Resonance degeneracy

We we now forego the case Z — fc = 1, where we have resonance degeneracy we note that the expression (25) is positive if — fc > 1, and it becomes smaller with increasing difference / —A . Dipoles that differ by more than one rotational quantum repel each other. 

Here — 0. This has the consequence that two solutions have to be taken into consideration, which coincide for weak interactions. This represents the fact that in this case the resonance degeneracy with the state Z = Z — 1, A = A +1 is considered, which leads to resonance splitting when the systems are coupled. The equation of fifth order takes the special form... 

The second term (first order) depends on the resonance degeneracy resulting from energy exchange (reflection symmetry). It obviously vanishes for the ground state (nj = =. .. = 0) and since we are not interested here in the... 

Moreover we assume that is a non-degenerate eigenvalue. As a matter of fact, this is never the case, since, because of the indistin-guishability of the electrons the resonance degeneracy, discovered by... 

As shown in Figure 27, an in-phase combination of type-V structures leads to another A] symmetry structures (type-VI), which is expected to be stabilized by allyl cation-type resonance. However, calculation shows that the two shuctures are isoenergetic. The electronic wave function preserves its phase when tr ansported through a complete loop around the degeneracy shown in Figure 25, so that no conical intersection (or an even number of conical intersections) should be enclosed in it. This is obviously in contrast with the Jahn-Teller theorem, that predicts splitting into A and states. 

The electron spin resonance spectrum of a free radical or coordination complex with one unpaired electron is the simplest of all forms of spectroscopy. The degeneracy of the electron spin states characterized by the quantum number, ms = 1/2, is lifted by the application of a magnetic field, and transitions between the spin levels are induced by radiation of the appropriate frequency (Figure 1.1). If unpaired electrons in radicals were indistinguishable from free electrons, the only information content of an ESR spectrum would be the integrated intensity, proportional to the radical concentration. Fortunately, an unpaired electron interacts with its environment, and the details of ESR spectra depend on the nature of those interactions. The arrow in Figure 1.1 shows the transitions induced by 0.315 cm-1 radiation. 

Because of this degeneracy and coexistence of these resonant structures one expects intrinsic conjugation defects to exist and be formed along the chain, the so-called Pople-Wamsley defects (34) which in the case of polyacenes and polydiacetylenes takes the form... 

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