HOMO-LUMO crossing

Inspection of the triptych of Fig. 15 shows that the Sj state of the cyclopropyl-dicarbinyl diradical is necessarily formed when starting with the pentadiene, that is, in the Di-7t-Methane rearrangement. This is seen in two ways. In the MO triptych of Fig. 14, we see no HOMO-LUMO crossing in this wing of the triptych. In the state triptych of Fig. 15, the surfaces then do not approach one another in this wing. Hence there is no mechanism for interconversion to ground state enroute to the diradical from the St diene. 

Additionally, if only S0 and Sx are considered, these configurations cannot mix as a consequence of Brillouin s theorem. Nevertheless, the situation is not as serious as it appears. Thus it is seen that in an MO approximation the S0 and Si configurations do become degenerate where HOMO-LUMO crossing occurs, and this signifies that where Mobius-Huckel theory predicts a degeneracy, surfaces will at least approach one another. 

From PE spectroscopy results for azomethane (Haselbach and Heilbron-ner, 1970) the energy of the n MO is known to lie between those of the n + and n orbitals. Thus, a HOMO-LUMO crossing results and the trans-cis... 

To apply the phase-change rule discussed in the previous section, we choose the reactant A with wave function A> and the two chemically equivalent products B and C with wave functions B> and C>, which differ by a rotation of the methylene group through 180, as anchors as indicated in Figure 6.7. The transition from B to C involves a HOMO-LUMO crossing and hence is phase-inverting, whereas the transitions from A to B or C are equivalent the total number of phase changes on the closed-loop A-B-C-A is thus odd, and a conical intersection must be contained within the loop. The... 

Figure 6. The HOMO-LUMO crossing occurring during the dsd rearrangement (Berry pseudorotation) of a trigonal bipyramid through a square pyramid intermediate.

It is important to remember that orbitals of different symmetry can and will cross each other along a reaction coordinate. The most important case where this occurs is when the highest occupied molecular orbital (HOMO) crosses the lowest unoccupied molecular orbital (LUMO). Such HOMO-LUMO crossings are said to be symmetry forbidden atid engender a high activation barrier. We shall sec many examples of this behavior in later chapters and the way molecules conspire to gel around the high barrier. 

MOs used in Figure 11.4 then transform as 2 and c symmetry, 11.61. This is the geometry where the HOMO—LUMO crossing occurs. The e set is half-filled and... 

The distinction between allowed" and "forbidden" reactions... seems to be one of topology rather than symmetry, there being a qualitative distinction between pairs of isomers that can be interconverted by a pericyclic reaction without a HOMO-LUMO crossing and pairs that cannot be so interconverted without a HOMO-LUMO crossing. ... 

Pairs of isomers that can be interconverted without a HOMO-LUMO crossing were termed HOMOMERS, while those whose interconversion requires a HOMO-LUMO crossing were termed LUMOMERS. In contrast to the other selection rules developed above, this classification system is independent of the path by which the interconversion takes place. 

Potential surfaces and HOMO/LUMO crossings in the isomerization of Dewar-benzene to benzene have been examined by the MINDO/3 method, and chemi-... 

MO and AD pictures (p. 805) reaction stages (p. 806) role of states DA, D+A , D+A (p. 811) HOMO-LUMO crossing (p. 815) nucleophilic attack (p. 816) electrophilic attack (p. 818) cycloaddition reaction (p. 823) Woodward-Hoffmann rules (p. 825) Diels-Alder reaction (p. 825) diabatic and adiabatic potentials (p. 828) inverse Marcus region (p. 833) collective coordinate (p. 836) mean force potential (p. 836) Franck-Condon factors (p. 840) reorganization energy (p. 841)... 

The experimental evidence cited above indicates that this does not occur. As suggested at the right of Fig. 6.6, the in-plane glide (6i) begins well before the intended HOMO-LUMO crossing, which is avoided because all four MOs have the same irrep (o ) in The HOMO and LUMO of the extended tran-soid zwitterion are qualitatively similar to those in the biradical illustrated in Fig. 6.4, but are more widely separated in energy As a result, the orbital approximation - and the symmetry analysis based upon it - is no less reliable than for the biradical mechanism. The zwitterionic mechanism can be accomodated by Fig. 6.5, with self-evident modifications arising from the polar nature of the tetramethylene intermediate. ... 

Dewar has applied the MINDO/3 method to a study of the thermal conversion of Dewar-benzene into benzene. The method gives an activation energy of 114.2 kJ mol , which is fairly close to the experimentally observed value of 96.2 kJ mol". The transition state has only symmetry. As a result, the HOMO/LUMO crossing occurs after the transition state. The charge distribution within the transition state shows that it tends towards a zwitterionic form and that either electron-attracting or -releasing substituents at the bridgehead should therefore facilitate the reaction. 

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