Localized bond treatments

III. Bonding In Boranes and Carboranes A. Localized Bond Treatments... 

That transition metal-carbonyl clusters, which contain an apparent abundance of electrons, might have much in common with boranes and carboranes, notorious for their deficiency of electrons, appears at first sight improbable. However, the structural and bonding relationship between them becomes apparent if one considers certain metal-carbonyl clusters for which localized bond treatments are unsatisfactory. 

In contrast to the limitations noted above in the value of localized bond treatments for closo carboranes, MO treatments and computations based thereon provide really useful insight into their bonding. An early illustration of their value for closo deltahedral borane dianions B 11 was provided in 1955 by... 

Higuchi, J., J. Chem. Phys. 27, 825, (ii) Semi-localized bond orbital treatment of the allyl radical. Extension of VB. 

A simple localized 2c, 2e bond treatment is adequate there are sufficient electrons for all the connections to be made by electron pairs. 

In the hands of Lipscomb and others 76,143, 145a, 153,189, 190), such localized bond schemes, particularly when obtained via self-consistent field (SCF) molecular orbital (MO) treatments, have proved particularly valuable for rationalizing the shapes and interatomic distances and estimating the charge distribution in many higher boranes. 

Manes and Manes-Pozzi have suggested a cluster of the type (Vq 2 Me ), which has been taken as the basis species for a statistical treatment aimed at the interpretation of the thermodynamic data on (Ui yPUy)02 x and Pu02 x. This cluster has later been called by Manes, Sdrensen et al. the tetrahedral defect The reason of this name lies in the fact that the local bond is supposed to occur in a coordination tetrahedron of an oxygen ion in the fluorite structure in this tetrahedron, one oxygen vacancy is formed, and the two electrons are shared with the four surrounding cations, giving rise (formally) to 2(Me ) locally bonded with the vacancy. Manes, Sorensen et al. showed that by... 

The discussion could be further elaborated by a consideration cf 5, p hybridization, which U undoubtedly of some importance here. For reasons of symmetry, this can affect only the [so-K -h U )j MO in the n ri-localized MO treatment the result must be that h<- 2so AO in (SO acquires some MO bonding properties and the bonding diameter of Rcd-(hH-l-s) j is further weakened but with an over-all gain in bonding. 5k3G,H-s) in Eos. (SI) now is replaced by a inear combination including S(2sq, s-t-s), the final 5 being easily computed as a function of the extent of hybridization if this were known. 

The localized bond model fails for odd conjugated systems (ions and radicals such as allyl or benzyl) the mesomeric stabilization of these can be estimated by the perturbation treatment of Section VIII. However, the localized bond model can still4 be used for other types of odd systems, i.e. ones where the... 

MO treatments are preferred in such cases. The manner in which these same cations, (CsHs) and (CeMce) can be treated in MO terms is worth illustrating here for the purpose of comparison with the localized bond schemes just discussed, and also to underline the relationship between these pyramidal systems and normal aromatic ring systems. 

The input requires the usual data of a quantum chemical treatment the starting geometry of the system and the basis set to be used, plus the L strictly localized bond orbitals expanded in the basis set chosen for the computation. 

A pair-function calculation, where each electron pair is associated to a quasi-localized bond function built from Lowdin orthogonalized Is orbitals. This is equivalent to the treatment of ethane mentioned above 14) ... 

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