_P.-Powell-auth.-Principles-of-Organometallic-Chemistry-Springer-Netherlands-1988

Cluster compounds
4
5
5
Trigonal
Octahedron
Pentagonal
Dodecahedron
bipyramid
bipyramid
1
4~2
8~
7 6
10
4
·~'
11~2
6
12
Tricapped
trigonal prism
Bicapped
square
antiprism
Octadecahedron
Eicosahedron
Fig. 11.2 The triangulated-polyhedral structures ofBnH~- and Bn- 2 C 2 Hn species with the
conventional numbering schemes also indicated.
p orbitals (P", three orbitals), d orbitals (D", up to a maximum of five orbitals,
depending on cluster size),f-orbitals (F", up to seven orbitals) etc. This is shown for
the eicosahedron B 12H~; (Fig. 11.3). Calculations predict that in this case the
three P (t 11 1 u) orbitals should be weakly bonding, but they are destabilized by
mixing with tangential bonding orbitals of the same symmetry. In general,
therefore, the n radial frontier orbitals of the n B-H groups in B"H" 2 - lead to o ne
bonding m.o. and (n- 1) antibonding m.o.s.
The 2n p orbitals tangential to the cluster give rise to n bonding and n
antibonding m.o.s. The 5 n m.o.s associated with B"H~- ( 4n B a.o.s and n H a.o.s)
are therefore divided up as follows:
Bonding m.o.s
n B-H m.o.s
1 radial m.o.
n tangential m.o.s
Total: 2n + 1 bonding m.o.s
338
Antibonding m.o.s
n B-H m.o.s
(n- 1) radial m.o.s
n tangential m.o.s
Total: 3n- 1 antibonding m.o.s