1 Electron counting rules and simple bonding descriptions for electron-poor materials  -SiB 3

2 Boron – the master of clusters B 4 Cl 4 B 8 Cl 8 B 9 Br 9 Icosahedral clusters in elemental B  -rhombohedral boron  -rhombohedral boron B n Clusters in halides and hydrides (boranes)

3 Boranes Hoffmann, R.; Lipscomb, W. N. J. Chem. Phys. 1962, 37, Wade K. J. Chem. Soc. Chem. Comm. 1971, 792. Wade, K. Inorg. Nucl. Chem. Lett. 1972, 8, 559. Bonding in boranes

4 Constructing MOs: B atoms: The two sets of skeleton bonding  combinations (12 basis functions) transform as: T 1g, T 2g, T 1u, T 2u Those combinations correspond already to (triply degenerated) MOs. The two sets of  combinations transform as: A 1g, E g, T 1u 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 A 1g, E g, T 1u ligand bonding skeleton bonding Number of electrons: 26 Number of basis functions: 30 Point group: O h Local coordinate system Dividing the orbitals: B atoms: two  type functions (p x and p y ) two  type orbitals (s, p z or better: two sp hybrid orbitals, one inward and one outward pointing) H ligand atoms: one  type orbital (s) B 6 H 6 2- Use of 12 basis functions and 12 electrons for terminal ligand bonding, six bonding MOs (a 1g, e g, t 2u ). For skeleton bonding 18 basis functions and 14 electrons remain.

5 T 1g T 2u T 1u T 2g B-  MO diagram B-  MO diagram  - and  type skeleton MOs with the same symmetry (T 1u ) interact which leads to a net stabilisation of the borane skeleton.

6 Wade’s rules 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. Wade’s rules link cluster geometries to certain electron counts 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.

7  -B 12 Electron counting for  - B electrons per icosahedron 26 for skeleton bonding 6 for 2c2e terminal bonding 6x2/3 = 4 for 3c2e bonding within layers

8  -B 12 G. Will et al. (2001)

9  -B 28 Electron counting for  -B 28 structure unitlinkage B 12 4 × 2c2e8 × 3c2e 264 × 2/28 × 2/3 B2B2 2 × 2c2e4 × 3c2e 22 × 2/24 × 2/3

10

11 From III-V to II-V semiconductors Sb GaSb and ZnSb IIIIIIVV EN: Sb = 1.7, Ga = 1.7, Zn = 1.6 GaSbZnSb  EN 00.1 E g [eV]0.81 direct 0.50 indirect vec43.5

12 Electronic structure of ZnSb The ZnSb framework has a modest polarity The optimum electron count is 3.5 e/atom Non-classical 4c4e bonding within rhomboid rings Zn 2 Sb 2 (localized multicentre bonding) A. Mikhaylushkin, J. Nylén, U. Häussermann, Chem. Eur. J, 11 (2005), 4912 ZnSb – An electron poor framework semiconductor

13 3 [Zn 2 Sb1 2/2 ] 2 [Sb2] Electronic structure of  -Zn 4 Sb 3 (Zn 6 Sb 5 ) Zn 6 Sb 5 = 3 ( /2) = 30 2 (4 x 2) = 8 38 e for electron precise conditions (3.454 e/atom); 37 e available electron count R-3c36 Zn18 Sb112 Sb2= Zn 36 Sb 30 (Zn 6 Sb 5 = Zn 3.6 Sb 3 ) H. W. Mayer, I. Mikhail, K. Schubert, J. Less-Common Met. 59 (1978), 43. Less electrons than ZnSb: rhomboid rings condense into chains

14  -SiB 3 Si 4 2+ B 12 2-

15  -boron?