Multifaceted aspects of charge transfer

Abstract

Charge transfer and charge transport are by far among the most important processes for sustaining life on Earth and for making our modern ways of living possible. Involving multiple electron-transfer steps, photosynthesis and cellular respiration have been principally responsible for managing the energy flow in the biosphere of our planet since the Great Oxygen Event. It is impossible to imagine living organisms without charge transport mediated by ion channels, or electron and proton transfer mediated by redox enzymes. Concurrently, transfer and transport of electrons and holes drive the functionalities of electronic and photonic devices that are intricate for our lives. While fueling advances in engineering, charge-transfer science has established itself as an important independent field, originating from physical chemistry and chemical physics, focusing on paradigms from biology, and gaining momentum from solar-energy research. Here, we review the fundamental concepts of charge transfer, and outline its core role in a broad range of unrelated fields, such as medicine, environmental science, catalysis, electronics and photonics. The ubiquitous nature of dipoles, for example, sets demands on deepening the understanding of how localized electric fields affect charge transfer. Charge-transfer electrets, thus, prove important for advancing the field and for interfacing fundamental science with engineering. Synergy between the vastly different aspects of charge-transfer science sets the stage for the broad global impacts that the advances in this field have.

Figure 1.

Molecular-orbital (MO) diagrams depicting examples of: (a) ground-state electron transfer, ET; (b) photoinduced electron transfer, PET; and (c) photoinduced hole transfer, PHT. In these examples, PET and PHT show a transition through locally excited, LE, states. A strong coupling between the ground and the CT states allows for direct photo excitation into the latter. Such MO diagrams provide excellent conceptual representation about the manner in which the electrons move between the orbitals during the various processes. Nevertheless, the depicted assumption that the energy level of each of the orbitals does not change as the electron donor, D, and acceptor, A, transition between their singlet and doublet states is a rough approximation at best. Furthermore, MO diagrams do not capture the dependence of the energies of the various states on (1) the solvating media and (2) permanent dipoles. State and Jabłoński diagrams address this issue.

Figure 2.

State diagrams, i.e., energy, 𝓔, vs. generalized coordinates, q, of (a) diabatic and (b) adiabatic electron transfer, depicting transitions between an initial, i, ground state and a final, f, charge-transfer state.

Figure 3.

State diagrams showing diabatic transitions between initial, i, and final, f, states: (a) in the Marcus normal region, (b) under activationless regime, and (c) in the Marcus inverted region, as depicted by varying the driving force, ΔG⁽⁰⁾, while keeping the reorganization energy, λ, constant. (d) Marcus curves for solvents with different polarity, i.e., CH₃CN and CH₂Cl₂, obtained using MH (eq. 4) and MLJ (eq. 6) formalisms, where H_if = 1 meV, λ_ν = 0.1 eV, hν_C = 0.2 eV, r_D = r_A = 4 Å, and R_DA = 9 Å

Figure 4.

State diagrams depicting ISC under: (a) Weak vibronic coupling, where the nested geometry leads to an overlap between the lowest-energy vibrational wavefunction of the S₁ electronic state with the central region of the upper vibrational wavefunctions of the triplet state. In each electronic state, inherently, the density of the wavefunctions in the middle decreases with an increase in the vibrational energy. That is, for nested states, the vibronic overlap decreases with an increase of the ISC driving force. (b) Strong vibronic coupling, where vibrational wave functions from the S₁ and T_n electronic sates overlap at the crossings of the potential-energy surfaces of the electronic states. The densities of the vibrational wavefunctions is, indeed, the highest at the potential-energy surfaces of the wells.

Figure 5.

MO diagrams depicting examples of long-range (a) photoinduced electron transfer, PET, and (b) photoinduced hole transfer, PHT, proceeding via superexchange mechanism with the electron transferring directly from the donor, D, to the acceptor, A, without residing on the bridging units, B. The state diagrams depict improved representation of the energetics of these processes (Figure 6a,c).

Figure 6.

State diagrams depicting long-range CT via: (a) superexchange mechanism; and (b) hopping mechanism. For simplicity, we show DBA systems with only two bridging units that have identical states when oxidized or reduced. (c) Charge distribution in the bridging states, b₁ and b₂, where the transferred electron is on the LUMOs, or the transferred hole is on the HOMOs, of the bridging unites.

Figure 7.

MO diagrams depicting examples of long-range (a) photoinduced electron transfer, PET, and (b) photoinduced hole transfer, PHT, proceeding via charge hopping mechanism where the transferred electron and hole reside, respectively, on the LUMOs and HOMOs of the bridging units. The MO diagrams do not capture all nuances of the energetics of the charge-hopping steps. For example, the Columbic term, W (eq. 1c), in the ΔG⁽⁰⁾ expressions (eq. 1 and 2) reveals that if the two bridging units, B, are identical the b₁ states will be energetically more favourable that b₂ ones, especially for low-polarity media. It can make CR transition from the b₁ to the ground state more likely that the ET or HT transition from the b₁ to the b₂ state. State and Jabłoński diagrams depict these energy-level nuances, such as on Figure 6b, where 𝓔(b₁) ≈ 𝓔(b₂), consistent with B units that are different or negligible Coulombic contributions, W, due to polar media or to large distances between the bridging units and the donor or acceptor.

Figure 8.

MO/band diagram of charge transport through metal-molecule-metal junction where the molecule comprises two bridging units connecting the two electrodes. Along with the electronic coupling between the electrodes and the molecule, the alignment between the Fermi energies, 𝓔_F, and the energy levels of the frontier orbitals determines the mechanism of CTr. (a) Off-resonance (nonresonant) CTr involving electron tunnelling from the cathode to the anode. (b) On-resonance (resonant) electron transport involving (1) electron injection from the cathode to the first bridging unit; (2) hopping along the bridging units; and (3) an electron hop from the reduced bridge to the anode. (c) On-resonance (resonant) hole transport involving (1) an electron hop from the bridge to the anode, i.e., hole injection in the bridge; (2) hole hopping along the HOMOs of the bridging units, i.e., electron transfer from a HOMO of one bridging unit to the vacancy on the HOMO of a neighbouring unit; (3) an electron hop from the cathode to bridge HOMO with a vacancy.

Figure 9.

Bioinspired molecular electret, based on an oligomer of anthranilamide, Aa, residues, along with its permanent electric dipole originating from ordered amide bonds and from the polarization due to the hydrogen-boned formation leading to a collective shift of electron density from the carbonyl oxygens to the amide hydrogens.

Figure 10.

Relative energy levels of the frontier orbitals of electron-rich electret Aa residues comprising different side chains, R₁ and R₂ (Figure 9), as estimated from their reduction potentials for acetonitrile and dichloromethane. The energy levels of the HOMOs are estimated from the half-wave reduction potentials of the oxidized residues, $E_{{\text{Aa}}^{·+}|\text{Aa}}^{\left(1/2\right)}$, i.e., $𝓔\left(\text{eV\hspace{0.17em}vs.\hspace{0.17em}vacuum}\right)=-4.68-F{E}_{{\text{Aa}}^{·+}|\text{Aa}}^{\left(1/2\right)}\left(\text{V\hspace{0.17em}vs.\hspace{0.17em}SCE}\right)$, where F is the Faraday constant. The optical HOMO-LUMO gap, 𝓔₀₀, allowed for estimating the energy levels of the LUMOs, i.e., $𝓔\left(\text{eV\hspace{0.17em}vs}.\text{\hspace{0.17em}vacuum}\right)\approx {𝓔}_{00}-4.68-F{E}_{A{a}^{·+}|\text{Aa}}^{\left(1/2\right)}\left(\text{V\hspace{0.17em}vs}.\text{\hspace{0.17em}\hspace{0.17em}SCE}\right)$.

Figure 11.

Electron-transfer diagram of natural aerobic photosynthesis. Photosystem I (PSI) and photosystem II (PSII) utilize solar energy to drive water splitting. The oxygen-evolving complex of PSII represents the anodic side of this natural photoelectrochecmial cell, and the ferredoxin (Fd) of PSI represents the cathodic side that catalyses the production of a hydride, NADPH, from nicotinamide adenine dinucleotide phosphate (NADP⁺). The diagram depicts only some of the key moieties that mediate the sequence of ET steps: P700 and P680 are the special pairs of PSI and PSII, respectively; PQ is a plastoquinone responsible not only for diffusive electron transport, but also for pumping protons across the membrane; cytb₆f is the cytochrome b₆f complex; and Pc is a copper-containing protein, plastocyanin.

Figure 12.

Principles of electrocardiography, EKG. Ion transport processes, resulting in collective charge shifts within the heart, lead to polarization and depolarization, depicted by the vector of a cumulative electric dipole moment. Changes in the angle and the magnitude of this vector yields measurable signals.

Figure 13.

CT with birnessite minerals drives the anaerobic respiration of Shawanella sp. As(III)|As(V) redox couple acts as a shuttle to carry holes from Mn(IV) from the birnessite to the bacterial cell respiratory oxidation of lactate, C₃H₅O₃^–. The CO2 produced from the respiration forms carbonic acid and leads to the precipitation of the Mn²⁺ ions released in the aqueous media from the reduction of Mn(IV) from the mineral.

Figure 14.

Photoredox catalysis proceeding via (a) an oxidative quenching cycle, and (b) a reductive quenching cycle. The rate constants, k_em and k_nd, depict the photoemission (radiative) and non-radiative decays of the excited photocatalyst, PC*: sub represents a substrate or a key intermediate; [red] and [ox] represent a sacrificial electron donor and acceptor, respectively, if needed.

Figure 15.

Photoelectrochemical cell, PEC, for water splitting. The electrodes are semiconductors with different bandgaps and band-edge energies that allow cathodic water reduction and anodic oxidation to O₂. For broad-band semiconductors, photo sensitization with dyes or QDs is paramount to bring the absorption to the visible and NIR spectral regions. Auxiliary catalysts on the electrode surfaces can also improve the kinetics of O₂ and H₂ production.