Second-Order Jahn-Teller Distortion

It was shown by several workers that in this case the first-order Jahn-Teller distortion is due to an ej vibration, and that the second-order distortion vanishes. Therefore, in terms of simple Jahn-Teller theoi, the moat around the symmetric point should be a Mexican hat type, without secondary minima. This expectation was borne out by high-level quantum chemical calculations, which showed that the energy difference between the two expected C2v structures ( A2 and Bi) were indeed very small [73]. 

A hysteresis cycle in the molar susceptibility measurements has been observed for [Ni2(Medpt)2(N3)2(/r-N3)2] (883). This has been ascribed to a phase transition caused by an asymmetrization process of the rhombus-like centrosymmetric [Ni-(N3)2-Ni] core that occurs with falling temperature. The asymmetrization transition can be explained in terms of a second-order Jahn-Teller distortion, taking into account the local symmetry of the dinuclear [Ni-(N3)2-Ni] entity (D2h, rhombic symmetry) before the arrangement.2128... 

Wade expanded the 1971 hypothesis to incorporate metal hydrocarbon 7T complexes, electron-rich aromatic ring systems, and aspects of transition metal cluster compounds [a parallel that had previously been noted by Corbett 19) for cationic bismuth clusters]. Rudolph and Pretzer chose to emphasize the redox nature of the closo, nido, and arachno interconversions within a given size framework, and based the attendant opening of the deltahedron after reduction (diagonally downward from left to right in Fig. 1) on first- and second-order Jahn-Teller distortions 115, 123). Rudolph and Pretzer have also successfully utilized the author s approach to predict the most stable configuration of SB9H9 (1-25) 115) and other thiaboranes. 

The proposed approach to static cooperative Jahn-Teller effect is based on the exact effective Hamiltonian (7), acting in the reduced space of active one-centre distortions only. It involves effective force constants, which are analytically related to the parameters of the full microscopic Hamiltonian. Direct electronic interactions between sites, such as orbital-dependent electrostatic and exchange interactions [28], can be added to the effective Hamiltonian without modifying it. This approach proves to be especially efficient in the case of strong Jahn-Teller distortions, when the effects of second-order Jahn-Teller coupling become important. 

Recently Krogh-Jespersen and Roth evaluated the potential stabilization of the 2B2 structure type by methyl substitution. For both mono- and gem-dimethyl derivatives the 2A, type structures are minima, whereas the 2B2 type structures are transition states. They undergo second-order Jahn-Teller distortion to unsym-metrical structures with one very long C—C bond. 

Rationalization for why ligand bending takes place in some tris(dithiolene) complexes has been addressed recently by Campbell and Harris (372) and previously by others (7, 357). In TP structures, the bend is thought to result from a second-order Jahn-Teller distortion where the highest occupied molecular orbital (HOMO) is lowered in energy as a result of improved overlap between the ligand nv and the metal dz2 orbitals as depicted in Fig. 23 (372). 

An extended Hiickel molecular orbital analysis on both of these complexes revealed that this structural difference between the chloride and the iodide can be traced to a second-order Jahn-Teller distortion, which is predicted to occur more readily for the chloride. Specifically,... 

In conclusion, these studies provide a theoretical foundation for rationalizing many of the trends in coordination geometry regularity (bond lengths and angles), which have been commented upon throughout this chapter. More simplified descriptions of second-order Jahn-Teller distortions in some of these systems can be found in Refs. 105 and 106. 

The cyclobutane radical cation was calculated by several groups, who evaluated Jahn-Teller distorted structures potentially arising upon ionization of cyclobutane [79, 83-87]. Four distorted local minima were considered (Figure 13). A rectangular structure with two weakened C-C bonds (type A) and a rhomboidal structure with four weakened C-C bonds (type B) result from first order Jahn-Teller distortion. Two further structures, a trapezoidal one (one weakened C-C bond type C), and an irregular structure shaped like a kite (two lengthened C-C bonds type D) can be envisaged as a consequence of second-order Jahn-Teller distortion [86]. A detailed recent study also considered puckered equivalents of the planar structure types, A-D... 

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