is called the Marcus inverted region, which is discussed in detail later [6]. The importance of the Marcus inverted region is well recognized in the function of the photosynthetic reaction center (vide infra) [7–9].
The photoinduced electron‐transfer processes occur in a membrane‐bound protein in the photosynthetic reaction center, which contains a number of cofactors, including four bacteriochlorophylls (BChl) as shown in Figure 1.1 [10]. The central part is referred to as the special pair [(BChl)2], while the other two bacteriochlorophylls (BChl) are referred to as “accessory” bacteriochlorophylls. There are also two bacteriopheophytins (BPhe), two ubiquinones (QA and QB), and a non‐heme iron atom (not shown in Figure 1.1), which together with the special pair are organized in pseudo‐C2 symmetry forming two branches (A and B). Light‐initiated charge separation occurs between the special pair [(BChl)2] and the neighboring pigments, leading to a radical cation [(BChl)2·+]. Despite the quasi‐symmetrical arrangement of the cofactors, the electrons are transported unidirectionally along the A‐branch of the reaction center [11–13], which suggests that the symmetry‐breaking specific interactions with the protein are fundamentally important. Light‐initiated charge separation occurs between the special pair [(BChl)2] and the neighboring pigment (BPhe), leading to the radical cation [(BChl)2·+] and the radical anion (BPhe·−). Without QA, back electron transfer from BPhe·− to (BChl)2·+ occurs with the lifetime of 10 ns to regenerate (BChl)2 and BPhe·−. In such a case there is no way for the energy conversion to occur when the photon energy is only converted to heat. In the presence of QA, electron transfer from BPhe·− to QA occurs at a much faster rate than the back electron transfer from BPhe·− to (BChl)2·+ despite the smaller driving force of the electron transfer than that of the back electron transfer. This has been made possible because of the Marcus inverted region. The subsequent electron transfer from QA·− to QB also occurs at a much faster rate than the back electron transfer from QA·− to (BChl)2·+ because of the much longer distance between QA·− and (BChl)2·+ than that between QA·− and QB. The final charge‐separated state [(BChl)2·+ and QB·−] is obtained with a nearly 100% quantum yield, having a lifetime of seconds, which is long enough for further chemical reactions [14,15]. Thus, the Marcus inverted region plays a pivotal role in the charge‐separation processes in the photosynthetic reaction center.
Figure 1.1 Cofactors and structure of photosynthetic reaction center of purple bacteria.
As the reverse process of photosynthesis, in which the four‐electron oxidation of water is achieved by using solar energy, the highly exergonic four‐electron reduction of oxygen to water is essential to maintain the life of an aerobic organism by respiration [16–18]. Cytochrome c oxidases (CcOs) catalyze efficiently the reduction of molecular oxygen to water by the soluble electron carrier, cytochrome c [16–18]. In both the four‐electron oxidation of water in photosynthesis and the four‐electron reduction of O2 in respiration, electron transfer is accompanied by proton transfer, which is referred to as proton‐coupled electron transfer (PCET) [19–24]. Metal ions also play important roles in controlling electron transfer in metal ion‐coupled electron transfer (MCET) [24–27].
This book describes mechanisms and applications of electron transfer inspired by electron‐transfer processes in photosynthesis and respiration. The first rational design of a variety of donor–acceptor covalently linked ensembles including dyads, triads, tetrads, and pentads is described based on the Marcus theory of electron transfer, enabling to mimic the energy‐transfer and electron‐transfer processes in the photosynthetic reaction center. A specific challenge involves construction of simple donor–acceptor dyads, which afford longer lived and higher energy charge separated (CS) states than the natural system. The photosynthetic reaction center model compounds can be applied as effective redox catalysts in various catalytic chemical transformations. Then, the fundamental concepts of PCET and MCET are discussed and they are applied to developing efficient catalysts for multi‐electron redox processes such as oxidation of water and reduction of dioxygen and carbon dioxide.
2 Marcus Theory of Electron Transfer
The dependence of rate constants of electron transfer on the driving force of electron transfer is well analyzed on the basis of the Franck–Condon principle (vide supra) by the Marcus theory of electron transfer, which provides basic principles to analyze the rate constant of electron transfer quantitatively [6]. According to the Marcus theory of electron transfer [6], the rate constant of nonadiabatic intramolecular electron transfer (kET) is given by Eq. (2.1):
(2.1)
where V is the electronic coupling matrix element, h is the Planck constant, T is the absolute temperature, ΔGET is the free energy change of electron transfer, and λ is the reorganization energy of electron transfer [6]. The ΔGET values are determined from the one‐electron oxidation potentials (Eox) of electron donors (D) and the one‐electron reduction potentials (Ered) of electron acceptors by Eq. (2.2):
(2.2)
where e is elementary charge. According to Eq. (2.1), the logarithm of the electron‐transfer rate constant (log kET) is related parabolically to the driving force of electron transfer from electron donors to acceptors (−ΔGET) and the reorganization energy (λ) of electron transfer, that is, the energy required to structurally reorganize the donor, acceptor, and their solvation spheres upon electron transfer [6].
When the magnitude of the driving force of electron transfer becomes the same as the reorganization energy (−ΔGET = λ), the electron‐transfer rate reaches a maximum and is basically controlled by the magnitude of electronic coupling (V) between the donor and acceptor moieties (Eq. (2.1)). Upon passing this thermodynamic maximum, the highly exothermic region of the parabola (−ΔGET > λ) is entered, in which an additional increase of the driving force results in an actual slowdown of the electron‐transfer rate, due to an increasingly poor vibrational overlap of the product and reactant wave functions. This highly exergonic range is generally referred to as the Marcus inverted region [6–8,28,29]. In such a case, the magnitude of the reorganization energy is the key parameter to control the electron‐transfer process. The smaller the reorganization energy, the faster is the forward photoinduced charge‐separation (CS) process, but the charge‐recombination (CR) process becomes slower when the driving force for back electron transfer (–ΔGET) is larger than the reorganization energy (λ) of electron transfer as shown in Figure 2.1. Among the
