2 as a

Review pubs.acs.org/Organometallics

Half-Wave Potential Splittings ΔE1/2 as a Measure of Electronic Coupling in Mixed-Valent Systems: Triumphs and Defeats Rainer F. Winter* Fachbereich Chemie, Universität Konstanz, Universitätsstraße 10, D-78457 Konstanz, Germany S Supporting Information *

ABSTRACT: This review is a cautionary note against the often purported direct relation between the half-wave potential splitting ΔE1/2 (or ΔE°) for stepwise, consecutive electron transfer from systems featuring two or more identical redox sites and the true electronic coupling HAB and charge or spin distribution in the ground state of intermittently formed mixed-valent (MV) systems. Several examples where these different quantities go in parallel are contrasted with other examples where this is not the case. Different kinds of such “non-conformist” behavior are outlined with the aid of representative examples. These include cases of fairly strong electronic couplings and large degrees of ground-state delocalization despite small values of ΔE1/2sometimes just above the statistical limit or even below thatas well as examples for just the opposite behavior of no detectable electronic coupling despite appreciable electrochemical half-wave potential splitting. The crucial roles of the nominal bridges that interconnect the individual redox sites and of the environment (solvent, supporting electrolyte) in determining ΔE1/2 and HAB are emphasized. We also seek to provide some guidelines for the practitioner as to how to discriminate between these various types of behaviors and how to determine the strength of the electronic coupling between the redox sites.

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AIM AND SCOPE The aim of this tutorial review is to critically evaluate the relation between the redox splitting ΔE1/2 and the degree of electronic interactions (electronic coupling) between identical, interconnected, redox-active moieties in mixed-valent (MV) compounds. First it will be briefly defined what we understand by a mixed-valent system and by the term “electronic coupling”. We will then discuss how the electronic coupling in such systems can be measured. This will be followed by representative examples of “conformists”compounds where the electronic coupling and ΔE1/2 value go in parallel. Next we will turn to MV systems, where no such correlation exists for one reason or another. Among these “non-conformists” are “ignorants”, MV compounds which, despite similar architectures and similar values of ΔE1/2, differ quite appreciably in terms of ground-state delocalization. The next group will be referred to as “still waters” and encompasses compounds that display rather large electronic coupling despite small ΔE1/2 values. Such compounds typically belong to mixed-valent (MV) systems of class II according to the Robin and Day classification scheme.1 Finally we will discuss some examples of systems showing only small degrees of ground-state delocalization or even full charge and valence localization despite appreciable ΔE1/2 values. Such systems are here referred to as the “pretenders” and belong to MV systems of class I or MV systems close to the class II/I borderline. It should be pointed out that this review is not meant to be comprehensive with respect to the examples provided for each different kind of © 2014 American Chemical Society

behavior. It is rather highly sellective and seeks to provide particularly illustrative examples. These examples are chosen such as to cover coordination compounds akin to the classical, paradigmatic Creutz−Taube ion,2 metal−organic mixed-valent systems where the nominal bridge binds the metal centers via metal−carbon σ or σ and π bonds, and fully organic MV systems. This is to convey a sense of generality of the underlying principles and to demonstrate that these various kinds of behaviors do not depend on the exact nature of the redox-active subunits that generate the MV states.

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SETTING THE STAGE Before entering the discussion we will briefly dwell on the term “half-wave potential”, which is usually symbolized by E1/2 and “half-wave potential splitting”, ΔE1/2. Particularly in cyclic voltammetry, E 1/2 is commonly used instead of the thermodynamically more meaningful “formal potential” E°′ or “standard potential” E°, which relate to one another as given by eq 1. A stringent definition and distinction of these values thus E°′ = E° + RT /nF ln(γOx /γRed)

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Special Issue: Organometallic Electrochemistry Received: January 14, 2014 Published: June 24, 2014 4517

dx.doi.org/10.1021/om500029x | Organometallics 2014, 33, 4517−4536

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requires consideration of the relevant activity coefficients γ. Any reader who is interested in the details of this matter is directed to instructive relevant textbooks on this topic.3−5 The term “half-wave potential”, which is usually symbolized as E1/2, originates from sampled-current voltammetry and polarography. The relation between the formal potential E°′ and the half-wave potential E1/2 is given by eq 2, where Dred and E1/2 = E 0 ′ + RT /nF ·ln(Dred /Dox )m

maximum peak current, Ep,fw/2. This is, however, not identical with the half-wave potential E1/2, which is the mean average of the peak positions of the forward and the reverse peaks (eq 4).13 While for an ideal electrochemically and chemically E1/2=(Ep,fw + Ep,rev )/2

reversible redox system, (E p,fw + E p,rev )/2 should be independent of the sweep rate v, the effects of double-layer charging current and uncompensated cell resistance will shift the forward peak slightly more than the reverse peak and hence cause some drift of E1/2 toward higher absolute values (i.e., anodically for an oxidation, cathodically for a reduction) as v increases. If no positive feedback resistance correction is applied, the value of (Ep,fw + Ep,rev)/2 = E1/2 will only be invariant to the sweep rate v at sufficiently low values of v. Considering the relation between the formal and half-wave potentials as given by eq 2, one should note that the diffusion coefficients of the two congeners of a redox couple are sufficiently similar to each other such that the term RT/nF ln(Dred/Dox) usually accounts for only a few millivolts. Considering that the accuracy with which the peak positions of a conventional cyclic voltammogram can be determined is mostly no better than ±1 mV and that of E1/2 is consequently no better than ±2 mV, the distinction among E1/2, E°′, and E° appears to be a somewhat academic one with not (so) much relevance for practical measurements as they are performed in everyday routine work. The same also pertains to differences in ΔE1/2, ΔE°′, and ΔE° for two consecutive one-electron processes. We will therefore employ the symbols E1/2 and ΔE1/2 throughout this review, simply because only these values are directly obtained from the experimental data and quoted in the original references. Central to this review is the shaky relation between ΔE1/2 and the electronic coupling in mixed-valent systems. We thus need to define what we understand by these terms. A mixedvalent system is any compound where two or more identical or very similar redox-active subunits are present in formally different oxidation states. The best investigated compounds of that type by far belong to the family of imine-bridged bis(pentaammine or -imine) ruthenium and osmium complexes, with the parent pyrazine-bridged system, the so-called Creutz−Taube ion, as the most prominent representative (Figure 2).2

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Dox denote the diffusion coefficients of the reduced or the oxidized form of the relevant redox couple (note that for an oxidation the logarithmic term has to be inverted). Electroanalytical methods giving sigmoidally shaped current/time responses such as polarography, normal pulse voltammetry, linear sweep voltammetry at ultramicroelectrodes under conditions of radial diffusion (i.e., at sufficiently low sweep rates v), or voltammetric measurements on rotating-disk electrodes (hydrodynamic measurements) provide half-wave potentials at half the diffusion-limited maximum current. The latter is measured when applying a potential to the working electrode that is sufficiently negative or positive of E° to quantitatively consume any analyte molecule arriving at the electrode surface such that the concentration of the analyte equals 0. Note that the exponent m of the (Dred/Dox)m term of eq 2 may vary from one method to another: e.g., 1/2 in polarography and 2/3 in hydrodynamic measurements. In square wave voltammetry or differential pulse voltammetry, the relevant potential information is drawn from the position of the peak maximum. While the peak potential equals E1/2 in square wave voltammetry,6 it is equal to the difference given in eq 3, Ep = E1/2 − ΔE/2

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where ΔE symbolizes the step height which is usually only a couple of millivolts, in differential pulse voltammetry.3−5 Cyclic voltammetry has by now evolved into the most broadly used electroanalytical technique.3,7 This is probably because cyclic voltammetry is nearly equally well adapted to provide thermodynamic information such as redox potentials and the numbers of electrons transferred during an electrochemical process, as well as kinetic information such as the rate of the charge transfer through the electrode/analyte interface or the rates of chemical processes preceding or following the electron transfer step.7−12 Considering an ideal Nernstian wave in cyclic voltammetry as displayed in Figure 1, the term “half-wave potential” might be easily misinterpreted as the potential at the point where the initial (forward) wave reaches half the

Figure 2. Creutz−Taube ion.

The charge state 5+ implies that one of the ruthenium atoms adopts the oxidation state +II while the other has the oxidation state +III. As for all mixed-valent (MV) systems, these are, however, only formal oxidation state assignments. The real (physical) oxidation state at each site as reflected by the electron density at the redox site (here the metal atom) may be anywhere between these extremes. Much of the discussion around any MV compound centers around the question of the so-called “electronic interaction” or “electronic coupling”, which directly relates to the degree of charge distribution

Figure 1. Ideal Nernstian wave in cyclic voltammetry and associated peak parameters. 4518


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Figure 3. Potential hypersurfaces for mixed-valent compounds of classes (a) I, (b) II, and (c) III or (d) hypersurface when a “non-innocent” bridge strongly participates in a redox process and offers a low-lying bridge state.

counterions. As long as 2HAB is larger than 0 but smaller than λ, the ground state of a mixed-valent system is characterized by a double-minimum hypersurface. This means that, in the MV ground state, the two redox-active moieties differ in terms of electron densities and, in most cases, also in terms of their equilibrium structures. This is what defines mixed-valent systems of class II.1 Intramolecular electron transfer can then occur by photochemical excitation from one local minimum into the antibonding hypersurface, from which the system can relax to the ground state with an inversion of redox states. The underlying absorption band is therefore called an intervalence charge transfer absorption (IVCT). Alternatively, intramolecular electron transfer can occur as a thermally activated process. In the harmonic approximation, the energy barrier for thermal electron transfer Eth is one-fourth of the total reorganization energy λ. If, however, 2HAB is larger than λ, the ground-state hypersurface has just one broad minimum at a value of the electron transfer coordinate that is midway between those for the minima of a class II system. This also means that both local redox sites adopt the same structure that is somewhere between the ground-state structures of the reduced and the oxidized states of a similar compound with just one redox-active subunit of the same kind or the bordering isovalent states. In that case optical excitation occurs between a delocalized ground state and a delocalized excited state and involves no net transfer of charge. The underlying transition is therefore termed a charge resonance (CR) band, an expression that was originally coined for transitions observed for radical ions of arenes dissolved in the neutral, uncharged arene itself.18−22 Considering the above, any of the individual redox sites of a MV system of class I has essentially the same properties as it would have in a similar compound with just one redox site in its respective oxidation state, and the spectroscopic properties are just the sum of those of the corresponding reduced and oxidized subunits. In systems of class II, electronic coupling renders the sites more similar, but they still differ with respect to their intrinsic electron and spin densities and, in most cases, with respect to their structure coordinates, as implied by the double-minimum ground-state hypersurface. Therefore, it is still possible to spectroscopically distinguish the individual sites on some experimental time scale. In MV compounds of class III, however, the valences, charges, and spin densities are totally averaged and both sites are structurally identical. Today it is agreed to assign compounds in the class II/III borderline regime as a class of their own, if the exact assignment to class II or class III depends on solvent friction: that is, the time constant at which the solvent shell can structurally reorient to accommodate the alteration in charge distribution.23−27 At this point it is important to consider how to obtain information on the electronic coupling matrix element HAB and

between the individual redox sites. Electronic coupling decreases the difference in intrinsic charges and valence states of the individual sites and renders them electronically similar, if not identical. The strength of this interaction therefore has a profound influence on the shape of the potential hypersurface that describes the ground state of a mixed-valent system and on its physical and spectroscopic properties. The energy of a system comprising two identical redox-active constituents, one in its reduced and one in its oxidized state, that are interconnected by a common bridge is usually described by one of the potential hypersurfaces of Figure 3. The x axis represents the so-called electron transfer (ET) coordinate, which in principle can be any structure parameter that is particularly sensitive to the change in oxidation state: for example, a specific bond length, bond angle, or dihedral angle. In metal-containing redox systems, the higher oxidized form has usually more contracted metal−ligand bonds owing to a smaller ionic radius while those bonds of the reduced form tend to be larger. Structural rearrangement accompanying the intramolecular electron transfer from the reduced to the oxidized site in a MV system creates the energy barrier Eth, the height of which usually relates to the net amplitude of the structural change.14−17 The potential hypersurface for each local redox site is conventionally drawn as a hyperbola. This is because electron transfer is most frequently coupled to certain vibrational modes that render the structure of the reduced form closer to that of the oxidized one and vice versa (some exceptions will be discussed with the phenomenon of “potential inversion” within Examples of “Still Waters”). If the common entity that links the spatially separated redox-active subunits, the so-called “bridge”, acts as an insulator, the redox sites are more or less independent of each other and the MV state is not stabilized by resonance effects or electronic coupling. This denotes the class I limit of noninteracting MV systems according to the original definition by Robin and Day.1 As we will show later, this does not mean, however, that ΔE1/2 is necessarily 0, since further oxidation/reduction from a mixedvalent to a homovalent state may still suffer an electrostatic penalty. In addition, there is still a statistical component to consider. Electronic coupling between the redox-active subunits across the common bridge leads to an avoided crossing of the individual diabatic potential hypersurfaces and generates two adiabatic hypersurfaces, one representing a bonding ground state and the other an antibonding excited state. The shape of the resulting ground state hypersurface depends on the ratio between the electronic coupling parameter HAB (or VAB) and the reorganization energy λ, which is the energy required for bringing about the necessary structural readjustment at the individual redox sites of the dissolved molecule and the surrounding solvent shell, including the solvent dipoles and the 4519


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charge due to electrostatic repulsion between the then likecharged redox sites. This contribution can be estimated on the basis of a model implying two point charges embedded in a peanut-shaped cavity of dielectric constant εi surrounded by a medium with the dielectric constant εo (Figure 4). Estimates on

the rate of intramolecular electron transfer (ET) in MV systems. Here we are confronted with the rule of thumb stating that an increase of electronic coupling between the individual redox sites should go hand in hand with increasing thermodynamic stabilization of the MV state, as measured by the comproportionation constant Kc. As is immediately apparent from eq 5, larger values of Kc translate into larger Kc = exp{(nF ΔE1/2)/(RT )}

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potential splittings ΔE1/2 for consecutive one-electron redox processes. In the simple case of a system with two identical redox sites, the first redox process changes a homovalent state into the mixed-valent (MV) state while the second changes the MV state into another homovalent state where both sites are oxidized or reduced by one electron. Here, however, one has to bear in mind that the value of Kc mirrors the relative free energy changes upon stepwise redox processes (eq 6). Kc is hence just

−ΔGc = nF ΔE1/2

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a measure of the thermodynamic stability of the mixed-valent state with respect to the bordering isovalent states. As a matter of fact, ΔE1/2 depends on a variety of different factors apart from the quantity of interest here, the resonance contribution ΔGres due to electronic coupling (eq 7, where ΔGstat = ΔGc = ΔGstat + ΔGind + ΔGex + ΔGel + ΔGres

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Figure 4. (top) Schematic drawing of the solvent shell and estimates of individual contributors to ΔE1/2 for a relative of the Creutz−Taube ion in aqueous solution.38 (bottom) Contributions of individual terms to ΔGc according to an analysis of diferrocenyl-substituted thiophene, furan, and N-substituted pyrroles (for structures see Figure 13). The bottom part of this figure is reproduced in part from ref 40 with permission.

statistical contribution → 2 ln 2 RT/F = 36 mV at room temperature, ΔGind = inductive contribution, ΔGex = magnetic exchange contribution, ΔGel = electrostatic contribution, and ΔGres = resonance contribution due to electronic coupling).28−31 This is first a statistical term, ΔGstat, which simply pays tribute to the fact that in a system comprising two identical redox sites the mixed-valent state is statistically favored with respect to a mixture of the bordering isovalent ones. This factor accounts for 2 ln 2 RT/F, which is 36 mV at room temperature.32,33 This may not seem much, but we will encounter some examples where ΔE1/2 is not far above the statistical limit despite measurable and significant degrees of ground-state delocalization as we go along. The second contributor is the inductive term ΔGind. It describes the fact that a redox process involving a redox site on one end of a molecule will affect its bonding to the bridging ligand and hence induce some shift of the intrinsic redox potential of another redox-active moiety, which is attached to the same ligand. Consider the case of a dimetal complex bridged by a π-accepting ligand with a low-lying LUMO such as 4,4′-bipyridine. As one of the attached metal sites is oxidized, its back-bonding to that ligand decreases. Hence, the bridging ligand becomes a stronger π acceptor to the second redox site. This in turn will increase the redox potential on that local site and thereby increase the redox splitting ΔE1/2.28,34,35 The third contributor to the free energy of comproportionation is electron exchange. In a simple two-state system, this factor is proportional to the antiferromagnetic exchange term. It may also be as large as some tens of millivolts.36,37 The next term to consider is the electrostatic contribution ΔGel. It simply expresses that, in a system undergoing a series of two consecutive one-electron transfer processes, the energy required to remove or add a unit charge increases with outer

analogues of the Creutz−Taube ion in aqueous solution gave contributions ΔGel of about 20−30 mV, but it was stated that it might be much larger in media of lower dielectric constant.38,39 Hildebrandt and Lang have more recently underpinned these predictions by quantifying the electrostatic and inductive contributions to ΔE1/2 for the stepwise oxidations of 2,5diferrocenyl-substituted thiophene, furan, and 4-substituted Nphenylpyrroles in the CH2Cl2/NBu4+ [B(C6F5)4]− supporting electrolyte (for structures see Figure 13). They estimated a much larger value of ca. 175 mV.40 Considering the additional statistical term of 36 mV, the nonresonance contributors to ΔE1/2 are thus likely to be on the order of 200 mV in apolar, weakly ion pairing media. This fact has been demonstrated in a rather dramatic way by Geiger and co-workers. One first, instructive example showed that ΔE1/2 for the stepwise oxidation of bis(fulvene)dinickel 1 in Figure 5 increases from 273 to 480 mV and finally to 744 mV

Figure 5. Bis(fulvene)dinickel (left) and bis(diferrocenyldithiolene)nickel (right) test systems investigated by Barriére, Geiger, et al.42 4520


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in CH2Cl2 and from 212 to 417 mV and then to 806 mV in anisole by simply replacing the chloride counterion of the [NBu4]+-based supporting electrolyte by [PF6]− or by [B(C6F5)4]−. This translates into changes in Kc of more than 7 orders of magnitude. Another, even more enlightening, example is that of the stepwise reduction of the dithiolene ligands of the bis(diferrocenyldithiolene)nickel complex 2 of Figure 5, where, depending on the cation of the supporting electrolyte, ΔE1/2 in CH2Cl2 as the solvent may vary from the nearly statistical limit of 40 mV (Na+) to 750 ± 10 mV for [NBu4]+ to nearly 800 mV for [N(hepytl)4]+.41,42 These investigations demonstrate how much the electrostatic term ΔGel may contribute to the experimentally observed ΔE1/2 and Kc values. They constitute a heraldic warning against relating ΔE1/2 and Kc in a quantitative manner to the true electronic coupling between the individual redox sites in a MV system without further proof. Therefore, it is always important to bear in mind that the resonance term is only one out of five contributors to the experimentally observed redox splitting, and often an only minor one. This makes ΔE1/2 and Kc only a qualitative measure of electronic coupling, even if compounds of similar architecture in the same solvent/ supporting electrolyte system are compared. An interesting account of how the solvent dielectricity constant εDK and the ion strength influence ΔE1/2 was provided by Bushby et al.43 This brings us now to the question of what means we have to experimentally measure the real degree of electronic coupling in a mixed-valent system. In the discussion of the potential hypersurface of class II MV systems it was already stated that intramolecular electron transfer, that is the transfer of an electron from the reduced to the oxidized site (or of a hole in the opposite direction), can be induced by excitation into the IVCT band. Indeed, the characteristic parameters of that band provide a rather direct access to the electronic coupling matrix element HAB (VAB) according to the familiar Mulliken−Hush expression (eq 8).44−46 Here, εmax denotes the extinction HAB = 0.0206(εmax νmax ̃ Δν1/2 ̃ )/RAB

Even if the assignment of a MV system as one belonging to class II has been secured, analysis of the IVCT band by eq 8 is not wholly without problems. For quantitative evaluation one needs to know the effective charge transfer distance RAB, which relates to the adiabatic dipole moment difference. Traditionally RAB is set equal to the spatial separation between the centers of the nominal redox sites, which, in the case of a transition-metalbased redox system, is the metal atom. Unfortunately, the adiabatic dipole moment difference and RAB are very difficult to measure experimentally, with electron absorption (Stark) spectroscopy being about the only means. Representative measurements revealed that even for rather clear-cut cases, such as analogues of the Creutz−Taube ion, the above geometrical approach grossly overestimates the charge-transfer distance and hence underestimates the electronic coupling term. Thus, in the 4,4′-bipyridine-bridged analogue of the Creutz−Taube ion of Figure 6, the experimentally determined charge-transfer

Figure 6. Comparison of the geometric and the experimental chargetransfer distances RAB in an extended verison of the Creutz−Taube ion and a bis(pentachlorophenyl)(tetrachlorophenyl)methyl dbis(anisyl)phenylamine conjugate.49

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distance is 6 Å, which is only about half the spatial separation between the ruthenium atoms of 11.3 Å. Discrepancies between geometrically estimated and measured charge-transfer distances even increase when the redox sites are less well-defined and also incorporate the nominal bridge.47,48 One example is the mixedvalent hybrid conjugate of a bis(pentachlorophenyl)(tetrachlorophenyl)methyl and a bis(anisyl)phenylamine radical of Figure 6, which constitutes one interesting and rare example of a neutral MV system with dissimilar but nearly isoenergetic redox sites. Here the experimental value of RAB of 4.2 Å is only about one-third of the geometric distance between the carbyl carbon and the nitrogen atom of 12.3 Å.49,50 The degree of ground-state delocalization of a MV system can also be measured spectroscopically. Applicable methods are vibrational spectroscopy, EPR spectroscopy, Mössbauer spectroscopy, and NMR spectroscopy. IR spectroscopy relies on “marker bands” whose positions are sensitive to the charge density at the local vibrator. Carbonyl, metal carbonyl, cyano, or isonitrile CN or alkynyl CC stretches may well serve this purpose, although in the last case no direct relation of the shift to the charge density change at the metal atom exists.51 Even C−H or B−H stretches can, however, qualify as such spectroscopic markers.52−54 For EPR spectroscopy, the relevant information can be obtained from hyperfine splittings to spinbearing centers close to the respective redox site, while for Mössbauer spectroscopy it is the number of signals and their

coefficient at the band maximum, ν̃max the energy at the band maximum in cm−1, Δν̃1/2 the bandwidth at half-height in cm−1, and RAB the effective charge transfer distance in Å. For strongly coupled MV systems of class III, HAB is simply half the energy at the band maximum (eq 9). HAB = νmax ̃ /2

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. A useful criterion to distinguish between these cases is the value of the parameter Γ as defined by Brunschwig, Creutz, and Sutin, which relates to the ratio between the experimental and theoretical value of Δν̃1/2 for a class II system as given by eq 10.45 For a class II system, Δν̃1/2,theor is given by eq 11. For a Γ = 1 − (Δν1/2,obsd /Δν1/2,theor ) ̃ ̃

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very weakly interacting system at the class I/II borderline, Γ approaches a value of 0. With increasing electronic coupling Γ steadily increases to reach a value of 0.5 at the class II/III borderline. Values of Γ exceeding 0.5 indicate strong electronic coupling between the individual redox sites, as is characteristic of MV systems of class III. Δν1/2,theor = (2310νmax ̃ ̃ )1/2

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Figure 7. (left) Bis(triarylamines) 3−8 studied by Lambert and co-workers. (right) IVCT bands of MV radical cations 3•+−8•+ (top) and plot of ΔE1/2 against HAB with best-fit line (bottom) (figure based and partially reproduced from ref 61 with permission).

s−1 in 3•+, the most weakly coupled MV system of this series, to 2.8 × 1012 s−1 in 8•+.61 In their initial analysis RAB was approximated as the spatial separation between the amine nitrogen atoms, and the phenylenediamine radical cation 8•+ was viewed as being close to the class II/III borderline but to be still a class II system. Later work by the same authors showed that 8•+ and the closely related N,N,N′,N′-tetraphenylphenylenediamine radical cation both have double-minimum adiabatic ground-state hypersurfaces with, however, a very low energy barrier to thermal ET of only 40−60 cm−1, which is well beyond the thermal energy at room temperature.60,61 Thus, they are effectively class III species. Moreover, X-ray crystallography and vibrational spectroscopy verified that the N,N,N′,N′-tetraphenylphenylenediamine radical cation possesses a centrosymmetric ground-state structure in the solid state and in solution, again in full agreement with a class III assignment. Other, more detailed studies also revealed that the biphenyl-bridged radical cation 6•+ and its relatives are also very close to the class II/III borderline with again a very low thermal energy barrier to intramolecular ET of only about 50 cm−1 and centrosymmetric structures in the solid state.62,63 This is because the expected decrease of the electronic coupling HAB from ca. 5500 cm−1 in 8•+ to about 3000 cm−1 in 6•+ is nearly offset by a substantial decrease of the reorganization energy λ from about 12000 cm−1 to ca. 7500 cm−1. A similar situation is found with Kubiak’s and Ito’s pyrazinebridged triruthenium clusters 9−14 shown in Figure 8.64 The diimine-bridged triruthenium clusters are reduced in consecutive one-electron steps that arise from the Ru(III/III/II) to Ru(III/II/II) transformations of each cluster. The analysis of the electronic coupling here also rests on the analysis of the intercluster IVCT band in the NIR. Additional NIR bands are due to intracluster IVCT transitions and are also observed in the direduced state. Intercluster electronic coupling across the bridge is strongly modulated by the ancillary pyridine ligand on each triruthenium cluster and increases as that ligand becomes more electron donating. Again an increase in ΔE1/2 and Kc is paralleled by an increase in HAB, as calculated from a Mulliken− Hush analysis of the IVCT band.

quadrupole splittings. NMR spectroscopy may also be instructive in distinguishing cases where either one or both redox sites have appreciable spin density and may be underutilized in the analysis of MV systems.55−59 Here one should be aware of the fact that each spectroscopic method is associated with its own time constant: i.e., 10−15 s for electronic transitions, 10−11−10−12 s for vibrational spectroscopy, ∼10−9 s for Mössbauer spectroscopy, 10−8 s for EPR spectroscopy, and 10−3−10−8 s for NMR spectroscopy.60 As a consequence, the dynamic window offered by one kind of molecular spectroscopy or the various pieces of information gathered from different spectroscopic methods can be used to map or even quantitatively determine the rates of intramolecular ET in a mixed-valent system. This will be illustrated by several of the following examples.

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SOME “CONFORMISTS” After preparing the groundwork, we will now turn to selected and instructive examples of the various kinds of behaviors when trying to relate the redox splitting ΔE1/2 and the electronic coupling HAB (VAB). We will start the discussion with some “conformists”: that is, compounds where these two quantities go in parallel. One set of compounds where such correlation is clearly observed comprises the arylene-bridged bis(triarylamine)-derived radical cations 3•+−8•+ of Figure 7, which were studied by Lambert and co-workers.61 The electronic coupling was derived from a Hush-type analysis of the observed IVCT band, which becomes narrower and intensifies as the electronic coupling increases. A linear correlation between HAB and the half-wave potential splitting was observed (see Figure 7). These authors also noted a lowenergy cutoff of the IVCT band as the electronic coupling approaches half the total reorganization energy λ and on entering the class II/III borderline regime. This cutoff results from inhomogeneous broadening of the underlying vibrations and from the fact that the IVCT transition energy cannot be smaller than λ/2. The rate of thermally induced intramolecular electron transfer as calculated on the basis of HAB and λ expectedly increases by more than 3 orders of magnitude from 9.3 × 108 4522


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Figure 8. Ito’s and Kubiak’s diimine-bridged triruthenium clusters 9− 14.58

Even more interestingly, these authors masterly utilized the Ru(CO) IR stretches to analyze ground-state electronic delocalization and the rate of intramolecular intercluster ET. In the 4,4′-bipyridine-bridged systems 12−14, where electronic coupling is only weak, the IR spectrum of the monoreduced MV Ru(III/III/II)/Ru(III/II/II) compound shows two separate, well-resolved IR bands at positions similar to those in the oxidized Ru(III/III/II)/Ru(III/III/II) and the direduced Ru(III/II/II)/Ru(III/II/II) states. This means that, in the MV state, the carbonyl-bearing ruthenium atom of the oxidized triruthenium cluster has nearly the same electron density as in the Ru(III/III/II)/Ru(III/III/II) state while that on the other atom strongly resembles that in the direduced Ru(III/II/II)/ Ru(III/II/II) state. This is exactly what one expects of weakly coupled MV systems of class II. The electronic coupling significantly increases as the 4,4′bipyridine bridge is shortened to pyrazine. This causes the two Ru(CO) bands to move closer together or even merge into a single, broad absorption. These patterns were simulated on the basis of a Bloch-type line shape analysis for IR coalescence, as shown in Figure 9 for the pyridine complex 10. Such analysis yielded the rate constant for IVCT. Therefore, in these examples, the values of ΔE1/2 and Kc, the electronic coupling parameter HAB, and the rate of intercluster electron transfer kET go all in parallel.64 From the above discussion it is clear that the Ru(CO) bands of the mixed-valent forms become more and more similar to each other as the electronic coupling increases. In the same vein, Geiger and co-workers have shown that the relative CO band shifts of a mixed-valent compound with respect to the bordering isovalent compounds even provide a quantitative measure of ground-state delocalization. The relative band shift can be derived from a comparison of the band positions of the formally reduced and the formally oxidized subunits of a MV system to those in the bordering homovalent reduced or oxidized states to the total CO band shift between the isovalent forms as shown in Figure 10. Such a comparison yields the charge distribution parameter Δρ, which in turn provides a measure of valence delocalization in the ground state of a mixed-valent system. As by its definition, Δρ scales between 0 for a fully localized MV compound of class I and 0.5 for a fully delocalized system of class III. A Δρ value of X according to the definition in Figure 10 indicates that one redox site of the MV system in its

Figure 9. (left) Experimental IR spectra of pyrazine-bridged triruthenium clusters 9−11 in their Ru(III/III/II)/Ru(III/III/II) (dotted line), Ru(III/II/II)/Ru(III/II/II) (broken line), and MV Ru(III/III/II)/Ru(III/II/II) (solid line) states. (right) Comparison of the observed and simulated IR spectra for various values of the electron transfer rate constant kET (reproduced from ref 64 with permission).

Figure 10. Definition of Geiger’s charge distribution parameter.65,66

ground state carries 100 × X% and the other 100 × (1 − X)% of the total charge residing on both sites. Geiger originally derived his definition of the charge distribution parameter Δρ with the half-sandwich manganese and chromium complexes 15−22 shown in Figure 11 and showed that his charge delocalization parameter linearly correlates with ΔE1/2 in these compounds.66,67 In an intuitive sequence, the weakest coupling was found for complexes 15•+ and 16•+ with a saturated methylene linker within the bridging ligand, followed by complexes 17•+ and 18•+ with torsional freedom for rotation around the C−C single bond of the common fulvalenediyl bridge, to complexes 20•+ and 21•+, where the two half-sandwich subunits are forced into coplanarity. The strongest coupling within this series was, however, observed for the doubly linked radical cations 19•+ and 22•+. Of note is that 19•+ is intrinsically delocalized on the EPR time scale of 10−9−10−8 s but is partially localized (Δρ = 0.29) on the faster IR time scale of 10−12 s while 22•+ retains full ground-state delocalization (Δρ = 0.50) even on the faster IR time scale. Similar studies on disandwich complexes 23, 23′ and 24, 24′ (see Figure 12) derived from alkyl-bridged, cyclobutadienederived superphanes showed a 79:21 charge distribution for the electronic ground state of the mixed-valent system derived from the propano-bridged complex 23•+, as measured by the IR band shifts of the ester substituents at the cyclopentadienyl rings.65 4523


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Figure 11. Half-sandwich manganese and chromium complexes studied by Geiger.7

studies also revealed that the charge and spin delocalization of MV systems are not necessarily the same. According to quantum chemical calculations, the unpaired spin of 23′•+ is strictly localized on just one cobalt sandwich subunit. Charge delocalization in that compound was suggested to be effected by inductive interactions through molecular orbitals other than the localized SOMO. During their investigations of the 2,5-diferrocenyl-substituted thiophene, furan, and N-substituted pyrroles 25−33 shown in Figure 13, Hildebrandt, Lang, and co-workers found a linear correlation between the ΔE1/2 value in the weakly ion pairing CH2Cl2/NBu4+{B(C6F5)4}− electrolyte and oscillator strength f of the IVCT transition for their corresponding MV radical cations as well as the HAB values derived from a Mulliken− Hush analysis (see Figure 13). Interestingly, for compounds 28−33 ΔE1/2 also scales linearly with the Hammett constant σ at the pyrrolic nitrogen atom, showing that electron-rich heterocycles serve as better conduits than less electron rich ones. These authors ingeneously utilized that correlation to determine the resonance and nonresonance contributions to the overall thermodynamic driving force for the comproportionation reaction (vide supra) and to derive the effective charge transfer distance RAB.68,69 This method constitutes a viable alternative to electron absorption spectroscopy or quantum chemical calculations to determine RAB from a series of closely related MV compounds of the same general structure with rigidly disposed redox centers. In a series of three consecutive papers, Kochi and co-workers examined the degrees of ground state delocalization, the

Figure 12. Propano- and pentano-bridged dicobaltasuperphanes investigated by Geiger, Gleiter, and co-workers.65

The above ratio resembles the quantum chemically calculated flow of electron density from the respective ligands to the cobalt ions in a broken-symmetry solution. In the pentanolinked counterpart 24•+ the coupling is expectedly much weaker at 98:2. This tapering off of intrinsic ground-state delocalization is mirrored by a decrease in half-wave potential splitting from 440 mV in 23, or 390 mV in the similar complex 23′ with unsubstituted cyclopentadienyl rings, to 145 mV in 24′, which also bears unsubstituted cyclopentadienyl ligands. Note that 24 and 24′ are already cases of nearly complete intrinsic ground-state localization despite substantial half-wave potential splitting. As we will see later, the paracyclophane architecture is very efficient at conveying electrostatic interactions between the parallel disposed, rigidly stacked decks, which leads to an exceptionally large contribution of the ΔGel term to the total ΔGc value of eq 7. Interestingly, these

Figure 13. 2,5-Diferrocenyl-substituted thiophene, furan, and pyrroles investigated by Hildebrandt and Lang (left) and the linear correlation between the oscillator strength f of the IVCT band and the half-wave potential splitting (reproduced in part from ref 40 with permission). 4524


Organometallics

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correlation between ΔE1/2 and structural parameters.70 The overall conclusions derived from structural studies were further corroborated by Hush-type analyses of the IVCT bands and the ET kinetics derived from line broadening of the EPR spectra.71,72 Further studies on the MV radical cations of the torsionally restricted tolyl (351Me), xylyl (352Me), and duryl (354Me) derivatives showed that forcing the phenyl rings of the terminal donors and the bridge out of direct conjugation into a more and more orthogonal orientation diminishes the rate of intramolecular ET more than lengthening the bridge by insertion of another phenylene unit. An at least qualitative correlation between the rate of intramolecular ET, the intensity of the IVCT band, and ΔE1/2 was observed. Moreover, the stilbenyl or tolanyl bridges of compounds 39•+ and 40•+ rendered intramolecular ET more facile than the shorter biphenyl bridge of 36•+ or even the rigid, planar fluorenyl bridge of 38•+. This was ascribed to an increase of conjugation and a higher propensity of these bridges to accommodate the unipositive charge. Of particular interest for the following discussion is, however, that the biphenylene- and triphenylenebridged systems 36•+ and 37•+, duryl-bridged 354Me•+, and even ethylene and propylene-bridged D•+−(CH2)n−D (n = 2, 3) all displayed an IVCT absorption in the near-infrared region, although their oxidation occurs as an unresolved two-electron process with intramolecular ET rates kET in the range of 3 × 107−3 × 109 s−1. This makes these systems already the first examples of “still waters”: i.e., MV compounds showing fairly large electronic couplings despite vanishingly small ΔE1/2 values.

kinetics of the intramolecular ET, the thermal energy barrier for thermal IVCT, and HAB values by analyzing the IVCT and bridge-to-donor charge-transfer bands in the near-infrared region for MV systems 34•+−40•+ (Figure 14).70−72 These

Figure 14. (Oligo)phenylene-, fluorenyl-, stilbenyl-, and tolanylbridged and nonbridged systems investigated by Kochi and coworkers.70−72

are composed of two terminal bis(2,5-dimethoxy-4-methyl)benzene donors D and oligophenylene (34−37) or phenylene bridges with various degrees of methylation (35nMe, n = 1, 2, 4), the rigidified fluorenyl-bridged 38, and the stilbenyl- or tolanylbridged compounds 39 and 40. The issue of ground-state delocalization was first addressed by comparing the structural properties of each donor site in the MV radical cations to those of the neutral precursor and the dication of propylene-bridged D•+−(CH2)3−D•+ with two mutually insulated oxidized donors. Taking the CAr−O(OMe) bond length as the structural parameter which is most strongly affected by oxidation, these authors noted that charge distribution between the donor sites is complete in 34•+ (ΔE1/2 = 290 mV), while it assumes a value of 80:20 in phenylene-bridged 35•+ (ΔE1/2 = 110 mV) and 100:0 in 36•+ (unresolved two-electron wave), with its longer biphenyl bridge. For 38•+, which can be viewed as a torsionally restricted analogue of biphenyl-bridged 36•+, the terminal donors become structurally similar but share only 55% of the total charge injected by one-electron oxidation. The remaining 45% are delocalized onto the fluorenyl bridge. For 34•−36•+, data points of a plot relating ΔGc to fractional charges on each individual site fall on a common line, thus establishing a direct

■

THE “NON-CONFORMISTS” After looking at examples of conformist behavior where ΔE1/2, Kc, and the electronic HAB coupling go in parallel, we will now turn to mixed-valent systems where this is not the case. We will first discuss some examples of “ignorants”: i.e., MV compounds that, despite very similar molecular architectures and similar half-wave potential splittings, differ substantially with respect to the degrees of electronic coupling. This will then be followed by examples of “still waters”, where rather substantial degrees of ground-state delocalization are observed despite very small values of ΔE1/2. Such MV systems consequently belong to class II according to the Robin and Day classification scheme. The final section will then provide some examples of systems with

Figure 15. IR spectra of the isomeric divinylphenylene-bridged diruthenium complexes 41 and 42 in their various oxidation states. 4525


Organometallics

Review

vanishingly small degrees of electronic coupling (i.e., class I or class I/II borderline behavior) despite substantial ΔE1/2 valuesthe “pretenders”. Some “Ignorants”. Examples of such systems are the isomeric 1,3- and 1,4-divinylphenylene-bridged diruthenium complexes 41 and 42, shown in Figure 15. Both isomers show about the same splitting of half-wave potentials with a slightly larger value of 270 mV for the less-well conjugated meta isomer 42 in comparison to that of 250 mV for para-substituted 41.73 In metal−organic alkenyl complexes of this type it is not easy to define the true redox sites. This becomes evident from the electronic spectra of the mixed-valent radical cations, which strongly resemble those of the radical ions of phenylenevinylene oligomers. This in essence means that the divinylphenylene unit (i.e. the nominal bridge) strongly contributes to the relevant redox orbital. According to Mulliken analysis, the contribution of the divinylphenylene ligand to the HOMO amounts to about 60−70%, while that of the metal centers and the other coligands is only about 25−30%.73−75 Calculated charge density differences upon the first and the second oxidations indicate that the charge lost from the bridge is about 3 times higher than that which is lost from the metal atoms. TD-DFT calculations on the MV radical cations helped to assign the near-infrared absorption bands as essentially π → π* transitions within a highly conjugated open-shell metal− organic π system with very little charge transfer involved,73,74 in analogy to Kochi’s systems of Figure 14. Owing to the dominant ligand character of the SOMO, the radical cations give well-resolved EPR spectra in fluid solution. The hyperfine splitting patterns indicate that the unpaired spin of 41•+ and 42•+ is evenly distributed over the entire molecule, including both vinyl ruthenium moieties. On the faster IR time scale of 10−11−10−12 s this picture changes, however. The radical cation of the meta isomer 42 gives an IR pattern of two resolved Ru(CO) bands. For the para isomer, the individual absorptions are merged into a slightly asymmetric, broad band, from which individual Ru(CO) bands can be derived by means of nonlinear curve fitting. For both species, the Ru(CO) bands of the MV forms are shifted to higher and lower energies in comparison to the bordering isovalent neutrals and dications. This is clearly the fingerprint of MV systems with moderate electronic coupling. For 42•+ the degree of intrinsic groundstate delocalization can be assessed through Geiger’s charge distribution parameter Δρ, which here assumes a value of 0.13. For 41•+ the picture is, however, less clear. Detailed quantum chemical studies with hybrid functionals that have been shown to perform well in treating strongly coupled, mixed-valent systems54,74,76−79 indicated that 41•+ constitutes an intrinsically delocalized MV system of class III. The weak IR band constituting the higher energy shoulder may hence arise from vibrational coupling or from another rotamer with stronger torsion around the vinyl arylene linkages. In fact, some cases where two conformers with differing degrees of ground-state delocalization between identical or nonidentical redox sites coexist in solution in thermal equilibria have been reported in the literature.78,80−82 Irrespective of the origin of the second, weaker Ru(CO) band in the IR spectrum of 41•+ it is nevertheless clear that the radical cation of the para isomer 41, despite the smaller redox splitting ΔE1/2, is significantly more delocalized than that of 42. A similar situation is met in the alkenyl- and alkynyl-linked bis(triarylamine)-derived radical cations 43•+ and 44•+ of Barlow and his co-workers (Figure 16).83 Both diamines show

Figure 16. Structures of diamines 43 and 44 and comparison of the IVCT (CR) bands in the NIR region (solid line, 43•+; dotted line, 44•+) (reproduced with permission from ref 83).

two separate one-electron oxidation waves with an only modest splitting of 140 (43) or 150 mV (44), respectively. Both radical cations are fully delocalized on the EPR time scale. The radical cation of the ethynyl-bridged system shows a strong CC IR stretch at 2135 cm−1, while there is none observed for the neutral or the diaction. This indicates that 44•+ has an unsymmetrical, intrinsically localized electronic ground state. The radical cation of the stilbenyl-bridged compound 43•+, however, has a symmetrical structure with shortened C−N bond lengths to the carbon atoms of the bridge in comparison to the C−N bonds to the peripheral anisyl substituents.83 The asymmetrical shape and narrowness of the IVCT band with its low-energy cutoff and its weak solvatochromism were originally taken as indications that 43•+ constitutes a fully delocalized MV system of class III. Later investigations, including in-depth quantum chemical studies, revealed a small but nonzero value of the charge-transfer distance RAB of about 1.9 Å, such that 43•+ was reassigned as a MV system right at the class II/III borderline.84 The IVCT band of the tolanyl derivative 44•+ with its symmetrical shape, its bandwidth matching the predictions of Hush theory, and its much larger solvatochromism argue for an assignment to class II. Thus again, the electronic coupling in these systems is quite different despite very similar ΔE1/2 values and is even appreciably larger for 43 with the smaller value of ΔE1/2. Examples of “Still Waters”. With the term “still waters” (running deep) we here denote compounds where two or more interconnected redox sites undergo electron transfer at very similar potentials despite showing fairly large degrees of electronic coupling in their mixed-valent states. In many such cases, individual E1/2 values are so close that they give rise to an unresolved two-electron (or more-electron) wave and a single, but broadened, peak in differential pulse or square wave voltammetry. The small values of ΔE1/2 and the concomitant low thermodynamic stabilities of the intermediate mixed-valent species as expressed by the comproportionation constant Kc (see eq 5) often render their detection and spectroscopic identification difficult. In these cases, digital simulation of the electrochemical responses is essential for determining the E1/2 values of each involved redox couple and ΔE1/2. This is a prerequisite for determining the individual Kc values, which in turn are needed as an input for quantitative interpretation of the spectra of the electrochemically or chemically generated mixed-valent forms. Only by accounting for the equilibrium 4526


Organometallics

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Figure 17. Carotenoids and tetraaminobenzenes investigated by Sáveant and Evans and co-workers.87,88

concentration(s) of the mixed-valent species in addition to those of the bordering homovalent states can one obtain meaningful values for the extinction coefficients of the IVCT band or the real positions of IR marker bands in the case of overlapping spectroscopic responses, which are then used to derive quantitative information on the electronic coupling. The phenomenon of unusually close spacings of individual redox processes in such compounds has been termed “potential compression”, in particular when they are merged into one unresolved wave or peak.85,86 Sáveant et al. have provided instructive examples of such behavior in a combined electrochemical and quantum chemical study on the carotenoids 45− 47 of Figure 17 and related polyenic model compounds of various chain lengths.87 These authors pointed out that such systems may even display potential inversion (i.e. the second electron transfer is thermodynamically favored and occurs at less positive (oxidation) or less negative (reduction) potential with respect to the first electron transfer) as the number of unsaturated, conjugated repeat units of the bridge exceeds a threshold value. This means that Kc assumes a value smaller than 1, although the intermediate MV radical ion is delocalized. Three factors were identified as crucial prerequisites of such behavior. (i) The sizable lengths and rigidities of the bridges keep the charge-bearing, terminal redox centers sufficiently far apart from each other such that Coulombic effects do not contribute to ΔGc. (ii) The charge of the radical ions is delocalized onto the nominal bridge. Such delocalization was inferred from the fact that (calculated) C−C bond lengths within polyenic bridges have a clear short−long CC−C alternance in the neutral forms but are nearly uniform for the radical ions while the redox-active end groups remain structurally equivalent and experience only minor structural change. (iii) Upon the second electron transfer, the charges move to the redox-active end groups with considerably less delocalization onto the bridge. This leads to a situation where the dioxidized or direduced homovalent systems are preferentially stabilized by solvation and ion pairing with respect to the MV radical ions. If, however, charge delocalization of the homovalent direduced or dioxidized systems is similar to that in the radical ions, the “normal” behavior of a diminishing value of ΔE1/2 with increasing number of repeat units of the bridge down to the statistical limit is observed. A similar situation was also met with tetraaminobenzenes 48−50 (Figure 17), particularly in more strongly ion pairing or polar media.88 Other examples showing an overall similar constellation can be found among dinitro-substituted arenes89,90 and tetraarylethenes.91,92

For tetraaminobenzenes 48−50, structural rearrangement on stepwise electron transfer and the concomitant increase of the inner reorganizational energy barrier for at least one of the electron transfer steps involved in the overall redox conversions also play a role, but only a minor one. There are, however, several cases where structure changes caused by a redox process are so profound that they cannot be accommodated by a single vibrational mode or a combination of several of them. In such cases the reactant is “vibrationally incompetent” to reach the transition state. In these cases, electron transfer and structural reorganization are decoupled and occur as two separate, consecutive steps. A sequence where electron uptake or release occurs first and is then followed by structural rearrangement seems to be more frequent than the inverse order, but there is precedence for both kinds of behavior, sometimes even as alternative pathways, depending on the conditions.93 While the interested reader is directed to instructive reviews on that subject,85,86 9,10-bis(1,3-dithiole-2-ylidene)-9,10-dihydroanthracene 51,94 the bis(phosphido)-bridged diiron hexacarbonyl complexes 52 (R = CH3, CF3, Ph),95 and fulvalenediyl dirhodium tetracarbonyl 5396 of Figure 18 are briefly discussed here as particularly instructive examples of such behavior. Due to repulsive steric interactions between the H atoms at the ortho positions, neutral 51 adopts a highly distorted saddlelike (or butterfly-like) structure where the 9,10-

Figure 18. Three examples of compounds showing the phenomenon of “potential inversion”. 4527


Organometallics

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electron transfer more facile than the first transfer, and hence for potential inversion, is thus attainment of a more favorable, stabilized structure for the ultimate product. For the aforementioned reasons, assessment of the electronic coupling in the mixed-valent state in such systems is not trivial or even impossible if Kc is so low that the equilibrium concentration of the mixed-valent intermediate decreases below the detection limit. Examples of “still waters” allowing for such analysis are the elongated versions of the divinylphenylenebridged diruthenium complex 41 of Figure 15, complexes 54− 56.98 The insertion of another styryl unit into the bridge creates two different stereoisomers with respect to the conformation of the central double bond, which may be trans or cis. Because of rapid electrocatalytic isomerization of oxidized 55, comparison of the intrinsic properties of these two stereoisomers required the synthesis of 56, where the cis stereochemistry of the central double bond is fixed by incorporation into a cyclohexenyl ring. Electrochemical oxidation of the trans isomer 54 occurs as two consecutive one-electron steps with a half-wave potential separation of only 49 mV, as was deduced by digital simulation of the cyclic voltammograms (Figure 20). This value is just

dihydroanthracene entity is folded around the central ring and the peripheral 1,3-dithione-2-ylidene moieties point in the opposite direction. Twofold oxidation to dication 512+ induces a major structural rearrangement as the inner 9,10-dihydroanthracene moiety flattens and the 1,3-dithione-2-ylidene substituents rotate out of that plane into an almost perpendicular orientation to the central ring (see Figure 19).

Figure 19. (left) Cyclic voltammogram of a 0.61 mM solution of compound 51 (upper curve) or of electrochemically generated 512+ (lower curve) at v = 2.0 V/s in 0.1 M DMF/NBu4+PF6−. Potentials are provided against the ferrocene/ferrocenium standard. (right) Computed structures of 51 in its relevant oxidation states. Figures are reproduced from ref 94 with permission.

Quantum chemical calculations indicated that radical cation 51•+ has a ground-state structure resembling that of 51, but with a more flattened central ring and a lesser upward bending of the dithione-2-ylidene appendices.94,97 Careful analysis of the cyclic voltammograms of 51 and their variation with sweep rate and concentration indicated that the second oxidation occurs at a potential ca. 285 mV negative of the first oxidation and that the second electron transfer step from the radical cation to the dication is slower than the first step. This latter finding is in agreement with the majority of the structural rearrangement occurring in the second step. For diiron complexes 52 (R = Me, CF3, Ph), the potential inversion is so large that no reliable estimate of ΔE1/2 was possible. Experimental and quantum chemical studies indicate that the overall two-electron reduction causes a major structural rearrangement within the Fe2P2 core of these complexes from a tetrahedron with an open vertex to a square. During this process the Fe−Fe distance changes from a bonding value of about 2.7 Å to a nonbonded value of ca. 3.6 Å. The calculated structure of the experimentally inaccessible mixed-valent radical anion is roughly intermediate, having a flattened-tetrahedral geometry with a Fe···Fe distance of ca. 3.3 Å.95 The structural changes involved in the overall conversion of 53 to 532+ involve rotation around the fulvalenediyl single bond from the preferred transoidal structure and contraction of the Rh−Rh distance from a nonbonded value to a Rh−Rh single-bond value. Geiger and co-workers have made a convincing case that the overall energy changes are almost evenly distributed over both individual electron transfer steps with bond rotation and formation of a partial Rh···Rh bond in the first step and further contraction of the Rh···Rh distance during the second step.96 In all of the above cases, the driving force for rendering the second

Figure 20. Distyrylethene-linked diruthenium complexes 54−56 and a comparison of experimental and simulated cyclic voltammograms.98

above the statistical limit of a system comprising two noninteracting redox sites. For the cyclohexenyl-fused cis isomer, ΔE1/2 is somewhat larger at 74 mV. The small ΔE1/2 values suggest that two very weakly coupled or even noninteracting redox sites are present and that the radical cations should be localized species on the verge of the class I/ class II borderline. It is therefore not surprising to see two Ru(CO) bands for the corresponding radical cations. Again, the low-energy Ru(CO) band of the MV radical cation is shifted to the blue from that of the neutral species, while the higher energy Ru(CO) band is shifted to the red from that of the dication. Geiger’s charge distribution parameters Δρ calculated from these shifts are 9% for the rigidified cis isomer 56•+ and 19% for trans-configured 54•+. Therefore, not only is the trend in ΔE1/2 again just opposite to the true degree of electronic coupling but also the ground-state delocalization of both isomers is clearly larger than one would have anticipated on the basis of redox splittings close to or slightly above the statistical limit. This is particularly emphasized by comparison to Geiger’s half4528


Organometallics

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Figure 21. (left) Structures of diamines 57−59 and comparison of geometric N−N separations and calculated charge-transfer distances RAB. (right) Electronic spectra of the MV radical cations (solid lines) and the homovalent dications (broken lines). Bridge-to-amine charge-transfer absorptions are marked by red stars and IVCT transitions by blue stars. Electronic spectra and formulas are reproduced from ref 83 with permission.

Figure 22. Polyene-, furan-, or thiophene-bridged analogues of the Creutz−Taube ion investigated by Launay, Spangler, et al.101

Despite the vanishingly low ΔE1/2 values, radical cations 57•+ and 58•+ clearly show an IVCT band in the near-infrared region in addition to a much more intense bridge-to-aminium chargetransfer band relating to a bridge-mediated ET.45,81,82 That IVCT band moves to higher energies and becomes less intense as the spatial separation between the triarylamine-based redox sites increases and is completely hidden underneath the bridgeto-amine charge-transfer band in 59•+. According to a Hushtype analysis and backed by quantum chemical calculations, the radical cations show appreciable electronic coupling with a nonzero value of HAB even for 59•+. These authors also noted that the calculated charge-transfer distances in these MV radical cations are much smaller than the physical separations between the nitrogen atoms d(N−N), which one would identify as the charge-bearing sites. In a further parallel to 54•+ and 56•+, EPR spectroscopy shows full spin delocalization for radical cations of the divinylphenylene and the divinylstilbenyl-bridged systems 57•+ and 58•+ with no signs of spin localization even at low temperature. Turning to relatives of the Creutz−Taube ion, Launay, Spangler, and co-workers have noted the appearance of interpretable IVCT bands of MV radical cations 60•+−64•+ (Figure 22) during titrations of the parent Ru(II)/Ru(II) tetracations with iodine as the oxidant in water or D2O.101 The derived HAB values of 60•+−62•+ are only modest at 180−240 cm−1 in water or 200−260 cm−1 in D2O and are about 250 cm−1 for 63•+ and 64•+ with heterocyclic bridges, but they are nevertheless worthy of note since none of these compounds showed any indication of a resolvable half-wave potential

sandwich manganese and chromium complexes of Figure 11. Complex 56•+ has the same charge distribution parameter Δρ as 17•+ with an ΔE1/2 value of 210 mV, while that of 54•+ strongly resembles those in complexes 18•+, 20•+, and 21•+, which all have ΔE1/2 values in the range 260−270 mV.66 Further demonstrating the large degree of electronic coupling, radical cations 54•+ and 56•+ are completely delocalized on the EPR time scale, as follows from the observation of identical hyperfine splittings to four equivalent phosphorus nuclei of the phosphine coligands at the metal atoms. Mixed-valent 54•+ and 56•+ thus show the same kind of behaviordelocalized on the EPR time scale but (partially) localized on the IR time scale as the radical cation of the doubly linked dimanganese complex 19•+ (Figure 11), where an ΔE1/2 value of 450 mV was observed. The same qualitative behavior of considerable electronic couplings despite the small ΔE1/2 values was found by Barlow et al. for bis(triarylamines) 57−59 (Figure 21).84 These latter compounds relate to diamine 43 of Figure 16 in the same way as complexes 54−56 relate to complexes 41 and 42: i.e., by insertion of additional styryl units into the nominal bridge. For the divinylphenylene-linked bis(triarylamine) 57 and its longer homologues 58 and 59 no splitting of the redox waves was observed. No attempts to digitally simulate the cyclic voltammograms and to determine ΔE1/2 have, however, been made in these cases. Considering the close resemblance between triarylamine- and alkenylruthenium-based redox systems,99,100 the ΔE1/2 values of 54 and 57 are probably very similar to each other. 4529


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splitting ΔE1/2 in cyclic voltammetry. Kc values derived from the spectroscopic changes during titrations are in the range of 9−11 for the polyene-bridged complexes but somewhat higher for the heterocyclically bridged species. The former Kc values translate into ΔE1/2 values in the range of 56−62 mV, which again is only slightly above the statistical limit of 36 mV. Other examples of “still waters” can be found among the oligoene-bridged diferrocenes 65•+−70•+ of Spangler, Launay, and co-workers (Figure 23). Voltammograms of these

two redox-active end groups are interconnected by a polyene, polyyne, polyenyne, oligo(arylenevinylene), or oligo(aryleneethynylene) bridge. Further examples of mixed-valent bridged biferrocenium radical cations behaving as “still waters” are the indacene- and trindene-derived compounds 71−74 in Figure 24 of Santi and his co-workers.103,104 Here, redox splitting is only observed in the presence of the very weakly ion pairing fluorinated tetraphenylborate counterion but not with the corresponding [PF6]− salt. When incremental amounts of acetylferrocenium ion were added to CH2Cl2 solutions containing 0.1 M [NBu4]+ [B(C6F5)4]−, the characteristic IVCT bands of the MV radical cations 71•+−74•+ were readily observed in addition to small amounts of fully oxidized 712+ to 732+ or 743+ (see Figure 24, right). These bands showed astoundingly large Γ values of 0.24, 0.25, 0.10, and 0.27 (see eq 10), which place these systems well into the regime of moderately to rather strongly coupled MV systems of class II. Most interestingly, the observability of the characteristic IVCT bands of the MV radical cations was intimately tied to the presence of the [NBu4]+[B(C6F5)4]− electrolyte. These bands were not observed in neat CH2Cl2 or in CH2Cl2 containing 0.1 M [NBu4]+[PF6]−, although statistics and the value of Kc still mandate that some amounts of the MV radical cations must also be present under these conditions. Similar examples are the heterocyclically bridged bis(ethynylferrocenes) 75−79 of Marken, Raithby and co-workers (Figure 25).105 Despite large Fe···Fe separations of over 13 Å

Figure 23. Oligoene-bridged diferrocenes investigated by Spangler and Launay.102

compounds showed two consecutive one-electron waves with ΔE1/2 values decreasing in the intuitive order 65 > 66 > 67 but only composite two-electron waves for 68−70 with their longer oligoenediyl bridges.102 Kc values derived from electrochemical measurements or from redox titrations and HAB values obtained from a Hush-type analysis of the IVCT bands steadily decrease with increasing metal-to-metal separation but still reach a value of about 200 cm−1 for 70•+, the longest member of this series. The Fe···Fe separation of 70 is 18.4−18.7 Å, depending on whether the ferrocenyl termini are cis-disposed (right in Figure 23) or trans-disposed (left in Figure 23) with respect to each other. From the plot of ln HAB versus the Fe···Fe distance an exceptionally small attenuation factor of only 0.087 Å−1 for the decay of the electronic coupling with increasing separation between the individual redox sites (or an even smaller value of 0.054 Å−1 for 65•+−67•+ and a larger value of 0.113 Å−1 for 67•+−70•+) was derived. Sizable electronic interactions in the MV states despite small half-wave potential splittings ΔE1/2 thus seem to be particularly common for compounds where

Figure 25. Bis(ferrocenylethynes) 75−79 with heterocyclic bridges and the HOMO of compound 76.105

Figure 24. (left) Indacene- and trindene-bridged bi- and triferrocenes 71−74. (right) Spectroscopic changes during stepwise oxidation of biferrocenes 71 and 72 and deconvolution of the LMCT and IVCT bands at the point of maximum concentration of the radical cations (reproduced from ref 103 with permission). 4530


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Figure 26. (left) Alkenyl ruthenium substituted cyclophanes 80−82. (right) Spectroscopic changes in the region of the Ru(CO) stretches in the IR during stepwise oxidation of compound 80. The inset shows the growth of the low-energy side of the IVCT band during the first oxidation and its intensity decrease during the second oxidation.106

Figure 27. (left) Isomeric bis(ferrocenyl)-substituted [2.2]paracyclophanes 83 and 84. (right) Changes in the vis/NIR spectra on stepwise oxidation of complex 83 to its dication.109,110

Ru(CO) bands at 1911 and 1972 cm−1, which, in terms of energies, are almost an exact superposition of that of neutral 80 (ν̃ 1911 cm−1) and that of fully oxidized 802+ (ν̃ 1973 cm−1). This result therefore points to complete charge localization on just one styryl ruthenium subunit of 80•+. Still, radical cation 80•+ shows a broad and weak electronic band that is specific to the MV state and has no counterpart in the similar complex 82•+ with just one vinyl ruthenium moiety. It hence fulfills all characteristics of an IVCT transition in a weakly coupled system.106 [2.2]Paracyclophane 81 constitutes an interesting counterpoint to [2.1]orthocyclophane 80. This compound has a redox splitting of 215 mV. For the derived MV radical cation 81•+, a ground-state charge delocalization of about 7% is derived from the Ru(CO) band shifts on applying Geiger’s charge distribution parameter Δρ (see Figure 10).65,66 This value is much larger than that of the half-open, ortho-linked 80•+ despite very similar through-bond distances between the charge-bearing sites but only about 14% of that in the para isomer and about 60% of that in the meta isomer of the divinylphenylene-bridged complexes 41•+ and 42•+ and even smaller than that in the stilbenyl-derived complexes 54•+ and

and small ΔE1/2 values of only 52−110 mV, the radical cations display very narrow IVCT bands. The Γ values (eq 10) derived from the original data in ref 105 are in the range of 0.5 and place these radical cations into the régime of strongly coupled mixed-valent systems. According to quantum chemical calculations, such strong couplings are fostered by the large contributions of the heterocyclic bridges to the corresponding HOMOs and the complete delocalization of that “redox orbital” over the entire molecule. Further accounts on the electronic coupling in mixed-valent bi- or oligoferrocenes with heterocyclic bridges have recently been reviewed by Hildebrandt and Lang.40 The “Pretenders”. After that collection of examples of “still waters”, which exhibit rather impressive degrees of electronic coupling despite only low ΔE1/2 values, we now turn to compounds that show the exactly opposite behavior: that is, no electronic coupling at all despite fairly large values of ΔE1/2. The half-open [2.1]orthocyclophane 80 of Figure 26 may be viewed as a borderline case of such systems. This compound has a redox splitting of 105 mV for the stepwise oxidation of the individual styryl ruthenium moieties. However, the IR spectrum of the singly oxidized radical cation 80•+ displays two resolved 4531


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Figure 28. Benzene- and pyridine-bridged bi- and triferrocenes and their cyclic voltammograms in CH2Cl2/0.1 M [NBu4]+[B(C6F5)4]−. The righthand part of this figure is reproduced with permission from ref 111.

56•+ with identical primary redox sites. This dichotomy most probably relates to the limited (in comparison to direct, through-bond conjugation), yet still operational, electronic coupling through space in the generic [2.2]paracyclophane architecture with parallel displaced decks (see also compounds 23/23′•+ and 24/24′•+ of Figure 12) which is essentially lost on going to the half-open clamshell-like structure of ortholinked 80•+. By simply changing the identity of the primary redox sites from alkenyl ruthenium to the ferrocenyl sites of compounds 83 and 84 (Figure 27), the same [2.2]paracyclophane architecture leads to complete charge localization on just one ferrocenyl site, irrespective of whether the ferrocenyl subunits are in the pseudo-para or the pseudo-ortho positions. In the weakly ion pairing supporting electrolyte [NBu 4 ] + [B{C6H3(CF3)2-3,5}4]− both complexes show two consecutive, resolved one-electron transfer waves with redox splittings of 112 and 60 mV, respectively. For both compounds a broad NIR band appears during progressive oxidation. This time, however, the NIR band continues to grow until full conversion to dications 832+ and 842+ and is hence not specific to the intermediate mixed-valent radical species. Quantum chemical calculations disclose that this band originates from d−d type transitions between the δ and the a1g (dz2) orbitals that are confined to the Fe atoms of the ferrocenium nuclei.107,108 Thus, despite resolvable redox splittings and despite the presence of an NIR band, radical cations 83•+ and 84•+ are fully localized species. It is the lack of conjugation between the peripheral redox sites and the [2.2]paracyclophane bridge which causes the difference from 81•+, whose phenyl decks are integral parts of the relevant redox sites.109,110 A similar situation is observed in 2,4,6-triferrocenyl-1,3,5triazine 85, where despite half-wave potential splittings of 140 and 185 mV, respectively, no IVCT bands were observed during stepwise oxidation inside a transparent thin-layer electrolysis cell. This is all the more remarkable since the radical cations and dications of 2,4,6-triferrocenyl-substituted benzene or pyridine species 86 and 87 as well as the radical cations of 2,5-diferrocenyl- and 2,6-diferrocenyl-substituted

pyridines 88 and 89 of Figure 28 all showed IVCT bands with the characteristics of weakly coupled MV systems of class II and half-widths that comply with the theoretical predictions given by eq 11. All of these compounds have ΔE1/2 values in essentially the same range as that for 85.111 Other examples of “pretenders” within the series of heterocyclically bridged oligoferrocenes are 2,3,4,5-tetraferrocenyl-substituted thiophene 90, furan 91, and pyrroles 92 and 93 (Figure 29). All four compounds are oxidized in four

Figure 29. Tetraferrocenyl-substituted thiophene, furan, and pyrroles investigated by Hildebrandt, Lang, and co-workers.

separate one-electron steps with half-wave potential separations of 186−331 mV for the first and the second or the third and the fourth oxidations, respectively. Here, the first two oxidations were assigned to the ferrocenyl substituents in positions 2 and 5, neighboring the heteroatom, and the third and the fourth oxidations to those in the 3- and 4-positions. The potential splittings between the second and the third oxidations hence include some contributions that account for the chemically different environments of the redox sites. Whereas radical cations and dications of 91−93 were found to exhibit interpretable IVCT bands, their further oxidation to mixedvalent 913+−933+ led to the complete disappearance of any NIR absorption. The half-wave potential splittings between the 2+/ 3+ and the 3+/4+ couples were therefore attributed to solely 4532


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Figure 30. Triarylamine-bridged dicobaltatetrahedrane clusters 94 and 95.112

Figure 31. Astruc’s oligo(ethynylferrocenyl)-substituted benzenes.113

[NBu4]+[B{C6H3(CF3)2-3,5}4]− as the supporting electrolyte were interpreted as being entirely due to electrostatic repulsions between spatially close or cisoid-arranged ferrocenyl redox sites.113 The above reasoning is mostly based on the observations of only one unresolved wave in the more ionpairing CH2Cl2/[NBu4]+[PF6]− supporting electrolyte and the fact that the para-disubstituted isomer 76 with transoiddisposed ferrocenyl subunits displays no redox splitting in both media. Sizable peak potential separations of up to 210 mV in some of the conformationally less restricted bis(ethynylferrocenes) were viewed as arising from slow electron transfer kinetics owing to redox-induced rotations around the Cp−CC axis (note that such rotation in the fulvalenediylbridged dirhodium complex 53 in Figure 18 occurs so rapidly that it does not lead to such slowing of electron transfer kinetics, though). The same reasoning was later employed to account for the observation of just one redox wave in rigid (ferrocenylethynyl)arylene dendrimers.114 As the example of the indacene- and trindene-bridged MV diferrocenes 71•+− 74•+ demonstrates,103,104 such reasoning should, however, be regarded as only tentative in lieu of spectroscopic data on the

electrostatic effects. Even more surprisingly, no IVCT transition was observed for thiophene-based 90n+ in any mixed-valent state (n = 1−3). This behavior thus is in marked contrast to that of 2,5-diferrocenylthiophene 25 in Figure 13. Another interesting case of a “pretender” has been reported by Low and co-workers.112 The triarylamine-bridged bis(dicobaltatetrahedrane) cluster 94 in Figure 30 undergoes two consecutive cluster-based one-electron oxidations with potential splittings of 100 and 220 mV, depending on whether the anion of the supporting electrolyte is [PF 6]− or [B(C6F5)4]−. IR spectra of the neutral and the radical cation and comparison with the results on the similar complex 95 with just one cluster unit clearly prove the valence-localized nature of 94•+. Again, this species has a weak, broad NIR band, but so do 95•+ with just one cluster subunit and dicationic 942+. This band is consequently due to an intra- but not an intercluster IVCT transition. Likewise, the redox splittings observed in 1,2-disubstituted or 1,3,5-trisubstituted benzene-bridged oligo(ethynylferrocenes) 96 and 97 and the observation of three consecutive twoelectron waves for 1,2,3,4,5,6-hexakis(ethynylferrocenyl)benzenes 99−101 (see Figure 31) in CH2Cl2 containing 4533


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provide valuable insight into the electronic coupling parameter HAB (VAB) or the degree of charge or spin delocalization between the individual redox sites of a MV compound. In particularly favorable cases, the change of spectra with temperature may even allow determining the rates of intramolecular electron transfer and the parameters ΔG, ΔH, and ΔS for that process. If such analyses rest on data extracted from the electronic spectra of MV species, one should be aware that NIR absorptions of open-shell systems may have origins other than IVCT. It is therefore important to verify the absence of such an absorption in any of the homovalent bordering states in order to avoid misinterpretation.

various, partially oxidized mixed-valent species featuring oxidized ferrocenium and reduced ferrocenyl subunits.

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AN ATTEMPT AT A BOTTOM LINE The preceding sections have provided various exemplary cases where ΔE1/2 scales with the degree of electronic coupling and other cases where this is clearly not the case. Among the latter are mixed-valent systems that exhibit strong electronic coupling despite small ΔE1/2 values and cases showing the exactly opposite behavior of no coupling at all despite appreciable values of ΔE1/2. Although the amendment of simple rules or a consistent rationale are not possible and would certainly be an oversimplification, some more general trends seem to emerge. Hence, the probability of finding a meaningful correlation between ΔE1/2 and the true electronic coupling in terms of ground state delocalization and charge or spin distribution in the MV state are highest in cases where the terminal redox sites and the bridge are well-defined and assume the roles that these terms imply. Even then, reliable comparisons between different compounds require that measurements are performed in similar electrolytes, since individual redox potentials and their separations strongly depend on any constituent of the electrolyte system.41,42 Particularly prone to failure of direct correlations between ΔE1/2 and HAB are systems where the nominal bridge actively participates in the redox processes or when the bridge just serves to hold the redox sites in spatial proximity but has no orbital overlap with the terminal redox sites. The first scenario is likely to produce large electronic couplings despite small halfwave potential splittings sometimes even just above the purely statistical limit or below. Typical examples are compounds where redox-active end groups with moderate intrinsic E1/2 values connect to fully π-conjugated bridges via direct arylene, alkenyl, or ethynyl functionalities and when these functionalities likewise contribute to the respective redox orbitals. Ironically enough, large bridge contributions seem to diminish ΔE1/2 although they place the effective redox sites in close spatial proximity by decreasing the effective RAB values. Sáveant has pointed out that the small magnitude of ΔE1/2 in such systems is often governed by large gains in solvation energies which stabilize the doubly oxidized or doubly reduced forms with respect to mixed-valent forms and that such extra stabilization may even lead to potential inversion.87 When, on the other hand, the bridge only serves as a scaffold to which the redox-active end groups are attached but has no orbital interaction with them, the redox splitting ΔE1/2 mainly arises from electrostatic repulsion between the charged sites. It is therefore strongly modulated by the abilities of the respective counterions to ion pair with and to intercalate between the charged sites so as to insulate one of them against the other or by the ability of the solvent to screen the charges at the individual redox sites against one another. In any event, it is clear that the value of ΔE1/2 for electron transfer from two or more interconnected redox sites provides at best a qualitative, but by no means quantitative, measure of ground-state delocalization of a MV system. It is not even a necessary condition for appreciable degrees of ground-state delocalization in the MV state. Any firm conclusions about the electronic coupling therefore need to be backed by spectroscopic measurements. In many cases, analysis of the IVCT band(s), the shifts and patterns of characteristic “marker” bands in vibrational spectroscopy, hyperfine splittings in EPR spectroscopy, or, if applicable, Mössbauer or NMR spectra

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ASSOCIATED CONTENT

* Supporting Information S

This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Notes

The authors declare no competing financial interest. Biography

Rainer F. Winter was born in Neustadt an der Weinstraße, a center of wine production in Germany. After studying Chemistry at the University of Kaiserslautern, he obtained a Ph.D. degree in 1993 under the auspices of Otto J. Scherer, working on niobium and tantalum complexes with substituent-free Pn and Asn ligands. During his postdoctoral studies with William E. Geiger (1993−1995) at the University of Vermont he was taught the ropes of electrochemistry and learned the power of an integrated approach combining electrochemistry with molecular spectroscopy. Coming back to Germany, he joined the group of Wolfgang Kaim at the University of Stuttgart for his habilitation, working on cumulenylidene complexes of ruthenium. In 2005 he became assistant professor at the University of Regensburg and in 2010 full professor at the University of Konstanz. His main research interests focus on mixed-valent compounds with metal− organic and organic redox sites, long-range electron transfer, (poly)electrochromic compounds, and dye-modified heavy-metal emitter molecules.

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ACKNOWLEDGMENTS This paper is dedicated to Claude Lapinte on the occasion of his retirement with best wishes. REFERENCES

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