Jahn-Teller-active species

Jahn-Teller distortion" occurs in LiMn204 at 7°C (280 K). This phase transition results in a transformation from the cubic space group Fd3m to the tetragonal group Mj/amd. The structural distortion results from interaction of the Jahn-Teller active species Mn + (t2 -e ), in contrast, Mn" " (t2/-e ) and Mn (t2/-e/) are not Jahn-Teller active. Because of the low temperature of this transition, and that modified spinels have in general lower transition temperatures, this mechanism may not be as relevant as others for currently used spinel materials. Related mechanisms can cause strain and structural failure, resulting in electrically disconnected particles. 

The above results mainly apply to the Longuet-Higgins E x e problem, but this historical survey would be incomplete without reference to early work on the much more challenging problems posed by threefold or higher electronic degeneracies in molecules with tetrahedral or octahedral symmetry [3]. For example, tetrahedral species, with electronic symmetry T or T2, have at least five Jahn-Teller active vibrations belonging to the representations E and T with individual coordinates (Qa,Qb) and (Qx. Qx. Q ) say. The linear terms in the nine Hamiltonian matrix elements were shown in 1957 [3] to be... 

The greatest utility of the Angular Overlap Model lies however in its ability to comprehend the Jahn-Teller activity in terms of a simple one-electron operator. The matrix elements of this operator must of course first be determined within the chosen basis set for the required symmetry and stoichiometry and the method is here applied to give a comprehensive coverage for dx systems resulting from ML6, Oh, species. In principle... 

The symmetry of the normal mode of vibration that can take the molecule out of the degenerate electronic state will have to be such as to satisfy Eq. (6-7). The direct product of E with itself (see Table 6-11) reduces to A + A 2 + E. The molecule has three normal modes of vibration [(3 x 3) - 6 = 3], and their symmetry species are A + E. A totally symmetric normal mode, A, does not reduce the molecular symmetry (this is the symmetric stretching mode), and thus the only possibility is a vibration of E symmetry. This matches one of the irreducible representations of the direct product E E therefore, this normal mode of vibration is capable of reducing th eZ)3/, symmetry of the H3 molecule. These types of vibrations are called Jahn-Teller active vibrations. 

Electron-transfer reactions of higher cycloalkanes were also studied. Electron transfer from C-C7H14 to unstable holes generated by radiolysis in Freon-113 gave rise to a stable radical cation, c-Ci A f its spectrum was interpreted in terms of a twisted chair form with C2 symmetry [37]. Finally, radiolysis of c-CgHie in a Freon-113 matrix generated a Jahn-Teller-active radical cation, c-CgHie, with three sets of non-equivalent protons [37]. A detailed discussion of these species exceeds the scope of this review. 

Radiolysis of 96 resulted in an interesting, temperature-dependent spectrum. At 4 K, the species is Jahn-Teller-active and exhibits a static distortion from D3/, to C2v symmetry. In contrast to the bicyclo[2.2.1]heptane radical cation, the SOMO of 96 + involves four endo-C-H bonds, an = 3.8 mT. At 77 K in perfluorocyclohexane or Freon-113, the radical cation is dynamically averaged, with splitting from 12 equivalent protons [235]. 

Small metal clusters have received considerable attention because of their possible involvement as "active sites" in a variety of catalyzed reactions. Although not particularly noted for their catalytic activity, alkali clusters have a simple chemical composition and may, therefore, model the more complicated systems in a manner analogous to the role played by the hydrogen atom in atomic structure. Less emphasized is the fundamental nature of alkali clusters per se. Since the ground state of Hj is not chemically bound, alkali trimers are the most elementary species which can exhibit a Jahn-Teller interaction. 

The additional oxazoline ligation is expected to deactivate the complexes in their Lewis acidity, as was shown in a theoretical study on (BOX)Cu catalysts [23]. The transformation of the resting state into the active (17e Cu ) species therefore necessitates the decoordination of an oxazoline unit and the opening up of the system (Scheme 15.3, top). The required hemilability is provided siereoe/ec-tronically by the strong dynamic Jahn-Teller effect of the d Cu" center. As a consequence of the threefold rotational symmetry of the system, all the possible dicoordinated catalytically active species (A-C) are equivalent (Scheme 15.3, bottom). 

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