The Potential Constants of Ethane
dc.contributor.author | Hansen, G. E. | en_US |
dc.contributor.author | Dennison, David M. | en_US |
dc.date.accessioned | 2010-05-06T21:46:46Z | |
dc.date.available | 2010-05-06T21:46:46Z | |
dc.date.issued | 1952-02 | en_US |
dc.identifier.citation | Hansen, G. E.; Dennison, D. M. (1952). "The Potential Constants of Ethane." The Journal of Chemical Physics 20(2): 313-326. <http://hdl.handle.net/2027.42/70194> | en_US |
dc.identifier.uri | https://hdl.handle.net/2027.42/70194 | |
dc.description.abstract | The infrared and Raman data of light and heavy ethane (C2H6 and C2D6) have been reexamined for the purpose of determining as accurately as possible the potential constants of the ethane molecule. In order to fill in some of the gaps in the spectroscopic data, additional high resolution measurements have been made on the infrared spectrum of heavy ethane which have given more precise values for the active fundamental frequencies and zeta‐values. Resolution of the fine structure associated with the parallel band ν5* has given the value of the large moment of inertia of C2D6, thus completing the information required for the spectroscopic determination of the dimensions of ethane. The data yield, C☒C distance=1.543A, C☒H distance=1.102A, H☒C☒C angle=109°37′, and H☒C☒H angle=109°19′. The twenty‐two distinct potential constants compatible with the D3d symmetry of ethane have been determined through their relationships to the normal frequencies and zeta‐values of C2H6 and C2D6. The normal frequencies have been obtained by addition of anharmonic corrections to the spectroscopically observed fundamental frequencies. These corrections were estimated by means of the known anharmonic corrections for methane and the conditions imposed by the Teller product rule. The fundamental frequencies and zeta‐values have been taken directly from the observed band centers and rotational spacings wherever possible. In the cases of resonance, the influence of the couplings were either calculated or estimated and the corresponding unperturbed values for the frequencies and zeta‐values selected. The potential function is determined first in terms of a set of simple symmetry coordinates, and then reexpressed in terms of valence coordinates to permit comparison of the valence force constants of ethane and methane. | en_US |
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dc.format.extent | 993901 bytes | |
dc.format.mimetype | text/plain | |
dc.format.mimetype | application/pdf | |
dc.publisher | The American Institute of Physics | en_US |
dc.rights | © The American Institute of Physics | en_US |
dc.title | The Potential Constants of Ethane | en_US |
dc.type | Article | en_US |
dc.subject.hlbsecondlevel | Physics | en_US |
dc.subject.hlbtoplevel | Science | en_US |
dc.description.peerreviewed | Peer Reviewed | en_US |
dc.contributor.affiliationum | Randall Laboratory of Physics, University of Michigan, Ann Arbor, Michigan | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/70194/2/JCPSA6-20-2-313-1.pdf | |
dc.identifier.doi | 10.1063/1.1700400 | en_US |
dc.identifier.source | The Journal of Chemical Physics | en_US |
dc.identifier.citedreference | A. Levin and C. F. Meyer, J. Opt. Soc. Am. 16, 137 (1928); P. Daure, Ann. Phys. 12, 375 (1929). | en_US |
dc.identifier.citedreference | G. Sutherland and D. M. Dennison, Proc. Roy. Soc. (London) A148, 250 (1935); J. B. Howard, J. Chem. Phys. 5, 442 (1937). | en_US |
dc.identifier.citedreference | Crawford, Avery, and Linnett, J. Chem. Phys. 6, 682 (1938). | en_US |
dc.identifier.citedreference | F. Stitt, J. Chem. Phys. 7, 297 (1939). | en_US |
dc.identifier.citedreference | L. G. Smith, J. Chem. Phys. 17, 139 (1949). | en_US |
dc.identifier.citedreference | D. M. Dennison, Revs. Modern Phys. 12, 175 (1940). | en_US |
dc.identifier.citedreference | W. E. Anderson, thesis (University of Michigan, 1948). | en_US |
dc.identifier.citedreference | G. Herzberg, Infrared and Raman Spectra of Polyatomic Molecules (D. Van Nostrand Company, Inc., New York, 1945). | en_US |
dc.identifier.citedreference | It is the measurement of the ν2+9ν2+9 by Smith which favors a value for ν2ν2 higher than the value ν2 = 1375 cm−1ν2=1375cm−1 originally given in reference 3. It then becomes preferable to assign the 2778 cm−12778cm−1 band as ν2+2ν2+2 rather than ν6+6ν6+6 as given also originally in reference 3. | en_US |
dc.identifier.citedreference | As mentioned by Smith, the appearance in the infrared spectrum of a perpendicular band with large rotational spacing at 2021.6 cm−12021.6cm−1 is the strongest argument in favor of the D3dD3d equilibrium configuration of ethane, since this position and rotational spacing forces the band’s assignment as ν9+12,ν9+12, a combination band infrared active for the D3dD3d model but infrared inactive for the D3hD3h model. | en_US |
dc.identifier.citedreference | Smith reported these spacings as 7.64 and 7.02 cm−17.02cm−1 respectively, but reexamination of his data seems to indicate the above listed values to be preferable. | en_US |
dc.identifier.citedreference | M. Johnston and D. M. Dennison, Phys. Rev. 48, 868 (1935) show that the dipole coupling between a combination level and the vibrational ground state is such that if l1,l2,⋯l1,l2,⋯ represent the internal angular momenta quantum numbers, the apparent zeta‐value for the combination band is ζ = +(Σliζi)ζ=+(Σliζi) or −(Σliζi)−(Σliζi) as ∣Σli∣ = 3n+1∣Σli∣=3n+1 or 3n−1,3n−1, where n is any integer. | en_US |
dc.identifier.citedreference | C. M. Lewis and W. V. Houston, Phys. Rev. 44, 903 (1933). | en_US |
dc.identifier.citedreference | Kistiakowsky, Lacher, and Stitt, J. Chem. Phys. 7, 289 (1939). | en_US |
dc.identifier.citedreference | L. G. Smith and W. N. Woodward, Phys. Rev. 61, 386(A) (1942). | en_US |
dc.identifier.citedreference | The choice of coordinates such that the kinetic energy expression for ethane has a diagonal form and equal coefficients gives rise to two simplifying features: first, the transformation matrix Siα,Siα, connecting the symmetry coordinates ξiξi with the normal coordinates (ξ10,ξ10, ξ11,ξ11, and ξ12,ξ12,) is unitary, and second, the matrix of the coefficients Zij,Zij, appearing in the expression for pzpz is symmetric and related to the zeta‐matrix, ζαβζαβ (i.e., the coefficients in the expression for pzpz in terms of normal coordinates), by the equation ζαβ=ΣZijSiαSiβ, where the diagonal elements ζααζαα are the observable values ζα = ζ10,ζ11,and ζ12.ζα=ζ10,ζ11,andζ12. The formal advantage of the use of a new set of coordinates ξi∗ξi∗ in accomplishing this same simplification for heavy ethane is offset by a consequent necessity for the introduction of a new set of potential constants bij∗bij∗ related but not equal to the bij.bij. | en_US |
dc.owningcollname | Physics, Department of |
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