Inhomogeneous electrochemiluminescence. I: Integral encounter theory of kinetics and yield

The generation of excited triplet luminophor by recombination of electrochemically injected ions is calculated. The reversibility of triplet production is shown to affect insignificantly the triplet accumulation and their quantum yield. The free energy dependence of the latter is specified and fitted to the available experimental data.The maximal quantum yield of triplet luminescence found experimentally is sometimes less than 1, even when the excitation is the sole result of charge recombination. This phenomenon may be a result of the biexcitonic annihilation of triplets produced in a narrow strip at the border between the space separated anions and cations. The kinetics of this process is calculated and the maximal yield of fluorescence is shown to decrease with excitation life time and increase with triplet diffusion out of the strip. Alternatively, the maximal quantum yield may be reduced due to the trivial triplet quenching by neutral precursors of ions.     

The theory of electron transfer

This article provides an overview of the theory of electron transfer. Emphasis is placed on the history of key ideas and on the definition of difficult terms. Among the topics considered are the quantum formulation of electron transfer, the role of thermal fluctuations, the structures of transition states, and the physical models of rate constants. The special case of electron transfer from a metal electrode to a molecule in solution is described in detail.     

Nonadiabatic theory of electron transfer

Tunneling between potential wells is considered as affected by random nonadiabatic change in the resonance condition. A general expression is derived for the transition probability on the assumption that the process involves only two states of the discrete spectrum. Detailed consideration is given to the case of an electron localized by the polarized layer it produces.     

A model for electrochemical electron transfer with strong electronic coupling

Electron exchange between a metal or semiconducting electrode and a solvated reactant is calculated by Green-function techniques. In the wide band approximation the time development of a system prepared in a definite electronic state can be calculated exactly. The results are valid for all coupling strengths, and are applied both to photoexcited and to thermally-induced transfer.     

Proton-coupled electron transfer from tyrosine: a strong rate dependence on intramolecular proton transfer distance

Proton-coupled electron transfer (PCET) was examined in a series of biomimetic, covalently linked Ru(II)(bpy)(3)-tyrosine complexes where the phenolic proton was H-bonded to an internal base (a benzimidazyl or pyridyl group). Photooxidation in laser flash/quench experiments generated the Ru(III) species, which triggered long-range electron transfer from the tyrosine group concerted with short-range proton transfer to the base. The results give an experimental demonstration of the strong dependence of the rate constant and kinetic isotope effect for this intramolecular PCET reaction on the effective proton transfer distance, as reflected by the experimentally determined proton donor-acceptor distance.     

Stereodifferentiation in the formation and decay of the encounter complex in bimolecular electron transfer with photoactivated acceptors

Experimental evidence has been obtained for the involvement of encounter complexes between both enantiomers of a pi,pi* triplet excited ketone and a chiral phenol or indole. Determination of the pre-equilibrium constants (K(EC)) and the intrinsic decay rate constants (kd) indicates a significant stereodifferentiation in both steps of the quenching process.     

Semiclassical treatments of electron transfer rate from weak to strong electronic coupling regime

Electron transfer (ET) rate is a fundamental parameter to characterize ET processes in physical, chemical, material and biologic sciences. It is affected by a number of quantum phenomena, such as nuclear tunneling, curve crossing, quantum interference, and the coupling to the environment. It is thus a challenge to accurately evaluate the ET rate since one has to incorporate both quantum effects and dissipation. In this review article, we present several semiclassical theories proposed in our group to cover the regime from weak to strong electronic coupling. Their applications to some concrete systems are also shown.     

On the theory of tunnelling in electron and proton transfer reactions

The concept of tunnelling in the theory of electron and proton transfer reactions has recently been questioned on the ground that the situation is a non-stationary one. It has been suggested that time-dependent perturbation theory should be applied to obtain the quantum mechanical transition probability. We have done this for a square barrier. The result for most reactions is the same as obtained by the WKB approximation.     

Biorthonormal electronic basis sets in the theory of electron transfer reactions

We have used the quantum-chemical concept of biorthonormal electronic basis functions to derive the two-centre electron exchange integrals in non-diabatic electron transfer reactions. It is shown that only non-diagonal parts induce the transfer corresponding to inclusion of the diagonal parts in the zero-order hamiltonians. This result coincides with the result derived previously by means of scattering theory.     

Direct calculation of electron transfer parameters through constrained density functional theory

It is shown that constrained density functional theory (DFT) can be used to access diabatic potential energy surfaces in the Marcus theory of electron transfer, thus providing a means to directly calculate the driving force and the inner-sphere reorganization energy. We present in this report an analytic expression for the forces in constrained DFT and their implementation in geometry optimization, a prerequisite for the calculation of electron transfer parameters. The method is then applied to study the symmetric mixed-valence complex tetrathiafulvalene-diquinone radical anion, which is observed experimentally to be a Robin-Day class II compound but found by DFT to be in class III. Constrained DFT avoids this pitfall of over-delocalization and provides a way to find the charge-localized structure. In another application, driving forces and inner-sphere reorganization energies are calculated for the charge recombination (CR) reactions in formanilide-anthraquinone (FA-AQ) and ferrocene-formanilide-anthraquinone (Fc-FA-AQ). While the two compounds have similar reorganization energies, the driving force in FA-AQ is 1 eV larger than in Fc-FA-AQ, in agreement with experimental observations and supporting the experimental conclusion that the anomalously long-lived FA-AQ charge-separated state arises because the electron transfer is in the Marcus inverted region.     

The sign of electron exchange in random radical encounter pairs

The electron spin polarization pattern observed in independently generated radicals (F-pairs) produced by both laser photolysis and pulse radiolysis in water, alcoholic, and hydrocarbon solvents is E/A, low-field emission, high-field enhanced absorption. Thus, the sign of the exchange coupling in F-pairs is negative contrary to the recent suggestion that exchange coupling is positive in F-pairs.     

The new theory of electron transfer: application to the photosynthetic reaction centre

Based on recent developments in the theory of electron transfer, we prove that a non-polar environment is needed to maintain the high efficiency and chemical integrity of the photosynthetic reaction centre. We also determine the Gibbs energy diagram for the primary act of charge separation in photosynthesis, and propose an equivalent circuit that captures the principal features of the entire acceptor side of the electron transport chain in photosystem II.     

Inhomogeneous electrochemiluminescence. II Markovian encounter theory of the phenomenon

The free energy dependence of the electro-chemiluminescence quantum yield is specified, with the Markovian encounter theory accounting for the reversibility of triplet production competing with the irreversible recombination to the ground state. It is shown that diffusional ion recombination is highly inhomogeneous in space. It proceeds at either large positive ionization free energy (mainly to the triplet product) or at large negative free energy when recombination to the ground state dominates. On the contrary at medium free energies, the quasi-resonant generation of triplets is under kinetic control and therefore much more homogeneous. In this case, both recombination products are generated in comparable amounts.The multiple reversible ionization is shown to act as an independent quenching mechanism previously unknown. The role of the triplet quenching at the electrode is also specified. These effects reduce noticeably the luminescence quantum yield but only at larger triplet life times and in different free energy regions.     

Photoinduced intramolecular electron transfer in ruthenium and osmium polyads: insights from theory

Ru(II) and Os(II) complexes (P) of [4'-(p-phenyl)]terpyridyl ligand (ptpy) derivatized with an electron acceptor (A) of the triphenylpyridinium (H3TP+) type have been recently proposed as functional models for electron-transfer (ET) processes in the context of artificial photosynthesis. These inorganic dyads, P-A, are expected to undergo intramolecular photoinduced ET to form a charge separated (CS) state of pivotal interest. To draw a complete picture of possible ET processes, the ground- and excited-state properties of these complexes, both in their native and monoreduced forms, have been studied by the means of density functional theory (DFT). A time-dependent-DFT approach (TDDFT) was used to interpret the electronic spectra, while additional spectroscopic measurements have been carried out in order to complete the available experimental information and to further confirm the theoretical issues. Besides the noticeable quantitative agreement between computed and experimental absorption spectra, our results allow us to clarify, by first principles, the actual nature and interplay of the electronic and geometrical coupling between the acceptor moiety and the photosensitizer. The possibility of a direct (optical) ET from the ground state to the targeted *[P+-A-] CS state is theoretically postulated and found to be consistent with available photophysical data (transient absorption spectroscopy). Concerning backward ET (from the CS state), the occurrence of a quinoidal-like electronic redistribution inherent to the photoreduced acceptor-ligand is proposed to favor efficient charge recombination.     

Tetrahalotetraazafulvalenes — New strong electron acceptors

Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 10, p. 1421, October, 1989.