Energy rearrangement

If VQ > 0, then the threshold for photoionization into a vacuum Eva( = -Ee(ls). If VQ < 0, then that additional energy has to be supplied. Delahay (1976) has summarized this process, but the actual mechanism is still debatable. If AH and Evac are experimentally known, one can get an experimental measure of the medium rearrangement energy in the ground state, EM(ls) = E - AH. On that basis, since EM is always positive, Kestner (1976) prefers the lower experimental value of AH for e. ... 

Much larger inner-shell rearrangement energy terms are involved in the CO J CO2 couple relating to linear CO2 but bent COf species. 

In competition, the C(6)-yl and C(5)-yl radicals may disproportionate, possibly via an adduct [reactions (80) and (81)]. This yields the hydrate via an enol [reaction (83)]. The other product is the glycol [reaction (82)]. In the original paper (Al-Sheikhly and von Sonntag 1983), it has been proposed that it maybe formed in an ET reaction. Due the considerable rearrangement energies involved in ET reactions as compared to radical recombination reactions, it is now considered that this ET reaction might occur via an addition/elimination process [reactions (80) and (81)] such as has also been found for other systems. 

A part of the activation energy will arise from the adjustment to a common value in both complexes (inner-sphere rearrangement energy). 

The calculated MINDO/3 LUMOs for these molecules are lower than the experimental Ea by 0.70 eV and for AMI are higher than the experimental Ea by about 0.1 eV. These are shown in Figure 7.2. The systematic uncertainties remain constant. Figure 7.3 provides the optimum values of the VEa for the linear acenes. The VEa are between the A Ea and MINDO/3 LUMO values. The calculated VEa for hexa-cene to novacene support the AEa values of 1.65 eV to 2.0 eV. The systematic difference is the rearrangement energy. It is approximately 0.2 eV for anthracene and above. 

Figure 7.2 Plot of the semi-empirical Ea versus the experimental Ea for the linear acenes 1 to 9. The x s are the CURES-EC values that are equal to the experimental values within the uncertainties. The circles are the calculated VEa and the triangles the LUMO. These are displaced from the CURES-EC values by a constant amount. This implies that the rearrangement energies are approximately the same for the linear acenes, as determined in [8] and this book.

Figure 3. Potential energy curve of the angular vibration of alcohol-metal (Mx) (1) and isocyanate-metal (Mx) (2). The rearrangement energy for that system is the collapse region of curves 1 and 2 CaErI. Similarly, in the case of M we have alcohol-metal (M)(V), isocyanate-metal (M.) (2 ), and AEk- < aEk.

Fig. 10.38. More-O Ferrall-Jencks diagram representing the variable transition structure for the Cope rearrangement. Energies (in kcal/mol) are from thermodynamic data, as quoted by D. A. Hrovat, J. Chen, K. N. Houk, and W. T. Borden, J. Am. Chem. Soc., 122, 7456 (2000).

Nuclear Rearrangement Energy Migration (fast, non radiative)... 

The standard interpretation for weakly coupled systems has assumed that the inner- and outer-sphere rearrangement energies are not dependent on the separation between the metal centers and that the distance dependence of Eqp and AG for electron transfer is due to the decrease in electronic coupling between the centers with increasing distance. This electronic factor will affect the probability of electron transfer and therefore is lumped together with AS in transition-state theory interpretations. The dependence of the electronic factor, k, on distance is taken to be related to that of the exchange integral, between the metal centers, and quantum mechanics predicts that... 

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