Closed-cluster composition and structure

The deltahedron for n = 10, a bicapped square antiprism, exhibits two four-connect and eight five-connect vertices. Hence, for one heteroatom in a ten vertex c/oso-cluster we have 1 - and 2-isomers and two heteroatoms in 1,10-, 1,6-1,2-, 2,3-, 2,4-, 2,6- 2,8-isomers. Different placements generate different cluster stabilities. A rule of thumb is that the more electronegative element prefers the lower-connectivity vertex. Multiple heteroatoms more electronegative than B prefer non-adjacent positions as far apart as possible. Rearrangement to the most stable isomeric form need not be fast. In the case of icosahedral clusters, for example, the barrier to rearrangement is large and isomers can be isolated. 

Answer. [BioHio]2- The number of valence electrons for B is three, H ligands are one-electron ligands, and the cluster charge is 2. eve =10x3 + 10x 1+2 = 42 = 4n +2. Consistent with the discussion above, the B-H external cluster bond is taken to involve one electron from H and one from B hence, the B-H fragment contributes two electrons to cluster bonding, sep = (10x2 + 2)/2 = 22/2 = ll = n + 1. 

A 12-vertex cluster with a bare N atom is NBnHn eve =1x5 + 11x3 + 

11 x 1 = 49 thus, one more electron is needed giving [NBnHn]-. 

Rationalization of known compounds provides a level of usefulness that justifies the rule. But the rule also permits observed molecular stoichiometries of newly synthesized compounds to be translated into acluster shape. For example, [Al Bu ]2-has eve = 50 or sep =13 consistent with n = 12 and a deltahedral structure. The compound has been synthesized and an X-ray diffraction study reveals an icosahe-dral shape. The ability to suggest reasonable structures based on knowledge of a molecular formula generated by a technique like mass spectrometry accelerated the development of cluster chemistry simply because rapid spectroscopic methods can be more productively applied. Although efficient X-ray crystallographic structure determination reduces its importance for compounds that can be isolated in pure crystalline forms, transient intermediates detected in a reaction mixture can now be given reasonable structures. 

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