Static Distortions

Kremer16 then went on to make a precise estimate of the social value of an innovation or surplus under a situation of competition and under a monopoly. Thus, for example, for a price five times higher than the price fixed according to the marginal price, we detect a static distortion of 1.5, that is, the social rate of return of an innovation in a situation with marginal cost prices will be 1.5 times the return on the investment under monopoly prices. In this situation the social value of an innovation in a competitive environment would be 9.35 times the social value in a monopoly, that is, when there is no welfare loss. Kremer thus provides an estimate of welfare loss from a more thorough analytical perspective, and shows that it can be sizeable. 

For the d9 configuration, with a 2II(a2 it3 S4) ground state, only one sandwich complex, Co(HMBz)2, is known (108). This was shown to have a moment of 1.86 0.08 B.M. at 83 and 295 K, and a permanent dipole moment of 1.78 D in benzene solution. Although there are no indications of a static distortion to be found from X-ray diffraction studies (7), this latter observation appears to afford clear cut evidence of an effective symmetry lower than Cxv, and the magnetic data were shown (101) to imply A 1100 cm-1 in order to reproduce the essentially temperature independent moment observed. However, two cautions should be observed in assessing this evidence. Firstly the predicted temperature... 

For these latter systems, the effects of static distortions have been considered for a separation, A, of the erstwhile degenerate components of the n or 5 levels, in the absence of spin-orbit coupling, and expressions for the g values are readily derived (68, 72,101). 

In the limit of strong vibronic coupling, F4S = 0, c = 5 /3, s=, c2 - s2 =, and the dynamic Jahn-Teller effect thus renders nugatory the orbital contributions to the angular momentum, and reduces the splitting, A, by a factor of two. Note in addition that the c and s quantities used in the vibronic treatment do not correspond to those of the adiabatic case, although the expressions are formally similar, so that the static distortion, A, cannot accurately be calculated from the c and s values deduced from the and 4 data. 

V 0.48), Ammeter and Swalen also calculated the adiabatic distortion parameter for the Co(Cp)2/Fe(Cp)2 system, finding A = 528 cm 1. In both cases however calculations were carried out to determine the value of the purely static distortion which would reproduce, via the vibronic coupling mechanism, the results for c and 45- For the Ru(Cp)2 host the corrected value of A proved to be 200 cm 1 and for the Fe(Cp)2 host 840 cm-1. Thus in the Ru(Cp)2 host, with a rather long metal to carbon distance, the vibronic effect... 

The interpretation of the results was hindered to some extent by the inability to observe more than the gz absorption, except in the Kr matrix, but it was found that although the Fermi contact term, k0, showed some lattice dependence, the main feature of the results was that whilst A ranged from 286 cm-1 in Ne to 668 cm-1 in Kr, the vibronic overlap term varied only between 0.30 and 0.25, thus bearing out the authors predictions concerning the origin of the static distortion, A. 

Inhomogeneous broadening in solids typically occurs as a result of nonequivalent static distortions in the crystalline environment of an optically active center. As can happen with the paving stones in a floor, the crystal reticules are not perfectly equal there is a distribution of crystalline environments for the absorbing atom, and consequently a distribution of resonance frequencies. 

Due to this mixing a Jahn-Teller molecule is expected to be rather fluxional and this often makes it difficult to detect the effect. It is usually observed in crystals where due to the so-called Jahn-Teller cooperativity a static distortion may occur in the crystal. The most typical examples are the tetragonally distorted octahedral structures, such as MnFs or KCuFs. 

The intensities of polarized ligand field spectra ns-n ) of V(ethyl-dtp)3 doped into the corresponding indium(III) compoimd exhibit a relatively small temperature dependence. The source of the large intensities of the d-d transition is the static distortion of the ligand field n ) and not vibronic effects to any appreciable extent. 

Lohr, L. L., and W. N. Lipscomb An LCAO—MO study of static distortions of transition metal complexes. Inorg. Chem. 2, 911 (1963). 

The mechanism by which the d-d transitions gain intensity still remains to be determined. For octahedral and square planar complexes which have a center of symmetry, the transitions are partly inhibited. Slightly disorted octahedral and square planar metal complexes may have a fractional part of a d-d transition allowed, and this static distortion mechanism may be responsible for some intensity in many cases (I, 2). The fact that when Co(acac)3 catalyst was utilized in the oxidation, its absorption wavelength remained unchanged and its coefficient increased,... 

Answer. A possible explanation for the observed diastereoselectivity of nucleophilic addition to the carbonyl involves a static distortion of the carbonyl group so as to improve n donation of the (1 C—C bonds into the n orbital of the carbonyl... 

Figure B8.1. (a, b) Static distortion of carbonyl group to favor overlap with the highlighted bonds. The bonds in a) are poorer n donors because of electrostatic effects of the quaternary N center and interaction with er R. Thus interaction (b) is favored, (c) Distortion in the transition state to favor...

Overall, such studies support the tendency for C60 molecules to undergo JTD according to the shapes predicted in the calculations and with very small amplitudes. It seems possible that an interaction with the solvent stabilizes a static distortion in the reported cases. The true nature of the JTD for a free molecule being intrinsically dynamic, this could explain why JTD have remained elusive in many other cases. 

When a Jahn-Teller-distorted C q molecule is placed in a solid-state environment, strain or crystal-field perturbations may play a decisive role in the selection and/or enhancement of the Jahn-Teller-distorted configuration. In an attempt to investigate the Jahn-Teller-distorted C6 0 molecules in the solid state, C60-tetraphenylphosphonium iodide has been synthesized and studied [40]. The well-known Flu(l) and Flu(2) modes were found to split into doublets at room temperature indicating a D5d or D3d and not a D2u Jahn-Teller configuration. These results are consistent with a dynamic Jahn-Teller effect in the strong coupling limit or with a static distortion stabilized by the low-symmetry perturbations. 

Another factor contributing to the asymmetry and breadth of absorption bands in crystal field spectra of transition metal ions is the dynamic Jahn-Teller effect, particularly for dissolved hexahydrated ions such as [Fe(H20)6]2+ and [Ti(H20)6]3+, which are not subjected to static distortions of a crystal structure. The degeneracies of the excited 5Eg and 2Eg crystal field states of Fe2+ and Ti3+, respectively, are resolved into two levels during the lifetime of the electronic transition. This is too short to induce static distortion of the ligand environment even when the cations occupy regular octahedral sites as in the periclase structure. A dual electronic transition to the resolved energy levels of the Eg excited states causes asymmetry and contributes to the broadened absorption bands in spectra of most Ti(m) and Fe(II) compounds and minerals (cf. figs 3.1,3.2 and 5.2). 

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