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Electron counting rules and simple bonding descriptions for electron-poor materials

Electron counting rules and simple bonding descriptions for electron-poor materials. b -SiB 3. Boron – the master of clusters. a -rhombohedral boron. B n Clusters in halides and hydrides (boranes). B 9 Br 9. B 4 Cl 4. B 8 Cl 8. Icosahedral clusters in elemental B. b -rhombohedral boron.

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Electron counting rules and simple bonding descriptions for electron-poor materials

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  1. Electron counting rules and simple bonding descriptions for electron-poor materials b-SiB3

  2. Boron – the master of clusters a-rhombohedral boron Bn Clusters in halides and hydrides (boranes) B9Br9 B4Cl4 B8Cl8 Icosahedral clusters in elemental B b-rhombohedral boron

  3. 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.

  4. ligand bonding 1 5 4 2 3 6 skeleton bonding B6H62- Number of electrons: 26 Number of basis functions: 30 Point group: Oh Local coordinate system Dividing the orbitals: B atoms: two  type functions (px and py) two  type orbitals (s, pz or better: two sp hybrid orbitals, one inward and one outward pointing) H ligand atoms: one  type orbital (s) Constructing MOs: B atoms: The two sets of skeleton bonding  combinations (12 basis functions) transform as: T1g, T2g, T1u, T2u Those combinations correspond already to (triply degenerated) MOs. 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 (a1g, eg, t2u). For skeleton bonding 18 basis functions and 14 electrons remain.

  5. B-p MO diagram B-s 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.

  6. 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.

  7. a-B12 Electron counting for a-B12 36 electrons per icosahedron 26 for skeleton bonding 6 for 2c2e terminal bonding 6x2/3 = 4 for 3c2e bonding within layers

  8. a-B12 G. Will et al. (2001)

  9. g-B28 Electron counting for g-B28

  10. From III-V to II-V semiconductors GaSb and ZnSb II III IV V EN: Sb = 1.7, Ga = 1.7, Zn = 1.6 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 Si42+ B122-

  14. b-boron?

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