Threefold degenerate

For a threefold degenerate MO occupied by three electrons, a configuration of a triradical having a quartet multiplicity is required hy Hund s rule. In organic chemistry, systems of this type occur rarely but with transition element complexes, quartets, quintets, and sextets, they are common. 

Scheme 3 Rearrangement of [C4H6R] + cations, for R = H a threefold degenerate interconversion of bicyclobutonium ion (54) and cyclopropylmethyl cations (55).

In contrast with 1, for which only four threefold degenerate modes are active, 30 and 33 exhibit 86 and 45 IR active modes, respectively, 58 and 31 of which are twofold degenerate. The lower symmetry of 30 and 33 as compared to 1 also results in a higher number of nonequivalent carbon atoms producing more expected signals... 

For the case of an undistorted octahedral field, as in MgO and CaO, the spin-orbit interaction produces a threefold degenerate ground state that behaves as an S= 1 spin system in a magnetic field with + (2.0023) for a... 

The twofold degenerate rearrangement of 51 may involve unpopulated puckered 1,2,4-trimethylcyclobutyl cation 52 as an intermediate. In the threefold degenerate rearrangement of 53, isomeric 54 may be involved as an NMR unpopulated intermediate80. 

The 3-homonortricyclyl cation 70 was prepared by the isomerization of bicyclo[3.2.1]oct-3-en-2-yl cation 71 at 20 °C in SbFs/SC ClF solution83. The ion shows a threefold degenerate rearrangement between -85 °C to 20 °C. At 20 °C the C4, C6, C8 and Cl, C3, C7 carbons become equivalent with an average of 36.19 ppm and 135.8 ppm, respectively (equation 43). Below -80 °C the cation is a static secondary cyclopropylcarbinyl cation with the cationic center chemical shift at <5I3C 234.1. 

The parent secondary cyclobutyl cation 47 undergoes threefold degenerate rearrangement viao-bond delocalization involving nonclassical bicyclobutonium ion-like system171,172 (see Section 3.5.2.5). Similar behavior is also observed for the 1-methylcyclobutyl cation 48a.173 176 The 1-phenylcyclobutyl cation 48b, on the other... 

Siehl and co-workers949 950 have used the matrix co-condensation technique to generate the l-(trimethylsilyl)bicyclobutonium ion 528 (Scheme 3.23). The 1H and 13 C NMR spectra of ion 528 show averaged methylene signals, which is in accord with a fast threefold degenerate rearrangement and a puckered hypercoordinate structure. 

For certainty, assume that, as in the earlier example of Section 2, the JT term is the orbital triplet T2a of Oh. The matrix JT Hamiltonian of the orbital triplet term linearly coupled to a threefold degenerate t2g mode can be written as ... 

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