65 years of electron transfer Free

Electron transfer (ET), as a simplest chemical reaction, is the fundamental step in the oxidation–reduction reaction, involved in a large class of electrochemistry, biochemistry, and organic and inorganic chemistry. 65 years have passed since the introduction of the series of work on the free energies and the rates for ET reactions.^1,2 This contribution began a rapid transformation of the field that advanced through experimental work by Sutin,³ Taube,⁴ and others and detailed theoretical treatments by Marcus, Hush, Levitch, Dogonadze, and Jortner.^5–11 For more than half of a century, ET has become an important ingredient in many modern research themes, which this special topic collection aimed to cover.

In the ET process, a charge is moved from one spatial part of the system to another, and thus, the energy difference of the two electronic states is coupled to the dielectric polarization from the environment, leading to the activation energy in the model of Rudy’s derivation. This concept serves as an important starting point for the quantum dissipative dynamics under various non-equilibrium statistical mechanical treatments, which is also generalized for linear and nonlinear spectroscopy. Discussions on various approximations, predictions, and extensions followed, such as the inner vs outer reorganization energy, inverted region behavior, adiabatic vs nonadiabatic models, solvent and solute dynamics, quantum vs classical treatment of nuclei motion, and strong vs weak coupling limit. The theoretical account of two-state and multi-state problems has been useful not only for ET, but it has also influenced the understanding of other processes, such as energy transfer, proton transfer, and proton-coupled electron transfer as well as nonlinear spectroscopy and, more recently, singlet fission.

Electronic structure characterization for ET has offered a solid base for the theoretical expressions of the rates and dynamic. With the availability of electronic structure tools, estimation of parameters determining the rate of ET, such as the electronic coupling and the reorganization energy, both inner and outer ones, has been possible. Systems with ET characteristics also pose challenges to electronic structure calculations. Excitations with charge-transfer characteristics are hard to describe with a low level of calculation, such as the typical time-dependent density functional theory (TDDFT), and improvements and discussion in this aspect have been an important area. Simulations for the dynamics of ET in various complex systems have also been an important ingredient in the ET literature.

ET is naturally important in biology, as many important redox reactions take place in living cells, from energy conversion processes of metabolism and photosynthesis to DNA synthesis and repair, and the function of photoreceptors. The conversion of solar energy involves an excited state charge transfer, which is the first chemical reaction in photosynthesis. Artificially designed systems to study ET across biological molecules, such as protein and DNA, have also been an important area of study, with important focus on superexchange vs hopping mechanisms.

ET and transport mechanisms have also been investigated in the context of molecular and organic electronics. In artificial systems, such as various kinds of solar cells and light-emitting organic devices, the interconversion of light and electric energy as well as the charge transport in semiconducting materials are also important areas with ET. The development of artificial photosynthetic systems and photoredox catalysis is another important and currently very active area, where ET is coupled to catalytic chemistry. Experimental and theoretical work in these areas have been important developments.

As a “snapshot” for the current status, much of the cutting-edge research development related to ET is included in this collection.

In addition to the free energy change, the Marcus rate expression requires two additional parameters, the electronic coupling and the reorganization energy, often denoted as λ. λ describes the extent of energy change due to nuclear degrees of freedom for both intra- and intermolecular motions. It is also called “electron–phonon coupling” in the condensed matter physics literature. λ plays an important role in determining the ET rates and the charge-transporting behavior, and understanding factors influencing the magnitudes of λ has been an important area of study. In the present collection, Nuraliev et al. and Peralta et al. reported different aspects of electron–phonon coupling, the association with Raman spectroscopy, and the perseveration of coherence.^12,13 Takeuchi et al. report on an experimental study of coherence in ultrafast electron transfer.¹⁴ The nuclear tunneling effect as well as formulation with semi-classical treatment are also reported.^15,16

To study ET with electronic structure methods, it is often necessary to include excited states for both charge-transfer states and photo-induced ET cases. TDDFT and its approximated version, the Tamm–Dancoff approximation (TDA), are often the “go-to” methods among very few affordable excited models for molecules of practical size. However, typical functionals are prone to large errors for states with charge-transfer characteristics. In this aspect, it is important to develop good long-range corrected density functionals, the simplest fix for the charge-transfer states, as reported in one work in this collection.¹⁷ 

Theoretical development on the ET rate expression under different regimes of physical conditions has been important, as seen in Parson’s work in this collection.¹⁸ The electronic coupling in the Marcus theory has been readily calculated with proper (but not unique) definition of the diabatic states. It has been possible to build machine-learning models for a quick calculation, as Wang et al. have shown with the use of artificial neural networks.¹⁹ Obtaining coupling with the fragment molecular orbital approach, a scheme for treating large systems, such as proteins and enzymes, is also discussed.²⁰ 

With the vast advancement of computational software and hardware, it has been possible to simulate the dynamics of a charge-transporting system with both electronic and nuclei degrees of freedom included. Such approaches are useful especially for complicated systems that cannot be easily described with standard ET theories. Systems with multiple sites, large electronic couplings, relatively weak electron–phonon couplings, or nuclear dynamics across different time scales can now be studied. In this collection, we are pleased to find methodological contributions for monitoring vibrational energy flows²¹ and for electronic excited states.²² It is important to analyze for the effects of charge-transfer in dynamics simulations,^23,24 where important application can be made for optoelectronic devices models, such as the photocatalytic effects in TiO₂.²⁵ 

ET has been a field that tightly coupled theories, computation, and experiments. The early proposal for molecular rectifier²⁶ has inspired much of single molecular junction studies. Works from Petrov et al. described the electroluminescence generation with a gate voltage.²⁷ A work from Sowa and Marcus described the system with entropic effects from the solvent.²⁸ A highly related subject is nanoparticles and quantum dots, where the Auger recombination and multiexciton generation was reported with halogenated Si nanocrystals.²⁹ A combined theoretical and experimental work on the photophysics graphene quantum dot assemblies with axially coordinated cobaloxime catalysts was also included in the present collection.³⁰ 

ET at the interfaces of electrolyte and electrode, or liquid–liquid interfaces, has been an active and important area, including problems in the lithium battery.³¹ Problems addressed here include the reorganization energy at the interface,³² the effect of density-of-states for non-metal electrodes,³³ and electric field effects, in this case at micelle surfaces.³⁴ Related work on the interfacial charge transfer dynamics of dye-sensitized semiconductors for use in solar cells or solar fuel devices are reported,³⁵ including the effects of increasing inner the reorganization energy on charge recombination.³⁶ Xie et al. report a computational study of ET in polymer blends in the context of organic solar cells.³⁷ The theory of ET has been indispensable in understanding experimental studies of photosynthesis, including the S-state transitions of the oxygen evolving complex³⁸ and in the charge transport in semiconducting polymers and arrays of organic molecules.^39,40 The electrocatalytic reduction of CO₂ is also a very active area of research that is included here.⁴¹ In achieving higher solar energy conversion efficiency, singlet fission has been an important area of study, in which both theoretical and experimental efforts are also tightly coupled. In singlet fission, much of the effort has been laid in the charge-transfer characteristic in the excited states involved,⁴² and the implication for nonlinear optics is also reported.⁴³ 

The study of charge separation and charge recombination has been carried out in a large array of different systems. In this collection, Angulo and Rosspeintner and Nançoz et al. reported photoinduced bimolecular ET with effects of diffusion and formation of weak vs strong exciplexes.^44,45 Observations for the autoxidation of tartaric acids is reported.⁴⁶ Studies on photoredox photosensitizers are also seen,⁴⁷ which is in the line of developing photoredox catalysis and artificial photosynthesis. Covalently tethered molecular dyads and triads^48–53 are important model systems for artificial photosynthesis that convert solar energy into chemical energy, where the understanding of photophysics and photochemistry heavily involves charge transfer. Various processes, such as light-harvesting,⁵⁴ spin-polarization and magnetic field effects,^49,53 photoisomerization,⁵⁵ vibrational decoherence,¹⁴ and excitonic quenching,⁵⁶ are reported with ET in various systems. This collection also includes a report on the excited state dynamics of metallo-DNA.⁵⁷ Megarity et al. report an experimental technique with protein film electrochemistry for studying redox chemistry with enzymes,⁵⁸ obtaining details that were not available in conventional kinetics studies.

Here, we must say a sad farewell to Bob Cave, one of the guest editors for this thematic collection. Bob was a widely accomplished giant in the field of electronic structure theory, covering many fundamental processes in physical chemistry and chemical physics. Bob had a broad impact promoting our understanding of molecular chemical behavior in vacuum and condensed phases, primarily chemical kinetics (especially charge transfer) and molecular spectroscopy. In extremely productive and insightful ways, he showed how the basic ingredients of these two fields can be related and captured in compact electronic structure models easily accessible to a broad component of the chemical community, with necessary model parameters easily extractable using current electronic structure computational techniques. While Bob was primarily a theorist, his work had the great value of being closely related to timely experimental results, and he had a joint NSF grant with an experimentalist to focus in depth on these interrelationships.

His contribution to science was conveyed not only by his extensive publications (more than 100 papers in top journals and book chapters) but also in the broader context through national and international meetings, via invited presentations, and as organizer of several sessions at the National American Chemical Society meetings and a Gordon Research Conference. He also received a prestigious Camille and Henry Dreyfus Teacher-Scholar Fellowship. An additional valuable benefit to science was his service as a National Science Foundation Visiting Program Director in Chemistry.

As successful as Bob was in implementing his primary passion, basic electronic structure, and associated computational efforts, his talent as a teacher and administrator led to a “tug of war” in which he was frequently asked to take time out, serving as the Associate Dean for Academic Affairs, Dean of the Faculty, and Vice President for Academic Affairs at his institution, Harvey Mudd College.

Bob came up with ground-breaking advances in his research, but with an endearing humility and ambiance and with down to earth common sense and humor, for example, the title of one of his invited talks, “Butadiene-the simplest of polyenes? Not by a long shot.” It was always a great pleasure for Bob’s collaborators to work with him, in some cases over several decades, relishing his wonderful friendly spirit present at all times. His many students also benefited immensely from his close contact, allowing them to interact with their colleagues through numerous presentations at regional and national meetings.

As we pay tribute to Bob Cave’s massive accomplishments, it is reassuring to know that their great impact for so many parts of the scientific community will live on.

This collection reflects some of the remarkable breadth of ET and its impact on chemistry, physics, and biology and the fundamental importance of electron transfer theory to guide our understanding of these processes. Marcus has personally contributed a note, as included in this collection,⁵⁹ which is a short description of the ideas being evolved during that time. On the other hand, we are saddened by the loss of Bob Cave. With Bob’s involvement in shaping the perspectives and in the invitations that eventually led to this JCP special topic collection, we believe that this collection will continue to remind us of his warm dedication and brilliant inspiration to science and education for many years to come.

We thank JCP editor Emily Weiss and Journal Managers Erinn Brigham and Jenny Stein for their assistance.