Long-range transfer

The electron transfer rates in biological systems differ from those between small transition metal complexes in solution because the electron transfer is generally long-range, often greater than 10 A [1]. For long-range transfer (the nonadiabatic limit), the rate constant is... 

The only reported application of the m,H-ADEQUATE experiment for structure elucidation was again in the initial report of the development of the experiment using 5,6-dihydrolamellarin 38 Only two correlations were reported by the authors. Both began with an initial 3/CH correlation from H19 and H22 to C17 and C2, respectively. The subsequent long-range transfers were also via three bonds from Cl 7 to ClOb and from C2 to ClOa, respectively as shown by 45. 

Quenching occurs by long-range interactions. In this model, the quencher molcule does not need to touch the tryptophan, but molecules at the surface of the protein can quench tryptophans some distance away—the long-range transfer model. The following equation would describe the results ... 

The long-range transfer model is formally the same as the second model, but now k, does not require penetration but instead indicates transfer at a distance. When k, < kd, the reaction rate will not depend upon kd. This model can therefore account for the viscosity dependence. Since penetration is not required, this model also predicts that quenching will not be critically dependent upon size and charge of the molecule. 

The rate constant for long range transfer by dipole-dipole mechanism is given by... 

The width of the encounter pair reactivity zone, 672, is to be considered small. There is no reason for this choice, save convenience. Probably rather larger widths would be more appropriate following work on gas-phase collision kinetics or long-range transfer processes (Chap. 4). In such circumstances, the partially reflecting boundary condition is no longer suitable and other techniques have to be used (see Chap. 8 Sect. 2.4 and Chap. 9 Sect. 4). 

The remainder of this section considers several experimental studies of reactions to which the Smoluchowski theory of diffusion-controlled chemical reaction rates may be applied. These are fluorescence quenching of aromatic molecules by the heavy atom effect or electron transfer, reactions of the solvated electron with oxidants (where no longe-range transfer is implicated), the recombination of photolytically generated radicals and the reaction of carbon monoxide with microperoxidase. 

Long-range Transfer Effects and Diffusion-controlled Reactions... 

In the remainder of this section, the general equations and theory appropriate for an incorporation of these long-range transfer effects into the diffusion-controlled reaction process are discussed. Later in this chapter, the specific cases of interest outlined above are developed and their relation to experimental work commented upon. 

In Chap. 2 and 3, the motion of two reactants was considered and a diffusion equation was derived based upon the equation of continuity and Fick s first law of diffusion (see, for instance, Chap. 2 and Chap. 3, Sect. 1.1). When one reactant (say D) can transfer energy or an electron to the other reactant (say A) over distances greater than the encounter separation, an additional term must be considered in the equation of continuity. The two-body density n (rj, r2, t) decays with a rate coefficient l(r, — r2) due to long-range transfer. Furthermore, if energy is being transferred from an excited donor to an acceptor, the donor molecular excited state will decay, even in the absence of acceptor molecules with a natural lifetime r0. Hence, the equation of continuity (42) becomes extended to include two such terms and is... 

Finally, since the long-range transfer probabilities are all, to some degree, dependent on mutual orientation of donor and acceptor, it is necessary to retain the facility to average over all orientations. Further attention is given in Chap. 5 to rotational effects during reactions between anisotropic molecules in solution. In Chap. 5, Sect. 4.2, the experimental evidence currently available indicates that molecules re-orient more rapidly than they react. 

Birks [6] has commented on several approaches to combined diffusion and long-range transfer which do not involve the use of a diffusion equation. These are generally ill-defined and require ad hoc assumptions. For instance, the Perrin [133] active sphere analysis is quite satisfactory once the assumptions are established from experiment [134]. 

On substituting these expressions into the rate coefficient for long-range transfer etc. and noting that collisional deactivation is improbable for these situations, eqn. (74), the rate coefficient can be shown to be... 

This is a much more severe condition than those discussed by Yokota and Tanimoto [140] or by Birks [6]. In the rate coefficient equation (83), x has an upper bound of (t/r0)2/3/10, which practically means thatx < 0.1, since for times longer than t r0 natural decay of the donor masks any long-range transfer effects. The term in square brackets and raised to the three quarter power in eqn. (83) is 1.15 for x 0.1. Consequently, the Yokota and Tanimoto [140] expression is only strictly valid under circumstances where it differs from the Forster [12] expression [that is where D = 0 in eqn. (83)] by little more than likely experimental errors The decay law of excited donor molecules concentration [D ], is... 

When electrons can transfer either by contact approach of the redox pair or long-range transfer, the appropriate equation for a scavenger (electron acceptor) of charge z is... 

As discussed in Chap. 3 Sect. 2.5, while observation of time-dependent rate coefficients does enable reliable estimates of the diffusion coefficient appropriate to reaction between donors and acceptors, the very ease of observation of these time-dependent effects masks much detail of diffusive motion in liquids. Estimates of i eff reflect more on the parameters appropriate to long-range transfer processes than on collisional events in... 

To show this connection, consider an ion-pair as above (Sect. 2.1). Not only may the ion-pair diffuse and drift in the presence of an electric field arising from the mutual coulomb interaction, but also charge-dipole, charge-induced dipole, potential of mean force and an external electric field may all be included in the potential energy term, U. Both the diffusion coefficient and drift mobility may be position-dependent and a long-range transfer process, Z(r), may lead to recombination of the ion-pair. Equation (141) for the ion-pair density distribution becomes... 

Equation (164) describes the evolution with time t0 of the survival probability of an ion-pair formed at time t with a separation r. In the general, case this equation cannot be solved, but if no long-range transfer occurs and the transport coefficients are constant, this reduces to... 

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