Allene, degenerate orbitals

Degenerate orbitals are also found in tetrasubstituted allenes, that is, allenes of symmetry Dm (cf. Fig. 9). However, the (e) degeneracy of these last molecules is due to symmetry. 

These new developments place allene-olefin and allene-allene thermal cycloadditions in a new context framed by the questions Are there reactive intermediates separating reactants and products in the cycloadditions, or in the degenerate rearrangements Might there be a common reactive intermediate for the allene-olefin addition and the methyl-enecyclobutane rearrangement, and another for the allene-allene addition and the 1,2-dimethylenecyclobutane rearrangement How may the experimentally observed stereochemical features of these four processes be reconciled with orbital symmetry theory ... 

In Fig. 9 an orbital diagram correlating the outermost (occupied and unoccupied) degenerate e orbitals of allene (11) with orbitals of corresponding symmetries in the molecules RH to give the outermost orbitals of a monosubstituted allene is displayed. 

For a discussion of the situation in complex allenes take for simplicity a 1,3-disubstituted allene with identical ligands. These molecules are (at least) of symmetry C2. Then, symmetry suffices to state that the electronic states (orbitals) have lost a typical feature of x systems They have no longer nodal planes. Furthermore, in allenes of symmetry C2, such as 3 or 72, the resulting a and b orbitals are accidentally degenerate (lc,66). 

Corresponding arguments apply to pentatetraenes. In all these Z>2rf-systems the chemically interesting (outermost) orbitals have no nodal planes. Then, of course, in isoelectronic l,3-di ubstituted carbodiimides the situation is comparable with that in 1,3-disubstituted allenes and corresponding reasonings apply and similar findings are expected. From pe spectra it has been shown recently (99) that, indeed, the outermost a and b orbitals in symmetric carbodiimides are degenerate. 

Section II briefly outlines the theory behind the /T method, while the IVO generation scheme is described in Section III for systems, such as allene, where there is a degenerate highest occupied molecular orbital in the SCF ground state wavefiinction. The computations are described in Section IV along with comparisons to experiment and other high level calculations. 

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