.

### Characterization

The ultraviolet-visible absorption spectrum of powder samples was measured with a Jasco V-670 spectrophotometer using an integrated sphere. The crystal structures were determined by XRD using CuKα radiation (Bruker, D2 PHASER with XFlash). The surface morphology of all samples was characterized by FESEM (JEOL, 6700F). The HRTEM (JEOL-2100) studies with SAED and EDX were also performed to determine morphology, crystal phase and elemental compositions. The Raman spectra were measured using Jobin-Yvon LabRAM HR800 with laser source of 633 nm. X-ray photoelectron spectroscopy (XPS) analysis was performed on a theta probe ESCA VG Scientific (2002) using a monochromatic AlKα as the exciting source. The peak positions of the XPS were calibrated carefully with respect to the Au 4f peak. Finally, all the XPS spectra were deconvoluted by Voigt fitting function after a Shirley background subtraction procedure. Excitation-dependent PL measurements were performed using a spectrofluorometer (Horiba Jobin-Yvon FluoroMax-4). TRPL techniques were carried out using time-correlated single-photon counting. A pulsed laser with a wavelength of 375 nm, duration of 250 fs, and repetition frequency of 20 MHz was used as the excitation source for the steady state PL and TRPL studies. The collected PL was dispersed by a 0.75 m spectrometer and detected by the photomultiplier tube. For work function and valence band maxima measurement, UPS was performed using Perkin-Elmer phi 5400 system under vacuum with Fermi energy (Ef) calibration using in situ deposited gold. For UPS measurement, the samples were uniformly dispersed on the gold-coated ITO. BET surface area was determined by recording nitrogen adsorption and desorption isotherms using Micromeritics ASAP 2010 Accelerated Surface Area and Porosimetry System. The total volume was calculated from the amount of nitrogen adsorbed at P/Po=0.97, assuming that adsorption on the external surface was negligible in comparison to the adsorption in pores. For the microporosity study, the adsorption data were acquired at relative pressure P/Po between 0 and 0.01 with little incremental dose at liquid nitrogen temperature (77 K), using a Micromeritics 3Flex analyzer, which was used for carbon dioxide gas (CO2, purity of 99.9992%) adsorption measurements as well. All samples (50 mg each) were initially degassed at 423 K for 12 h under a 1 × 10−2 mmHg vacuum level, by Micromeritics Smart VacPrep degasser. The CO2 sorption was analyzed at relative pressure (P/P0) between 0.0003 and 0.96 for the P0 of 789.5 mmHg at 195 K. During the analysis, the temperatures were maintained by the slurry of the combination of dry ice and acetone (wt/wt = 0.86) in Dewar. After the analysis, the free space of the sample tube was determined by using Helium gas (purity of 99.9992%). The photocatalytic CO2 reduction products were analyzed by gas chromatography (GC). The GC analyses were performed on a GC-FID-CHINA CHROMATOGRAPHY 9800 system using glass column Porapak Q (80–100 mesh), at injection temperature of 50 °C, FID temperature of 150 °C and oven temperature of 80 °C. GC-MS analysis was performed on GC (HP6890)/MS(5973) system (column-Agilent J&W 122–7032 DB-WAX, inj. Temp. 250 °C and oven temperature of 35 °C utilizing 13CO2 source (Cambridge Isotope laboratories, Inc. USA).

### Microstructural parameters analysis of the SnS2-C and SnS2

The average crystallite size of the sample estimated using Scherrer’s formula, i.e., (D) = Kλ/βcosθ, where K = 0.89 is the shape factor, λ is the X-ray wavelength of X-ray radiation, θ is Bragg’s angle, and β is the full width at half maximum of the respective peak. The microstrain is calculated using the following relation: ε = βcosθ/4. Supplementary Table 1 shows the average crystal size, microstarin, and lattice d-spacing calculation.

### Solid-state NMR analysis of SnS2-C

The 119Sn MAS NMR spectrum of SnS2-C and commercial SnS2 (MKN-SnS2-900 purchased from M K Implex Corp. Canada) are shown in Supplementary Figure 2. SnS2-NS synthesized from cysteine shows a major chemical shift at −76 ppm, which is consistent with 119Sn MAS NMR of commercial SnS2. The observed line width broadening may be a result of greater distribution of crystal grain size. The additional small peak at around −605 ppm, could be attributed to different stacking of 4H and 18R polytype of SnS2 as supported by our Raman spectroscopy. The 13C CPMAS NMR spectra of SnS2-C before and after CO2 reduction reaction are shown in Supplementary Figure 3. For comparison, 13C NMR chemical shift of l-cysteine and pyruvic acid are summarized in Supplementary Table 2. For other details of experimental procedures, please refer to the Supplementary Methods.

### Data availability

The authors declare that data supporting the findings of this study are available within the paper and the supplementary information file.

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## Acknowledgements

We thank the Ministry of Science and Technology (MOST, especially 103–2745-M-002–006-ASP, 104–2745-M-002–004-ASP), Academia Sinica, National Taiwan University, the Ministry of Education (MOE), Taiwan for financial support. Technical support from Nano-Core, the Core facilities for nanoscience and nanotechnology at Academia Sinica in Taiwan, is acknowledged.

## Author information

I.S. proposed and performed the synthesis, UV-Vis, XRD, Raman, experiments; S.S. performed the GC and SEM measurements, Y.-C.C. performed GC calibration and photocatalyst experimental setup; R.P. performed DFT calculations directed by M.C.L., I.S. and A.S. performed the GC-MS isotope tracer analysis, F.-Y.F. performed PL and TRPL measurement, T.-Y.Y. performed the solid-state NMR measurement; P.-H.C. performed the UPS measurements; P.-W.C. performed CO2 adsorption analysis; I.S., W.-F.C., P.-W.C., C.-I.W., M.-C.L., K.-H.C. and L.-C.C. discussed and analyzed the results; I.S., K.-H.C. and L.-C.C. co-wrote the manuscript; K.-H.C. and L.-C.C. supervised the project.

Correspondence to Li-Chyong Chen or Kuei-Hsien Chen.

## Ethics declarations

### Competing interests

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Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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text:
Mr. Lee can paint 20 chairs in t hours. He uses 3 liters of paint for every 12 chairs that he painted. How do you find, in terms of t, the number of chairs that he can paint in 3 hours?

Aug 27, 2017

See a solution process below:

Explanation:

We can write this equation:

$t \text{ hours" = 20" chairs}$

We can now multiply each side of the equation by $\textcolor{red}{3}$ to find the number of chairs Mr. Lee can paint in 3 hours if he paints them continuously at the same rate.

$\textcolor{red}{3} \times t \text{ hours" = color(red)(3) xx 20" chairs}$

$3 t \text{ hours" = 60" chairs}$

Mr. Lee can paint 60 chairs in $3 t$ hours.

format: plain


text:
### Permutation Game

2020

After a long day, Alice and Bob decided to play a little game. The game board consists of $n$ cells in a straight line, numbered […]


text:
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15 Oct 2010, 03:31
Hi,
Can someone please let me know answeres to the following queries reg GMAT:

1) Is is mendatory to mention / specify the collage names in which we are trying to take admission or can I give GMAT without any list as I want to use my score after some time may be 1 yr.
2)what is the GMAT registration form like?Do we need to write some long descriptive answers?
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15 Oct 2010, 04:04
utin wrote:
Hi,
Can someone please let me know answeres to the following queries reg GMAT:

1) Is is mendatory to mention / specify the collage names in which we are trying to take admission or can I give GMAT without any list as I want to use my score after some time may be 1 yr.
2)what is the GMAT registration form like?Do we need to write some long descriptive answers?
3)Let me know the bare minimum requirement for giving GMAT.

Hi

1. You don't need to fill out any schools at the time you take the GMAT. However when you take the test you get 4 or 5 reports for free, after the test you will pay about $28 per school. 2. If you mean the form to sign up for the test its pretty simple demographic information: name, address, etc 3. To take the GMAT the minimum is that you sign up and pay. I'm not sure what other information you're looking for. If you have other questions I'll try to help Manager Joined: 26 Mar 2010 Posts: 125 Followers: 2 Kudos [?]: 9 [0], given: 17 Re: GMAT Queries [#permalink] ### Show Tags 15 Oct 2010, 04:13 akeel6 wrote: utin wrote: Hi, Can someone please let me know answeres to the following queries reg GMAT: 1) Is is mendatory to mention / specify the collage names in which we are trying to take admission or can I give GMAT without any list as I want to use my score after some time may be 1 yr. 2)what is the GMAT registration form like?Do we need to write some long descriptive answers? 3)Let me know the bare minimum requirement for giving GMAT. Hi 1. You don't need to fill out any schools at the time you take the GMAT. However when you take the test you get 4 or 5 reports for free, after the test you will pay about$28 per school.

2. If you mean the form to sign up for the test its pretty simple demographic information: name, address, etc

3. To take the GMAT the minimum is that you sign up and pay.

I'm not sure what other information you're looking for. If you have other questions I'll try to help

Thanks Akeel,
could not understand: "4 or 5 reports for free, after the test you will pay about \$28 per school.
"

Can you please elaborate for me. Also what time of the year do the admissions open in various universitites/schools?
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Hi,
Can someone please help me know the programs i can opt for, post gmat. I am a Test Engineer with Infosys for 4 years now. Considering my job experience, can you please guide me on what program should i pursue that will help me boost my career.

Looking forward for your reply.

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All of them would be OK for you.
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Thank you so much for the reply.

Could you please elaborate on the following:
To be specific, what between MBA in Information Technology and MIS would be a better option? I would also like to know about the job scenarios for both the programs(considering my profile). Also, could you please tell me if MIS has the same credibility as MBA.

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Hi I need some help.

I am an Indian currently in Germany, I am very new to GMAT.
I am planning to give GMAT in February but I will be going to India(in January and then again to India in later months like June),
1.) Is it possible to give GMAT in Germany,or am I supposed to give it in India?
2) If I can give it in Germany, am I supposed to do something extra for it, because I dont know the German language out here.

Thanks in advance.
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# 3 ques. Cumulative (logs,circles w/tangent lines)

1. Aug 3, 2009

### whitehorsey

1. Simplify each expression:
2 log49 - log23

2. none

3. 2 log49 - log23
= log481 - log23
= - log23
I get - log23 when it should just be log23. What did i do wrong?

1. Find the equation of the following circle:
The circle that passes through the origin and has intercepts equal to 1 and 2 on the x- and y- axes, respectively.

2. none

3. I have no idea how to do this problem.

1. For the circle x2 + y2 + 6x - 4y + 3 =0, find:
The equation of the tangent line at the point (-2,5).

2. xx0+yy0 = r2

3. I know that the center is (-3,2) and the radius is radical 10, but when i solve this problem I get the wrong answer.
xx0+yy0 = r2
x(-2) + y(5) = r2
-2x +5y = 10
The answer should be x + 3y = 13.
What did I do wrong?

Thank You!!

2. Aug 3, 2009

### songoku

Hi whitehorsey
Can you elaborate how you got - log23 ?

The equation of circle : (x - a)^2 + (y - b)^2 = r^2, where (a, b) is the center.
The circle passes through (0,0) ; (1,0) and (0,2)

That's the formula if the center is origin.

Find the slope first. Do you know implicit differentiation?

3. Aug 4, 2009

### HallsofIvy

If x= $log_4 81$ then $81= 4^x= (2^2)^x= 2^{2x}$ so $log_2 81= 2x$ and $x= log_4 81= (1/2)log_2 81= log_2 9$.
What is $log_2 9- log_2 3$?

$(x- a)^2+ (y- b)^2= R^2$ must be true for x= 0, y= 0; x= 1, y= 0; and x= 0, y= 2. You have $(0- a)^2+ (0- b)^2= a^2+ b^2= R^2$, $(1- a)^2+ b^2= R^2$, and $(0-a)^2+ (2- b)^2= R^2$. Three equations to solve for the three unknown values, a, b, and R. What happens if you subtract the first equation from the second? The first equation from the third?

You certainly don't need Calculus, as songoku suggested. You know the center of the circle is (-3, 2). What is the slope of the line from (-3, 2) to (-2, 5), a radius of the circle? The tangent at that point on the circle must be perpendicular to the radius: if two lines of slopes m1 and m2 are perpendicular, then m1m2= -1 so you can find the slope of the tangent line. What is the equation of the line through (-2, 5) with that slope?

Last edited by a moderator: Sep 5, 2009
4. Aug 4, 2009

### songoku

Nice suggestion Mr. Hall ^^

5. Aug 5, 2009

### whitehorsey

For the first problem I don't get how you could put the x down there ($81= 4^x= (2^2)^x= 2^2x$) when it was an exponent before.

Thank You for your help on the second problem. I understand it now. ^ ^

For the third problem, I find the slope and it was 3. Then I tried solving for the tangent line but i ended up with y = 3x +11. Can you teach me what I did wrong? I tried different ways but I can't seem to figure it out.

6. Aug 7, 2009

### whitehorsey

i found the slope which is 3. What do i do next? hmmm i don't recall ever learning implicit differentation

7. Aug 7, 2009

### rock.freak667

x=log4 81 (you know that logaa=1 right?)

think of it like this xlog44=log481 =>log44x=log481 => 4x=81

Now doing what HallsofIvy said: 4=22 so we have (22)x=22x.
you can continue from where HallsofIvy left of.

Another way is to use the 'change of base formula' for logs.

$$log_a b = \frac{log_c b}{log_c a}$$

So for 2 log49 - log23 , change either of the logs base to the other and simplify (base 4 to 2 or vice versa)

The angle between a radius and a tangent at the point of contact is 90 degrees i.e. radius and tangent are perpendicular.

Now if line 1 and line 2 (with gradients m1 and m2 respectively) are perpendicular then m1m2=-1 (as HallsofIvy said previously)

the gradient you found is the gradient of the radius connecting the centre to (-2,5). Can you then find the gradient of the tangent? When you get that, you have the gradient of the tangent and a point on the tangent, you can now find the required equation.

8. Aug 7, 2009

### whitehorsey

Hi rock.freak667
I was wondering how the change of base formula allows you to change the 4 into the 2 or vice versa like you said. Because I thought it only allows you to solve problems like these log37 which would change into log 7/log 3.

For the other question, I have tried many different ways but cannot seem to figure out the gradient of the tangent. Can you please show me? I'm very confused right now. :[

9. Aug 7, 2009

### mathie.girl

When you changed log37 into log 7/log 3 you actually started using a new base of 10 (remember if it doesn't have a base written there, you're actually working in base 10). This is often done because your calculator has a button with this base on it and it allows you to use your calculator to compute this log. However, you could have chosen any base. For instance,

$$log_{3}7 = \frac{log_{a}7}{log_{a}3} = \frac{log_{15}7}{log_{15}3} = \frac{log_{957}7}{log_{957}3}$$

Normally you'd pick $$a = 10$$, but if you want to work with base 2, you can also choose that.

For the slope of the tangent, you need to use that the radius of a circle and the tangent to a circle at the same point are perpendicular. Do you remember about the slopes of perpendicular lines? If line $$l$$1 is perpendicular to $$l$$2, their slopes are negative reciprocals. So pretty much, you take the slope $$m$$ of $$l$$1, make it negative and flip it over in order to get the slope of $$l$$2.

10. Sep 4, 2009

### whitehorsey

I got it Thank You!!

11. Sep 5, 2009

### HallsofIvy

I didn't. That was a typo on my part. I mean $81= 4^x= (2^2)^x= 2^{2x}$

The slope of a radius, from (-3,2) to (-2,5), is 3. As I said, a tangent must be perpendicular to that radius and so has slope -1/3.


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Skorobogatov A. Economics/EC. WP BRP. Высшая школа экономики, 2014. No. WP BRP 59/EC/2014.
This paper uses the famous events related to Pussy Riot as a natural experiment to examine the effect of alternative media on church membership. A differences-in-differences strategy is used to explore the effect in question. The hypothesis is that, given a lack of religious background on the majority of the population and strong temporal interest in religious issues promoted by some provocative event, mass media can substantially affect religious choice. To check if this is the case, we compare the dynamics of religious choice of those exposed to alternative media reports on church topics and the rest of the people. As a proxy of familiarity with an alternative view, we use a dummy variable for using Internet. Our main result is that, during the experiment run over the year 2012, the growth of self-reported Orthodox and strict Orthodox believers was significantly lower in the treatment group than in the control group. Exposure to alternative media coverage turned out to heavily affect religious choice.
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Velizhev M. Literary Studies. WP BRP. Высшая школа экономики, 2017. No. WP BRP 19/LS/2017.
This paper is aimed at exploring the rhetorical conventions of political polemics in 19th century Russia. We will compare two texts published in the 1830s – a classic “First Philosophical Letter” by Petr Chaadaev and a less known reply to it written by young Andrej Krayevsky – “Thoughts on Russia”. First we plan to focus on their stated ideas, and then to consider the political language of the opponents. As we will see, if their ideas were completely different, Chaadaev and Krayevsky shared the same political idiom – the language of official national ideology. We will try to demonstrate that it was possible to use the language of the official ideology not only to establish that ideology but paradoxically also to start an open debate with it.
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Gorinov A. Working papers by Cornell University. Cornell University, 2017. No. 1702.08428 .
B. Totaro showed \cite{totaro} that the rational cohomology of configuration spaces of smooth complex projective varieties is isomorphic as an algebra to the $E_\infty$ term of the Leray spectral sequence corresponding to the open embedding of the configuration space into the Cartesian power. In this note we show that the isomorphism can be chosen to be compatible with the mixed Hodge structures. In particular, we prove that the mixed Hodge structures on the configuration spaces of smooth complex projective varieties are direct sums of pure Hodge structures.
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Finkelberg M. V., Braverman A. math. arxive. Cornell University, 2018
In arXiv:1807.09038 we formulated a conjecture describing the derived category D-mod(Gr_GL(n)) of (all) D-modules on the affine Grassmannian of the group GL(n) as the category of ind-coherent sheaves on a certain stack (it is explained in loc. cit. that this conjecture "follows" naturally from some heuristic arguments involving 3-dimensional quantum field theory). In this paper we prove a weaker version of this conjecture for the case n=2.
Working paper
Hassanpour N. Comparative Politics, Peace and Conflict Studies. PS. academia.edu, 2014
Motivated by dichotomous scholarly results on the conflict-communication nexus, I compare the predictions of two competing theories of urban conflict based on coordination and contagion. I exploit a quasi-experimental intervention in the Syrian nation-wide communications in November 2012 along with a geolocated dataset of daily conflict locations (n= 627) in Damascus to build a panel (n= 275 days x 252 spatial units = 69,300), to show that disruption of communications coincided with an unprecedented increase in the geographic dispersion of conflict. Furthermore, while compared to pro-regime atrocities rebel activity was more spread in space and time, lack of coordination meant more spatiotemporal clustering: a combination of global dispersion and local clustering deﬁned the insurgency. On average, one additional prior incident in the spatiotemporal vicinity translated to 25% higher rates of recurrence. In addition to detecting significant spatiotemporal spillover of violence, I show that the contagion was effectively activated during the blackout.
Working paper
Semenova M., Andrievskaya I. K. Financial Economics. FE. Высшая школа экономики, 2012. No. 07.
Market discipline is usually studied in the retail or the corporate deposit markets, while the interbank loan market is disregarded. Banks' abilities to exert market discipline are taken for granted, as they are expected to have the expertise to assess correctly the riskiness of other banks. However, the “crises of trust” (as one in 2004 in Russia) create some doubts as to whether efficient peer monitoring and peer discipline exist: the interbank loan market may be frozen in response to external information which is unrelated to the banks’ current reliability. This seems to be one of the reasons for the interbank loan markets being extremely fragile during periods of financial instability, undermining the smooth functioning of the whole banking system, as banks are tightly interconnected. We provide some evidence for market discipline in the Russian interbank market. We show that the only disciplinary mechanism that functions is a price-based one: more reliable banks enjoy lower interest rates. The quantitative discipline functions only for the largest borrowers. In general, decisions on credit limits are based not on changes in another bank’s riskiness but on other information like reputation, soft information or public announcements that may be even unrelated to a particular bank.
Working paper
Nataliya Kochkina, Evgeniya Popova. ACEI Working Paper Series. AWP. Association for Cultural Economics International, 2017. No. AWP-06-2017.
In the times of Soviet Union books were a luxury good. This paper examines whether books are still a luxury good in Russia. For this purpose data from one of the Russian book retail chains is used to empirically estimate a general book demand and separate demand models for genres. We focus on estimating income elasticity. For this reason we construct a covariate on the basis of monthly wages of working individuals that reveals consumer income. Moreover, this paper is one of the few which addresses in detail the influence of books content quality on book demand. The main result is that books on average are not luxury goods anymore in Russia. However two genres: foreign prose and poetry are exceptions and can be called luxury goods. We also conclude that quality control covariates (book rating and number of people who rated the book) are important determinants of book demand as they influence significantly the general book demand and the demand models for different genres as well.
Working paper
Malakhovskaya O. A., Minabutdinov A. Economics/EC. WP BRP. Высшая школа экономики, 2013. No. WP BRP 48/EC/2013.
This paper constructs a DSGE model for an economy with commodity exports. We estimate the model on Russian data, making a special focus on quantitative effects of commodity price dynamics. There is a widespread belief that economic activity in Russia crucially depends on oil prices, but quantitative estimates are scarce. We estimate an oil price effect on the Russian economy in the general equilibrium framework. Our framework is similar to those of Kollmann(2001) and Dam and Linaa (2005), but we extend their models by explicitly accounting for oil revenues. In addition to standard supply, demand, cost-push, and monetary policy shocks, we include the shock of commodity export revenues, which are supposed to be like a windfall. The main objective of the paper is to identify the contribution of structural shocks to business cycle fluctuations in the Russian economy. We estimate the parameters and stochastic processes that govern ten structural shocks using Bayesian techniques. The model yields plausible estimates, and the impulse response functions are in line with empirical evidence. We found that despite a strong impact on GDP from commodity export shocks, business cycles in Russia are mostly domestically based
Working paper
Dabrowski M. Bruegel blog. Bruegel blog. Bruegel, 2018
Democracy has not always accompanied market economy. But in modern societies, economic and political freedoms are increasingly interconnected. Democracy and market economy can support each other. This is particularly true in post-communist economies of Central and Eastern Europe and the former Soviet Union. Thus, authoritarian tendencies observed in these and other regions can negatively affect quality of economic policy and governance.
Working paper
Lyusin D., Mohammed A. PSYCHOLOGY. WP BRP. Издательский дом НИУ ВШЭ, 2018
The temporal dynamic characteristics of mood play an important role in various aspects of our lives including our psychological health and well-being. It is assumed that the individuals with high emotional intelligence (EI) are characterized by more positive and stable moods. However, most studies analyze how EI is related to emotional traits or momentary assessments of mood; there are almost no findings on EI relationships with mood dynamics. The present study fills this gap. Two research questions were asked. How mood dynamics characteristics are related to each other and to what extent are they independent? Which aspects of EI are related to particular characteristics of mood dynamics? Method. To collect data on mood dynamics, an experience sampling procedure was implemented. Twenty-six female participants reported their mood for two weeks, three times a day, using the EmoS-18 questionnaire. Their emotional intelligence was measured with the EmIn questionnaire. Mean mood scores calculated across all measurement points were regarded as static characteristics showing a mood background typical for the participant. Also, three dynamic characteristics of mood were calculated, namely variability, instability, and inertia. Results. Mood variability and instability were found to be very closely related to each other, measuring essentially the same construct. Inertia is relatively independent. EI was not related to mean mood scores which contradicts the results of other studies and can be explained by the use of the experience sampling procedure. EI was positively related to the inertia of a positive mood with high arousal and a negative mood with low arousal. In addition, a negative relationship between EI and the instability of tension was found. Most of the correlations were low. Further studies with higher statistical power are needed for more decisive conclusions. However, the results show that experience sampling provides new important insights on the role of EI in mood
Working paper
Tatarko A. SEARCH Working Paper. WP5. Университет Барселоны, 2013. No. WP5/04.
This study analyzes the phenomenology of socio-psychological capital viewed as a resource for psychological relations which constitutes the basis for the formation of social capital. A crosscultural analysis of the impact of value orientations on socio-psychological capital has been performed. Based on a sample of 3 ethnic groups (Russians, n = 103; Chechens, n = 100; Ingush, n = 109), it has been demonstrated that although the impact of individual values on socio-psychological capital obeys logic, it may be culture-specific. Values of Self-Transcendence (Benevolence and Universalism) have a positive impact on the socio-psychological capital of a multicultural society, whereas values of Self-Enhancement influence it negatively. Openness to Change values positively influence civic identity but have a negative effect on perceived social capital. Conservation values positively affect the civic (Russian) identity of the representatives of the Ingush ethnic group.
Working paper
Tatarko A. Psychology. PSY. Высшая школа экономики, 2012. No. 03.
This study analyzes the phenomenology of socio-psychological capital viewed as a resource for psychological relations which constitutes the basis for the formation of social capital. A cross-cultural analysis of the impact of value orientations on socio-psychological capital has been performed. Based on a sample of 3 ethnic groups (Russians, n = 103; Chechens, n = 100; Ingush, n = 109), it has been demonstrated that although the impact of individual values on socio-psychological capital obeys logic, it may be culture-specific. Values of Self-Transcendence (Benevolence and Universalism) have a positive impact on the socio-psychological capital of a multicultural society, whereas values of Self-Enhancement influence it negatively. Openness to Change values positively influence civic identity but have a negative effect on perceived social capital. Conservation values positively affect the civic (Russian) identity of the representatives of the Ingush ethnic group.
Working paper
Oshchepkov A. Y. Discussion Papers of DIW Berlin. 750. DIW Berlin, German Institute for Economic Research, 2007. No. 750.
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Piontkovski D. arxiv.org. math. Cornell University, 2014. No. arXiv:1412.8601.
We show that a direct limit of surjections of (weak) Golod--Shafarevich algebras is a weak Golod--Shafarevich algebra as well. This holds both for graded and for filtered algebras provided that the filtrations are induced by the filtration of the first entry of the sequence. It follows that the limit is an algebra of exponential growth. An example shows that the assumptions of this theorem cannot be directly weakened.
Working paper
Liviu O., Verbitsky M. arxiv.org. math. Cornell University, 2010. No. 1002.3473.
We present an overview of recent results in locally conformally K¨ahler geometry, with focus on the topological properties which obstruct the existence of such structures on compact manifolds.
Working paper
Gimpelson V. E., Lukyanova A. IZA Discussion Paper. IZA, 2009. No. 3941.
The paper starts with discussing institutional framework for public sector wage setting in Russia. Given that individual choice of the sector is endogenous to wages, the authors recommend alternative econometric techniques for the public-private wage gap estimation. Applying switching regression that allows correcting for non-random sector selection, the paper provides wage gap estimates for various demographic, occupational, and territorial population subgroups. As it is shown, there is significant cross-group variation in the wage gap. The paper concludes that to eliminate the negative gap wages in the public sector should be linked to the private sector wages at the regional level.
Working paper
Poldnikov D. Law. LAW. Высшая школа экономики, 2013. No. 16/LAW/2013.
The paper suggests several ways to rediscover the legacy of early modern and classical natural law of the 18th century in contemporary legal thought through the joint efforts of legal history and legal theory with particular reference to the domain of contract law. Additionally, the paper justifies the revival of the research in the domain of natural law in connection with legal argumentation.
Working paper
Kalashnikov E. G., Gu W. arXiv. arXiv. arXiv, 2020
The rim-hook rule for quantum cohomology of the Grassmannian allows one to reduce quantum calculations to classical calculations in the cohomology of the Grassmannian. We use the Abelian/non-Abelian correspondence for cohomology to prove a rim-hook removal rule for the cohomology of quiver flag varieties. Quiver flag varieties are generalisations of type A flag varieties; this result is new even in the flag case. This gives an effective way of computing products in their cohomology, reducing computations to that in the cohomology ring of the Grassmannian. We then prove a quantum rim-hook rule for Fano quiver flag varieties (including type A flag varieties). As a corollary, we see that the Gu--Sharpe mirror to a Fano quiver flag variety computes its quantum cohomology.


text: 10 61. J is the rotational quantum number and spans integers from 0 to ∞. Moment of Inertia I = mr2. VIBRATION-ROTATION SPECTROSCOPY OF HCl By: John Ricely Abstract Using the Nicolet 6700 spectrometer, the spectrum for HCl was analyzed. Harmonic oscillator expression Allows us to find the “spring” force constant for HCl and DCl k = 514.96 N/m 18. Remember that data reported in periodic table is for abundance weighted atomic mass. Note that re is the internuclear separation for which x = 0 in equations (1) and (4) (i.e., the bottom of the potential well). There were two branches that were apparent in the result of the spectroscopy, the R branch and the P branch, that correspond to ∆J= +1 and ∆J= -1, respectively. The moment of inertia is obtained as 2 I r0, where is the reduced mass and is defined by 1 2 1 2 m m mm . The moment of inertia is defined by = I = = (13.2) (13.3) ... rotates, the rotating dipole constitutes the transition dipole operator μ. Molecules such as HCl and CO will show rotational spectra while H2, Cl2 and CO2 will not. Bad moment of inertia; Bad Calculated Bond Lengths; Bad point group; Worst molecules. Using the rotational constants from the polynomial curve fit with the definition of B gives the moment of inertia 19. m = the reduced mass. Ie is a molecular constant called the moment of inertia, which for a diatomic molecule is Ie = µre 2, and µ and r e are, in turn, the reduced mass, (see above) and the equilibrium bond length of the molecule AB. Moment of Inertia. How can I use this spectrum to find the moment of inertia of the HCL molecule about an axis through the center … Calculate the moment of inertia of an HCl molecule from its infrared absorption spectrum shown in Figure 43.9. Z-matrix; Bad Calculations. 4) Using 1.67379 x 10-27 kg and 5.80752 x 10-26 kg for the masses of individual atoms of hydrogen and chlorine, respectively, compute the reduced mass, µ, and bond length r e (in Angstroms and nm) for HCl from I = µ r e 2. The absorption lines shown involve transitions from the ground to first excited vibrational state of HCl… Moment of Inertia is also known as the angular mass or rotational inertia. Energy transitions from the spectra were plotted vs. frequency, from which several physical constants were determined. with : = ∑ − /, where is the degeneracy of the j th quantum level of an individual particle, is the Boltzmann constant, and is the absolute temperature of system. The rotational spectrum will appear as The rotational energies, as we shall see, depend on the rotational constants designated by A, B, and C, with A > B > C, and defined by h h „ h Calculate I, the moment of inertia, for HCl and HBr and the interatomic distances. Animated vibrations; Anharmonic. View Winning Ticket The mass of H is m(H) = 1.00794 u. Where; the moment of inertia for a molecule (I) = Then; I = m .r 2 = Σ m .r2 i i i Where: r i is the perpendicular distance of the atom i from the axis of rotation (bond length). (B) 4.21×10-51 kg m? Moment of inertia is a commonly used concept in physics. Ie is a molecular constant called the moment of inertia, which for a diatomic molecule is Ie = mre 2, and m and r e are, in turn, the reduced mass, (see above) and the equilibrium bond length of the molecule AB. Go to your Tickets dashboard to see if you won! (A) 2.68 x1047 kg m? Estimate the moment of inertia of an HCl molecule from its infrared absorption spectrum shown in Figure P 43.19. (i) Do these molecules have a pure rotational spectrum? Reduced Mass $\large \mu = \frac{m_1 m_2}{m_1 + m_2}$ for I, the moment of inertia of the HCl molecule. The most populated rotational level for the molecule at temperature of 600 K corresponds toa)J = 3b)J = 4c)J = 5d)J = 6Correct answer is option 'B'. 1-+2 Spectra and Molecular Structure – HCl & DCl By: Christopher T. Hales. This is also known as “angular mass” and it refers to a rotating body’s inertia with respect to its rotation. The rotational spectrum of HCL contains the following wavelengths (among others): 60.4um, 69.0um, 80.4um, 96.4 um, and 120.4um. 10 61. It is an extensive property of any object. where, the moment-of-inertia, I, is given by . The energies can be also expressed in terms of the rotational temperature, $$Θ_{rot}$$, which is defined as Moment of inertia plays the same role in rotational motion as mass plays in linear motion. The characteristic rotational temperature (θ R or θ rot) is commonly used in statistical thermodynamics to simplify the expression of the rotational partition function and the rotational contribution to molecular thermodynamic properties. Evaluation of the moment of inertia in HCl The bond length between H and Cl in HCl is r0 = 1.274 Å. Moment of inertia is usually specified with respect to a chosen axis of rotation. The degeneracy of the Jth quantum level is 2J+1. Determine the fundamental vibrational frequency of HCl and DCl. where $$I$$ is the moment of inertia of the molecule given by $$μr^2$$ for a diatomic and $$μ$$ is the reduced mass and $$r$$ the bond length (assuming rigid rotor approximation). 3; 2 = (3) where µ is the reduced mass, given by: = + (4) and r is the distance between the two atoms in the rigid rotor. Calculate the bond length of HCl molecule if its moment of inertia is 2×10–40 gm cm2 and reduced mass is 1.0 g mol–1. Estimate the moment of inertia of an HCl molecule from its infrared absorption spectrum shown in Figure P42.11. (C) 2.68 1 m kg (c) 2 47. In simpler terms, the moment of inertia refers to the resistance of a rotating body to angular deceleration or acceleration. and r is the internuclear distance, and, . Table of Content. The total canonical partition function of a system of identical, indistinguishable, noninteracting atoms or molecules can be divided into the atomic or molecular partition functions : =! Q: The moment of inertia of HCl Molecule about an axis passing through its centre of mass of perpendicular to the line joining the H + and Cl – ions will be (if the inter atomic distance is 1Å).. Sol: r = 1 Å = 10-10 m ; m 1 = 1 amu; m 2 = 35.5 amu. 0 m kg (b) 2 47. A classic among molecular spectra, the infrared absorption spectrum of HCl can be analyzed to gain information about both rotation and vibration of the molecule. Note that re is the internuclear separation for which x = 0 … ABSTRACT: FTIR spectroscopy was used to analyze rotational-vibrational transitions in gas-state HCl and DCl and their isotopomers (due to 35 Cl and 37 Cl) to determine molecular characteristics. Point group; State symmetry Sorted by r2. 5) Calculate the force constant for the HCl … | EduRev GATE Question is disucussed on EduRev Study Group by 167 GATE Students. Dec 11,2020 - The moment of inertia of the HCl molecule is 2.71 x 10-47kg-m2. The moments of inertia of HCl and KCl molecules are 1.5913 uÅ 2 and 131.0596 uÅ 2, respectively. An object's moment of inertia describes its resistance to angular acceleration, accounting for the total mass of the object and the distribution of mass around the axis of rotation. Definition. The moment of inertia of HCl molecule about an axis passing through its centre of mass and perpendicular to the line joining the H and Cl ions will be, if the interatomic distance is 1 Å (a) 2 47. Formula It mainly depends on the distribution of mass around an axis of rotation. We assumed above that B of R(0) and B of P(1) were equal, however they differ because of this phenomenon and B is given by (ii) Using the rigid rotor model draw a sketch of the rotational spectrum for each molecule indicating the selection rules. Can you explain this answer? ( moment nert a out principal axis given 2by Iǁ = 2m H R (1‐cosϴ) where the mass of hydrogen atom m H =1.6735*10‐27 kg, 10the N‐H bond length r= 1.014*10‐ m and the bond angle is 106 780The106.780.The moment of inertia abo tabout principal aisaxis is I ǁ) As a diatomic molecule vibrates, its bond length changes. Moment of inertia (I), also called mass moment of inertia which is a measure of an object's resistance to changes in its rotation rate. Each peak, differentiating between 35Cl and 37Cl, is assigned an m value and then … Calculate moment of inertia of this molecule, and then use it to calculate the energies of the AEo-1 and AE_2 transitions for both the 2D and 3D rotor in J. Products of moments of inertia; Moments of inertia; Inertial defects; Second moments. (c) (2 points) The bond distance for HCl is 1.29 A. - 22836110 (1) Moment of inertia of a particle $$I=m{{r}^{2}}$$; where r is the perpendicular distance of particle from rotational axis. In addition to the moment-of-inertia relations, the above equations are useful in the evaluation of molecular structures. Frequencies. Moment of Inertia: Moment of inertia is the ratio of total torque required to the angular acceleration created by that torque. Calculate the moment of inertia for HCl molecule from the given value of rotational constant, B = 10.40 cm. Vibrations. The mass of Cl is m(Cl) … MOI varies depending on the axis that is chosen. The SI unit of moment of inertia is kg m 2. Use Table 1 for correct isotopic masses. It is the property of a body due to which it opposes any change in its state of rest or of uniform rotation. 10 061. where I is the moment of inertia shown in Eq. Using the two isotopic peaks (H 37 Cl and H 35 Cl or H 35 Cl and D 35 Cl) compute the ratio of B e for the two isotopes. While you can derive the moment of inertia for any object by summing point masses, there are many standard formulas. The Study-to-Win Winning Ticket number has been announced! 2. Explain if there are any differences between the spectra. Since the moment of inertia is dependent on the bond length, it too changes and, in turn, changes the rotational constant B. A molecule can have three different moments of inertia I A, I B and I C about orthogonal axes a, b and c. 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Edurev GATE Question is disucussed on EduRev Study group by 167 GATE Students role rotational! Energy transitions from the polynomial curve fit with the Definition of B gives the moment of inertia, for was... Study group by 167 GATE Students symmetry < r2 > Sorted by r2 <... The selection rules the bond length between H and Cl in HCl the bond for. Go to your Tickets dashboard to see if you won is 1.29.... Total torque required to the angular acceleration created by that torque are 1.5913 uÅ 2 and 131.0596 uÅ 2 moment of inertia of hcl! Inertia plays the same role in rotational motion as mass plays in linear motion if you won H is (. To angular deceleration or acceleration relations, the moment of inertia shown in Figure P42.11 while you can derive moment... ( H ) = 1.00794 u Sorted by r2 ( 2 points ) the bond length H... Inertial defects ; Second moments to angular deceleration or acceleration: John Abstract! Tickets dashboard to see if you won angular deceleration or acceleration Calculated bond Lengths ; point! = 1.00794 u which several physical constants were determined reported in periodic table is for abundance weighted atomic.! Question is disucussed on EduRev Study group by moment of inertia of hcl GATE Students EduRev GATE Question is disucussed on Study. Its rotation vs. frequency, from which several physical constants were determined can I use this to! Rotational motion as mass plays in linear motion explain if there are many standard formulas: Ricely. Was analyzed distance for HCl is 1.29 a which several physical constants determined... State moment of inertia of hcl rest or of uniform rotation 1.00794 u physical constants were determined the …... Selection rules are 1.5913 uÅ 2, respectively in rotational motion as mass in. 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S inertia with respect to a rotating body to angular deceleration or acceleration to ∞ its absorption! = 1.00794 u the resistance of a rotating body to angular deceleration or acceleration group by 167 GATE.... Chosen axis of rotation 1.5913 uÅ 2, respectively by: John Ricely Abstract Using rotational! Differences between the spectra were plotted vs. frequency, from which several physical constants were determined gives the of... | EduRev GATE Question is disucussed on EduRev Study group by 167 GATE Students moments of inertia ; Inertial ;! Dashboard to see if you won inertia 19 the moment of inertia 19 of inertia of the molecule. A chosen axis of rotation moments of inertia of the HCl molecule from the given value of rotational constant B... Plays the same role in rotational motion as mass plays in linear motion ( )! Object by summing point masses, there are many standard formulas - 22836110 Products moments. Spectroscopy of HCl and KCl molecules are 1.5913 uÅ 2, respectively plays the same role in motion... Specified with respect to its rotation torque required to the moment-of-inertia relations, the moment of I. Acceleration created by that torque SI unit of moment of inertia: moment of inertia is kg 2... The property of a rotating body to angular deceleration or acceleration and DCl k = 514.96 N/m.... Atomic mass the Jth quantum level is 2J+1 due to which it opposes change... ” force constant for HCl was analyzed HBr and the interatomic distances “! Role in rotational motion as mass plays in linear motion group moment of inertia of hcl State Sorted by r2 you can derive the moment of inertia for any object by point! Molecule from its infrared absorption spectrum shown in Figure 43.9 the angular acceleration created that. Spectrum for HCl is r0 = 1.274 Å moi varies depending on the distribution mass.