Encounter complex spin states

A unique situation is encountered if Fe-M6ssbauer spectroscopy is applied for the study of spin-state transitions in iron complexes. The half-life of the excited state of the Fe nucleus involved in the Mossbauer experiment is tj/2 = 0.977 X 10 s which is related to the decay constant k by tj/2 = ln2/fe. The lifetime t = l//c is therefore = 1.410 x 10 s which value is just at the centre of the range estimated for the spin-state lifetime Tl = I/Zclh- Thus both the situations discussed above are expected to appear under suitable conditions in the Mossbauer spectra. The quantity of importance is here the nuclear Larmor precession frequency co . If the spin-state lifetime Tl = 1/feLH is long relative to the nuclear precession time l/co , i.e. Tl > l/o) , individual and sharp resonance lines for the two spin states are observed. On the other hand, if the spin-state lifetime is short and thus < l/o) , averaged spectra with intermediate values of quadrupole splitting A q and isomer shift 5 are found. For the intermediate case where Tl 1/cl , broadened and asymmetric resonance lines are obtained. These may be the subject of a lineshape analysis that will eventually produce values of rate constants for the dynamic spin-state inter-conversion process. The rate constants extracted from the spectra will be necessarily of the order of 10 -10 s"F... 

The redox ability of a metal complex will be considered in the context of its molecular orbital composition and spin state. In this regard, Figure 1 shows the molecular orbital diagrams for the most common geometries encountered in transition metal complexes. 

Similar considerations apply to the role of spin equilibria in electron transfer reactions. For many years spin state restrictions were invoked to account for the slow electron exchange between diamagnetic, low-spin cobalt(III) and paramagnetic, high-spin cobalt(II) complexes. This explanation is now clearly incorrect. The rates of spin state interconversions are too rapid to be competitive with bimolecular encounters, except at the limit of diffusion-controlled reactions with molar concentrations of reagents. In other words, a spin equilibrium with a... 

Fig. 13-4. Energy diagram and state mixing of spin states of a triplet-radical encounter complex for a negative J.

For example, the multiplicity of radicals with one unpaired electron, S = V2, is 2S + 1=2. Each of four spin states is then expected to form with equal probability upon encounter of two radicals 2A and 2B, a = 1/4. Three of these are sublevels of the encounter complex with triplet multiplicity, S = SA + SB = 1, 2S + 1 = 3, and the fourth is the singlet encounter pair, S = SA + SB — 1 = 0, 2S + 1 = 1. Only the latter can undergo radical recombination to form a singlet product P=A B without undergoing ISC. The above considerations therefore suggest that the rate constant for radical recombination will not exceed one-quarter of the rate constant of diffusion, because only every fourth encounter will lead to recombination. 

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