Electron Transfer. Shunichi Fukuzumi

(2.2):

(2.2)

      where e is elementary charge. According to Eq. (2.1), the logarithm of the electron‐transfer rate constant (log k_ET) is related parabolically to the driving force of electron transfer from electron donors to acceptors (−ΔG_ET) 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 (−ΔG_ET = 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 (−ΔG_ET > 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 (–ΔG_ET) is larger than the reorganization energy (λ) of electron transfer as shown in Figure 2.1. Among the key parameters that govern electron‐transfer reactions (V, ΔG_ET, and λ), the reorganization energy (λ) imposes the most important impact. The primary electron‐transfer processes of photosynthesis are, for example, characterized by an extremely small reorganization energy (λ ∼ 0.2 eV), attained by the protein environment. This aspect is essential to achieving ultrafast charge separation and retarding the energy‐wasting charge recombination, which is highly exergonic (−ΔG = 1.2 eV) [11–15]. Thus, the components of artificial photosynthesis, which are not necessarily natural components in photosynthesis, must have small λ values of electron transfer.

Figure 2.1 (a) Schematic diagram of photoinduced electron transfer of an electron donor–acceptor (D–A) dyad. (b) Driving force dependence of log k_ET with different λ values (for the meaning of λ, see text).

3 Photosynthetic Reaction Center Models

The first candidates of artificial photosynthetic reaction centers are porphyrins, which have been involved in a number of important biological electron‐transfer systems including the primary photochemical reactions of chlorophylls in the photosynthetic reaction centers. Porphyrins contain an extensively conjugated two‐dimensional π‐system and are thereby suitable for efficient electron transfer, because the uptake or release of electrons results in minimal structural and solvation change upon electron transfer, resulting in a small λ value of electron transfer [30]. In addition, rich and extensive absorption features of porphyrinoid systems guarantee increased absorption cross sections and efficient use of the solar spectrum [30]. In contrast with the two‐dimensional porphyrin π‐system, fullerenes contain an extensively conjugated three‐dimensional π‐system [31]. Electron transfer to C₆₀ is highly efficient because of the minimal changes of structure and solvation associated with the electron‐transfer reduction [31–33]. Thus, a series of porphyrin–fullerene linked molecules have been designed and synthesized to mimic the charge‐separation processes in the photosynthetic reaction center, starting from a zinc porphyrin–C₆₀ dyad (ZnP–C₆₀), a ferrocene–zinc porphpyrin–C₆₀ triad (Fc–ZnP–C₆₀), a zinc porphyrin‐free base porphyrin–C₆₀ triad, up to a tetrad (Fc–ZnP–H₂P–C₆₀) [34–39].

The driving force dependence of the electron‐transfer rate constants (k_ET) of these dyad, triad, and tetrad molecules for CS and CR processes is shown in Figure 3.1, where log k_ET is plotted against the driving force (−ΔG_ET) [39]. The lines in Figure 3.1 represent the best fit to Eq. (2.1) (ZnP–C₆₀: λ = 0.66 eV, V = 3.9 cm⁻¹; Fc–ZnP–C₆₀, Fc–H₂P–C₆₀, and ZnP–H₂P–C₆₀: λ = 1.09 eV, V = 0.019 cm⁻¹; Fc–ZnP–H₂P–C₆₀: λ = 1.32 eV, V = 0.00017 cm⁻¹) [39]. The λ‐value increases, whereas the V value decreases with increasing edge‐to‐edge distance in the order of the dyad (R_ee = 11.9 Å), the triad (R_ee = 30.3 Å), and the tetrad (R_ee = 48.9 Å). Such an increase in the λ value with increasing distance results from an increase in the solvent reorganization energy (λ_s), because the λ_s value is known to increase with increasing distance between an electron donor and an acceptor as given by Eq. (3.1):

(3.1)

      where r₁ and r₂ are the radii of the donor and acceptor, r₁₂ is the donor–acceptor distance, ε is the dielectric constant, and n is the refractive index [6,40].

Figure 3.1 Driving force (−ΔG_ET) dependence of intramolecular electron‐transfer rate constants (k_ET) in ZnP–C₆₀ (CS [○]; CR [□]), Fc–ZnP–C₆₀ (•), Fc–H₂P–C₆₀ (▴), ZnP–H₂P–C₆₀ (▪), and Fc–ZnP–H₂P–C₆₀ (△).

      Source: Imahori et al. 2001 [39]. Reproduced with permission of American Chemical Society.

Figure 3.2 Edge‐to‐edge distance (R_ee) dependence of optimal electron‐transfer rate constants (log[k_ET(optimal)/s⁻¹]) in ZnP–C₆₀ dyad, Fc–ZnP–C₆₀ triad, Fc–H₂P–C₆₀ triad, ZnP–H₂P–C₆₀ triad, and Fc–ZnP–H₂P–C₆₀ tetrad. The line represents the best fit to Eq. (2.1) (β = 0.60 Å⁻¹, V₀ = 210 cm⁻¹).

In the case of