160
6 Interactions
the UV region, corresponding to the long-axis polarized transitions of the naphthyl units (indicated by the arrows in the figure). Construct the appropriate exciton states and determine the CD profile of the two enantiomers of binaphthyl.
6.5 A diradical is a molecule with two open orbitals, each containing one electron.
Consider as an example twisted ethylene (D 2d symmetry, see Fig. 3.9). The
HOMO is a degenerate e-orbital, occupied by two electrons. Construct the e 2
diradical states for this molecule, and determine their symmetries.
6.6 Planar trimethylenemethane (TMM), C 4 H 6 , is a diradical with trigonal symmetry. Determine the Hückel spectrum for the four carbon p z -orbitals perpendicular to the plane of the molecule. The HOMO in D 3h has e ′′ symmetry and is
also occupied by two electrons. Determine the corresponding diradical states,
and compare with the results for twisted ethylene. How would you describe the
valence bond structure of this molecule?
References
1. Wigner, E.P.: Group Theory. Academic Press, New York (1959)
2. Griffith, J.S.: The Irreducible Tensor Method for Molecular Symmetry Groups. Prentice Hall,
Englewood-Cliffs (1962)
3. Butler, P.H.: Point Group Symmetry Applications, Methods and Tables. Plenum Press, New
York (1981)
4. Ceulemans, A., Beyens, D.: Monomial representations of point-group symmetries. Phys. Rev.
A 27, 621 (1983)
5. Lijnen, E., Ceulemans, A.: The permutational symmetry of the icosahedral orbital quintuplet
and its implication for vibronic interactions. Europhys. Lett. 80, 67006 (2007)
6 Interactions
the UV region, corresponding to the long-axis polarized transitions of the naphthyl units (indicated by the arrows in the figure). Construct the appropriate exciton states and determine the CD profile of the two enantiomers of binaphthyl.
6.5 A diradical is a molecule with two open orbitals, each containing one electron.
Consider as an example twisted ethylene (D 2d symmetry, see Fig. 3.9). The
HOMO is a degenerate e-orbital, occupied by two electrons. Construct the e 2
diradical states for this molecule, and determine their symmetries.
6.6 Planar trimethylenemethane (TMM), C 4 H 6 , is a diradical with trigonal symmetry. Determine the Hückel spectrum for the four carbon p z -orbitals perpendicular to the plane of the molecule. The HOMO in D 3h has e ′′ symmetry and is
also occupied by two electrons. Determine the corresponding diradical states,
and compare with the results for twisted ethylene. How would you describe the
valence bond structure of this molecule?
References
1. Wigner, E.P.: Group Theory. Academic Press, New York (1959)
2. Griffith, J.S.: The Irreducible Tensor Method for Molecular Symmetry Groups. Prentice Hall,
Englewood-Cliffs (1962)
3. Butler, P.H.: Point Group Symmetry Applications, Methods and Tables. Plenum Press, New
York (1981)
4. Ceulemans, A., Beyens, D.: Monomial representations of point-group symmetries. Phys. Rev.
A 27, 621 (1983)
5. Lijnen, E., Ceulemans, A.: The permutational symmetry of the icosahedral orbital quintuplet
and its implication for vibronic interactions. Europhys. Lett. 80, 67006 (2007)