Mixed-Valence Systems E-Book

• Herausgeber: Wiley-VCH GmbH
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 999

Veröffentlichungsjahr: 2023

Beschreibung

Mixed-Valence Systems

Comprehensive overview on the advanced development of mixed-valence chemistry

Mixed-Valence Systems: Fundamentals, Synthesis, Electron Transfer, and Applications covers all topics related to the theory and experimental results of mixed-valence systems, including the design, synthesis, and applications of mixed-valence compounds containing inorganic, organometallic and organic redox-active centers. The text also covers the recent advances in mixed-valence chemistry, including the development of new mixed-valence systems, transition of mixed valency, better understanding of the spectral characteristics of intervalence charge transfer, and controllable electron transfer related to molecular electronics.

In Mixed-Valence Systems, readers can expect to find detailed information on sample topics such as:

• Characterization and evaluation of mixed-valence systems, electron paramagnetic resonance spectroscopy, and electrochemical methods
• Optical analysis, important issues in mixed-valence chemistry, transition of mixed valency from localized to delocalized, and solvent control of electron transfer
• Theoretical background, potential energy surfaces from classical two-state model, and quantum description of the potential energy surfaces
• Reorganization energies, electronic coupling matrix element and the transition moments, generalized Mulliken–Hush theory, and analysis of the band shape of intervalence charge transfer

Strengthening the relationship of mixed-valence electron transfer and molecular electronics, Mixed-Valence Systems is of immense value to researchers and professionals working in the field of electron transfer, molecular electronics, and optoelectronics.

Leseprobe

Mixed‐Valence Systems

Fundamentals, Synthesis, Electron Transfer, and Applications

Edited by Yu‐Wu Zhong, Chun Y. Liu, and Jeffrey R. Reimers

Editors

Prof. Yu-Wu ZhongInstitute of Chemistry, CASLaboratory of Photochemistry2 Bei Yi JieZhong Guan Cun100190 BeijingChina

Prof. Chun Y. LiuJinan UniversityDepartment of Chemistry601 Huang-Pu Avenue West510632 GuangzhouChina

Prof. Jeffrey R. ReimersShanghai UniversityInternational Centre for Quantum and Molecular Structures and School of Physics99 Shangda Lu200444 ShanghaiChina

and

University of Technology SydneyDepartment of Mathematical & Physical Sciences15 Broadway2007 SydneyAustralia

Cover Image: Courtesy of Prof. Tianfei Liu, Nankai University, Tianjin, China

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Print ISBN: 978-3-527-34980-7ePDF ISBN: 978-3-527-83526-3ePub ISBN: 978-3-527-83527-0oBook ISBN: 978-3-527-83528-7

Dedicated to Noel S. Hush AO FAA FRS (1924–2019)

Noel Hush completed his BSc (1945) and MSc (1948) at the University of Sydney, moving then to the United Kingdom to a lectureship at Manchester and then readership at Bristol, completing a DSc under the guidance of C. Longuet-Higgins and M.H.L. Pyrce. His career spanned over 70 years, from his first publication in 1947 in Nature on reduction reactions to his last paper in 2019 in J. Chem. Phys. on a simple theory for understanding attosecond spectroscopy.

In 1952–1953, Hush introduced the use of harmonic diabatic potential-energy surfaces for the description of electron-transfer reactions, these being much simpler than the diabatic Morse potentials that had dominated the previous two decades, in which focus had been primarily on the understanding of dissociative chemical reactions. Then, in 1958, he introduced the notion that intramolecular vibrations within molecules, or else the inner coordination spheres of ions, were just as important as long-range solvent interactions. Controversially, he then also introduced the concept that quantum mechanics was needed to understand electron-transfer reactions, focusing on the continuous transfer of charge that takes place along the reaction coordinate through a transition state. This led to another controversial proposition, that the burgeoning Molecular Orbital Theory could be used to make quantitative predictions concerning reaction and spectroscopic outcomes. Given the widespread application of Quantum Mechanics, supported by high-level calculations of electronic structure that pervade this book, and indeed all modern literature, it is hard to imagine that these basics were not immediately embraced by the community.

His theories concerning electron transfer became accepted following his 1967 paper in Prog. Inorg. Chem. that linked the reactivity and spectroscopy of mixed-valence compounds. This led to simple explanations for observed properties, paralleling the Robin–Day classification scheme introduced in the same year. The synthesis of the Creutz–Taube ion two years later, which demonstrated unprecedented chemical features that were only interpretable using quantum mechanics, was central to the acceptance of Hush's theories. It led to the award of the Nobel Prize to Taube in 1982, with the works of Hush, and Robin and Day defining much of the field of Mixed-Valence Chemistry unto this day.

During the 1970s, Hush pioneered computational methods that allowed the responses of quantum systems to an externally applied electric field to be studied, facilitating quantitative analysis of the Stark effect. During the 1980s, his focus was on the interpretation of new experiments demonstrating intramolecular photoinduced charge separation, works that were to form a platform for understanding the quantum aspects of biological photosynthesis. This led, during the next two decades, to quantitative theories for the operation of primary charge separation in purple bacteria, as well as to the development of the field of Molecular Electronics. These and many parallel achievements have brought the field of Mixed-Valence Chemistry to where it is today, providing a backbone for the understanding of many commercial processes including dyes, sensors, medicines, light-harvesting, and electron-transport systems.

Preface

In the simplest form, mixed-valence (MV) compounds refer to redox-active molecular systems in which the same chemical element is present in different oxidation states. In more generalized forms, differing ions, or indeed differing chemical groups, may be involved, the core idea being the presence of two groups that may exchange electron(s) internally to create isomeric forms of the compound. One famous example is the Creutz–Taube ion, {[(Ru(NH3)5](μ-pz)[(Ru(NH3)5]}5+ (pz = 1,4-pyrazine), which, applying classical valence theory, can be envisaged as containing one Ru2+ (d6) and one Ru3+ (d5) center connected via a pyrazine bridge. The principle applies not just to compounds but also to materials, the classic example being the dye Prussian blue that contains charge-localized Fe2+ and Fe3+ centers bridged by cyanide ligands.

MV compounds provide simple model system for the examination of the fundamental electron-transfer (ET) processes in donor–bridge–acceptor molecular systems. A prominent feature of MV compounds is the observation of the intervalence charge-transfer (IVCT) transition in a broad range from the visible to infrared region, depending on the nature of the system and the strength of electronic coupling. By analyzing the IVCT band, important parameters of the ET process between mixed-valent redox sites can be derived, including the reorganization energy (λ), the electronic coupling parameter (Hab), and the thermal activation barrier (ΔG*). Along with these studies, enormous information on the influence of the chemical structures and environments on ET processes is obtained. This field has become increasingly important when molecular electronics and artificial photosynthesis emerge as the research frontiers in physical sciences across the globe.

In 1979 and 1990, two monographs with the title Mixed-Valence Compounds: Theory and Applications in Chemistry, Physics, Geology, and Biology and Mixed Valency Compounds: Applications in Chemistry, Physics and Biology were published as the NATO Advanced Science Institutes Series. From then on, no monograph on the topic of MV compounds has been published. Considering that a great deal of progress has been made in recent decades and this field has received continuous interest to date, we felt it necessary and important to organize an updated book to reflect the current state of studies on MV compounds. We proposed this book in December 2020 and started to invite contributions a few months later. Thanks to the professional, enthusiastic, and timely contributions from the co-authors, we've been able to complete it on schedule.

This edited book invited contributions from the main experts who are currently actively working in the field of MV compounds. Chapters 1–3 describe the fundamentals and recent theoretical progress on the understanding and analysis of MV compounds. Chapters 4–9 present updated results, in particular the ET properties, of covalently connected MV compounds, including bridged diruthenium complexes and metal alkynyls, ferrocenyl-functionalized heterocycles, covalently bonded dimetal (M2) complexes, cyanide-bridged multimetallic systems, and organic MV systems. Chapters 10–15 describe various nonclassical aspects of MV compounds, including the MV complexes in biological and biomimetic systems, the ET of noncovalent systems, materials with stimulus-responsive IVCT or metal-to-metal charge transfer absorptions, mixed valency in extended materials, and the applications of MV compounds in near infrared (NIR) electrochromism. These topics cover the important advances in the theory, synthesis, ET, and application of conventional and nonclassical MV systems. We believe this book will be an essential reference for a wide range of scientific researchers and graduate students interested in MV systems and electron-transfer studies.

July 2022

Yu-Wu Zhong (Beijing)Chun Y. Liu (Guangzhou)Jeffrey R. Reimers (Sydney)

1Introduction and Fundamentals of Mixed-Valence Chemistry

Chun Y. Liu and Miao Meng

Jinan University, College of Chemistry and Materials Science, Department of Chemistry, 601 Huang-Pu Avenue West, Guangzhou 510632, China

1.1 Introduction

The term mixed valence (MV) is used to describe chemical systems in condensed media and solids in which the same chemical element exists in different oxidation states [1–3]. Thus, MV compounds refer to the category of unimolecular systems consisting of more than one redox center derived from the same element but formally having different oxidation levels in the ground state. In this context, molecules or solids having the same chemical constitutions but different oxidation states for the nonequivalent atoms should be viewed as distinct chemical identities or materials, but those having the same oxidation level are chemically identical. Prussian blue, the prototype of MV compound, is identical to Turnbull's blue [4]. It should be addressed that in MV compounds, the oxidation states of individual redox-active atoms that share the same elemental redox potential depend upon the electronic properties of the chemically bonded atoms or groups. For example, a high oxidation level is given to a redox center surrounded by more or stronger electron-withdrawing atoms or groups, and vice versa, a lesson learned from text book chemistry. However, mixed valency of MV compounds, which concerns charge distribution over the molecular ground state, is a very comprehensive issue pertaining to electrons and nuclei in motion that compasses a number of fundamental chemical problems, including energetic, dynamic, kinetic, and mechanistic of chemical transformations [5–8]. Moreover, MV compounds possess a unique optical property resulting from charge transfer between the spatially separated (chemically bonded or nonbonded) atoms with different valence electron shells. The interplays of electronic and nuclear dynamics within the molecule and between molecules (MV molecules and solvent molecules) are implicated through their optical behaviors, which are translated into the dynamics and energetics of the interpenetrated chemical and physical systems. With its enriched scientific contents, mixed-valent chemistry has evolved into one of the major playgrounds in modern chemistry in its own right for experimental and theoretical practitioners [6–10].

The attraction of mixed-valence systems is largely enforced by the fact that the valences of the discrete redox centers are intramolecularly self-exchangeable, thus representing the most elementary chemical reaction: intramolecular electron transfer (ET). In the middle of last century, the theoretical framework for ET was constructed and expanding rapidly, as marked by a series of profound progresses made in a relatively short period of time. Kubo and Toyozawa derived the general expression of activation energy (1955) [11]; Levich and Dogonadze presented the rate equation for ET reaction in the nonadiabatic limit (1960) [12, 13]; Marcus introduced the dielectric continuum model of solvation and the classical ET kinetic formalism (1956) [14, 15]; McConnell developed the superexchange model (1961) [16]; and Hush described the intramolecular effects using coupled harmonic surfaces (1958) [17] and calculations of the electronic coupling integral from intervalence optical parameters (1967) [5]. In the two-state description, the energy profiles of initial and final states of the system are approximated with a harmonic oscillator, which models the incorporated electron–nuclei dynamics in chemical transformation from reactant to product along the reaction coordinate. This simplified theoretical model on ET demands an experimental model that has single transferring electrons and well-defined electronic configuration. Thus, research work on MV chemistry gained a strong impetus to experimentally monitor the ET processes and to validate the semiclassical theories.

The follow-up experimental study was pioneered by Taube and Creutz with the elegantly designed, pyrazine (pz)-bridged diruthenium complex (I), {[(Ru(NH3)5](μ-pz)[(Ru(NH3)5]}5+, known as the Creutz–Taube ion [18], in which the two bridged Ru ions have formal oxidation numbers +2 and +3.

In a formal sense, the Ru2+(d6) and Ru3+(d5) centers in I serve the electronic donor (D) and acceptor (A), respectively, and electron self-exchange crossing the pz bridge (B) occurs without change of the free energy (ΔG = 0). In the mixed-valent D–B–A molecular system, electron migrating from D to A and nuclear motion conform energetically and dynamically to the semiclassical two-state models [19, 20]. The Creutz–Taube ion allowed the first observation of Frank–Condon transition that induces ET between two metal centers in a molecular complex, namely, intervalence charge transfer or IVCT [18, 21]. Inspired by the Creutz–Taube complex, a large number of MV compounds in form of D–B–A with various transition metal complex and organic charge-bearing units for the D and A sites have been synthesized, and studied in terms of electronic coupling (EC) and ET [6, 8, 22–24].

Electron transfer in MV systems may proceed via one of the two reaction pathways, thermal or optical [6, 22, 25–27]. By thermal ET pathway, the system overcomes the thermal energy barrier (ΔG*) and reaches the transition state through thermal fluctuations. In the transition state, designated as [D–B–A]≠ and [A–B–D]≠ in Figure 1.1 for the forward and reverse reactions, respectively, the system has an averaged nuclear configuration for the MV molecule (the activated complex) and solvation. From the reactant to the product, the system experiences an adiabatic process. Optical ET in MV compounds is initiated by vertical transition of the reactant state (with the extra electron on the donor) to the vibrational excited states of the product (with the extra electron transferred to the acceptor) (Figure 1.1). This transition occurs between two diabatic states and is governed by the Frank–Condon principle. Radiationless relaxation of the system from the nuclear excited state to the ground states completes the ET process [6, 19, 25].

For the ET event to occur, no matter which pathway is taken, the donor and acceptor electronic states must be coupled. It is the extent of coupling that controls the ET dynamics and kinetics, which is quantified by the coupling matrix element in quantum mechanics, i.e. Hab. Hush demonstrated that this crucial quantity can be derived from the IVCT spectrum of the MV compound [5, 6, 9, 19]. The Hush model connects the spectral data (transition energy, intensity, and absorption bandwidth) of the molecular system and the energetic parameters of the ET reaction (coupling integral and thermal ET barrier), and paves the way to optical determination of ET rate constant (kET). This optically determined coupling integral (Hab) can be incorporated into adiabatic and nonadiabatic ET kinetic expressions in the classical and semiclassical formalisms, which have been successfully applied in strongly and weakly coupled MV systems, respectively. Advances in time-resolved spectroscopic techniques allow the photoexcited states to be monitored, thus providing a powerful means for study of the photoinduced ET process in systems involving electronic excited states, D*–B–A or D–B–A*. Optical study of MV compounds and transient spectroscopic investigations of photoinitiated ET are complemented in development, validation, and refinement of the contemporary ET theories [19, 20, 25]. The gained understanding allows control of electron (charge) transfer in molecular systems and elucidation of the long-range charge transport processes in biological system and is beneficial to development of innovative technologies such as conductive materials, molecular electronics, and catalysts for solar–chemical energy conversion.

Figure 1.1 Optical (top) and thermal (bottom) ET pathways in mixed-valence D–B–A compounds. [A–B–D]* represents the vibrational excited state of the product. EIT is the intervalence charge transfer transition energy. [D–B–A]≠ and [A–B–D]≠ refers to the transition complex for the reactant and product, respectively. ΔG*F and ΔG*R is activation energy of the forward and reverse ET reaction, respectively.

1.2 Brief History

Historically, mixed-valence solids were found several centuries ago in various minerals, such as metal oxides, sulfates, and phosphates, in which the metal elements exist in different valence states [1, 3, 28]. These minerals usually show intense colors. The coloration of vivianite crystal with the chemical formula Fe3(PO4)2·8H2O is one of the interesting examples [5]. Vivianite is colorless when freshly exposed, as expected for the Fe2+ ion; after being exposed to air, it shows varying colors from light blue, light green, to dark blue or green, depending on the length of exposure due to oxidation of Fe2+ to Fe3+. As early as in the eighteenth century, it was realized that the blue color of ceramic glaze on vases was produced from ferrous iron (Fe3+) in reducing conditions. In nearly the same period of time, Prussian blue became a popular pigment for artists, which contains Fe3+ ions and negatively charged hexacyanoferrate ions [Fe(CN)6]4–, formulated as Fe4[Fe(CN)6]3, as described in the chemistry text book at entry level. However, chemists at that time were unable to explain the coloration of this material because both ferrous and ferric ions in aqueous solution do not show strong absorptions in this particular spectral range. It was generally observed that solutions or solids containing an element in two different valence states often exhibit unusual intense coloration, which does not appear when either of the elements is present alone [3]. This recognition connected coloration of the complexes to the valences of its ingredients [1], importantly, beginning to be aware that the distribution of oxidation states within the molecule can exchange under the influence of light so as to produce the light absorption and hence the color. For these systems, “valency oscillation” and “resonant valency” were proposed to describe the physical origin of intense color presented by one element in different valence states [29], which is more or less close to today's understanding. In 1950s, long-distance electron transfer between metal ions was assumed to explain “valency oscillation.” Weyl first noted that light absorption in MV systems is related to the interactions between two valence states of the same element [30].

Mixed-valence phenomena are also widely seen in enzymes and cofactors of biological systems where the active sites consist of multiple metal centers in variable oxidization states. For example, naturally occurring photosynthesis produces energy materials from low-potential molecules such as H2O and CO2 by absorption of visible light. The energy conversion processes involve two protein cofactor complexes, namely, photosystems (PS) II and I. In PS II, the oxygen-evolving complex (OEC), which conducts oxidation of water to molecular oxygen, is an ox-tetramanganese cluster with the Mn atoms in different oxidation levels [31]. In PS I, ferredoxin {(Cys)2FeII-(μ-S)2FeIII(Cys)2}+ ([2Fe2S]) is the electron carrier that transports electrons to the enzymatic reductive reaction center, the ferredoxin([2Fe2S])-nicotinamide adenine dinucleotide (NADP/H) reductase (FNR) [32]. Accomplishments of these biochemical reactions depend on intramolecular and intermolecular electron transfer with the driving force ultimately from sunlight [33].

In 1960–1970s, three important publications by Hush (1967) [5], Robin and Day (1968) [34], and Creutz and Taube (1969) [35] marked the cornerstone in development of mixed-valence chemistry. Based on the Mulliken charge transfer theory, Hush demonstrated [36, 37] that the electronic coupling matrix element (Hab) can be calculated from the IVCT parameters [5–7], transition energy EIT, molar extinction coefficient εIT, and half-height bandwidth Δν1/2 (Eq. 1.1).

(1.1)

where EIT and Δν1/2 are in wavenumber (cm−1) and rab is the effective electron transfer distance in angstrom (Å). This Mulliken–Hush expression, developed in the pure classical two-state regime, can be used in broad range of double-well charge transfer systems. The Hush model also reveals the correlation between optical (radiative) and thermal (radiationless) electron transfer for symmetric MV systems [5, 7, 14, 38].

(1.2)

Equation (1.2) suggests that the kinetics and energetics for the ET process can be described through optical analysis of the intervalence charge transition of MV compounds [19]. It is interesting that this fundamental energetic relationship concerning activation energy of ET reaction was revealed by Kubo and Toyozawa [11], Marcus [14], and Hush [5] from their independent works.

Robin and Day provided a scheme that classifies the MV compounds in terms of the extent of electronic coupling [34]. According to them, within the semiclassical framework, there are three regimes that MV compounds in different coupling strength belong to, that is, noncoupled (fully localized) Class I, strongly coupled or fully delocalized Class III, and the intermediate Class II that encompasses systems from weakly to moderately strongly coupled. In Robin–Day's classification [34], for MV compounds in Class I, thermal exchange of the oxidation states for the element in different sites is very slow, and the optical transition occurs by weak absorption of high-energy photons, while in Class III compounds, the valence states for the element in the multiple sites are averaged and thus crystallographically indistinguishable [1]. Class II compounds are those for which the electronic wave functions of the ground state and the excited state are significantly mixed, and the valence states are interchangeable in response to external stimulations, such as light and heat [1, 34].

Synthesis of the Creutz–Taube complex in 1969 initiated experimental studies of intramolecular EC and ET. For the Creutz–Taube ion, a broad, asymmetric absorption band was observed at 6369 cm−1, which was attributed to electron transfer from Ru2+ to Ru3+ crossing the pyrazine molecule. However, it took many years to characterize this MV compound in terms of the Robin–Day's scheme, that is, whether it belongs to localized Class II with +2 for one Ru center and +3 for the other or to delocalized Class III with an averaged oxidation state of +2.5 for each of the two Ru centers. Now, it is generally accepted that the Creutz–Taube ion is best placed on the Class II–III borderline [39, 40].

A prominent feature of MV compounds is the observation of characteristic IVCT transition that occurs in a broad region from visible to infrared depending on the strength of electronic coupling between the redox centers. By analyzing the IVCT band, important parameters of the ET process between mixed-valent redox sites can be extracted, including the reorganization energy (λ), the electronic coupling parameter (Hab), and the thermal activation barrier (ΔG*). These concepts arose from the seminal works of Kubo and Toyozawa, Marcus, and Hush concerning the activation energy, Marcus and Hush regarding the intermolecular and intramolecular contributions to the reorganization energy, and Hush and Levich and Dogonadze to the electronic coupling [12, 41]. McConnell's theory is then applied to understand the dependence of the coupling, and hence the spectra, on systematic extension of the separation between the mixed-valence centers. These pioneering works established the theoretic framework of mixed-valence chemistry, which has inspired and guided research in this field for a half century [1, 2, 6, 8].

1.3 Diversity of Mixed-Valence Systems – Some Examples

Following the Creutz–Taube ion, various mixed-valence D–B–A compounds were synthesized with different d5-6 transition metal ions (Ru, Os, and Fe) by substituting the auxiliary ligands NH3 with inorganic anions, e.g. Cl−, CN−, or organic molecules, e.g. bipyridine (bpy) and terpyridine (tpy), or by modifying the bridging ligand (BL) [6, 8, 40]. For these analogues, broad, low-energy IVCT absorptions are observed typically in the near-infrared region. Asymmetrical compounds derived from heterodinuclear metal centers [42], or from homodinuclear metal ions coordinatively saturated with different supporting ligands [43], exhibited distinct energetic profiles in the two-state framework, i.e. ΔG0 ≠ 0, and attracted significant attention. However, for dinuclear d5-6 systems with building blocks that have distorted octahedral geometry, the intervalence spectrum must be carefully assigned because the d orbitals between the two metal centers interact through dπ–dπ conjugations across BL [39, 40]. As a result, multiple electronic transitions, including three intervalence transitions (IT) and two interconfigurational (IC) transitions occurring at the acceptor, may appear, as shown in Figure 1.2, and may overlap with each other [40]. In this case, only the lowest energy IT band, IT(1) in Figure 1.2, arises from pure donor–acceptor ET that accounts for the reorganization energy (λ) [39].

When multidentate pyridyl and phenyl ligands are used, the degeneracy of d orbitals in an octahedral field is removed, which gives rise to single intervalence band for the mixed-valence complexes. Organometallic Ru (II/III) building blocks prepared with multidentate phenyl ligands feature five-membered ring structures involving a Ru—C bond (II). The cyclometalated Ru redox centers are able to increase the molecular rigidity and stability of the assembled D–B–A complexes and to strengthen the d(Ru)–π(phenyl ligand) orbital interactions [44]. Aligning the Ru—C bonds on the donor and acceptor sites with the IVCT axis substantially enhances the electronic coupling by favoring the BL-mediated hole transfer pathway [45].

Figure 1.2 Multiple transitions occurring in d5-6 mixed-valence M–BL–M systems (M = Ru and Os).

The first reported dinuclear MV complex with nonoctahedral redox sites was the biferrocenium cation [(C5H5)Fe-(C5H4-C5H4)-Fe(C5H5)]+ (III), synthesized by Cowan and coworkers in 1973 [46]. This molecule exhibits a broad IVCT band at 1900 nm. With different BLs, a series of ferrocenium MV organometallics have been studied in terms of electronic coupling [47]. In earlier studies, few other transition metals were used to construct binuclear MV systems. For example, transition metal ions in group VIB of the periodic table were exploited as the redox centers, typically, [M(CO)3(PR3)2]2(μ-pz) (M = Mo and W) (IV) [48, 49] and [Mo(tp*)(NO)Cl]2(μ-BL)] (tp* = tris(3,5-dimethylpyrazolyl)hydroborate) (V) [50]. These dinuclear organometallic complexes feature an 18 e− configuration for each metal center and present redox properties sensitive to the coordination environment due to the strong π back-bonding from the ligand to the metal center [51]. {[Mo(CO)3(PR3)2]2(μ-pz)}+ with an electronic configuration 4d5/4d6 exhibits a relatively narrow (Δν1/2 700 cm−1), symmetric IVCT band (4650 cm−l) in the near-IR region [49].

In the 1990s, unimolecular mixed-valence D–B–A systems were extended from metal-containing inorganic complexes to pure organic compounds. The bistriarylamine (VI) [52, 53] and bishydrazine (VII) [54, 55] derivatives involving redox-active sp3 nitrogen atoms are the prototypes of organic MV D–B–A systems, which were studied systematically by Nelsen and Lambert, respectively. Following these works, another organic radical system, namely, D–BL–D⋅+ (VIII), was developed in Kochi's group, with a redox-active group 2,5-dimethoxy-4-methylphenyl (D) as the donor and acceptor [56]. By employing redox-active organic groups, the concepts of mixed-valence chemistry are generalized. Compared to metal complex systems, the organic systems possess several features that favor study of EC. In these radical systems, electronic coupling and electron transfer involve single electrons that are specified with respect to orbital and electronic state, which facilitates the assignment and analysis of the IVCT bands. Study of organic systems concerns all aspects of mixed-valence chemistry, which has contributed to advance our knowledge in this field [24, 57].

The family of bridged MV compounds was further expanded with involvement of redox-active metal clusters containing more than one metal atom, used as a whole to be a building block for assembling the D–B–A molecule. Linking two quadruply-bonded dimetal units, M2 (M = Mo and W), with a tetradentate bridging ligand was first achieved in Chisolm's group in 1989 [58], yielding the dimers of dimers of form of M2–BL–M2, which has a formal oxidation state +4 for each of the M2 centers, as shown in IX. The MV complexes [M2–BL–M2]+ are prepared by one-electron oxidation using appropriate oxidizing reagents [58, 59]. Cotton and coworkers optimized the synthetic method with the designed dimolybdenum building block [Mo2(DAniF)3]+ (DAniF = N,N′-di(p-anisyl)formamidinate) for converged assembly [60, 61], which led to the synthesis and structural characterization of many Mo2 dimers with diverse bridging ligands. A quadruply-bonded M2 unit has a well-defined, distinct electronic configuration, σ2π4δ2 [62]. For this M2 MV complex system, electron delocalization within the M2 unit is assumed. In a view of electron localization, the donor site (M24+) has a close shell with the valence electrons paired in the δ orbital, while in the acceptor (M25+), the δ orbital is singly occupied. Therefore, in the M2 dimers, EC and ET involve only the δ electrons. Recently, Liu and coworkers systematically studied EC and ET in the Mo2 MV systems under the contemporary ET theories [63, 64]. Covalently bonded diruthenium complexes were exploited by Ren and coworkers as the redox centers to assemble Ru2 dimers through an axial linkage. For the Ru2–BL–Ru2 systems, polyyn-diyl chains –(C2)n– are the favorable bridging ligands to link two Ru2(ap)4 (ap = 2-anilinopyridinate) complex molecules (X) with the number of alkynyl units (n) up to 6 [65].

The oxygen (O)-centered triruthenium cluster, [Ru3O(acetate)6-(CO)L2], has been used as the electron donor or acceptor for construction of the MV D–B–A complexes by Ito and Kubiak [66]. In a [Ru3O(acetate)6-(CO)L2] complex, the three Ru atoms are in formal oxidation states III, III, and II, which presumably are fully delocalized through the acetate bridging ligands. Replacing one of the L ligands with a pyridyl ligand modifies the redox potential of the Ru3 center, which controls the properties of donor and acceptor; the other L position is replaced by a pyridyl bridging ligand, resulting in the dimer of trimers (XI). The mixed-valence system results from one-electron reduction of the Ru3 dimers, {Ru3(III, II, II)–BL–Ru3(III, III, II)}−. In this system, the electronic coupling can be tuned by alternation of the remaining L ligand, besides variation of the BL. Uniquely, the CO groups function as an IR probe, which has been successfully used to study the ET kinetics by analysis of vibrational band broadening of the carbonyl group [66, 67].

It is generally recognized that in MV D–B–A molecules, the bridging ligand plays a dominant role in control of D–A electron transfer. For decades, much of the work has focused on BL mediation of electronic coupling [23, 24, 47, 68]. In these studies, the main goals are to evaluate efficiency of various BL in coupling the electronic states, to determine its ability of transporting electrons, and to explore how the electronic event takes place. The study encompasses three crucial aspects of electron transfer reactions: energetics, kinetics, and mechanism. Approaches to these issues include variation of the BL structures, mainly through changes in length, conformation, and conjugation. Distance dependence of EC is the characteristic property for a given MV system [69], determined by the nature of the donor and acceptor. For a homologous series with varying BL length, the distance dependence of EC and ET can be evaluated by an attenuation factor β