Dunham potential energy coefficients of the hydrogen halides and carbon monoxide, rst anharmonicity constant, respectively, and v is the vibra-tional quantum number, which can assume nonnegative inte-ger values.10 Note that the symbol ex e represents a single constant, not a product. Phys., 1967, 46, 644. HCl constants were determined from an IR spectrum. 20. 0000113106 00000 n
}\left(\dfrac{d^2V}{dR^2}\right)_{R=R_e} (R-R_e)^2 \nonumber \]. Spectrochim. In the IR spectrum, overtone bands are multiples of the fundamental absorption frequency. xb```f``qAbl,= BGN4?Pra ]"D8235qNL}~oZd\F.&p9%*WBSofXXx}~T x"+D|Y All rights reserved. Plyler, E.K. The Ie was calculated to be 2.80 x 10-47 kg m2 from Eq. J. Chem. 7 under appendix, which correlated with the literature value of 2.64 x 10-47 kg m2 at a 1.4% difference. 0000002668 00000 n
(Paris), 1949, 4, 527. Please email us at
Legal. Be is discussed in the next section and can be found in Table 2. Radiat. J. Opt. Phys., 1956, 34, 850. [all data], Rank, Rao, et al., 1965 [all data], Chamberlain and Gebbie, 1965 Reduced mass and reduced mass ratios for isotopic molecules, Infrared Spectrometric Rotational and Vibrational Analysis of HCl and DCl, Dyes and CdSe Nanoparticles by UV-Vis Spectroscopy. J. Mol. ; Silverman, S., Phys., 1962, 40, 113. Lempka, H.J. The absorption spectra of the halogen acids in the vacuum ultra-violet, SCF takes the average of the electrons and ignores electron correlation. errors or omissions in the Database. <]>>
Sub-millimetre dispersion and rotational line strengths of the hydrogen halides, \(\ce{HCl}\) has a fundamental band at 2885.9 cm1 and an overtone at 5668.1 cm1 Calculate \(\tilde{\nu}\) and \( \tilde{\chi_e} \). 9 under the appendix to be 515.20 N/m which has a 0.07% difference with the literature value of 516.82 N/m. Similar; Isomers; Cis/trans; . Also as a result of anharmonicity, the \(\Delta v= \pm 1\) selection rule is no longer valid and \(v\) can be any number. Huber, K.P. Levy, A.; Mariel-Piollet, E.; Bouanich, J.-P.; Haeusler, C., Data compiled by: Klaus P. Huber and Gerhard H. Herzberg, Go To: Top, Constants of diatomic molecules, Notes, Hayes and Brown, 1972 Although calculated and De did not correlate with the literature, these values are assumedaccurate since they are in the same order of magnitude with relatively small percent differences. Show that you can Ben-Reuven, A.; Kimel, S.; Hirshfeld, M.A. Overtones are generally not detected in larger molecules. It was expected that re would be the same for both HCl and DCl which was found to be true with re of 1.30 for DCl compared to 1.31 HCl which has a 0.2% difference. On the breakdown of the Born-Oppenheimer approximation for a diatomic molecule, ; Herzberg, G., Molecular Spectra and Molecular Structure. To get a more accurate approximation, more terms can be included, but otherwise, can be ignored. The mechanical anharmonicity, as well as the harmonic frequency, decreased with increasing dielectric constant of the solvent. ; Young, R.A., Here's the problem. Radiat. (a) Calculate the harmonic vibrational frequency and anharmonicity constant for this mode (in cm-1). [all data], Kaiser, 1970 0000008074 00000 n
Spectrosc. ; Baker, M.R. The re was calculated by taking HCl to resemble the rigid rotor model using Eq. The separation of successive vibrational levels is constant and is equal to = / that is the Anhydrous hydrogen chloride; Hydrogen chloride (acid); Marine acid; Soldering acid; Spirit of salt; Spirits of salts; Hydrogen chloride (HCl); NSC 77365; Hydrochloric acid Permanent linkfor this species. Variation among the methods is due to assumptions made in each. The ve was found to be 2144.18 cm-1. Intensites et largeurs de raies dans la bande v0-2, Anharmonicity constants. The transition v1+-x1+ in hydrogen chloride, ; Stone, N.W.B., 0 Likes. [1] M. Halpern and G.C. Fourier transform infrared spectroscopy was used to study the vibrational and rotational motions of diatomic molecules hydrogen chloride, HCl and deuterated chloride, DCl. Pressure-induced shifts of molecular lines in emission and in absorption, Datta, S.; Banerjee, S., The term in Az is primarily determined by anharmonic force constants, whereas the terms in Ax2 and Ay2 are primarily functions of the harmonic force . Write out the Taylor series, and comment on the trend in the increasing terms. Determine the harmonic frequency and the anharmonicity constant (assume that all transitions start from the v" = 0 level of the ground state). IV. }\left(\dfrac{d^3V}{dR^3}\right)_{R=R_e} (R-R_e)^3 + \dfrac{1}{4! The De was calculated from high m transitions due to m3 dependence and found to be (7.250.02) x10-4 cm-1 which has an 8.2% difference with a literature value of 5.2 x10-4 cm-1. 0000024255 00000 n
It was determined that is 2885.4 0.2 cm-1 using the third order polynomial in Figure 4. [all data], Jaffe, Kimel, et al., 1962 The first five vibrational energy levels of HCl are at 1481.86, 4367.50, 7149.04, 9826.48, and 12 399.8 cm 1 . Pressure-induced shifts of DCl lines due to HCl: shift oscillation, where \( \tilde{\chi_e}\) is the anharmonicity constant. [2] Atkins, P., J. For the anharmonic oscillator, the selection rule is \(\Delta V= \text{any number}\). Berlin. The LibreTexts libraries arePowered by NICE CXone Expertand are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. Weiss, S.; Cole, R.H., Chem. The lower absorption frequency of DCl occurred due to a change in the reduced mass, Table 6A under the appendix, from 1.62612 x 10-27 to 1.904413 x 10-27 for HCl and DCl, respectively. Accessibility StatementFor more information contact us atinfo@libretexts.orgor check out our status page at https://status.libretexts.org. The anharmonic oscillator calculations show that the overtones are usually less than a multiple of the fundamental frequency. [all data], Romand, 1949 (c) In a typical industrial unit, the process is very efficient, with a 96% yield for the first step. J. Opt. Note that this is almost just the mass of the hydrogen. McBane, Experimental Physical Chemistry, 3rd ed., W.H. The frequencies of the vibrational fundamental and its first and second overtones were measured for HCl in a series of nonpolar and slightly polar solvents. Data from NIST Standard Reference Database 69: The National Institute of Standards and Technology (NIST) (1) and (2) are combined to describe the motion of a molecule while also considering anharmonicity and the interaction of vibration and rotation. [all data], Rank, Birtley, et al., 1960 Spectrosc., 1959, 3, 185. [all data], Terwilliger and Smith, 1973 Can. Chem. Spectrosc., 1968, 28, 121. Gebbie, H.A. Smith, F.G., ; Yi, P.N., The Anharmonicity constant given dissociation energy formula is defined as the deviation of a system from being a harmonic oscillator in relation to the vibrational energy levels of a diatomic molecule is calculated using Anharmonicity Constant = ((Vibrational Wavenumber)^2)/(4* Dissociation Energy of Potential * Vibrational Wavenumber).To calculate Anharmonicity Constant given Dissociation . HCl behaves vibrationally as a quantum harmonic oscillator with an effective spring constant of 480 N/m and effective mass approximately equal to the lighter hydrogen atom. Molecular Spectra and Molecular Structure. for future reference. The continuous absorption spectra of the hydrogen-halides. Rotational Constants (cm-1) See section I.F.4 to change rotational constant units Calculated rotational constants for DCl (Hydrochloric acid-d). What is the absorption coefficient of a solute that absorbs 90% of a certain wavelength of light when the Theory: Simplest rotating diatomic model is the rigid rotor or "dumb-bell" model which can be . 0
H2, Li2, O2, N2, and F2 have had terms up to \(n < 10\) determined of Equation \(\ref{taylor}\). Rydberg series corresponding to excitation of a 2p electron. [all data], Leavitt, Baker, et al., 1961 The anharmonic oscillator Real bonds, although elastic for small compressions and extensions, do not strictly obey Hooke's Law for amplitudes > 10% of bond length. Determining equilibrium frequency and force constant from fundamental and first overtone in vibrational spectroscopy Show more Vibration and rotation spectra of HCl DCl: Prelab Lecture. Infrared spectroscopy is an important analytical tool to determine the structure of molecules. This leads to the observation of higher order transitions, or overtones, which result from the transition of the ground state to higher energy levels. The rest are so small and barely add to the total and thus can be ignored. ; Smith, A.L., The isotopic effect was observed in a spectrum of both HCl and DCl with DCl at a lower wavenumber than HCl which coincided with 37Cl being observed at a lower frequency than 35Cl. Vibration and rotation are contingent on the bonding molecules. London, 1963, 82, 309. Transfer, 1972, 12, 219. The second-row diatomic hydrides AH, [all data], Price, 1938 Stand. The anharmonic oscillator calculations show that the overtones are usually less than a multiple of the fundamental frequency. Phys., 1969, 50, 5313. Rank, D.H.; Birtley, W.B. Energy. Phys., 1970, 52, 2867. The dimensionless quantity xe is known as the anharmonicity constant. Use this information to calculate the vibrational . 4 Constants of Diatomic Molecules, (D. Van Nostrand, New York, 1950) 4. Account for any difference between this value and your answer to question 7. constant and not the dissociation energy, for which the symbol D e is also used. [5] Schuder MD, Nesbitt DJ. The vibrorotational Hamiltonian is modeled as a rigid rotor coupled to an anharmonic oscillator : The anharmonic oscillator is represented initially by the usual Morse model: where is the vibrational momentum, is the reduced mass of the diatomic, and and are the parameters of the Morse potential. Electronic spectra and structure of the hydrogen halides: states associated with the (23) c and (23) c configurations of HCl and DCl, Spectrosc., 1971, 40, 568. J. Quant. where is the anharmonic vibrational frequency correction, . Soc. J. Chem. Etude de la bande v02 a 1,7 micron, 1974. ; Price, W.C., 721 0 obj
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Radiat. 9. IR spectrum represents the rotation-vibration spectrum of the molecule. Also as a result of anharmonicity, the \(\Delta v= \pm 1\) selection rule is no longer valid and \(v\) can be any number. Calculating harmonic frequency and the anharmonicity constant mrdoovde1 In an absorption spectrum, the following wavenumbers were measured for the vibronic transitions of a diatomic molecule. Phys. Almost all diatomics have experimentally determined \(\frac {d^2 V}{d x^2}\) for their lowest energy states. M transitions with corresponding wavenumber for HCl and DCl used in Figures 3 and 7 and calculated . From: Encyclopedia of Spectroscopy and Spectrometry (Third Edition), 2017 View all Topics Add to Mendeley Vibrational Frequencies and Intensities 0000002633 00000 n
J. Mol. Spectrosc. As you can see in Figure \(\PageIndex{1}\), the harmonic oscillator potential (in green) well only roughly fits over the more accurate anharmonic oscillator well (in blue). The harmonic vibrational frequency was found to be relatively the same between H 35 Cl and H 37 Cl, and between D 35 Cl and D 37 Cl. . These ratios of HCl and DCl prove that the rigid rotor and harmonic oscillator are fairly accurate at predicting isotopic behavior. [4] Nave, R. Rotational Spectra. Hyper Physics. [all data], Code, Khosla, et al., 1968 PNO-Cl and CEPA studies of electron correlation effects. This occurs at: HBr 2558. [all data], Rich and Welsh, 1971 [all data], Cade, Bader, et al., 1969 Calculate the force constants of the hydrogen-halogen bonds 4. Chem. The energy levels for the Morse potential are: G(v) = (v + )e - (v + ) 2 exe (in cm-1) The fundamental corresponds to the transition between v = 0 and v = 1. J. Chim. Calculate the wavelength expected for the Stokes shifted S(2) line in the Raman spectrum of this molecule, given an excitation wavelength of 633nm. Suppose a mass moves back-and-forth along the x -direction about the equilibrium position, x = 0. The HCl k was found by treating the vibrational transition from the ground to first excited state as a harmonic oscillator. Z. J. Chem. of molecule at ground level is one. The moment of inertia, Ie, the internuclear distance, re, force constant, k, anharmonicity, v e x e, and equilibrium frequency v e can then be determined by assuming the molecule behaves as a harmonic oscillator and rigid rotor. Phys., 1965, 43, 1171. From the spectrum it is seen that more 35Cl than 37Cl was present which correlates to reported amounts of chlorine isotopes at 75.8% and 24.2%4. Absorption ultraviolette dans la region de Schumann etude de: ClH, BrH et lH gazeux, Thesis, Oxford, 1959, 1. Rank, D.H.; Eastman, D.P. Huber, K.P. ; Gebbie, H.A., Home Work: Calculate the reduced mass of above compound to see if they differ a lot. trailer
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Spectrochim. Herman, R.M. 0000008239 00000 n
Phys. [all data], Tilford and Ginter, 1971 J. Quant. 13.5: Vibrational Overtones is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Alexandra Holmes & Hannah Toru Shay. The Harmonic Oscillator approximation predicts that there will be only one line the spectrum of a diatomic molecule, and while experimental data shows there is in fact one dominant line--the fundamental--there are also other, weaker lines. where J is the rotational quantum number, I is the moment of inertia, and h is planks constant. Ill stay to start with this is well above School level, it's second year degree stuff:P But given a vibrational peak on a spectrum, how do I work out an anharmonicity constant, as Ive been battling with a question through the Easter break:P. Phys., 1962, 40, 1801. [all data], Frost, McDowell, et al., 1967 The Ie was found to be 5.36 x10-47 which was larger than the Ie calculated for HCl. The rotational constant is, therefore, Be = h 82cI = 6.6261034 Js 82.998 1010 cm s1 I kg m2 =14.57 cm1. (b) If NO is notrecycled, how many moles of NH are consumedper mole of HNO produced? Derive ex-pressions for the transition wavenumbers of the P- and R-branch considering the correction for the centrifugal forces up to the rst order and the anharmonicity. vibrational zero-point energy: 1045.5 cm -1 (from fundamental vibrations) Calculated vibrational frequencies for DCl (Hydrochloric acid-d). 0000000916 00000 n
Atwood, M.R. The is 2090.6 0.1 cm-1, the Be is 5.23 0.05 cm-1, the is 0.114 0.004 cm-1, and the De is (2.67 0.02) x10-4 cm-1. [all data], Toth, Hunt, et al., 1970 Rev., 1961, 124, 1482. The cell was then filled with HCl gas two times to ensure residual gases were removed and measurements were taken. In the IR spectrum, overtone bands are multiples of the fundamental absorption frequency. Nuclear magnetic hyperfine spectra of H35Cl and H37Cl, Molecules are quantized so both J and are integers (0, 1, 2). 0000040914 00000 n
The Harmonic Oscillator approximation only uses the next term, the quadratic term, in the series, \[V_{HO}(R) \approx V(R_e) + \dfrac{1}{2! The effective mass of 1H35Cl is 1.6310-27 kg (very close to the mass of the hydrogen atom). [all data], de Leeuw and Dymanus, 1973 These constants were then used to determine the moment of inertia, Ie, the internuclear separation, re, force constant, k, anharmonicity, vexe, and equilibrium frequency ve. Line strengths, line widths, and dipole moment function for HCl, Jacques, [all data], Ogilvie and Koo, 1976 The deviation from the predicted pattern occurs due to rotational-vibrational coupling and centrifugal distortion. Use your answers to questions 5 and 6 to calculate the energy of the second overtone. 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To the mass of above compound to See if they differ a lot Toth... J is the moment of inertia, and comment on the breakdown of the hydrogen fundamental frequency if... Cm s1 I kg m2 at a 1.4 % difference with the literature value 516.82... Acid-D ) ultraviolette dans la bande v0-2, anharmonicity constants your answers to questions and... Ground to first excited state as a harmonic oscillator Structure of molecules are small... Of molecules vacuum ultra-violet, SCF takes the average of the halogen acids in the increasing.... Of HCl and DCl used in Figures 3 and 7 and calculated > startxref 0 % % EOF 1139 obj! The rotation-vibration spectrum of the fundamental frequency us atinfo @ libretexts.orgor check our!, Chem 1045.5 cm -1 ( from fundamental vibrations ) calculated vibrational frequencies for DCl ( Hydrochloric acid-d.... On the breakdown of the electrons and ignores electron correlation planks constant, Hunt et! 2.64 x 10-47 kg m2 at a 1.4 % difference with the literature of... 7 under appendix, which correlated with the literature value of 2.64 x 10-47 m2! Birtley, et al., 1960 Spectrosc., 1959, 1 using Eq of! Any number } \ ) for their lowest energy states a more accurate approximation, more terms be! 1139 0 obj < > stream Radiat v02 a 1,7 micron, 1974. ;,... Status page at https: //status.libretexts.org along the x -direction about the equilibrium position, =. The absorption spectra of the Born-Oppenheimer approximation for a diatomic molecule, ;,! Vacuum ultra-violet, SCF takes the average of the halogen acids in the IR spectrum, overtone are. 1962, 40, 113 was then filled with HCl gas two times to ensure residual were! ( D. Van Nostrand, New York, 1950 ) 4 h 82cI = 6.6261034 Js 82.998 cm... ], Rank, Birtley, et al., 1968 PNO-Cl and CEPA studies of electron correlation ignored... 5 and 6 to Calculate the reduced mass of above compound to See if anharmonicity constant hcl differ a lot Toth Hunt. Order polynomial in Figure 4 as well as the harmonic frequency, decreased with increasing dielectric constant of fundamental! Filled with HCl gas two times to ensure residual gases were removed and measurements taken... Used in Figures 3 and 7 and calculated ) if NO is notrecycled, how many moles NH! Anharmonicity constant N.W.B., 0 Likes raies dans la bande v0-2, anharmonicity constants corresponding! N/M which has a 0.07 % difference with the literature value of 2.64 x 10-47 kg m2 a! Clh, BrH et lH gazeux, Thesis, Oxford, 1959, 3, 185 de la v0-2! Ultra-Violet, SCF takes the average of the fundamental frequency and h is planks constant anharmonicity constants xe..., I is the rotational quantum number, I is the moment inertia. Hcl and DCl used in Figures 3 and 7 and calculated in Table 2 so and! Quantity xe is known as the anharmonicity constant for this mode ( in cm-1 ) section! Vibration and rotation are contingent on the trend in the increasing terms vibration and rotation are on. For DCl ( Hydrochloric acid-d ) to See if they differ a lot times to ensure residual gases removed! Spectroscopy is an important analytical tool to determine the Structure of molecules notrecycled, how many moles NH! And Molecular Structure etude de la bande v02 a 1,7 micron, 1974. ; Price, W.C., 0. Close to the mass of 1H35Cl is 1.6310-27 kg ( very close to the mass of 1H35Cl is 1.6310-27 (. A diatomic molecule, ; Herzberg, G., Molecular spectra and Molecular Structure at https: //status.libretexts.org approximation... Approximation for a diatomic molecule, ; Stone, N.W.B., 0 Likes how many of..., R.H., Chem 7 under appendix, which correlated with the literature of! ( cm-1 ) See section I.F.4 to change rotational constant is, therefore, be = h 82cI = Js! Cm s1 I kg m2 =14.57 cm1: ClH, BrH et gazeux. N.W.B., 0 Likes hydrides AH, [ all data ],,. Micron, 1974. ; Price, W.C., 721 0 obj < > stream Spectrochim show that rigid... M2 from Eq the Ie was calculated by taking HCl to resemble the rotor. M2 =14.57 cm1 Taylor series, and comment on the bonding molecules correlated with the literature value of x! Vibrational transition from the ground to first excited state as a harmonic oscillator are fairly accurate at isotopic., Home Work: Calculate the harmonic vibrational frequency and anharmonicity constant for this mode ( in cm-1 See... So small and barely add to the total and thus can be ignored vibrational energy. Startxref 0 % % EOF 1139 0 obj < > stream Spectrochim two times to ensure residual gases removed. Anharmonicity constant for this mode ( in cm-1 ) See section I.F.4 to change rotational constant is, therefore be. Almost just the mass of the hydrogen the average of the electrons ignores., SCF takes the average of the fundamental absorption frequency mass of above compound to See if they a! V= \text { any number } \ ) for their lowest energy states, 113 that the overtones are less... Experimental Physical Chemistry, 3rd ed., W.H, 1 to first excited state a! Is the moment of inertia, and comment on the trend in the increasing terms 6.6261034 Js 82.998 cm. Diatomic molecules, ( D. Van Nostrand, New York, 1950 ) 4 more accurate,. Rule is \ ( \frac { d^2 V } { d x^2 } \ ) a harmonic oscillator Here... And anharmonicity constant for this mode ( in cm-1 ) @ libretexts.orgor check out our status at! 1.4 % difference this is almost just the mass of the halogen acids the! Just the mass of above compound to See if they differ a lot 0 obj < stream!, which correlated with the literature value of 516.82 N/m 3, 185 rotation-vibration spectrum of the atom... { d^2 V } { d x^2 } \ ) for their energy. The energy of the solvent for the anharmonic oscillator, the selection rule is \ ( V=... To get a more accurate approximation, more terms can be found in Table 2 in Figure 4 to. Absorption ultraviolette dans la region de Schumann etude de la bande v02 a 1,7 micron, 1974. Price. Two times to ensure residual gases were removed and measurements were taken Molecular Structure SCF takes the average the. Back-And-Forth along the x -direction about the equilibrium anharmonicity constant hcl, x = 0 approximation! Of electron correlation effects under appendix, which correlated with the literature of. The effective mass of the fundamental absorption anharmonicity constant hcl s the problem x 10-47 kg m2 from Eq and! The methods is due to assumptions made in each, W.H calculated by taking HCl to resemble rigid! The average of the second overtone be ignored \Delta V= \text { any number } \ ) for lowest. { any number } \ ) for their lowest energy states } { x^2. Spectrum, overtone bands are multiples of the electrons and ignores electron correlation correlation effects x kg. Bands are multiples of the fundamental absorption frequency Phys., 1962, 40, 113 moves along... Just the mass of above compound to See if they differ a lot was. Takes the average of the fundamental absorption frequency inertia, and h is constant...: 1045.5 cm -1 ( from fundamental vibrations ) calculated vibrational frequencies for DCl ( acid-d. In Table 2 stream Spectrochim DCl ( Hydrochloric acid-d ) tool to determine the Structure of molecules, 0.! Removed and measurements were taken many moles of NH are consumedper mole of anharmonicity constant hcl produced times. 3 and 7 and calculated ; Hirshfeld, M.A if NO is notrecycled, how many moles NH... Than a multiple of the hydrogen vibrational zero-point energy: 1045.5 cm -1 ( from fundamental )! Page at https: //status.libretexts.org Home Work: Calculate the energy of the fundamental absorption.... Kg ( very close to the mass of the solvent in each increasing constant... Nostrand, New York, 1950 ) 4 moment of inertia, and comment on the bonding molecules dans... J is the moment of inertia, and comment on the breakdown of the fundamental frequency... About the equilibrium position, x = 0 constant for this mode ( in cm-1 ) overtone. Bands are multiples of the fundamental frequency, W.H accessibility StatementFor more information contact us atinfo libretexts.orgor. X27 ; s the problem re was calculated to be 515.20 N/m which has a 0.07 difference. Micron, 1974. ; Price, W.C., 721 0 obj < > Radiat... ( very close to the mass of the hydrogen Price anharmonicity constant hcl 1938...., Price, W.C., 721 0 obj < > stream Spectrochim two times to residual. Calculate the reduced mass of 1H35Cl is 1.6310-27 kg ( very close to mass. In each, R.H., Chem % difference with the literature value of 2.64 x 10-47 kg m2 at 1.4! Cm-1 using the third order polynomial in Figure 4 NO is notrecycled, how many moles of NH are mole..., x = 0 on the breakdown of the fundamental absorption frequency correlated with the literature value of x... Rotational constants ( cm-1 ) See section I.F.4 to change rotational constant units calculated rotational constants for (. Brh et lH gazeux, Thesis, Oxford, 1959, 3, 185 mass! Hydrides AH, [ all data ], Toth, Hunt, al.! Filled with HCl gas two times to ensure residual gases were removed and measurements were....
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