Electron counting rules and simple bonding descriptions for electron-poor materials
b-SiB3
1
Boron – the master of clusters
a-rhombohedral boron
Bn Clusters in halides and hydrides (boranes)
B4Cl4
B8Cl8
B9Br9
Icosahedral clusters in elemental B
b-rhombohedral boron
2
Boranes
Bonding in boranes
Hoffmann, R.; Lipscomb, W. N. J. Chem. Phys. 1962, 37, 2872.
Wade K. J. Chem. Soc. Chem. Comm. 1971, 792.
Wade, K. Inorg. Nucl. Chem. Lett. 1972, 8, 559.
3
B6H62-
Point group:
Oh
Number of electrons: 26
Number of basis functions: 30
1
px
5
2
Local coordinate system
5
4
3
y
2
4
py
6
x
3
Dividing the orbitals:
B atoms:
H ligand atoms:
two  type functions (px and py)
two  type orbitals (s, pz or better: two sp hybrid orbitals, one inward and one outward pointing)
one  type orbital (s)
Constructing MOs:
B atoms:
H
The two sets of skeleton bonding  combinations (12 basis functions) transform as:
ligand bonding
T1g, T2g, T1u, T2u
B
H
H
Those combinations correspond already to (triply degenerated) MOs.
skeleton bonding
The two sets of  combinations transform as:
A1g, Eg, T1u
A1g, Eg, T1u
of which one is skeleton bonding (the set of inward pointing sp hybrid orbitals) and thus already represent MOs.
H atoms:
One set of  type SALCs A1g, Eg, T1u
Use of 12 basis functions and 12 electrons for terminal ligand bonding, six bonding MOs
4
(a1g, eg, t2u). For skeleton bonding 18 basis functions and 14 electrons remain.
B- MO diagram
B- MO diagram
T1g
T2u
T1u
T2g
- and  type skeleton MOs with the same symmetry (T1u) interact which leads to a net stabilisation of the borane skeleton.
5
Wade’s rules
Wade’s rules link cluster geometries to certain electron counts
A closo deltahedral cluster cage (parent poyhedron) with n vertices requires (n+1) pairs of electrons for skeleton bonding.
From a parent closo page with n vertices, a set of more open cages (nido, arachno, hypho) can be derived with a formally unchanged
skeleton bonding picture
Thus, for a parent closo deltahedron with n vertices, the related nido-cluster has (n-1) vertices, but still (n+1) skeleton bonding MOs.
Thus, for a parent closo deltahedron with n vertices, the related arachno-cluster has (n-2) vertices, but still (n+1) skeleton bonding MOs.
Thus, for a parent closo deltahedron with n vertices, the related hypho-cluster has (n-3) vertices, but still (n+1) skeleton bonding MOs.
A entity BH in boranes may be replaced by a entity CH (carboranes) or P.
Alternatively:
 Closo deltahedral clusters with n entities (vertices) (BH, CH, P) are stable with (4n+2) electrons.
 Nido clusters with n entities are stable with (4n+4) electrons.
 Arachno clusters with n entities are stable with (4n+6) electrons.
6
Electron counting for aB12
a-B12
36 electrons per icosahedron
26 for skeleton bonding
6 for 2c2e terminal bonding
6x2/3 = 4 for 3c2e bonding within layers
7
a-B12
G. Will et al. (2001)
8
g-B28
Electron counting for g-B28
structure unit
linkage
B12
4 × 2c2e
8 × 3c2e
26
4 × 2/2
8 × 2/3
B2
2 × 2c2e
4 × 3c2e
2
2 × 2/2
4 × 2/3
9
10
From III-V to II-V semiconductors
II
III IV
V
GaSb and ZnSb
EN:
Sb = 1.7, Ga = 1.7, Zn = 1.6
GaSb
ZnSb
DEN
0
0.1
Eg [eV]
0.81
direct
0.50
indirect
vec
4
3.5
Sb
11
Electronic structure of ZnSb
ZnSb – An electron poor framework semiconductor
The ZnSb framework has a modest polarity
The optimum electron count is 3.5 e/atom
Non-classical 4c4e bonding within rhomboid rings Zn2Sb2 (localized multicentre bonding)
A. Mikhaylushkin, J. Nylén, U. Häussermann, Chem. Eur. J, 11 (2005), 4912
12
Electronic structure of b-Zn4Sb3 (Zn6Sb5 )
R-3c
36 Zn
18 Sb1
12 Sb2
=
Zn36Sb30 (Zn6Sb5 = Zn3.6Sb3)
H. W. Mayer, I. Mikhail, K. Schubert, J. Less-Common Met. 59 (1978), 43.
Less electrons than ZnSb: rhomboid rings condense into chains
electron count
Zn6Sb5 =
3 [Zn2Sb12/2]
3 (4 + 4 + 4/2) = 30
2 [Sb2]
2 (4 x 2) = 8
38 e for electron precise conditions (3.454 e/atom);
37 e available
13
b-SiB3
b
c
a
Si42+
B122-
14
b-boron?
15