By Mellor J.W.
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Additional info for A comprehensive treatise on inorganic and theoretical chemistry vol.VIII N, Cl
Answer. As a crude approximation, let the Xe atom in XeF2 use one np AO to form one three-center–four-electron bond with one p orbital from each of the F atoms. The other nine ns and np AOs contain 18 of the 22 valence electrons as lone pairs. 14 with the remaining four electrons occupying the bonding and non-bonding three-center orbitals applies. Thus, at the Xe center, we have three Problems 29 lone pairs (six electrons) and one three-center–four-electron bond (two electrons in the only orbital with Xe character) giving a total of eight electrons associated with the Xe atom.
The C–H fragment contributes three electrons to cluster bonding – C is one step to the right of B. 1,10-B10 H8 (N2 )2 : cve = 10 × 3 + 8 × 1 + 2 × 2 = 42. The end-on bound dinitrogen ligand is a two-electron ligand to the cluster. sep = (8 × 2 + 2 × 3)/ 2 = 11. The B–H are two-electron fragments but the two B–N≡N fragments are three-electron fragments as its two-electron donor ligand allows the B atom to use all three valence electrons in cluster bonding. [CB11 H12 ]− : cve = 1 × 4 + 11 × 3 + 12 × 1 + 1 = 50 = 4n + 2.
However, the remaining 3n orbitals associated with the skeletal bonding are no longer divided equally between filled and empty. In fact, the number of high-lying cluster core MOs is n − 2 larger (2n − 1 − n −1) than the number of low-lying cluster core orbitals. As only the latter are filled, the number of sep is n + 1 vs. 3/2n for three-connect clusters whereas the number of cve is 4n + 2 vs. 5n for three-connect clusters. For the n = 6 and 12 clusters with 12 and 20 bonding edges the cluster bonding is accomplished with 7 and 13 bonding pairs, respectively.
A comprehensive treatise on inorganic and theoretical chemistry vol.VIII N, Cl by Mellor J.W.