Quantum Symmetry of the Vibrational States and Electronic π-Orbitals in a Benzene Molecule C6H6. The Fine Structure of Spin-Dependent Splitting


  • V.O. Gubanov Taras Shevchenko National University of Kyiv
  • A.P. Naumenko Taras Shevchenko National University of Kyiv
  • D.V. Gryn Taras Shevchenko National University of Kyiv
  • L.A. Bulavin Taras Shevchenko National University of Kyiv




benzene, vector and spinor representations of symmetry groups, normal-vibration patterns, classes of symmetry-group projective representations, electronic states, spin-dependent splitting


Analytical expressions and vector images have been constructed for all patterns of the normal vibrations, including doubly degenerate ones, of a benzene molecule C6H6 using the projection operator on the matrix elements of irreducible representations of the point symmetry group 6/mmm (D6ℎ). The characters of representations corresponding to the symmetry of both the electronic п-orbitals in a benzene molecule (without taking the electron spin into account) and the projective representations of its spinor п′-orbitals are found. The representations of the spinor п′-orbitals of a benzene molecule C6H6 belong to the projective class K1 and describe the fine structure of spin-dependent splitting of the degenerate spinless п-orbitals, which are revealed for the first time.


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How to Cite

Gubanov, V., Naumenko, A., Gryn, D., & Bulavin, L. (2021). Quantum Symmetry of the Vibrational States and Electronic π-Orbitals in a Benzene Molecule C6H6. The Fine Structure of Spin-Dependent Splitting. Ukrainian Journal of Physics, 66(1), 28. https://doi.org/10.15407/ujpe66.1.28



Optics, atoms and molecules