On the Coherent Description of Diffusion-Influenced Fluorescence Quenching Experiments

Bimolecular photo-induced electron transfer enlightened by diffusion

Photochemical electron transfer between freely diffusing molecules has been studied extensively. Here, we try to elucidate how much these works have contributed to the understanding of electron transfer. To this end, we have revisited the work performed in the experimental and theoretical areas of concern from the beginning of the 20th century up to the present day. We present a critical look at the major contributions and compile the current picture of a variety of phenomena around electron transfer in solution. This is based on two main developments, besides the theory of Marcus: encounter theories of diffusion and laser techniques in time-resolved spectroscopy.

Bimolecular photoinduced electron transfer in non-polar solvents beyond the diffusion limit

Electron transfer (ET) quenching dynamics in non-polar solvents are investigated using ultrafast spectroscopy with a series of six fluorophore/quencher pairs, covering a driving force range of more than 1.3 eV. The intrinsic ET rate constants, k₀, deduced from the quenching dynamics in the static regime, are of the order of 10¹²-10¹³ M^-1 s^-1, i.e., at least as large as in acetonitrile, and do not exhibit any marked dependence on the driving force. A combination of transient electronic and vibrational absorption spectroscopy measurements reveals that the primary product of static quenching is a strongly coupled exciplex that decays within a few picoseconds. More weakly coupled exciplexes with a longer lifetime are generated subsequently, during the dynamic, diffusion-controlled, stage of the quenching. The results suggest that static ET quenching in non-polar solvents should be viewed as an internal conversion from a locally excited state to a charge-transfer state of a supermolecule rather than as a non-adiabatic ET process.

Magnetic field effect on ion pair dynamics upon bimolecular photoinduced electron transfer in solution

The dynamics of the ion pairs produced upon fluorescence quenching of the electron donor 9,10-dimethylanthracene (DMeA) by phthalonitrile have been investigated in acetonitrile and tetrahydrofuran using transient absorption spectroscopy. Charge recombination to both the neutral ground state and the triplet excited state of DMeA is observed in both solvents. The relative efficiency of the triplet recombination pathway decreases substantially in the presence of an external magnetic field. These results were analyzed theoretically within the differential encounter theory, with the spin conversion of the geminate ion pairs described as a coherent process driven by the hyperfine interaction. The early temporal evolution of ion pair and triplet state populations with and without magnetic field could be well reproduced in acetonitrile, but not in tetrahydrofuran where fluorescence quenching involves the formation of an exciplex. A description of the spin conversion in terms of rates, i.e., incoherent spin transitions, leads to an overestimation of the magnetic field effect.

Photoinduced Bimolecular Electron Transfer in Ionic Liquids: Cationic Electron Donors

Recently, we have reported a systematic study of photoinduced electron-transfer reactions in ionic liquid solvents using neutral and anionic electron donors and a series of cyano-substituted anthracene acceptors [ Wu , B. ; Maroncelli , M. ; Castner , E. W. Jr Photoinduced Bimolecular Electron Transfer in Ionic Liquids . J. Am. Chem. Soc. 139 , 2017 , 14568 ]. Herein, we report complementary results for a cationic class of 1-alkyl-4-dimethylaminopyridinium electron donors. Reductive quenching of cyano-substituted anthracene fluorophores by these cationic quenchers is studied in solutions of acetonitrile and the ionic liquid 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide. Varying the length of the alkyl chain permits tuning of the quencher diffusivities in solution. The observed quenching kinetics are interpreted using a diffusion-reaction analysis. Together with results from the prior study, these results show that the intrinsic electron-transfer rate constant does not depend on the quencher charge in this family of reactions.

Optical transient absorption experiments reveal the failure of formal kinetics in diffusion assisted electron transfer reactions

The charge separation yield is shown to be strongly influenced by the distance dependence of the reactivity, viscosity and concentration and cannot be disentangled from the preceding events.

Influence of the excitation light intensity on the rate of fluorescence quenching reactions: pulsed experiments

The effect of multiple light excitation events on bimolecular photo-induced electron transfer reactions in liquid solution is studied experimentally. It is found that the decay of fluorescence can be up to 25% faster if a second photon is absorbed after a first cycle of quenching and recombination. A theoretical model is presented which ascribes this effect to the enrichment of the concentration of quenchers in the immediate vicinity of fluorophores that have been previously excited. Despite its simplicity, the model delivers a qualitative agreement with the observed experimental trends. The original theory by Burshtein and Igoshin (J. Chem. Phys., 2000, 112, 10930-10940) was created for continuous light excitation though. A qualitative extrapolation from the here presented pulse experiments to the continuous excitation conditions lead us to conclude that in the latter the order of magnitude of the increase of the quenching efficiency upon increasing the light intensity of excitation, must also be on the order of tens of percent. These results mean that the rate constant for photo-induced bimolecular reactions depends not only on the usual known factors, such as temperature, viscosity and other properties of the medium, but also on the intensity of the excitation light.

Characterization of dimethylsulfoxide/glycerol mixtures: a binary solvent system for the study of “friction-dependent” chemical reactivity

The properties of binary mixtures of dimethylsulfoxide and glycerol, measured using several techniques, are reported.

Bimolecular photoinduced electron transfer reactions in liquids under the gaze of ultrafast spectroscopy

Because of their key role in many areas of science and technology, bimolecular photoinduced electron transfer reactions have been intensively studied over the past five decades. Despite this, several important questions, such as the absence of the Marcus inverted region or the structure of the primary reaction product, have only recently been solved while others still remain unanswered. Ultrafast spectroscopy has proven to be extremely powerful to monitor the entire electron transfer process and to access, with the help of state-of-the-art theoretical models of diffusion-assisted reactions, crucial information like e.g. the intrinsic charge separation dynamics beyond the diffusion limit. Additionally, extension of these experimental techniques to other spectral regions than the UV-visible, such as the infrared, has given a totally new insight into the nature, the structure and the dynamics of the key reaction intermediates, like exciplexes and ions pairs. In this perspective, we highlight these recent progresses and discuss several aspects that still need to be addressed before a thorough understanding of these processes can be attained.

Exciplexes versus Loose Ion Pairs: How Does the Driving Force Impact the Initial Product Ratio of Photoinduced Charge Separation Reactions?

Many donor-acceptor systems can undergo a photoinduced charge separation reaction, yielding loose ion pairs (LIPs). LIPs can be formed either directly via (distant) electron transfer (ET) or indirectly via the dissociation of an initially formed exciplex or tight ion pair. Establishing the prevalence of one of the reaction pathways is challenging because differentiating initially formed exciplexes from LIPs is difficult due to similar spectroscopic footprints. Hence, no comprehensive reaction model has been established for moderately polar solvents. Here, we employ an approach based on the time-resolved magnetic field effect (MFE) of the delayed exciplex luminescence to distinguish the two reaction channels. We focus on the effects of the driving force of ET and the solvent permittivity. We show that, surprisingly, the exciplex channel is significant even for an exergonic ET system with a free energy of ET of -0.58 eV and for the most polar solutions studied (butyronitrile). Our findings demonstrate that exciplexes play a crucial role even in polar solvents and at moderate driving forces, contrary to what is usually assumed.

Bimolecular photoinduced electron transfer beyond the diffusion limit: the Rehm-Weller experiment revisited with femtosecond time resolution

To access the intrinsic, diffusion free, rate constant of bimolecular photoinduced electron transfer reactions, fluorescence quenching experiments have been performed with 14 donor/acceptor pairs, covering a driving-force range going from 0.6 to 2.4 eV, using steady-state and femtosecond time-resolved emission, and applying a diffusion-reaction model that accounts for the static and transient stages of the quenching for the analysis. The intrinsic electron transfer rate constants are up to 2 orders of magnitude larger than the diffusion rate constant in acetonitrile. Above ∼1.5 eV, a slight decrease of the rate constant is observed, pointing to a much weaker Marcus inverted region than those reported for other types of electron transfer reactions, such as charge recombination. Despite this, the driving force dependence can be rationalized in terms of Marcus theory.

Magnetic field effects on exciplex-forming systems: the effect on the locally excited fluorophore and its dependence on free energy

This study addresses magnetic field effects in exciplex forming donor-acceptor systems. For moderately exergonic systems, the exciplex and the locally excited fluorophore emission are found to be magneto-sensitive. A previously introduced model attributing this finding to excited state reversibility is confirmed. Systems characterised by a free energy of charge separation up to approximately -0.35 eV are found to exhibit a magnetic field effect on the fluorophore. A simple three-state model of the exciplex is introduced, which uses the reaction distance and the asymmetric electron transfer reaction coordinate as pertinent variables. Comparing the experimental emission band shapes with those predicted by the model, a semi-quantitative picture of the formation of the magnetic field effect is developed based on energy hypersurfaces. The model can also be applied to estimate the indirect contribution of the exchange interaction, even if the perturbative approach fails. The energetic parameters that are essential for the formation of large magnetic field effects on the exciplex are discussed.

Contact and Distant Luminescence Quenching in Solutions

The limitations and advantages of modern encounter theories of remote transfer are discussed, as well as their application to particular transfer reactions assisted by encounter diffusion. Comparison is made with contact multiparticle theories, Brownian dynamic simulations, and the actual experimental data requiring a distant description of energy and/or electron transfer.

The Rehm-Weller experiment in view of distant electron transfer

The driving-force dependence of bimolecular fluorescence quenching by electron transfer in solution, the Rehm-Weller experiment, is revisited. One of the three long-standing unsolved questions about the features of this experiment is carefully analysed here, that is, is there a diffusional plateau? New experimental quenching rates are compiled for a single electron donor, 2,5-bis(dimethylamino)-1,3-benzenedicarbonitrile, and eighteen electron acceptors in acetonitrile. The data are analysed in the framework of differential encounter theory by using an extended version of the Marcus theory to model the intrinsic electron-transfer step. Only by including the hydrodynamic effect and the solvent structure can the experimental findings be well modelled. The diffusional control region, the "plateau", reveals the inherent distance dependence of the reaction, which is shown to be a general feature of electron transfer in solution.