Experimental results

It is difficult to measure the distance dependence of k_et when the reactants are ions or molecules that are free to move in solution. In such cases, electron transfer occurs after a donor–acceptor complex forms and it is not possible to exert control over r, the edge-to-edge distance. The most meaningful experimental tests of the dependence of ket on r are those in which the same donor and acceptor are positioned at a variety of distances, perhaps by covalent attachment to molecular linkers (see 1 for an example). Under these conditions, the term e^{−∆‡G/RT} becomes a constant and, after taking the natural logarithm of eqn 24.81 and using eqn 24.80, we obtain ln ket =−βr + constant which implies that a plot of ln ket against r should be a straight line with slope −β. The value of β depends on the medium through which the electron must travel from donor to acceptor. In a vacuum, 28 nm⁻¹ < β < 35 nm−1, whereas β ≈ 9 nm⁻¹ when the intervening medium is a molecular link between donor and acceptor. The dependence of k_et on the standard reaction Gibbs energy has been investigated in systems where the edge-to-edge distance, the reorganization energy, and κν are constant for a series of reactions. Then eqn 24.81 becomes

and a plot of ln ket (or log k_et) against ∆rG⁰ (or −∆rG⁰) is predicted to be shaped like a downward parabola. Equation 24.84 implies that the rate constant increases as ∆rG⁰ decreases but only up to −∆rG⁰ = λ. Beyond that, the reaction enters the inverted region, in which the rate constant decreases as the reaction becomes more exergonic (∆rG⁰ becomes more negative). The inverted region has been observed in a series of

special compounds in which the electron donor and acceptor are linked covalently to a molecular spacer of known and fixed size (Fig. 24.29).

The behaviour predicted by eqn 24.84 and observed experimentally in Fig. 24.29 can be explained by considering the dependence of the activation Gibbs energy on the standard Gibbs energy of electron transfer. We suppose that the energies of the reactant and product complexes can be characterized by parabolas with identical curvatures and fixed but distinct q0 R and q0 P. Now we let the minimum energy of the product complex change while keeping q0 P constant, which corresponds to changing the magnitude of ∆rG⁰. Figure 24.30 shows the effect of increasing the exergonicity of the process. In Fig. 24.30a we see that, for a range of values of ∆rG⁰, ∆‡G > 0 and the transition state is at qa * > q₀^R. As the process becomes more exergonic, the activation Gibbs energy decreases and the rate constant increases. (This behaviour is another example of a ‘linear free-energy relation’, first discussed in Section 24.5.) Figure 24.30b shows that, when ∆‡G = 0 and qb* = q0 R, the rate constant for the process reaches a maximum as there is no activation barrier to overcome. According to eqn 24.81, this condition occurs when −∆rG⁰ = λ. Finally, Fig. 24.30c shows that, as the process becomes even more exergonic, ∆‡G becomes positive again but now the transition state is at qc * < q0 R. The rate constant for the process decreases steadily as the activation barrier for the process increases with decreasing ∆rG⁰. This is the explanation for the ‘inverted region’ observed in Fig. 24.29.

Some of the key features of electron transfer theory have been tested by experiments, showing in particular the predicted dependence of ket on the standard reaction Gibbs energy and the edge-to-edge distance between electron donor and acceptor. The basic theory presented in Section 24.11 has been extended to transfer of other light particles, such as protons.

We saw in Impact I7.2 and I21.2 that exergonic electron transfer processes drive the synthesis of ATP in the mitochondrion during oxidative phosphorylation. Electron transfer between protein-bound cofactors or between proteins also plays a role in other biological processes, such as photosynthesis (Impact I23.2), nitrogen fixation, the reduction of atmospheric N2 to NH3 by certain microorganisms, and the mechanisms of action of oxidoreductases, which are enzymes that catalyse redox reactions. Equation 24.78 applies to a large number of biological systems, such as cytochrome c and cytochrome c oxidase (Impact I7.2), which must form an encounter complex before electron transfer can take place. Electron transfer between protein-bound co factors can occur at distances of up to about 2.0 nm, a relatively long distance on a molecular scale, with the protein providing an intervening medium between donor and acceptor.

When the electron donor and acceptor are anchored at fixed distances within a single protein, only ket needs to be considered when calculating the rate of electron transfer by using eqn 24.81. Cytochrome c oxidase is an example of a system where such intraprotein electron transfer is important. In that enzyme, bound copper ions and haem groups work together to reduce O₂ to water in the final step of respiration. However, there is a great deal of controversy surrounding the interpretation of pro tein electron transfer data in the light of the theory that leads to eqn 24.81. Much of the available data may be interpreted with β ≈ 14 nm⁻¹, a value that appears to be insensitive to the primary and secondary structures of the protein but does depend slightly on the density of atoms in the section of protein that separates donor from acceptor. More detailed work on the specific effect of secondary structure suggests that 12.5 nm⁻¹ < β < 16.0 nm⁻¹ when the intervening medium consists primarily of α helices and 9.0 nm⁻¹ < β < 11.5 nm⁻¹ when the medium is primarily β sheet. Yet another view suggests that the electron takes specific paths through covalent bonds and hydrogen bonds that exist in the protein for the purpose of optimizing the rate of electron transfer.

A value of β is not necessary for the prediction of the rate constants for electron transfer processes between proteins if we take a different approach. It follows from eqns 24.78 and 24.79 that the rate constant k_obs may be written as

kobs = Ze^{−∆‡G/RT}

where Z=K_DA κν. It is difficult to estimate kobs because we often lack knowledge of β, λ, and κν. However, when λ >> | ∆ rG⁰|, kobs may be estimated by a special case of the Marcus cross-relation, which we derive in Further information 24.1:

k_obs = (k_DDk_AAK)^1/2

where Kis the equilibrium constant for the net electron transfer reaction (eqn 24.75) and k_DD and k_AA are the experimental rate constants for the electron self-exchange processes (with the asterisks distinguishing one molecule from another)

*D+D+→*D⁺+D

 *A⁻ +A→*A+A⁻

The rate constants estimated by eqn 24.86 agree fairly well with experimental rate constants for electron transfer between proteins, as we see in the following Example.

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مواضيع ذات صلة

Surface composition

Surface growth

Electron tunnelling

Controlling chemical reactions with lasers

Spectroscopic observation of the activated complex

Quantum mechanical scattering theory

Classical trajectories

Attractive and repulsive surfaces

The direction of attack and separation

Potential energy surfaces

State-to-state dynamics

Experimental probes of reactive collisions