Inverted effect

Owing to the existence of two centers for nucleophilic attack (at C2 and C5) in radical cations (220) obtained from the oxidation of 4-H -imidazole-1,3-dioxides (219), the formation of two products of methoxy group addition was observed, namely NNR (221) and NR of 3-imidazoline-3-oxide (222). The ratio of the products depends on the electronic nature of substitutes R1 and R2. Both, the donor character of R1 and acceptor character of R2 facilitate the formation of nitroxyl radicals (222) with the yield of (221) increasing with the inverted effect of the substituents. As was mentioned in Section 2.4, the results of preparative electrochemical oxidative methoxylation of 4H -imidazole-1,3-dioxides are similar to the results of chemical oxidation. 

For the experimental conditions investigated thus far, the steady-state solution is an excellent approximation to the solution of eq 1 and we consider this case. However, in proposing some experiments in the picosecond regime to enhance the chance of observing the inverted effect, we consider the time-dependent equation 1. 

The details of these short-time calculations, made for the case that U(r) = 0, are given elsewhere (28). Searching for the inverted effect in unimolecular systems (reactants linked to each other) would also be very desirable since their rates would not be diffusion limited. 

In a series of papers between 1956 and 1965, Marcus solved much of the mystery by outlining a description of the probability of fluctuations in the geometry of reactants and their solvents. These fluctuations lead to changes in the energy barriers that the reactants must surmount before an electron can be transferred from one molecule to another. Marcus extended the theory to other systems, such as electrochemical rate constants at electrodes, and to chemiluminescent electron transfer reactions. The by-now famous inverted effect is a consequence of his theory after a certain point, adding more energy to an electron transfer reaction actually slows the process. Scientists believe photosynthesis can occur because of the inverted effect. 

Most of the predictions were confirmed experimentally (apart from some anomalous cases), but one prediction, the inverted effect , (the decrease of rate constant with increasingly favorable (increasingly negative) AG°, when AG° is very large) was counterintuitive, but clearly evident in equation (1.4) and took 25 years before it was confirmed [26]. This story has been told many times and so I will not describe it here. However, the inverted effect is believed to have implications for efficiency of solar energy conversion in photosynthetic systems, as discussed elsewhere. Also, the ET theory had spin-offs for ion, atom and group transfer reactions considered in the next section. 

In order to lower the proximity effects caused by the solvent, C chemical shift values of compounds 75 and 76 have also been collected in CDCI3 solutions (Table 40). In the compound 75 series, electron-withdrawing and -repelling substituents cause shielding and deshielding of C-3 (ASCS 3.27 ppm), respectively, while the usual inverted effect can be evidenced for C-2 (ASCS 2.74 ppm). 

Figure 1 Driving-force dependence of ET rates predicted by semiclassical theory (equation 1). Rates increase with driving force until they reach a maximum value (A -]-) at —AG° = X. Rates then decrease at higher driving forces (inverted effect)...

Similar to other d -d systems, the drnuclear iridium(I) complex [Ir(/x-pz)(COD)]2 (23) showed spin-allowed and spin-forbidden (da — pa) absorption bands at 498 and 585 nm, respectively. Under ambient conditions, the complex displayed fluorescence at 564 nm and phosphorescence at 687 nm, which were assigned to singlet and triplet excited states of (da — pa) character. The triplet excited state of the complex was a powerful reductant with an excited-state reduction potential E° (Ir2+ ) of-1.81 V vs. SSCE. Facile electron transfer reactions occurred between the excited complex and methyl viologen and other pyridinium acceptors. The absence of an inverted effect for the forward electron transfer reactions, and the presence of such inverted behavior for the back-electron-transfer reactions were observed and explained. ... 

Some of the new theoretical relations, the cross-relation between the rates of a cross-reaction of two difierent redox species with those of the two relevant selfexchange reactions, were later adapted to non-electron transfer reactions involving simultaneous bond rupture and formation of a new bond (atom, ion, or group transfer reactions). The theory had to be modified, but relations such as the crossrelation or the effect of driving force (—AG°) on the reaction rate constant were again obtained in the theory, in a somewhat modified form. For example, apart from some proton or hydride transfers under special circumstances, there is no predicted inverted effect. Experimental confirmation of the cross-relation followed, and an inverted effect has only been reported for an H+ transfer in some nonpolar solvents. The various results provide an interesting example of how ideas obtained for a simple, but analyzable, process can prompt related, yet different, ideas for a formalism for more complicated processes. 

Further increase in Afi° causes a rate decrease. The inverted effect is now established with certainty. It corresponds to the region in which A,G > X. These ideas were strongly supported by P. L. Dutton, professor at the University of Pennsylvania, Philadelphia. Dutton studied electron-transfer reactions in bacterial photosynthetic centers. The first step in bacterial photosynthesis is a light excitation in bacteriochlorophyll. The excited electron is first transferred to bacteriopheophytin and then to a quinone, and again to another quinone. Electron transfer to the first quinone occurred at a distance of about 1 nm. Dutton and coworkers systematically changed quinones as electron acceptors and thereby also reaction distances. Additional distances were 0.46 and 2.34 nm. A variation of 2 nm (20 A) in the distance between electron donors and acceptors in protein changed the electron-transfer rate by a factor of 10. A linear distance dependence of the maximum electron trans-... 

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