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The rotational energy levels of four methyl groups

An application to X(CH3)4 type molecules

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Zeitschrift für Physik B Condensed Matter

Abstract

The energy level spectrum for a system of four interacting methyl groups belonging to an X(CH3)4 type molecule is calculated by numerical methods. The rotational potential at the site of each methyl group is assumed to be of a three-fold symmetry. The torsion-torsion interaction is defined as a term in the multipole expansion of the electrostatic interaction of two rigid charge distributions. It is shown, that the tunneling frequency characterizing the ground state manifold in the absence of methyl-methyl interaction, splits into a set of closely spaced frequencies.

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References

  1. Press, W.: Single-particle rotations in molecular crystals. In: Springer Tracts in Modern Physics. Vol. 92. Berlin, Heidelberg, New York: Springer 1981

    Google Scholar 

  2. Haupt, J.: Z. Naturforsch. 26a, 1578 (1971);

    Google Scholar 

  3. Punkkinen, M., Clough, S.: J. Phys. C7, 3403 (1974)

    Google Scholar 

  4. Emid, S., Wind, R.A.: Chem. Phys. Lett.33, 269 (1975)

    Google Scholar 

  5. Wind, R.A., Emid, S., Lightheim, D.J., Pourquie, F.P., Smith, J.: Bull. Magn. Res.6, 71 (1984)

    Google Scholar 

  6. Swalen, J.D., Costain, C.C.: J. Chem. Phys.31, 1562 (1959)

    Google Scholar 

  7. Grant, D.M., Pugmire, R.J., Livingstone, R.C., Strong, K.A., McMurry, H.L., Brugger, R.M.: J. Chem. Phys.52, 4424 (1970)

    Google Scholar 

  8. Lide, D.R. Jr., Mann, D.E.: J. Chem. Phys.28, 572 (1958)

    Google Scholar 

  9. Clough, S., Heidemann, A., Horsewill, A.H., Paley, M.N.J.: Z. Phys. B — Condensed Matter55, 1 (1984)

    Google Scholar 

  10. Prager, M., Heidemann, A., Häusler, W.: Z. Phys. B — Condensed Matter64, 447 (1986)

    Google Scholar 

  11. Häusler, W., Hüller, A.: Z. Phys. B — Condensed Matter59, 177 (1985)

    Google Scholar 

  12. Hirschfelder, J.O., Curtis, C.F., Bird, R.B.: Molecular theory of gases and liquids. p. 932. New York: John Wiley 1954

    Google Scholar 

  13. Peternelj, J., Jenčič, I., Cvikl, B., Pintar, M.M.: Phys. Rev. B36, 25 (1987)

    Google Scholar 

  14. Prager, M., Duprée, K.-H., Müller-Warmuth, W.: Z. Phys. B — Condensed Matter51, 309 (1983);

    Google Scholar 

  15. Müller-Warmuth, W., Duprée, K.-H., Prager, M.: Z. Naturforsch.39a, 66 (1983)

    Google Scholar 

  16. Prager, M., Langel, W.: J. Chem. Phys.85, 5279 (1986);

    Google Scholar 

  17. Langel, W., Prager, M., Schrems, O., Knözinger, E.: Quantum aspects of molecular motions in Solids. Springer Proceedings in Physics. Heidemann, A., Magerl, A., Prager, M., Richter, D., Springer, T. (eds.), Vol. 17, p. 93. Berlin, Heidelberg, New York: Springer 1987

    Google Scholar 

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Jenčič, I., Peternelj, J., Cvikl, B. et al. The rotational energy levels of four methyl groups. Z. Physik B - Condensed Matter 79, 251–254 (1990). https://doi.org/10.1007/BF01406591

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  • DOI: https://doi.org/10.1007/BF01406591

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