8 Electronic Properties of Transition Metal-Benzene Sandwich Clusters
341
Fig. 8.27 (a) Valence orbital pictures in the majority (α) spin part of the neutral Mn 18 Bz 18 cluster.
The number of nodes k is given for each delocalized orbital. Inset shows top and side views of the
partially magnified α-HOMO. The isosurface value of 0.01 was adopted unless otherwise noted.
(b) Orbital pictures of [18]annulene (C 18 H 18 ) with an isosurface value = 0.01, having the same k
values as depicted in (a) for comparison. (c) Orbital energies plotted against k for the Mn 18 Bz 18
α-HOMO and lower-lying isomorphous orbitals, and (d) those for the C 18 H 18 orbitals composed
of delocalized π electrons. Blue curves are obtained by a curve-fitting analysis using Eq. (8.1).
(Reproduced from Ref. [116] with permission from the Royal Society of Chemistry)
For an intelligible explanation of such delocalized electron systems, we use a
simple Hückel model: for cyclic conjugated systems, each molecular orbital energy
ε k is given as
341
Fig. 8.27 (a) Valence orbital pictures in the majority (α) spin part of the neutral Mn 18 Bz 18 cluster.
The number of nodes k is given for each delocalized orbital. Inset shows top and side views of the
partially magnified α-HOMO. The isosurface value of 0.01 was adopted unless otherwise noted.
(b) Orbital pictures of [18]annulene (C 18 H 18 ) with an isosurface value = 0.01, having the same k
values as depicted in (a) for comparison. (c) Orbital energies plotted against k for the Mn 18 Bz 18
α-HOMO and lower-lying isomorphous orbitals, and (d) those for the C 18 H 18 orbitals composed
of delocalized π electrons. Blue curves are obtained by a curve-fitting analysis using Eq. (8.1).
(Reproduced from Ref. [116] with permission from the Royal Society of Chemistry)
For an intelligible explanation of such delocalized electron systems, we use a
simple Hückel model: for cyclic conjugated systems, each molecular orbital energy
ε k is given as