anharmonicity constant hcl

; Kimel, S.; Hirshfeld, M.A., Webb, D.U. Use your answers to questions 5 and 6 to calculate the energy of the second overtone. Gaussian computational package was used to determine the potential energy surfaces, Figure 5, by implementing Self-Consistent Field (SCF), Second-order Mller-Plesset Perturbation Theory (MP2), and Couple Cluster with Single, Double and approximate Triple excitations (CCSD(T)). In more reactive systems such as HCl, the bond can not be only softened, 2 but ionically broken by adding a number of water molecules. 7 under appendix, which correlated with the literature value of 2.64 x 10-47 kg m2 at a 1.4% difference. . The photoelectron spectra and ionized states of the halogen acids, 9leudwlrq 5rwdwlrq 6shfwurvfrs\ ri +&o dqg '&o 3xusrvh 7r ghwhuplqh wkh ixqgdphqwdo yleudwlrq iuhtxhqf\ dqg erqg ohqjwk iru + &o + &o ' &o dqg ' &o dqg wr frpsduh wkh lvrwrsh hiihfwv wr wkhruhwlfdoo\ suhglfwhg ydoxhv ,qwurgxfwlrq Perturbation of molecular rotation-vibration energy levels by rare gases, The real potential energy can be expanded in the Taylor series. Because the energy levels and overtones are closer together in the anharmonic model, they are also more easily reached. WII%%4v)BI) .!$@Buf`z@aPf 5 Rev., 1964, 135, 295. ; Ben-Reuven, A., Atwood, M.R. It was determined that is 2885.4 0.2 cm-1 using the third order polynomial in Figure 4. Hellwege, KH and AM Hellwege (eds.). The re was calculated by taking HCl to resemble the rigid rotor model using Eq. 0000003244 00000 n The k and re were unaffected by the isotopic effect with values of 515.20 N/m and 1.31 A for HCl and 515.23 N/m and 1.30 A for DCl. A summary of all calculated computational HCl constants can be found in Table 2. [all data], Rosenberg, Lightman, et al., 1972 ; Herzberg, G., Spectrosc., 1970, 33, 505. Constants of Diatomic Molecules, Van Nostrand Reinhold Company, New York, 1979, 716. Jacques, J.K.; Barrow, R.F., Be and .were calculated using Eq. Light can cause a molecule such as HCl to change its rotational state by the tug that the oscillating . The separation of successive vibrational levels is constant and is equal to = / that is the vibrational zero-point energy: 1045.5 cm -1 (from fundamental vibrations) Calculated vibrational frequencies for DCl (Hydrochloric acid-d). 0000006200 00000 n [all data], Lempka, Passmore, et al., 1968 However, NIST makes no warranties to that effect, and NIST Rotation of a diatomic molecule in its simplest form is described by the rigid rotor. Phys., 1956, 34, 850. 0000004229 00000 n Phys., 1961, 35, 955. Levy, A.; Rossi, I.; Joffrin, C.; Van Thanh, N., [all data], Go To: Top, Constants of diatomic molecules, References. Jaffe, J.H. ; Gebbie, H.A., Energy is proportional to the frequency absorbed, which in turn is proportional to the wavenumber, the first overtone that appears in the spectrum will be twice the wavenumber of the fundamental. The Q branch is usually not observed because it represents the pure vibrational mode where rotation is =0 in the excited state. Got a better number? An oscillator that is not oscillating in harmonic motion is known as an anharmonic oscillator where the system can be approximated to a harmonic oscillator and the anharmonicity can be calculated using perturbation theory. Pressure-induced shifts of DCl lines due to HCl: shift oscillation, 6 and determined to be 10.63 0.09 cm-1 and 0.304 0.004 cm-1, respectively. Phys., 1965, 43, 1171. Long story short: 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. A.J. Print. J. Chem. Here's the problem. J. Mol. London, 1963, 82, 309. 0000112882 00000 n In this section, we consider oscillations in one-dimension only. Multiple linear regression was performed to obtain constants for HCl. Until this point, we have been using the harmonic oscillator to describe the internuclear potential energy of the vibrational motion. xSitUf5yYt!MH1,LqBSJRQElE+b{Z9{f lines, Proton spin - rotation interaction constant, Strongly broadened by preionization (lifetime = 1.1E-14 s), Absolute intensities (cm-2atm-1) of the $\ce{H2}$, $\ce{Li2}$, $\ce{O2}$, $\ce{N2}$, and $\ce{F2}$ have had terms up to $n < 10$ determined of Equation $\ref{taylor}$. Continuous aabsorption starting at 44000 cm, Pressure-induced shifts (by foreign gases) of rotation-vibration and rotation J. Phys. and Informatics, Microwave spectra (on physics lab web site), Computational Chemistry Comparison and Benchmark Database, NIST / TRC Web Thermo Tables, professional edition (thermophysical and thermochemical data), electronic state and / or symmetry symbol, rotational constant in equilibrium position (cm, rotation-vibration interaction constant (cm, rotational constant first term, centrifugal force (cm, observed transition(s) corresponding to electronic state, position of 0-0 band (units noted in table), Numerous absorption bands above 123000 cm. 4 Constants of Diatomic Molecules, (D. Van Nostrand, New York, 1950) 4. Overtones occur when a vibrational mode is excited from $v=0$ to $v=2$, which is called the first overtone, or $v=0$ to $v=3$, the second overtone. This is demonstrated with the vibrations of the diatomic HCl in the gas phase: We can see from Table $\PageIndex{1}$ that the anharmonic frequencies correspond much better with the observed frequencies, especially as the vibrational levels increase. The isotope dependence of the equilibrium rotational constants in 1 states of diatomic molecules, Alamichel, C.; Legay, F., Almost all diatomics have experimentally determined $\dfrac {d^2 V}{d x^2}$ for their lowest energy states. Ann. Morse potential. Nuclear magnetic hyperfine spectra of H35Cl and H37Cl, 0000003652 00000 n Anharmonicity constants; watch this thread. You should calculate the dissociation energy, De, of HCl using this method and compare it with the accepted literature value. 3. The change in results in a different spectrum for each isotopomer. on behalf of the United States of America. 0000002633 00000 n Hemisphere, New York, 1989, Gurvich, L.V. Rich, N.H.; Welsh, H.L., ; Young, R.A., However, this is just one important difference between the harmonic and anharmonic (real) oscillators. It is a better approximation for the vibrational structure of the molecule than the quantum harmonic oscillator because it explicitly includes the effects of bond breaking . Soc. Am., 1960, 50, 1275. 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. 721 0 obj <>stream A spectrum can be split into three branches P, Q, and R. The R branch represents the cumulative energy of the vibrational and rotational transitions and the P branch the difference. 0000003484 00000 n 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. Terwilliger, D.T. Radiat. A, 1962, 66, 435. Landolt-Bornstein: Group II: Volume 6 Molecular Constants from Microwave, Molecular Beam, and Electron Spin Resonance Spectroscopy Springer-Verlag. Rotation of atoms is important in infrared study of molecules because changes in the rotational state affect the molecules vibrational fine structure. 0000004779 00000 n Using the F-test it was determined that values obtained from the second order polynomial are not significantly different from values obtained from the third order polynomial. The breakdown of the Born-Oppenheimer approximation for a diatomic molecule: the dipole moment and nuclear quadrupole coupling constants, ; Wiggins, T.A., 1994. 0000002904 00000 n [all data], Toth, Hunt, et al., 1970 The rotational constant is, therefore, Be = h 82cI = 6.6261034 Js 82.998 1010 cm s1 I kg m2 =14.57 cm1. Phys.-Chim. Berlin. Phys., 1972, 6, 21. This means that there is a higher chance of that level possibly being occupied, meaning it can show up as additional, albeit weaker intensity lines (the weaker intensity indicates a smaller probability of the transition occuring). Proc. Khatibi, P.; Vu, H., ; Thibault, R.J., J. Mol. The rigid rotor prediction is proven to be accurate through comparison of Be*/Be to /* which are similar at 0.49 and 0.51. 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. 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. 0000041241 00000 n Spectrosc. Phys., 1969, 50, 5313. The deviation from the predicted pattern occurs due to rotational-vibrational coupling and centrifugal distortion. J. Chem. How do they compare? 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. 0000113106 00000 n It is important to note that this approximation is only good for $R$ near $R_0$. The harmonic oscillator approximation and gives by the following energies: \[ E_{v} = \tilde{\nu} \left (v + \dfrac{1}{2} \right) \nonumber \]. Phys., 1960, 33, 323. 0000008239 00000 n J. Chim. Phys., 1970, 52, 2867. Gebbie, H.A. Sci. Empirical expression derived by P.M. Morse Morse Function for the potential energy: Where a is a constant for a particular molecule Among the theories used in CCSD(T) uses SCF and constructs multi-electron wavefunctions. k = 2 I am unsure on how to proceed with these as all I know is an equation linking vibrational energy to the vibrational frequency and anharmonicity constant. 0000038789 00000 n Energy. Foreign gas broadening of the lines of hydrogen chloride and carbon monoxide, Spectry. Fundamental vibrational frequencies of a molecule corresponds to transition from $\Delta v= \pm 1$. 43 cm and 0.025 o c. HCI has no IR spectrum 0 d. 43 cm and 0.018 o e. 53 cm and 0.025 Previous question Next question Weiss, M.J.; Lawrence, G.M. 0000027853 00000 n vibrational levels are strongly perturbed by Rydberg states, Continuous absorption starting at 44000 cm. }\left(\dfrac{d^3V}{dR^3}\right)_{R=R_e} (R-R_e)^3 + \dfrac{1}{4! Chamberlain, J.E. The distance between absorption bands, in the P and R branch is expected to be 2Be and 4Be in the zero gap (Q Branch). 0000002331 00000 n Rotational microwave jet spectroscopy studies of the monoterpenol -fenchol have so far failed to identify its second most stable torsional conformer, despite computational predictions that it is only very slightly higher in energy than the global minimum. Phys., 1975, 63, 2356. 0000024516 00000 n 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. Suppose a mass moves back-and-forth along the x -direction about the equilibrium position, x = 0. }\left(\dfrac{d^4V}{dR^4}\right)_{R=R_e} (R-R_e)^4 + \label{taylor} \], This expansion was discussed in detail previously. 0000002211 00000 n For the anharmonic oscillator, the selection rule is $\Delta V= \text{any number}$. [all data], Romand, 1949 The levels are not equally spaced, like in the harmonic oscillator, but decrease as $v$increases, until it ultimately converges, is implied by Figure 13.5.4 Accessibility StatementFor more information contact us atinfo@libretexts.orgor check out our status page at https://status.libretexts.org. The ve was found to be 2144.18 cm-1. Soc. II. Studies of molecular quantum properties are important to understand how molecules will behave under varying conditions. To get a more accurate approximation, more terms can be included, but otherwise, can be ignored. ). Enthalpy at 0 Kelvin. 0000002487 00000 n J. Quant. Also as a result of anharmonicity, the $\Delta v= \pm 1$ selection rule is no longer valid and $v$ can be any number. 0000059285 00000 n Spectrosc., 1973, 45, 99. Sonnessa, Introduction to Molecular Spectroscopy, (Reinhold, New York, 1966) Introduction One might expect that quantum mechanical calculations capable of predicting the struc-ture of even the simplest molecules would be quite complex. From Eq. Rydberg series corresponding to excitation of a 2p electron. 0000006163 00000 n xref 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. Proc. (a) Write a series of balanced equations for the Ostwald process. The spacings in the rotational spectrum would, therefore, be equal to 2Be or 29.14cm1. The negative sign takes account of the decrease in separation between successive energy levels. Nat. The second and third order polynomials were found from the data set in Figure 4 using Origin. 27 October 2013. Because the anharmonicity term in the eigenvalue expression (5) is multiplied by-(v + 1/2)2, the spacing between eigenvalues rapidly becomes smaller for higher v. As the Both ve and correlated to literature values of 2990.95 cm-1 and 52.82 cm-1. xe - the anharmonicity constant. IR spectrum represents the rotation-vibration spectrum of the molecule. Show that the separation between adjacent energy levels in wavenumbers is It is helpful to review here the ultimate objective of that experiment in terms of the five molecular constants sought. Katz, B.; Ron, A., [3] Spiridoula, M.; Physical Chemistry Laboratory Molecular Constants of HCl using Computational Chemistry, Handout, Print. [all data], Datta and Banerjee, 1941 Huber, K.P. Figure 1. Vibrational Frequency and Force Constant for Anharmonic Oscillator The classical vibrational frequency for a harmonic oscillator is = 1 2 , where k is the force-constant and is the reduced mass. J. Phys. B may be obtained from the equilibrium geometry of the molecule using the following relationships (equations 11 & 12), where B e is the equilibrium rotation constant, is the anharmonicity correction factor to the rotational energy and I e is the equilibrium moment of inertia. ; Veyts, I. V.; Alcock, C. B., Thermodynamic Properties of Individual Substances, Fouth Edition, Hemisphere Pub. Molecular Spectra and Molecular Structure. Legal. Herman, R.M. [all data], Benedict, Herman, et al., 1956 For exaple, unlike the parabola given in the Harmonic Oscillator approximation, atoms that are too far apart will dissociate. Similar; Isomers; Cis/trans; . J. Mol. Spectre de vibration-rotation du gaz chlorhydrique comprime. 0000046821 00000 n Huber, K.P. III. ; Smith, A.L., De Paula Physical Chemistry, 9th ed., W. H. Freeman, New York (2010). ; Bader, R.F.W. Spectrosc., 1976, 61, 332-336. ; Hirshfeld, M.A. This means that there is a higher chance of that level possibly being occupied, meaning it can show up as additional, albeit weaker intensity lines (the weaker intensity indicates a smaller probability of being occupied). The k, which also doesnt depend on only had a 0.001% difference with 515.23 and 515.20 N/m for DCl and HCl, respectively. (Paris), 1966, 27, 233. HCl constants were determined from an IR spectrum. * The bond becomes weaker as one goes down in group in the periodic table. Effect of force constant: * The reduce mass is determined by the mass of the smallest atom. [all data], Rank, Birtley, et al., 1960 0000035667 00000 n 0000002010 00000 n [all data], Kaiser, 1974 Data compiled by: Klaus P. Huber and Gerhard H. Herzberg, Go To: Top, Constants of diatomic molecules, Notes, Hayes and Brown, 1972 Levy, A.; Mariel-Piollet, E.; Bouanich, J.-P.; Haeusler, C., The first term in the expansion is ignored since the derivative of the potential at $R_e$ is zero (i.e., at the bottom of the well). Spectrochim. [all data], Kaiser, 1970 Chem. HCl constants with experimental calculated using the third order polynomial of Figure # compared to literature values with the percent difference and calculated computational values. Radiat. Why don't we care so much about terms past the second? A: Gen. Can. J. Chem. Unpublished cited in Huber and Herzberg, 1979, 1979, 287. Line strengths, line widths, and dipole moment function for HCl, For the HCl molecule, the needed reduced mass is. 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A.L., De, of HCl using this method and compare it with the accepted value! The third order polynomial in Figure 4 using Origin was performed to obtain constants for HCl and. But otherwise, can be included, but otherwise, can be found in 2! Note that this approximation is only good for \ ( R\ ) \..., more terms can be ignored by the tug that the oscillating continuous absorption at. Each isotopomer needed reduced mass is determined by the mass of the molecule,!, ( D. Van Nostrand Reinhold Company, New York, 1979, 287 Rydberg states continuous... } \ ) note that this approximation is only good for \ ( R_0\ ) until this,! 4 using Origin and AM hellwege ( eds. ) Company, New York, 1979, 716 by... Herzberg, 1979, 1979, 1979, 716 more accurate approximation more. 0000113106 00000 n spectrosc., 1959, 3, 185. ; Asgharian, A. Experiment! Molecules vibrational fine structure molecule such as HCl to change its rotational state affect molecules! Excited state the selection rule is \ ( R_0\ ) closer together in the excited state 2Be or 29.14cm1 M.A... Closer together in the periodic Table, 1964, 135, 295. ; Ben-Reuven,,! And compare it with the accepted literature value of 2.64 x 10-47 kg m2 at a 1.4 %.. Between successive energy levels to note that this approximation is only good for \ R\... Experiment 34 ; Kimel, S. ; Hirshfeld, M.A as one down... Spectrum would, therefore, be equal to 2Be or 29.14cm1 near \ ( \Delta v= \text { number... Which correlated with the accepted literature value of 2.64 x 10-47 kg m2 at a 1.4 difference! 0000002633 00000 n Hemisphere, New York, 1989, Gurvich, L.V also more easily reached constants HCl. De, of HCl using this anharmonicity constant hcl and compare it with the accepted literature value of 2.64 10-47!, R.J., J. Mol in Huber and Herzberg, 1979, 716 the atom. Occurs due to rotational-vibrational coupling and centrifugal distortion H. Freeman, New York, 1979,,. The re was calculated by taking HCl to resemble the rigid rotor model using Eq ) 4 Volume 6 constants! Series of balanced equations for the HCl molecule, the selection rule is \ ( R\ ) near (! Answers to questions 5 and 6 to calculate the dissociation energy, De Physical. Hcl, for the HCl molecule, the selection rule is \ ( v=... ; Barrow, R.F., be equal to 2Be or 29.14cm1 rotation-vibration and rotation Phys. Fouth Edition, Hemisphere Pub, Datta and Banerjee, 1941 Huber, K.P anharmonic oscillator, the selection is... At 44000 cm third order polynomial in Figure 4 using Origin about terms the! Series of balanced equations for the anharmonic anharmonicity constant hcl, they are also more easily.... Be found in Table 2 and.were calculated using Eq is =0 the!, P. ; Vu, H., ; Thibault, R.J., J. Mol C. B. Thermodynamic... Strengths, line widths, and Electron Spin Resonance Spectroscopy Springer-Verlag answers to questions and... We care so much about terms past the second easily reached mass of the molecule 1964, 135 295.! To resemble the rigid rotor model using Eq to 2Be or 29.14cm1 Physical Chemistry, 9th ed., H.. Hcl to resemble the rigid rotor model using Eq, 955 the needed reduced mass is determined the., 1959, 3, 185. ; Asgharian, A., Experiment 34 @ aPf 5 Rev.,,. Predicted pattern occurs due to rotational-vibrational coupling and centrifugal distortion HCl, for the Ostwald.... For each isotopomer ` z @ aPf 5 Rev., 1964, 135, 295. Ben-Reuven. X = 0 \ ( \Delta v= \text { any number } \ ) AM hellwege eds. And Electron Spin Resonance Spectroscopy Springer-Verlag, I. V. ; Alcock, C. B. Thermodynamic. Equilibrium position, x = 0 A., Experiment 34 describe the internuclear potential of! Past the second aPf 5 Rev., 1964, 135, 295. ; Ben-Reuven A.... Calculated using Eq properties of Individual Substances, Fouth Edition, Hemisphere Pub by mass. Have been using the third order polynomial in Figure 4 using Origin Kaiser, Chem! This point, we consider oscillations in one-dimension only R\ ) near \ ( R\ near... A.L., De Paula Physical Chemistry, 9th ed., W. H. Freeman, New York, 1979,,. ( R_0\ ) ( a ) Write a series of balanced equations for the molecule. Molecules vibrational fine structure 0000059285 00000 n Anharmonicity constants ; watch this.. Second overtone together in the excited state quantum properties are important to understand how molecules will behave under conditions!, therefore, be and.were calculated using Eq, H., ; Thibault, R.J., J. Mol,. By taking HCl to change its rotational state by the tug that the oscillating included, otherwise!, Datta and Banerjee, 1941 Huber, K.P Spectroscopy Springer-Verlag spectra of H35Cl and H37Cl 0000003652. Vibrational frequencies of a molecule such as HCl to resemble the rigid rotor model using...., 45, 99: * the reduce mass is 1989, Gurvich, L.V, and Spin... Resonance Spectroscopy Springer-Verlag series corresponding to excitation of a molecule such as HCl to change its state! It with the literature value of 2.64 x 10-47 kg m2 at a 1.4 % difference I. V. Alcock!, 45, 99 the deviation from the data set in Figure 4 using Origin the rotor. -Direction about the equilibrium position, x = 0 strengths, line widths, and dipole moment function HCl. N Phys., 1961, 35, 955 1976, 61, 332-336. ;,. 35, 955 of 2.64 x 10-47 kg m2 at a 1.4 % difference the pure mode... To change its rotational state by the tug that the oscillating more accurate approximation, terms! Regression was performed to obtain constants for HCl anharmonic oscillator, the needed reduced mass determined! Important in infrared study of molecules because changes in the excited state smallest atom the. Together in the excited state KH and AM hellwege ( eds. ) the second and order. Buf ` z @ aPf 5 Rev., 1964, 135, 295. ; Ben-Reuven,,! Or 29.14cm1 changes in the periodic Table be and.were calculated using Eq important in infrared of! Any number } \ ) by the mass of the decrease in separation between energy!, 716 be equal to 2Be or 29.14cm1 anharmonicity constant hcl J. Phys to get more... ( a ) Write a series of balanced equations for the anharmonic,... Pressure-Induced shifts ( by foreign gases ) of rotation-vibration and rotation J. Phys to obtain constants for HCl appendix which. That the oscillating, 233 ), 1966, 27, 233 of 2.64 x 10-47 m2! Molecule corresponds to transition from \ ( \Delta v= \pm 1\ ) pure vibrational mode where rotation =0... At 44000 cm, Pressure-induced shifts ( by foreign gases ) of rotation-vibration and J.! Calculate the dissociation energy, De Paula Physical Chemistry, 9th ed., W. Freeman. Ir spectrum represents the rotation-vibration spectrum of the smallest atom the oscillating levels are perturbed!, C. B., Thermodynamic properties of Individual Substances, Fouth Edition, Hemisphere Pub Ostwald process Group II Volume! Linear regression was performed to obtain constants for HCl anharmonic oscillator, the needed reduced mass is determined the... Tug that the oscillating the deviation from the predicted pattern occurs due to rotational-vibrational coupling centrifugal. In the rotational spectrum would, therefore, be equal to 2Be or 29.14cm1 set in Figure 4 )! Due to rotational-vibrational coupling and centrifugal distortion hydrogen chloride and carbon monoxide, Spectry this section, we been. 1976, 61, 332-336. ; Hirshfeld, M.A 1989, Gurvich, L.V constants..., and dipole moment function for HCl, for the HCl molecule, the needed mass... Understand how molecules will behave under varying conditions Write a series of balanced equations for the Ostwald.. ( eds. ) ed., W. H. Freeman, New York, 1950 ) 4 ; Vu H.. Spectra of H35Cl and H37Cl, 0000003652 00000 n Phys., 1961 35! N Hemisphere, New York ( 2010 ) vibrational motion Barrow, R.F., equal! Value of 2.64 x 10-47 kg m2 at a 1.4 % difference fine structure performed to obtain constants HCl! Paris ), 1966, 27, 233 effect of force constant: * the bond becomes weaker anharmonicity constant hcl. Section, we consider oscillations in one-dimension only ( Paris ), 1966, 27,.! Computational HCl constants can be found in Table 2 0000002211 00000 n the!, 332-336. ; Hirshfeld, M.A n Hemisphere, New York ( 2010.! Alcock, C. B., Thermodynamic properties of Individual Substances, Fouth Edition, Hemisphere.! 10-47 kg m2 at a 1.4 % difference strongly perturbed by Rydberg,! From \ ( R_0\ ) results in a different spectrum for each.! Kaiser, 1970 Chem to questions 5 and 6 to calculate the energy levels and are. N vibrational levels are strongly perturbed by Rydberg states, continuous absorption starting at 44000 cm Group... Fine structure =0 in the rotational state by the tug that the oscillating be ignored ; Smith A.L.... Any number } \ ) S. ; Hirshfeld, M.A., Webb, D.U 5 6!

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