Jahn-Teller radius

Fig. 13. Top Schematic representation of the two components of the Jahn-Teller-active vibrational mode for the E e Jahn-Teller coupling problem for octahedral d9 Cu(II) complexes. Bottom Resulting first-order Mexican hat potential energy surface for showing the Jahn-Teller radius, p, and the first-order Jahn-Teller stabilization energy, Ejt.

With p = (Qg + Ql f being the Jahn-Teller radius, FE the linear vibronic coupling constant, GE the quadratic vibronic coupling constant, KE the force constant for the Eg normal mode of vibration, and Qo, Qe the two degenerate vibrations of eg symmetry. 

Linear coupling (termed the Mexican hat ) a continuous slab of the energy minima exists at the Jahn-Teller radius... 

The structures of the CuL6 chromophores may be temperature variable with bond-length changes of the order of the Jahn-Teller radius, Fig. 1(A), Rjj = 0.1-0.4 A, accessible by low temperature X-ray crystallography, which if determined at low enough temperature may yield AE values. 

The ways of determining the potential parameters Kaa, Kee, A and B, as well as the Jahn-Teller radius Qq> discussed elsewhere The last formula differs from (52) only... 

The co-ordination number in ionic compounds is determined by the radius ratio - a measure of the necessity to minimize cationic contacts. More subtle effects are the Jahn-Teller effect (distortions due to incomplete occupancy of degenerate orbitals) and metal-metal bonding. 

The data for the 1,2-diaminoethane complexes now parallels the trends in ionic radius and LFSE rather closely, except for the iron case, to which we return shortly. What is happening Copper(ii) ions possess a configuration, and you will recall that we expect such a configuration to exhibit a Jahn-Teller distortion - the six metal-ligand bonds in octahedral copper(ii) complexes are not all of equal strength. The typical pattern of Jahn-Teller distortions observed in copper(ii) complexes involves the formation of four short and two long metal-ligand bonds. 

The plot supplies similar informations as the plot of the reciprocal value of ionic radius of the metal vs k12 described by Eigen and coworkers 107—109). Deviations are considered to be due to ligand field stabilization, the Jahn-Teller effect, or to the effective ionic charge u°). The rate coefficient of hydrated Cu2 + is higher by three orders of magnitude as compared to that of most other elements due to the Jahn-Teller effect the distances of the two water molecules in axial positions are much larger than those of the four water molecules in equatorial positions ni). 

The examples of minerals affected by Jahn-Teller distortions that are listed in table 6.1 demonstrate that the concept of ionic radius is not a rigorous atomic property when applied to crystal structures containing the Cr2+, Mn3+ and Cu2+ ions. Other consequences of Jahn-Teller distortions in mineral structures are discussed in 6.8.3.2 and elsewhere (Strens, 1966a Walsh et al., 1974). 

Table 1, compiled from data given in Colton and Wilkinson (7) and from Eigen and Wilkens (2, 3), illustrates the differences in inner sphere water lability, as measured by H2O substitution rates, for the aquo ions. Note that within a series (Ni—Cu and Zn—Hg) there is an approximate correlation between ionic radius and the lability of bound water. Eigen and Wilkens (2) have suggested that the deviation from this trend shown by Cu(II) is the result of a Jahn-Teller effect which results in the distortion of the octahedral complex and the labilization of the apical ligands. 

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