Molecular orbital bond order

Proposer (Ref.) Method used Rh—Rh bond order Molecular orbitals ordering... 

The boranes are electron-deficient compounds (Section 3.8) we cannot write valid Lewis structures for them, because too few electrons are available. For instance, there are 8 atoms in diborane, so we need at least 7 bonds however, there are only 12 valence electrons, and so we can form at most 6 electron-pair bonds. In molecular orbital theory, these electron pairs are regarded as delocalized over the entire molecule, and their bonding power is shared by several atoms. In diborane, for instance, a single electron pair is delocalized over a B—H—B unit. It binds all three atoms together with bond order of 4 for each of the B—H bridging bonds. The molecule has two such bridging three-center bonds (9). 

Figure 2 Zeroth-order molecular orbital picture of the bonding in MoSi.

I. Molecules containing one to four electrons. We have already seen the H2 molecule in which there are two electrons in the ou orbital. Two bonding electrons constitute a chemical bond The molecular orbital theory does not restrict itself to even numbers of bonding electrons, and so the bond order is given as one-half the difference between the number of bonding electrons and the number of antibonding electrons ... 

The difference in reactivity between the a-stannyl sulfide 16A and the a-silyl sulfide 16B can be explained by comparing the two-center energies of their carbon-metal bonds. Semiempirical molecular orbital calculation revealed that the bond energies decrease in the order of 2-silyl, 2-germyl, and 2-stannyl-1,3-dithiane cation radicals. As the silyl dithiane was completely consumed by the oxidation under the... 

Suppose one wanted to consider whether He2 is likely to be a stable molecule. This molecule, if it existed, would have a similar molecular orbital energy level diagram to H2 (in both cases, only Is atomic orbitals are involved) but it would have four electrons two in the bonding als molecular orbital and two in the antibonding cru orbital. Its bond order would be = (2 - 2) = 0, or no bond. In other words, He2 would have no bond at all not surprisingly, molecules of He2 have not been observed except under demanding experimental conditions.5... 

The angular-overlap model (AOM) is one such specific model whose parameters have been chosen so as to refer to the central ion-to-ligand bonding process (9). However, it must be remembered that AOM still is a first-order perturbation model (70) but, one may say, a zeroth-order molecular orbital model (5). 

The characters of these matrices for all R can be obtained in a simple manner without ever writing out the matrices. If Ta interchanges one basis function with another, then no diagonal entry appears in the rows corresponding to these basis functions. The representation so formed is reducible. We may similarly obtain a representation with the nine basis vectors Oi(2px), 0-2(2px), OsCip ) Oi(2p ), 0>(2py), 03(2p ) Oi(2px), 0 (2px), Oj(2px). These could be taken three at a time or as a nine-rowed column vector. In any particular problem it is advisable to write out some of the matrices of Tr in order to keep track of the functions by associating them with the row of a matrix. Since Oi, O2, and O3 are indistinguishable in D3 symmetry, the resulting reps correspond to states that are composites of Oi, O2, and O3 atomic symmetry. However, whatever valence description of XOl" is employed, the valence bonds, or molecular orbitals, must retain the transformation properties shown in Tables 7.3 and 7.4. 

The question is the nature of the tt orbitals associated with the two double bonds. A molecular orbital analysis would begin with linear combinations of the tt orbitals an in-phase (symmetric, S) and an out-of-phase (antisymmetric. A). To the extent that there is any direct interaction between the double bonds, one would expect S to lie below A. Such a direct mixing is termed through space. The problem is that a number of observations lead to the conclusion that the actual orbital ordering in 1,4-cyclohexadiene is A < S. What has gone wrong This is a planar molecule, so there is a tt system that can be confidently treated as separate from the a framework. Isn t it always better to mix orbitals in-phase ... 

Write and sketch zero-order molecular orbital wave-functions by combining atomic orbital wavefunctions. Sketch the appearance of a bonding molecular orbital formed by combining in equal proportions a Is orbital on nucleus A with a 2p orbital on nucleus B. Show nodes if there are any. 

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