Isotopic Frequency Ratios Research Articles

Observation and Characterization of the Hg-O Diatomic Molecule: A Matrix-Isolation and Quantum-Chemical Investigation.

Mercuric oxide is a well-known and stable solid, but the diatomic molecule Hg-O is very fragile and does not survive detection in the gas phase. However, laser ablation of Hg atoms from a dental amalgam alloy target into argon or neon containing about 0.3 % of 16 O2 or of 18 O2 during their condensation into a cryogenic matrix at 4 K allows the formation of O atoms which react on annealing to make ozone and new IR absorptions in solid argon at 521.2 cm-1 for Hg-16 O or at 496.4 cm-1 for Hg-18 O with the oxygen isotopic frequency ratio 521.2/496.4=1.0499. Solid neon gives a 529.0 cm-1 absorption with a small 7.8 cm-1 blue shift. CCSD(T) calculations found 594 cm-1 for Hg16 O and 562 cm-1 for Hg18 O (frequency ratio=1.0569). Such calculations usually produce harmonic frequencies that are slightly higher than the anharmonic (observed) values, which supports their relationship. These observed frequencies have the isotopic shift predicted for Hg-O and are within the range of recent high-level frequency calculations for the Hg-O molecule. Spectra for the related mercury superoxide and ozonide species are also considered for the first time.

Preparation of Group 3 Metal Sulfur Monoxide Complexes via Oxidation of Metal Atoms using SOF2 in Cryogenic Matrixes

AbstractSide‐on sulfur monoxide complexes of scandium, yttrium, and lanthanum difluorides [MF2(η2‐SO)] were prepared via oxidation of metal atoms by SOF2 in cryogenic matrixes. The structures of these SO complexes are determined by characteristic infrared absorptions as well as isotopic frequency ratios, and the assignments are further supported by density functional theory calculations. A doublet ground state with nonplanar Cs symmetry was established for all the complexes with side‐on SO ligands. The S−O bond lengths as well as the S−O stretching vibrational frequencies approach those of SO−, suggesting that the group 3 metal MF2(η2‐SO) complexes can be considered as (MF2)+(SO)−. Consistent with this notion, the interaction between MF2 and SO is mainly ionic with SO negatively charged by about −0.60 e, and the unpaired electron is located in the SO 3π orbital that is antibonding in character. It is highly exothermic to form MF2(η2‐SO) mediated by a single fluorine transfer MF(SOF) intermediate from the reactions of SOF2 and metal atoms. The absence of group 3 metal sulfur monoxide complexes using SO2F2 as a precursor is because the resulting complexes would require a metal center with the oxidation state higher than III.

(Noble Gas)n -NC+ Molecular Ions in Noble Gas Matrices: Matrix Infrared Spectra and Electronic Structure Calculations.

An investigation of pulsed‐laser‐ablated Zn, Cd and Hg metal atom reactions with HCN under excess argon during co‐deposition with laser‐ablated Hg atoms from a dental amalgam target also provided Hg emissions capable of photoionization of the CN photo‐dissociation product. A new band at 1933.4 cm−1 in the region of the CN and CN+ gas‐phase fundamental absorptions that appeared upon annealing the matrix to 20 K after sample deposition, and disappeared upon UV photolysis is assigned to (Ar) n CN+, our key finding. It is not possible to determine the n coefficient exactly, but structure calculations suggest that one, two, three or four argon atoms can solvate the CN+ cation in an argon matrix with C−N absorptions calculated (B3LYP) to be between 2317.2 and 2319.8 cm−1. Similar bands were observed in solid krypton at 1920.5, in solid xenon at 1935.4 and in solid neon at 1947.8 cm−1. H13CN reagent gave an 1892.3 absorption with shift instead, and a 12/13 isotopic frequency ratio–nearly the same as found for 13CN+ itself in the gas phase and in the argon matrix. The CN+ molecular ion serves as a useful infrared probe to examine Ng clusters. The following ion reactions are believed to occur here: the first step upon sample deposition is assisted by a focused pulsed YAG laser, and the second step occurs on sample annealing: (Ar)2 ++CN→Ar+CN+→(Ar) n CN+.

Formation of Cerium and Neodymium Isocyanides in the Reactions of Cyanogen with Ce and Nd Atoms in Argon Matrices.

Laser ablation of metallic Ce and Nd reacting with cyanogen in excess argon during codeposition at 4 K forms Ce(NC)x and Nd(NC)x for x = 1-3, which are identified from their matrix infrared spectra using cyanogen substituted with 13C and 15N. The electronic structure calculations were performed for isocyano and cyano Cd and Nd compounds for up to n = 4. The frequencies were calculated at the density functional theory level with three different functionals as well as correlated molecular orbital theory (MP2) and are consistent with the experimental assignments and the corresponding 12C/13C isotopic frequency ratios for the isocyano species. The computed frequencies for the analogous cyanide complexes are significantly higher than those for the isocyano isomers, and they are not observed in the spectra. The high spin isocyano complexes are the lowest energy structures. On the basis of the natural population analysis results, the bonding in 4CeNC and 6NdNC is essentially purely ionic with the Ce/Nd in the +I-oxidation state. The bonding for disocyano (3Ce(NC)2 and 5Nd(NC)2) and triisocyano (2Ce(NC)3 and 4Nd(NC)3) complexes is still quite ionic with the lanthanide in the +II and +III formal oxidation states, respectively. For 1Ce(NC)4, the oxidation state is best described as being between +III and +IV. Formation of 5Nd(NC)4 does not really change the electron configuration on the Nd from that in 4Nd(NC)3 and the oxidation state on the Nd remains at +III. Although Nd compounds with up to 3 NC- groups have more ionic binding than do the corresponding Ce compounds, Ce(NC)4 has more ionic binding than does Nd(NC)4. The ionic nature of isocyano Ce and Nd complexes decreases as the number of isocyano groups increases. The energetics of formation of the isocyano Ce and Nd complexes using cyanogen or CN radicals are calculated to be mostly due to exothermic processes, with the exothermicity decreasing as the number of isocyano groups increases.

Bidentate Sulfur Dioxide Complexes of Scandium, Yttrium, and Lanthanum Difluorides.

The SO2 complexes of scandium, yttrium, and lanthanum difluorides [MF2(O2S)] were prepared via the reactions of laser-ablated metal atoms and SO2F2 upon UV-vis irradiation in cryogenic matrixes. The presence of bidentate SO2 ligand in the products was demonstrated by the characteristic infrared absorptions as well as isotopic frequency ratios from both S18O2F2 and 34SO2F2 experiments and is further supported by DFT calculations. All three product molecules were predicted to have nonplanar C2 v symmetry with the SO2 ligand bound to the metal center through both oxygens. The computed S-O bond length and stretching frequencies of ligated SO2 approach those of SO2- as a result of electron transfer from metal center to the 1π* orbital of SO2, in agreement with the results from bonding analysis. On the basis of DFT calculations, fluorine transfer from SO2F2 to the metal center to form the MF2(O2S) complexes is highly exothermic. Although a proposed intermediate in the form of MF(O2SF) was predicted to be stable, it was not observed in the experiments, presumably because of the low energy barrier for further isomerization to MF2(O2S).

Side-On Sulfur Monoxide Complexes of Tantalum, Niobium, and Vanadium Oxyfluorides.

Side-on sulfur monoxide complexes of tantalum, niobium, and vanadium oxyfluorides OMF2(η2-SO) were prepared via the reactions of metal atoms and SO2F2 upon UV-vis irradiation in a cryogenic matrix. The product structures were identified by the characteristic infrared absorptions and isotopic frequency ratios of terminal M-O, F-M-F, and M-(SO) stretches, which were further supported by density functional theory calculations at the B3LYP level. All of the three complexes were predicted to have doublet ground states with the S-O bond nearly perpendicular to the terminal metal-oxygen bond. Although end-on bonded isomers with either M-OS or M-SO geometry are stable as well, they are higher in energy than the side-on isomers, and their vibrational frequencies do not match the experimental values. For the OMF2(η2-SO) complexes, the S-O bond length approaches that of SO-, but it is longer than that of neutral SO due to the electron transfer from the metal d orbital to the in-plane π* orbital of SO. The metal-SO bonding in the side-on complex is mainly ionic, but covalent interactions play some role between the two parts. On the basis of the calculation results, the OMF2(η2-SO) complexes can be considered as (OMF2)+(SO)- in which the unpaired electron is mainly located in the out-of-plane π* orbital of SO. In addition to the complexes containing SO ligand, a series of other stable isomers were obtained by the B3LYP calculations, and they were proposed as intermediates involved in the formation of the OMF2(η2-SO) products via fluorine and oxygen transfer reactions between metal atoms and SO2F2 under UV-vis irradiation.

Infrared Spectra of the SO2F2- Anion in Solid Argon and Neon.

Sulfonyl fluoride anion (SO2F2-) was produced during codeposition of laser-ablated metal atoms, ions, and electrons with SO2F2 in argon and neon matrixes at 4 K. The structure of SO2F2- was determined by infrared spectroscopy and density functional theory calculations. On the basis of the experiments using 34SO2F2 and S18O2F2 samples, the three absorptions at 1284.9, 1109.3, and 567.0 cm-1 in argon and 1289.0, 1116.2, and 576.8 cm-1 in neon were assigned to the antisymmetric and symmetric O-S-O stretching and SO2 wagging modes of SO2F2-, respectively. These assignments were further supported by frequency and isotopic frequency ratio calculations. The SO2F2- anion possesses a 2A1 ground state with nonplanar C2 v symmetry. Compared with the neutral SO2F2 molecule, dramatic increases in the S-F bond length (0.295 Å) and F-S-F bond angle (41.0°) were found for the anion, which result from the S-F antibonding character of the singly occupied molecular orbital. The SO2F2- anion was formed via electron capture by SO2F2 in the gas phase before being deposited into the cryogenic matrix. The matrix environment stabilized this anion, but it was destroyed by UV-vis irradiation and presumably converted to the neutral SO2F2 molecule.

Infrared Spectroscopic and Theoretical Studies of Group 3 Metal Isocyanide Molecules.

A series of group 3 metal isocyanide complexes were prepared via the reactions of laser ablated scandium, yttrium, and lanthanum atoms with (CN)2 in an argon matrix. The product structures were identified on the basis of their characteristic infrared absorptions from isotopically labeled (CN)2 samples as well as the calculated frequencies and isotopic frequency ratios. Group 3 metal atoms reacted with (CN)2 to form M(NC)2 (M = Sc, Y, La) when the samples were subjected to λ > 220 nm irradiation. Other products such as M(NC)3 and MNC were produced together with M(NC)2 through either the reactions of M(NC)2 and (CN)2 or the loss of one CN ligand from M(NC)2. CCSD(T)//B3LYP calculations reveal that ScNC possesses a 3Δ ground state, while 1Σ+ is most stable for YNC and LaNC. All of the M(NC)2 and M(NC)3 complexes were predicted to have doublet and singlet ground states, respectively. Group 3 metal cyanides are less stable than the isocyanides by at least 4 kcal/mol at the CCSD(T) level, and their C-N stretches are much weaker than the N-C stretches of the isocyanides. No absorption can be assigned to the M(CN) x complex, which would appear between 2100 and 2250 cm-1.

Laser-Ablated U Atom Reactions with (CN)2 to Form UNC, U(NC)2, and U(NC)4: Matrix Infrared Spectra and Quantum Chemical Calculations.

Laser-ablated U atoms react with (CN)2 in excess argon and neon during codeposition at 4 K to form UNC, U(NC)2, and U(NC)4 as the major uranium-bearing products, which are identified from their matrix infrared spectra using cyanogen substituted with 13C and 15N and from quantum chemical calculations. The 12/13CN and C14/15N isotopic frequency ratios computed for the U(NC)1,2,4 molecules agree better with the observed values than those calculated for the U(CN)1,2,4 isomers. Multiplets using mixed isotopic cyanogens reveal the stoichiometries of these products, and the band positions and quantum chemical calculations confirm the isocyanide bonding arrangements, which are 14 and 51 kJ/mol more stable than the cyanide isomers for UNC and U(NC)2, respectively, and 62 kJ/mol for U(NC)4 in the isolated gas phase at the CCSD(T)/CBS level. The studies further demonstrate that the isocyano nitrogen is a better π donor, so it interacts with U(VI) better than carbon. Although the higher isocyanides are more stable than the corresponding cyanides, U(NC)5 and U(NC)6 were not observed here most likely because unfavorable or endothermic routes are required for their production from U(NC)4. The computed U-NC bond dissociation energies decrease from 581 kJ/mol for 4[UNC] to 168 kJ/mol for 1[U(NC)6 ]. The ionic nature of U(NC)n decreases as the number of isocyano groups increases.

Potassium acceptor doping of ZnO crystals

ZnO bulk single crystals were doped with potassium by diffusion at 950°C. Positron annihilation spectroscopy confirms the filling of zinc vacancies and a different trapping center for positrons. Secondary ion mass spectroscopy measurements show the diffusion of potassium up to 10 μm with concentration ∼1 × 1016 cm−3. IR measurements show a local vibrational mode (LVM) at 3226 cm−1, at a temperature of 9 K, in a potassium doped sample that was subsequently hydrogenated. The LVM is attributed to an O–H bond-stretching mode adjacent to a potassium acceptor. When deuterium substitutes for hydrogen, a peak is observed at 2378 cm−1. The O-H peak is much broader than the O-D peak, perhaps due to an unusually low vibrational lifetime. The isotopic frequency ratio is similar to values found in other hydrogen complexes. Potassium doping increases the resistivity up to 3 orders of magnitude at room temperature. The doped sample has a donor level at 0.30 eV.

Vibrational Spectroscopy of Na–H Complexes in ZnO

Sodium acceptors were diffused into ZnO bulk single crystals to a depth of ~1μm, with a near-surface concentration of ~1018–cm3. An O–H local vibrational mode (LVM) was observed at 3304–cm–1, at a temperature of 9 K, in hydrogenated samples. The LVM is attributed to an O–H bond-stretching mode adjacent to a Na acceptor. When deuterium substitutes for hydrogen, a peak is observed at 2466–cm–1. The isotopic frequency ratio is similar to values found in other hydrogen complexes. In the deuterated sample, a sideband at 2461–cm–1 is attributed to a Fermi resonance.

Infrared spectra and quantum chemical calculations of the uranium-carbon molecules UC, CUC, UCH, and U(CC)2

Laser evaporation of carbon rich uranium/carbon alloy targets into condensing argon or neon matrix samples gives weak infrared absorptions that increase on annealing, which can be assigned to new uranium carbon bearing species. New bands at 827.6 cm(-1) in solid argon or 871.7 cm(-1) in neon become doublets with mixed carbon 12 and 13 isotopes and exhibit the 1.0381 carbon isotopic frequency ratio for the UC diatomic molecule. Another new band at 891.4 cm(-1) in argon gives a three-band mixed isotopic spectrum with the 1.0366 carbon isotopic frequency ratio, which is characteristic of the anti-symmetric stretching vibration of a linear CUC molecule. No evidence was found for the lower energy cyclic U(CC) isomer. Other bands at 798.6 and 544.0 cm(-1) are identified as UCH, which has a uranium-carbon triple bond similar to that in UC. Evidence is found for bicyclic U(CC)(2) and tricyclic U(CC)(3). This work shows that U and C atoms react spontaneously to form the uranium carbide U≡C and C≡U≡C molecules with uranium-carbon triple bonds.

On the molecular and electronic structure of GaO4

We report the results of computational studies performed on the lowest doublet and quartet states of GaO4. Using density functional theory (DFT) and coupled cluster approach with 6-311+G(2df) basis set, the Cs end-on bonded superoxo complex proposed earlier for GaO4, from matrix experiments and computational studies, is thermodynamically unstable with respect to GaO4(2A′)→OGaO(2Πg) + O2(3Σg-) reaction. A kite-like C2v ground state geometry has been computed for GaO4. The energies of the low-lying states, harmonic vibrational frequencies and isotopic frequency ratios are reported for the GaO4 molecule. The adiabatic electron affinity of GaO4 is computed to be 3.74eV and 3.81eV at the B3LYP and CCSD(T)//B3LYP levels, respectively.

Infrared Spectra and Quantum Chemical Calculations of the Uranium Carbide Molecules UC and CUC with Triple Bonds

Laser evaporation of carbon-rich uranium/carbon alloys followed by atom reactions in a solid argon matrix and trapping at 8 K gives weak infrared absorptions for CUO at 852 and 804 cm(-1). A new band at 827 cm(-1) becomes a doublet with mixed carbon 12 and 13 isotopes and exhibits the 1.0381 isotopic frequency ratio, which is appropriate for the UC diatomic molecule, and another new band at 891 cm(-1) gives a three-band mixed isotopic spectrum with the 1.0366 isotopic frequency ratio, which is characteristic of the linear CUC molecule. CASPT2 calculations with dynamical correlation find the C[triple bond]U[triple bond]C ground state as linear 3Sigma(u)+ with 1.840 A bond length and molecular orbital occupancies for an effective bond order of 2.83. Similar calculations with spin-orbit coupling show that the U[triple bond]C diatomic molecule has a quintet (Lambda = 5, Omega = 3) ground state, a similar 1.855 A bond length, and a fully developed triple bond of 2.82 effective bond order.

Infrared Spectra and Density Functional Theory Calculations of Group 10 Transition Metal Sulfide Molecules and Complexes

Laser-ablated Ni, Pd, and Pt atoms were reacted with sulfur molecules emerging from a microwave discharge in argon during condensation at 7 K. Reaction products were identified from matrix infrared spectra, sulfur isotopic shifts, spectra of sulfur isotopic mixtures, and frequencies from density functional calculations. The strongest absorptions are observed at 597.9, 596.1, and 583.6 cm(-1), respectively, for the group 10 metals. These absorptions show large sulfur-34 shifts and 32/34 isotopic frequency ratios (1.0282, 1.0285, 1.0298) that are appropriate for S-S stretching modes. Of most importance, mixed 32/34 isotopic 1/4/4/2/4/1 sextets identify this product with two equivalent S(2) molecules containing equivalent atomic positions as the bisdisulfur pi complexes M(S(2))(2). Our DFT calculations find stable D(2h) structures with B(1u) ground states and intense b(1u) infrared active modes a few wavenumbers higher than the observed values. A minor Ni product at 505.8, 502.7 cm(-1) shows the proper sulfur-34 shift for assignment to (58)NiS, (60)NiS. Another major product with Pt at 512.2 cm(-1) reveals an asymmetric triplet absorption with mixed sulfur 32/34, which is appropriate for assignment to the SPtS disulfide molecule. A weak 491.7 cm(-1) peak exhibits the sulfur-34 shift expected for PtS, and this assignment follows.

D/H isotopic fractionation between brucite Mg(OH) 2 and water from first-principles vibrational modeling

Isotopic fractionation between two phases can be calculated if the vibrational properties of isotopic end-members are fully characterized. We assessed a theoretical approach based on first-principles density-functional density (DFT) prediction of vibrational frequencies by comparing with spectroscopic data on isotopically substituted brucite, a model mineral for which detailed experimental data on isotopic effects and brucite–water D/H partitioning exist. The deviation from experimental values averages to less than 1% for lattice modes, and 4% for OH stretching modes. The reduced partition function ratio (RPFR) for D/H substitution in brucite was combined with experimental RPFR for water to calculate D/H fractionation factor between water and brucite. Results within the harmonic approximation systematically deviate from experimental data by + 20–25‰. RPFR is very sensitive to the frequency and isotopic shift of high frequency OH stretching modes, for which anharmonic effects are important and usually not explicitly taken introduced in calculations for minerals. The asymmetry of the O–H potential was calculated by DFT and accounts for spectroscopic measurements of the anharmonic shifts of OH stretching mode overtones and isotopic frequency ratio. Calculations of D/H fractionation introducing anharmonic corrections to the RPFR of brucite are fitted with the expression 1000ln α D/H(brucite/H 2O) = − 23.3 10 3 / T + 2.55 10 6 / T 2 − 1.51 10 9 / T 3, that yields an improved agreement with experiments at high temperature, but the deviation at 25 °C is − 30‰. Uncertainties in calculated fractionation factors can arise from dispersion effects or from DFT errors. For instance, a 1% change of the stretching mode frequencies or a 3% change of lattice mode frequencies could account for the discrepancy between model and experimental fractionation factors. The pressure dependence of brucite RPRF was calculated, and is given by 1000ln Г Pbrucite = P (− 1.005 10 3 / T + 2.18 10 6 / T 2 − 0.213 10 9 / T 3), with P in GPa. The large calculated temperature dependence of the fractionation factor suggests that a single experimental fractionation curve can be fitted to a partial consistent set of experimental data as 1000ln α D/H(brucite/H 2O) = − 27.9(30) 10 3 / T + 8.8(29) 10 6 / T 2 − 2.24(63) 10 9 / T 3. These equations allow calculating the temperature and pressure dependence of the D/H fractionation factor between brucite and water in the 300–900 K and 0.1–100 MPa range when combined with the pressure correction for water RPFR [Polyakov, V.B., Horita, J. and Cole, D.R., 2006. Pressure effects on the reduced partition function ratio for hydrogen isotopes in water. Geochimica Cosmochimica Acta, 70: 1904–1913.] for geochemical applications. The DFT model used here for estimating RPFR of the model mineral brucite can be extended to other hydrous minerals using vibrational spectroscopy as a test for the accuracy of the DFT prediction, and the brucite–water equations proposed here as a reference for determining mineral–water fractionation factors and geochemical applications.

IR spectral density of H-bonds. Both intrinsic anharmonicity of the fast mode and the H-bond bridge. Part II: Isotopic effect

Anomalous isotopic effects on the position and the shape of the υ s ( X – H → … Y ) stretching vibration bond of hydrogen-bonded systems have been studied theoretically by applying a previous model [N. Rekik, N. Issaoui, H. Ghalla, B. Oujia, M.J. Wojcik, J. Mol. Struct. (Theochem) 821 (2007) 9–29]. The study of this effect is undertaken for weak to medium-strong H-bonded systems. Numerical results show that the relation between the isotopic frequency ratio, 〈 ω 〉 H / 〈 ω 〉 D and ω ° H / 〈 ω 〉 H , derived in this paper is confirmed by published experimental data.

Experimental and Theoretical Investigations of IR Spectra and Electronic Structures of the U(OH)2, UO2(OH), and UO2(OH)2 Molecules

Reactions of laser-ablated U atoms and H2O2 molecules produce UO2, H2UO2, and UO2(OH)2 as major products and U(OH)2 and HU(O)OH as minor products. Complementary information is obtained from similar reactions of U atoms with D2O2, with H2 + O2 mixtures, and with H2O in excess Ar. Through extensive relativistic density functional theory calculations, we have determined the geometry structures and ground states of these U species with a variety of oxidation states U(II), U(IV), U(V), and U(VI). The calculated vibrational frequencies, IR intensities, and isotopic frequency ratios are in good agreement with the experimental values, thus supporting assignments of the observed matrix IR spectra. We propose that the reactions proceed by forming an energized [U(OH)4] intermediate from reactions of the excited U atom with two H2O2 molecules. Because of the special stability of the U(VI) oxidation state, this intermediate decomposes to the UO2(OH)2 molecule, which reveals a distinctive difference between the chemistries of U and Th, where the major product in analogous Th reactions is the tetrahedral Th(OH)4 molecule owing to the stable Th(IV) oxidation state.

Isotope effects for molecules in a cavity

A model problem of the motion of a particle in an impenetrable cavity is considered in order to establish how the energy levels and transition energies between them depend on the linear size, R, of the cavity and on the particle mass. In the case of one particle problem with a uniform potential inside the cavity there exists a simple qualitative solution that describes the effect of the cavity size and shows that a decrease in R can cause the isotopic frequency shift to increase as compared to the free system. The estimates obtained were used to interpret the results of numerical calculations of low lying energy states of hydrogen molecule and its isotopomers confined within impenetrable spherical cavity. The effect of the cavity radius on the structure of the low lying part of the energy spectra of H2, D2, and HD molecules and on the reliability of adiabatic separation of nuclear variables are considered. The approach provides a qualitatively correct description of the changes in the energy level positions but the behavior of the isotopic frequency ratio is too smooth compared with results of more accurate calculations.

Infrared Spectra of (CS2)2- Anion in Solid Neon and Argon

Charged transient species produced from high-frequency discharge of CS2 have been trapped in solid argon and neon. Besides the previously identified CS2-, CS2+, and (CS2)2+ species, new absorptions at 909.0 cm-1 in solid neon and 908.0 cm-1 in solid argon were observed. Isotopic substitutions (13CS2, C34S2, and mixtures) showed that the new species involves two equivalent CS2 subunits. The photosensitive behavior and the agreement with frequencies and isotopic frequency ratios from quantum chemical calculations substantiate assignment of these absorptions to the most stable isomer of the (CS2)2- anion, which was predicted to have a planar C−C chemically bonded D2h structure.