MO treatment localized

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. 

For c/rwo-boranes and for the larger open-cluster boranes it becomes increasingly difficult to write a simple satisfactory localized orbital structure, and a full MO treatment is required. Intermediate cases, such a.s B5H9, require several resonance hybrids in the localized orbital... 

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. 

Electrophilic aromatic substitution is a typical reaction for BHs. In the MO treatment, some indices such as free valence [40], localization energy [41], and other quantities [42,43] have been introduced to predict the orientation of electrophilic aromatic substitution. Within the VB framework, several indices have also been formulated [44]. Here we introduce an alternative index, which is available from accurate VB wave functions, and demonstrate its applicability in accounting for the electrophilic aromatic substitution. 

A MO treatment of SiF 62) predicts the sequence Ia2al7r3a27r, the la orbital having 2s(F) character. The upper orbitals 3a and 27r are mainly localized at the silicon atom. The ground state of SiF is therefore. .. lir43o22ir — X2Ut molecular constants of the ground and excited states are summarized in Table 12... 

MO treatments at all levels, from extended HuckeP and CNDO to ab initio calculations, show that the central bond is composed mainly of atomic p orbitals on the bridgehead carbons. According to the classic paper of Newton and hulman, the C(l)-C(3) bond is formed from hybrid orbitals with 96% p character (or sp " ) as compared to cyclopropane where the percentage of p character is 86. Analysis of the localized MO employed in this study reveals also that the hybridization in the C(l)-C(2) bond is sp on C(l) and sp on C(2). Obviously, as a result of the extensive use made of the atomic p orbitals in the construction of the C-C bonds, the C-H bond of the bridgehead carbon contains a higher degree of s character (sp - ). 

In the simplest case, i.e. in going from (4) to (5), we see that two jr-electrons from the hexatriene are used to form the new o-bond, leaving a butadiene system in (5). The localization approximation concept appropriate for a simple Hiickel MO treatment should work well here, yielding useful semiquantitative information8. ... 

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. 

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... 

The alternative of exclusively using the AO basis operationally in CC calculations, as the most local basis possible (avoiding any kind of local MO description for the occupied orbitals), has also been considered [192,193], but has not yet been shown to pay dividends. In fact, unpublished work on polymers [194,195] suggests that AO methods actually do not compare very well with the standard delocal, Bloch periodic symmetry treatment. By the way CCSD has now been applied with periodic symmetry to simple polymers at the CCSD level [196,197]. 

Full MO treatments can, of course, be carried out even for the boranes in which the localized structure/bonding elements used in the semitopological... 

An orbital correlation diagram can be constructed by examining the symmetry of the reactant and product orbitals with respect to this plane, as shown in Figure 10.1. An additional feature must be taken into account in the case of cyclohexene. The cyclohexene orbitals CTj, a2, CTi, and (T2 are called symmetry-adapted orbitals. We might be inclined to think of the ct and a orbitals as being localized between specific pairs of carbon atoms, but this is not the case for the MO treatment because localized... 

The localized orbital approach is probably not the best choice today however, since LCAO-MO treatments at different levels of sophistication... 

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