Marcus and Co

Remark After this work was completed, a theory of blinking manocrystals was proposed by Marcus and co-workers [49,50]. 

From a tabulation of selected values kindly supplied by Prof. Y. Marcus, The Hebrew University, Jerusalem, Israel. Most of the listed standard molar Gibbs energies of transfer A Gfr may he found in earlier works by Marcus and co-workers [130,135,136,137,138]. Additional values are taken from the following references 1-hexanol [139], 2,2,2-trifluoroethanol (Cs ) [139], N,N-diethylformamide [140], trimethylphosphatc [140], butyrolactone [140], tetrahydrofu-ran [140], isobutyronitrile [140], pyridine (Li, K", Cs ) [141], dichloromethane [141], 1,2-dichloroethane [142], benzonitrile [143], and pyrrole [139]. All values are given in kj/mol. 

Assuming that the concept of a rate constant is valid, we might consider using a microscopic theory of unimolecular chemical reactions to predict what the reaction rate should be and then check to see whether the theory is in agreement with that obtained from the computer simulation. The theory most widely used for this purpose is the RRKM theory developed by Rice and Ramsperger,36 Kassel,and Marcus and co-workers. As has been discussed in detail elsewhere,RRKM theory contains the same essential dynamical assumptions contained in transition-state theory. We discuss these assumptions briefly in the next section. 

Marcus and co-workers have calculated nonadiabatic transfer probabilities for a model system consisting of ellipsoidal oxidant and reductant ions, at various mutual orientations. The model is designed to apply to large molecules such as proteins, and is a simplification of earlier work. " Selection rules (i.e., transfer probabilities) have been calculated for various 3d transition metal ions embedded in oxide lattices. For example, the reaction + Mn — + Mn " " is forbidden... 

This work has been carried out by Marcus and his co-workersand deals with the influence of sulphur on the passivation of Ni-Fe alloys. For sulphur-containing Ni-Fe alloys, sulphur segregates on the surface during anodic dissolution. Above a critical sulphur content a non-protective thin sulphide film is formed on the surface instead of the passive oxide film. 

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). 

Rate and equilibrium constants have been measured for representative intramolecular aldol condensations of dicarbonyls.60a For the four substrates studied (32 n = 2, R = Me n = 3, R = H/Me/Ph), results have been obtained for both the aldol addition to give ketol (33), and the elimination to the enone (34). A rate-equilibrium mismatch for the overall process is examined in the context of Baldwin s rales. The data are also compared with Richard and co-workers study of 2-(2-oxopropyl)benzaldehyde (35), for which the enone condensation product tautomerizes to the dienol60b (i.e. /(-naphthol). In all cases, Marcus theory can be applied to these intramolecular aldol reactions, and it predicts essentially the same intrinsic barrier as for their intermolecular counterparts. 

Thus, the model incorporating the direct hole trapping by adsorbed dichloroacetate molecules, which has been proposed by Bahnemann and co-workers, appears to be probable [7]. Moreover, calculations using the Marcus electron transfer theory for adiabatic processes which result in a reorientation energy of 0.64 eV suggest that also in the case of SCN- the hole transfer occurs in the adsorbed state [7]. 

Nowadays, the basic framework of our understanding of elementary processes is the transition state or activated complex theory. Formulations of this theory may be found in refs. 1—13. Recent achievements have been the Rice—Ramsperger—Kassel—Marcus (RRKM) theory of unimol-ecular reactions (see, for example, ref. 14 and Chap. 4 of this volume) and the so-called thermochemical kinetics developed by Benson and co-workers [15] for estimating thermodynamic and kinetic parameters of gas phase reactions. Computers are used in the theory of elementary processes for quantum mechanical and statistical mechanical computations. However, this theme will not be discussed further here. 

There are several rough experimental values for the decomposition of chemically activated CH4. Some older data on the reaction D + CH3 — CH3D, studied at 25°C. by Taylor and co-workers,38 correspond to (tf) 3 keal. (the zero-point energy difference for C—H and C—D is 2 keal.). These experiments correspond to the low-pressure limit, for which the calculated value in Table XI is kao 1.7 X 1010 sec.-1 at this energy. Marcus14 analyzed these data to obtain ka = 8 X 108 sec.-1 which, if we correct for the presence of a primary and secondary isotope effect due to the D atom, would be ka 1.5 X 109 sec.-1. He estimated a possible error of a factor of 5-10 in these values. We believe that the collision number used by Marcus in the calculation of ka is too low by a factor of 3-5 which would raise the experimental value to >5 X 10 sec.-1. The agreement is adequate, but the desirability of redoing these experiments with improved techniques is evident. 

Bemasconi and co-workers have studied the kinetics of disproportion-ation-comproportionation in azaviolene systems by temperature jump, stopped-flow, and pH jump techniques, examining the electron transfer process in the light of Marcus theory.316-318... 

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