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Benzene Vibrational Exciton Spectrum
dc.contributor.authorKopelman, Raoulen_US
dc.date.accessioned2010-05-06T23:32:12Z
dc.date.available2010-05-06T23:32:12Z
dc.date.issued1967-11-01en_US
dc.identifier.citationKopelman, Raoul (1967). "Benzene Vibrational Exciton Spectrum." The Journal of Chemical Physics 47(9): 3227-3230. <http://hdl.handle.net/2027.42/71308>en_US
dc.identifier.urihttps://hdl.handle.net/2027.42/71308
dc.description.abstractA critical discussion of the infrared polarization assignments of Zwerdling and Halford, in view of the now accepted benzene crystal structure, leads to acceptance of their results, though with somewhat reduced credibility. The controversial 707‐cm−1 absorption is assigned as the B2 interchange component (b axis polarized) of the a2u fundamental (674‐cm−1 gas‐phase) exciton band. The resulting, unusually large, static and dynamic exciton interaction terms are tabulated. Recent calculations based on atom—atom interactions are in reasonable agreement with the above results.en_US
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dc.publisherThe American Institute of Physicsen_US
dc.rights© The American Institute of Physicsen_US
dc.titleBenzene Vibrational Exciton Spectrumen_US
dc.typeArticleen_US
dc.subject.hlbsecondlevelPhysicsen_US
dc.subject.hlbtoplevelScienceen_US
dc.description.peerreviewedPeer Revieweden_US
dc.contributor.affiliationumDepartment of Chemistry, California Institute of Technology, Pasadena, California and Department of Chemistry, University of Michigan, Ann Arbor, Michiganen_US
dc.description.bitstreamurlhttp://deepblue.lib.umich.edu/bitstream/2027.42/71308/2/JCPSA6-47-9-3227-1.pdf
dc.identifier.doi10.1063/1.1712380en_US
dc.identifier.sourceThe Journal of Chemical Physicsen_US
dc.identifier.citedreference(a) E. R. Bernstein, S. D. Colson, R. Kopelman, and G. W. Robinson (unpublished data). (b) Proc. Intern. Symp. Mol. Struct. Spectry., Columbus, Ohio, 1965, Paper M2.en_US
dc.identifier.citedreference(a) S. D. Colson, R. Kopelman, and G. W. Robinson, J. Chem. Phys. 47, 27, (1967). (b) R. Gee, J. Chem. Phys. 46, 4847 (1967). (c) R. Kopelman, “The Interchange Symmetry I: Molecules and Crystals,” J. Chem. Phys. 47, 2631 (1967).en_US
dc.identifier.citedreferenceS. Zwerdling and R. S. Halford, J. Chem. Phys. 23, 2221 (1955).en_US
dc.identifier.citedreference(a) R. S. Halford and O. H. Schafer, J. Chem. Phys. 14, 141 (1946). (b) R. D. Mair and D. F. Hornig, J. Chem. Phys. 17, 1236 (1949).en_US
dc.identifier.citedreferenceE. G. Cox, Proc. Roy. Soc. (London) A135, 491 (1932).en_US
dc.identifier.citedreferenceZH stressed, correctly, that this conclusion was derived from the “accidental” structure (which turned out to be wrong), and not from selection rules based on the space group (which are correctly stated in their paper and are still applicable because only the structure, but not the space group, of benzene has been modified since—Ref. 7).en_US
dc.identifier.citedreferenceE. G. Cox, Rev. Mod. Phys. 10, 159 (1958); E. G. Cox, D. W. J. Cruichshank, and J. A. S. Smith, Proc. Roy. Soc. (London) A247, 1 (1958); G. E. Bacon, N. A. Curry, and S. A. Wilson, Proc. Roy. Soc. (London) A279, 98 (1964).en_US
dc.identifier.citedreferenceJ. L. Hollenberg and D. A. Dows, J. Chem. Phys. 37, 1300 (1962). Also E. Bernstein (private communication).en_US
dc.identifier.citedreferenceWisely, they took as their criterion for this identification only the non‐crystal‐induced bands. In view of later evidence (Ref. 8) that the intensity of these bands changes little upon condensation; it may still be a valid criterion.en_US
dc.identifier.citedreferenceHowever, only because the dichroic ratio c∕a is expected, for intrinsically allowed fundamentals, to be close to unity (oriented gas model) while the ratio b∕a or b∕c is expected to be much smaller. For instance, for an out‐of‐plane (A2u)(A2u) band, a/c ≅ 1.1,a∕c≅1.1, b/a ≅ 0.1.b∕a≅0.1. This seems to lend much more weight to ZH’s identification of the ac plane than to their specific identification of the a and c axes.en_US
dc.identifier.citedreferenceR. M. Hexter and D. A. Dows, J. Chem. Phys. 25, 504 (1956). A suggestion in this direction is found in Ref. 3, too.en_US
dc.identifier.citedreferenceS. C. Sirkar and A. K. Ray, Ind. J. Phys. 24, 189 (1950). S. C. Sirkar, D. K. Mukherjee, and P. K. Bishue, Ind. J. Phys. 38, 181 (1964). M. Ito, J. Chem. Phys. 42, 2844 (1965). The claim made in this work that the site selection rules are violated is unjustified in our opinion. The 1012‐cm−11012‐cm−1 band can be easily interpreted as the b2gb2g fundamental, ν5.ν5. It is observed12a at 1004 cm11004cm1 in a mixed crystal. The relatively large shift from the liquid value of 995 cm1995cm1 (if indeed 995 is correctly assigned as ν5ν5!) could be explained as due to Fermi resonance of ν5ν5 with the totally symmetric ν1ν1 (992 cm−1),(992cm−1), as in the site CiCi they have the same symmetry (Ag).(Ag). Very recently a similar conclusion has been reached independently by M. Ito and T. Shigeoka, Spectrochim. Acta 22, 1029 (1966). The difference between the liquid value (995 cm−1)(995cm−1) and the solid value may also be partly due to crystal splittings, not shift. Such splittings [see Ref. 2(b)] could also account for the difference between the solid value inferred from ir combinations and the one observed in the Raman, assuming that not all interchange (factor) group components have been observed in the Raman spectrum. a G. C. Nieman, Ph.D. thesis, California Institute of Technology (1964).en_US
dc.identifier.citedreferenceD. W. J. Cruickshank, Rev. Mod. Phys. 30, 163 (1958).en_US
dc.identifier.citedreferenceW. B. Person and D. A. Olsen, J. Chem. Phys. 32, 1268 (1960).en_US
dc.identifier.citedreferenceTheir conclusion is based on the observation that in a 10% mole solid solution of C6H6C6H6 in C6D6,C6D6, the absorption moved to a value halfway between 690 and 705 cm−1.705cm−1. In a fourfold factor‐group structure, as that of benzene, such a “half‐way” requirement is neither a necessary result of, nor a sufficient condition for, such an assignment. Even in a twofold factor‐group structure such a “half‐way” absorption is not a necessary result, due to the “translational (Ref. 1) shift” (and also quasiresonance). However, the observed drastic shift (15 cm−1)(15cm−1) upon dilution (a 10% mole solution certainly does not isolate the solute statistically) does indicate a wide “exciton band” and thus, indirectly, argues for the inclusion of the 705‐cm−1705‐cm−1 absorption in the multiplet structure of the 680‐cm−1680‐cm−1 band. Another good argument is the analogous behavior of the spectra of C6D6C6D6 and of C6D6C6D6 diluted in C6H6.C6H6. Their term “correlation doubling” should not be taken literally.en_US
dc.identifier.citedreferenceJ. L. Hollenberg and D. A. Dows, J. Chem. Phys. 39, 495 (1963).en_US
dc.identifier.citedreferenceHere n is the index of refraction. A helpful comment by I. Freund is gratefully acknowledged.en_US
dc.identifier.citedreferenceMeasured roughly from the spectra of Ref. 16.en_US
dc.identifier.citedreference0.001×0.06×9200  =  0.6.0.001×0.06×9200=0.6. As the c axis makes a 30° angle with the “vertical” (the slit direction), the “c” polarization spectrum should reveal the b component more intensely than the “a” polarization. This seems indeed to be the case. Obviously, an additional misalignment between the b axis and the center‐of‐beam axis cannot be ruled out.en_US
dc.identifier.citedreferenceIndeed, the 680‐cm−1680‐cm−1 component (9000 darks) is given as “9,” that of the 24 darks ν14ν14 is given as “6,” that of 705 cm−1705cm−1 as “3” by ZH. (These are very rough intensity designations.)en_US
dc.identifier.citedreferenceThe only reasonable alternative is to account for the 705‐cm−1705‐cm−1 peak as an “artifact” (impurity, imperfection). Such an “artifact” level may find itself inside the azuazu exciton band and may, therefore, be able to “borrow” from its intensity—see E. I. Rashba, Soviet Phys.‐Solid state 4, 2417 (1963) [Fiz. Tverd. Tela 4, 3301 (1962)]. With such an alternative one is tempted to assign the b component to the shoulder discernible in Hollenberg and Dows8,16 spectrum at about 690 cm−1.690cm−1. Such alternative assignment would not affect drastically the M terms calculated in the next paragraph.en_US
dc.identifier.citedreferenceA preliminary discussion was given — Ref. 1 (b).en_US
dc.identifier.citedreferenceIt should be pointed out that β of Table I is of the same order as that of the 1B2u1B2u electronic state (Ref. 1) and the 3B1u3B1u electronic state: G. C. Nieman and G. W. Robenson, J. Chem. Phys. 39, 1298 (1963).en_US
dc.identifier.citedreferenceI. Harada and T. Shimanouchi, J. Chem. Phys. 44, 2016 (1966). Similar conclusions have been drawn by N. H. Rich and D. A. Dows, Proc. Intern. Symp. Mol. Struct. Spectry., Columbus, Ohio, 1965. Paper V11.en_US
dc.identifier.citedreferenceThe literature value [i.e., Ref. 4(b)] for the liquid, at room temperature. 675 cm−1,675cm−1, may not be very accurate (due to calibration problems in this region, CO2,CO2, and the intensity of the band), but is still significantly lower then the lowest crystal bands, especially when taken under similar experimental conditions and at a comparable temperature of −12 °C−12°C [Ref. 4(b)].en_US
dc.identifier.citedreferenceR. Kopelman, J. Chem. Phys. 44, 3547 (1966).en_US
dc.identifier.citedreference(a) W. V. F. Brooks, S. J. Cyvin, and P. C. Kvande, J. Phys. Chem. 69, 1489 (1965). (a) W. V. F. Brooks and S. J. Cyvin, Spectrochim. Acta 18, 397 (1962). (a) W. V. F. Brooks and S. J. Cyvin, Acta Chem. Scand. 16, 820 (1962). See also: A. C. Albrecht, J. Mol. Spectry. 5, 236 (1960). A quantitative comparison of the various normal mode amplitudes and the experimentally known vibrational exciton bands seems to be premature at this point.en_US
dc.owningcollnamePhysics, Department of


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