Marcus theory structural effects

This discussion of sources of curvature in Br insted-type plots should suggest caution in the interpretation of observed curvature. There is a related matter, concerning particularly item 5 in this list, namely, the effect of a change in transition state structure. Br nsted-type plots are sometimes linear over quite remarkable ranges, of the order 10 pK units, and this linearity has evoked interest because it seems to be incompatible with Marcus theory, which we reviewed in Section 5.3. The Marcus equation (Eq. 5-69) for the plot of log k against log K of the same reaction series requires curvature, the slope of the plot being the coefficient a. given by Eq. (5-67). A Brjinsted plot, however, is not a Marcus plot, because it correlates rates and equilibria of different reactions. The slope p of a Br nsted plot is defined p = d log kobs/d pK, which we can expand as... 

The extent to which steric effects adversely affect the attainment of such intimate ion-pair structures would be reflected in an increase in the work term and concomitant diminution of the inner-sphere rate. This qualitative conclusion accords with the reactivity trend in Figure 16. However, Marcus theory does not provide a quantitative basis for evaluating the variation in the work term of such ion pairs. To obtain the latter we now turn to the Mulliken theory of charge transfer in which the energetics of ion-pair formation evolve directly, and provide quantitative informa-... 

Marcus theory (15) has been applied to the study of the reductions of the jU,2-superoxo complexes [Co2(NH3)8(/u.2-02)(/i2-NH2)]4+ and [Co2(NH3)10(ju.2-O2)]6+ with the well-characterized outer-sphere reagents [Co(bipy)3]2+, [Co(phen)3]2+, and [Co(terpy)2]2+, where bipy = 2,2 -bipyridine, phen = 1,10-phenanthroline, and terpy = 2,2 6, 2"-terpyridine (16a). The kinetics of these reactions could be adequately described using a simple outer-sphere pathway, as predicted by Marcus theory. However, the differences in reactivity between the mono-bridged and di-bridged systems do not appear to be explicable in purely structural terms. Rather, the reactivity differences appear to be caused by charge-dependent effects during the formation of the precursor complex. Some of the values for reduction potentials reported earlier for these species (16a) have been revised and corrected by later work (16b). 

The next two chapters are devoted to ultrafast radiationless transitions. In Chapter 5, the generalized linear response theory is used to treat the non-equilibrium dynamics of molecular systems. This method, based on the density matrix method, can also be used to calculate the transient spectroscopic signals that are often monitored experimentally. As an application of the method, the authors present the study of the interfadal photo-induced electron transfer in dye-sensitized solar cell as observed by transient absorption spectroscopy. Chapter 6 uses the density matrix method to discuss important processes that occur in the bacterial photosynthetic reaction center, which has congested electronic structure within 200-1500cm 1 and weak interactions between these electronic states. Therefore, this biological system is an ideal system to examine theoretical models (memory effect, coherence effect, vibrational relaxation, etc.) and techniques (generalized linear response theory, Forster-Dexter theory, Marcus theory, internal conversion theory, etc.) for treating ultrafast radiationless transition phenomena. 

These driving forces are exergonic and considerably more favorable than those involved in the electron-transfer reactions of the simple, monosub-stituted carbonylmanganese cations Mn(CO)5L+ and anions Mn(CO)4P-(where L and P are both monodentate phosphines and phosphites). Nonetheless, the rate constants for cis- and ra -Mn(CO)2( DPPE )2+ with Mn(CO)2(DPPE)2 are considerably slower than those qualitatively observed between Mn(CO)5L+ and Mn(CO)4P- (67). Such large rate differences that belie thermodynamics can be attributed to steric hindrance in the tetrasubstituted carbonylmanganese cations and the anion which are absent in the simpler ions. Such structural effects, even in these apparently outer-sphere electron transfers, merit a further quantitative evaluation as in the application of Marcus theory (83). 

Structure on hydrogel properties of 2-hydroxyethyl acrylate determined. " Polymers bearing tertiary amino groups have been synthesised and their fluorescence spectra found to be significantly quenched while maleic anhydride " and cyclododecanones have been found to be effective initiators of the photopolymerisation of styrene. Poly(methylphenylsilane) is also an effective photoinitiator for styrenes and acrylates via a photolytic process to give silyl radicals. Iron oxalate is also an effective photo initiator for acrylate monomers while a theoretical description of the kinetics of free radical dye-initiated polymerisation via an electron transfer process has been proposed. Using the Marcus theory it has been shown that the rate of electron transfer can affect the rate of initiation. 

It is curious that the striking deviations of electrochemical kinetic behavior from that expected conventionally, which are the subject of this review, have not been recognized or treated in the recent quantum-mechanical approaches, e.g., of Levich et al (e.g., see Refs. 66 and 105) to the interpretation of electrode reaction rates. The reasons for this may be traced to the emphasis which is placed in such treatments on (1) quantal effects in the energy of the system and (2) continuum modeling of the solution with consequent neglect of the specific solvational- and solvent-structure aspects that can lead, in aqueous media, to the important entropic factor in the kinetics and in other interactions in water solutions. However, the work of Hupp and Weaver, referred to on p. 153, showed that the results could be interpreted in terms of Marcus theory, with regard to potential dependence of AS, when there was a substantial net reaction entropy change in the process. 

---