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## Polyhedral skeletal electron pair theoryIn chemistry the ## Additional recommended knowledge
## The rules for boranes and carboranesThe skeletal electron counts for the four types of deltahedral cluster are:- - n vertex closo (n+1)
- n vertex nido (n+2)
- n vertex arachno (n+3)
- n vertex hypho (n+4)
The skeletal electron counts are determined by totalling the following:- - 2 from each BH unit
- 3 from each CH unit
- 1 from each additional hydrogen atom (over and above the ones on the BH and CH units)
- the anionic charge electrons
- Example of C
_{2}B_{7}H_{13} - Framework electron count: 14(7 X BH) + 6 (2 X CH)+ 4 (additional H) = 24
- As the number of vertices is 9 the prediction is
**arachno**(24 = 2(9+3))
- Example of B
_{6}H_{6}^{2-} - Framework electron count: 12(6 X BH) + 2 (anionic charge) = 14
- As the number of vertices is 6 the prediction is
**closo**(14 = 2(6+1))
## Total electron count formulation for boranes and carboranesThere is an alternative and more straightforward version of the rules that uses a total valence electron count. For boranes and carboranes the total valence electrons are counted plus any charge electrons,the rules are simply:- - n vertex closo (4n+2) electrons
- n vertex nido (4n+4) electrons
- n vertex arachno (4n+6) electrons
- n vertex hypho (4n+8) electrons
- Example of C
_{2}B_{7}H_{13} - Total valence electrons = (2 X 4) + (3 X 7) + (13X1)= 42
- As 42 = (4 X 9) + 6 the structure is predicted to be
**arachno**
- Example of B
_{6}H_{6}^{2-} - Total valence electrons = (6 X 3) + (6 X 1) + 2 = 26
- As 26 = (4 X 6) + 2 the structure is predicted to be
**closo**
## Theoretical basis for the rules for boranesA brief insight into the theory behind the rules through a consideration of the anionic closo cluster B - 1 sp hybrid orbital pointing radially into the center of the cluster
- 2 p orbitals tangential to the surface
The 18 framework molecular orbitals, (MOs), derived from the 18 boron atomic orbitals are :- - 1 bonding MO at the center of the cluster and 5 antibonding MOs from the 6 sp radial hybrid orbitals
- 6 bonding MOs and 6 antibonding MOs from the 12 tangential p orbitals.
The total skeletal bonding orbitals is therefore 7 i.e (n+1). ## Isolobal vertex unitsProvided a vertex unit is isolobal with BH then it can, in principle at least, be substituted for a BH unit. The CH - Fe has 8 valence electrons.
- Each carbonyl group is a net 2 electron donor after the internal σ and π bonding are taken into account making 14 electrons.
- 3 pairs are considered to be involved in Fe - CO σ-bonding and 3 pairs are involved in π back bonding from Fe to CO reducing the 14 to 2.
## Transition metal clustersAs for boranes and carboranes there is an alternative and more straightforward version of the rules that uses a total valence electron count. The total valence electrons are counted plus any charge electrons. The rules are simply:- - n vertex closo (14n+2) electrons
- n vertex nido (14n+4) electrons
- n vertex arachno (14n+6) electrons
- n vertex hypho (14n+8) electrons
- Example Rh
_{6}CO_{16} - Rhodium is group 9 with 9 valence electrons
- Total electron count = (6 X 9) + (16 X 2)= 86
- 86 = (14 x 6) + 2
- Therefore the prediction is
**closo**
## General References- WebElements
- Greenwood, N. N.; Earnshaw, A. (1997).
*Chemistry of the Elements*, 2nd Edition, Oxford:Butterworth-Heinemann.__ISBN 0-7506-3365-4__. - Cotton, F. Albert; Wilkinson, Geoffrey; Murillo, Carlos A.; Bochmann, Manfred (1999).
*Advanced Inorganic Chemistry (6th Edn.)*New York:Wiley-Interscience.__ISBN 0-471-19957-5__.
Categories: Chemical bonding | Inorganic chemistry | Organometallic chemistry |
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This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Polyhedral_skeletal_electron_pair_theory". A list of authors is available in Wikipedia. |