Wannier functions representing the bonding pattern of a filled pentagon for the C3 17-3 isomer. The 3c-2e Wannier functions are represented in red and the 4c-2e Wannier functions are in blue. The neighboring filled hexagons are shaded to clarify the local environment. A schematic representation of this pentagonal environment is shown at the bottom right. This coloring scheme is reused in Figure 2 .
The different B80 isomers with increasing number of filled pentagons. They were chosen to exemplify the role of the filled pentagonal unit inside these structures. The different local environments of the filled pentagons which are present in each isomer are sketched below them along with their frequency. The colored sections of these sketches represent a neighboring filled hexagon. Also displayed is the energy difference ( ΔE in meV) between the isomer and the Ih 20-0, its HOMO-LUMO gap (E G in eV) and its average pyramidalization angle ( ).
Schlegel diagrams with superposed Wannier states for the Ih 20-0 and both C3v 14-6 structures. The 3c-2e bonds are in red and the 4c-2e bonds are in blue. The delocalized π z bonds are displayed in green on the right panels. For clarity, the filling atoms are shown as big purple circles. The Ih 20-0 is formed of alternating 3c-2e bonds and 4c-2e bonds in the same Kékulé structure then the one observed in C 60. In the case of the D3d 14-6, we can see a complete percolation of the π z states on the equator. For the D3d 14-6(B), the π z states span out of the poles in three lightning shaped arms that do not meet.
Projection of the electron density of the Sc3N@B80 for the Ih 20-0 (left) and the D3d 14-6 (right) upon two planes : (a) the plane of the Sc atoms and (b) a plane containing both the N atom and the closest B atom. For clarity, thick bonds are used for inward displaced filling boron atoms.
Binding energies and HOMO-LUMO separation for the endohedral Sc3N@B80 fullerene and the ion. Binding energies are measured with respect to the energy of the pristine cage (plus the energy of the added cluster).
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