Symmetry Orbital correlation Orbitals

Fig. 13 a—c. A correlation diagram for the Huckel a MO s of (a) S3N3 and (b) a hypothetical SjNj" ion. In (c), the ab initio HFS energy levels of a planar HjPS Nj molecule are shown. For purposes of clarity, only the n symmetry orbitals are labelled. Unoccupied orbitals are indicated by an asterisk... 

Molecular orbital models are valuable aids in understanding the reactivity, regioselectivity, and stereospecificity phenomena exhibited by cycloaddition reactions and in predicting reactivity and product identities for addend pairs. Symmetry-energy correlation diagrams indicate that the 1,3-dipolar cyclo-... 

Alternative approaches have been suggested by Langlet and Malrieu22 and by Trindle.23-25 Langlet and Malrieu point out that although the correlation diagram method requires the use of symmetry orbitals, which must therefore be delocalized,... 

Fig. 8. Conversion of oyclobutene to s-eis-butadiene, Conrotatory changes are on the left disrotatory changes are on the right. Upper section alternative modes of ring opening of oyclobutene. Middle section orbital correlation. Bottom section symmetry state correlation.

Although the state correlation diagram is physically more meaningful than the orbital correlation diagram, usually the latter is used because of its simplicity. This is similar to the kind of approximation made when the electronic wave function is replaced by the products of one-electron wave functions in MO theory. The physical basis for the rule that only orbitals of the same symmetry can correlate is that only in this case can constructive overlap occur. This again has its analogy in the construction of molecular orbitals. The physical basis for the noncrossing rule is electron repulsion. It is important that this applies to orbitals—or states—of the same symmetry only. Orbitals of different symmetry cannot interact anyway, so their correlation lines are allowed to cross. 

It is now clearly established that potassium chemisorbed on transition metals functions as an unusually powerful donor. This increases the density of surface electron states available for back-bonding with certain adsorbates, if they possess orbitals with energy and symmetry that correlate near the Fermi energy of the metal. Examples of such orbitals would be the 27t of CO and N2. The important general consequences of this interaction include increased heat of molecular adsorption and increased dissociation probability. 

Three common labeling conventions are used in Fig. 7-17. A level may be labeled with reference to the separated atom AOs to which it correlates. The separated atom AO symbol is placed to the right of the MO symmetry symbol (e.g., a 2s). Note the absence of square brackets, which we used to symbolize the SO (2s -I- 2s5>. The symbol (7g2s means the MO of ag symmetry that correlates with 2s AOs at / = oo. An alternative label indicates the united-atom orbital with which the MO correlates. Here the AO label is placed to the left of the symmetry symbol (e.g., 3punited-atom notation are redundant and are often omitted. However, they are helpful in drawing correlation diagrams. Finally, the MOs may be simply numbered in their energy order within each symmetry type, as mentioned earlier (e.g., 2af). 

The Woodward-Hoffmann method [52], which assumes conservation of orbital symmetry, is another variant of the same idea. In it, the emphasis is put on the symmetries of molecular orbitals. Longuet-Higgins and Abramson [53] noted the necessity of state-to-state correlation, rather than the orbital correlation, which is not rigorously justified (see also, [30,44]). However, the orbital symmetry conservation rules appear to be very useful for most themial reactions. 

To see how and under what conditions stability is enhanced or diminished, we need to consider the symmetry of the orbital (9-32), Flectrons in the antisymmetric orbital r r have a 7ero probability of occurring at the node in u where U] = rj. Electron mutual avoidance of the node due to spin correlation reduces the total energy of the system because it reduces electron repulsion energy due to charge... 

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