Marcus theory definition

A very brief introduction to the important topic of bioinorganic electron transfer mechanisms has been included in Section 1.8 (Electron Transfer) of Chapter 1. Discussions of Marcus theory for protein-protein electron transfer and electron or nuclear tunneling are included in the texts mentioned in Chapter 1 (references 3-7). A definitive explanation of the underlying theory is found in the article entitled Electron-Transfer in Chemistry and Biology, written by R. A. Marcus and N. Sutin and published in Biochem. Biophys. Acta, 1985, 811, 265-322. 

The use of the energy-gap reaction coordinate allows us to calculate solvent reorganization energies in a way analogous to that in the Marcus theory for electron transfer reactions.19 The major difference here is that the diabatic states for electron transfer reactions are well-defined, whereas for chemical reactions, the definition of the effective diabatic states is not straightforward. The Marcus theory predicts that... 

Magnetic moment, 153, 155, 160 Magnetic quantum number, 153 Magnetization, 160 Magnetogyric ratio, 153, 160 Main reaction, 237 Marcus equation, 227, 238, 314 Marcus plot, slope of, 227, 354 Marcus theory, applicability of, 358 reactivity-selectivity principle and, 375 Mass, reduced, 189, 294 Mass action law, 11, 60, 125, 428 Mass balance relationships, 19, 21, 34, 60, 64, 67, 89, 103, 140, 147 Maximum velocity, enzyme-catalyzed, 103 Mean, harmonic, 370 Mechanism classification of. 8 definition of, 3 study of, 6, 115 Medium effects, 385, 418, 420 physical theories of, 405 Meisenheimer eomplex, 129 Menschutkin reaction, 404, 407, 422 Mesomerism, 323 Method of residuals, 73 Michaelis constant, 103 Michaelis—Menten equation, 103 Microscopic reversibility, 125... 

Perhaps the point to emphasise in discussing theories of translational energy release is that the quasiequilibrium theory (QET) neither predicts nor seeks to describe energy release [576, 720], Neither does the Rice— Ramspergei Kassel—Marcus (RRKM) theory, which for the purposes of this discussion is equivalent to QET. Additional assumptions are necessary before QET can provide a basis for prediction of energy release (see Sect. 8.1.1) and the nature of these assumptions is as fundamental as the assumption of energy randomisation (ergodic hypothesis) or that of separability of the transition state reaction coordinate (Sect. 2.1). The only exception arises, in a sense by definition, with the case of the loose transition state [Sect. 8.1.1(a)]. 

The parabolic form of the Marcus surfaces was obtained from a linear response theory applied to a dielectric continuum model, and we are now in a position to verify this form by using the microscopic definition (16.76) of the reaction coordinate, that is, by verifying that ln(P(A)), where P X) is defined by (16.77), is quadratic in A. Evaluating PIA) is relatively simple in systems where the initial and final charge distributions po and pi are well localized at the donor and acceptor sites so that /)o(r) = - a) + <7b <5(r - rs) and pi (r) = - fa) +... 

A second approach to this problem of multiple asymptotia is to introduce specialized coordinates which change smoothly from one arrangement to the others in such a way as to enable one to analyze the wavefunction in the various arrangement limits. This leads to the definition of generalized "reaction coordinates". (10-16) The leading examples of these are the natural collision coordinates first introduced by Marcus (12) and the hyperspherical coordinates pioneered by Delves (10). These have led to important advances in reactive scattering theory but are discussed by others active in their study so we do not pursue them further here. 

If carried through, the physicist s and chemist s theories should lead to the same results. Some concepts are definitely irreconcilable, however. Typical for ET reactions is the exponential dependence on the rate. At a decreasing temperature, nuclear tunneling leads to a weaker decrease of the rate and finally to a constant rate as a function of 1". This is interpreted as a tunneling through the Marcus barrier. In solid-state physics, this is referred to as variable range hopping, which leads to a log(rate) dependence proportional to 1. ... 

The classical theory of electron transfer developed by Marcus starts with the same kind of hard spheres in a dielectric continuum model that is used to derive the free energy of solvation of an ion. A central role in the theory is played by the reorganisation energy X, which in its simplest definition is given by... 

Although the 17 Century was a time of notable scientific progress, the scientists of the day were themselves far less respected and far less listened to than today s scientists. Some of them, such as Newton and Leibniz who are responsible for the introduction of many modem theories, were also devoted alchemists. The idea of " fire fluiglobular particles that attach easily only to combustible objects) persisted for another two hundred years and assumed that when a substance is burnt, the non-substantial essence ( terra pinguis ) escapes. The definition of the laws of conservation needed more precision on account of the action of traditional vital and mortal forces. Conservation was assumed to be something general between and within the system as probably first noted by the non-cited Czech educator Marcus Marci [121 ]. 

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