Low Reorganization Energy for Electron Self-Exchange by a Formally Copper(III,II) Redox Couple

Abstract

The rate constant for electron self-exchange (k₁₁) between LCuOH and [LCuOH]⁻ (L = bis-2,6-(2,6-diisopropylphenyl)carboximido-pyridine) was determined using the Marcus cross relation. This work involved measurement of the rate of the cross-reaction between [Bu₄N][LCuOH] and [Fc][BAr₄^F] (Fc⁺ = ferrocenium; BAr₄^F = tetrakis[3,5-bis(trifluoromethyl)-phenyl]borate)) by stopped-flow methods at −88 °C in CH₂Cl₂ and measurement of the equilibrium constant for the redox process by UV–vis titrations under the same conditions. A value of k₁₁ = 3 × 10⁴ M⁻¹ s⁻¹ (−88 °C) led to estimation of a value 9 × 10⁶ M⁻¹ s⁻¹ at 25 °C, which is among the highest values known for copper redox couples. Further Marcus analysis enabled determination of a low reorganization energy, λ = 0.95 ± 0.17 eV, attributed to minimal structural variation between the redox partners. In addition, the reaction entropy (ΔS°) associated with the LCuOH/[LCuOH]⁻ self-exchange was determined from the temperature dependence of the redox potentials, and found to be dependent upon ionic strength. Comparisons to other Cu redox systems and potential new applications for the formally Cu^III,II system are discussed.

Graphical Abstract

INTRODUCTION

With the aim of evaluating proposals for intermediates involved in catalytic oxidations by enzymes,¹ materials,² and molecular systems,^3,4 copper complexes at high formal oxidation states (>II) have been targeted for characterization and evaluation of their reactivity.⁵ Notable examples include complexes with [Cu₂(μ-O)₂)]²⁺,⁶ [Cu₂(μ-OH)]ⁿ⁺ (n = 4 or 5),⁷ [CuO₂]⁺,⁸ and [CuOH]²⁺⁹ cores postulated to contain formally Cu(III) ions; Cu(III) ions also have been stabilized by a variety of tetradentate anionic ligands¹⁰ and isolated with a metal–carbon bond.¹¹ In recent work, we found that LCuOH (Figure 1) and derivatives rapidly attack C–H and O–H bonds, and through detailed kinetic, thermodynamic, and computational studies, we evaluated the mechanisms and key underlying reasons for their fast reactions.⁹ Typically, the complexes abstract H atoms in a concerted proton–electron transfer (CPET) process driven by the formation of a strong O–H bond in the product complex comprising the [Cu(OH₂)]²⁺ core (bond dissociation enthalpy, BDE, ~ 90 kcal/mol for complex supported by L²⁻).^9b,c This high BDE was determined through a square-scheme analysis (Figure 1) for LCuOH, with the low E_1/2 for the Cu^III,II couple (−0.074 V vs [Fc]⁺/Fc) being offset by the high pK_a for [LCuOH]⁻ (~19 in THF). Through application of an Evans–Polanyi (linear free energy) relationship, we proposed that the strength of the O–H bond in LCu(OH₂) is a key contributor to the fast CPET reactions observed.^9b,c

Figure 1.

(Top) Redox couple examined in this study, with formal oxidation states noted in the structures. (Bottom) Thermodynamic square scheme.

To explore other kinetic factors that may be at play, we have more closely examined the formally Cu^III,II redox process by which LCuOH and [LCuOH]⁻ interconvert. In particular, noting that the two complexes appear to have similar square planar geometries with structures that differ only with respect to the metal–ligand bond distances (average Cu–N/O bond shortens by 0.09 Å upon oxidation),^9a we wondered if electron transfer (ET) self-exchange rates would be fast and the associated reorganization energy (λ) would be low. Kinetic studies of ET reactions involving Cu^III,II couples are rare, the only examples of which we are aware being those of oligopeptide¹² and imine–oxime complexes.¹³ Self-exchange rate constants k₁₁ ~ 5 × 10⁴ M⁻¹ s⁻¹ and ~5 × 10⁵ M⁻¹ s⁻¹ at 25 °C, respectively, were measured for these complexes in H₂O.^12a,13 Reaction entropies for the reduction of Cu^III to Cu^II were also determined for some oligopeptide complexes, using temperature-dependent cyclic voltammetry in H₂O and CH₃CN. These results were interpreted to indicate differences in solvent coordination between the two redox states (no binding to Cu^III, axial binding to Cu^II).¹⁴ The paucity of data on Cu^III,II systems contrasts with extensive information on Cu^II,I couples.¹⁵ Among the various factors that impact ET rates in such systems, geometry differences between the Cu^II and Cu^I states are particularly important. For example, ligand-induced distortions toward geometries intermediate between those favored for Cu^II (square planar) or Cu^I (tetrahedral) lowers λ and results in fast ET rates.¹⁵ Such effects have implications for understanding fast rates of ET in biological type 1 sites¹⁶ and for uses of copper complexes as redox mediators, such as in dye-sensitized solar cells.^17–19

Herein, we describe the determination of k₁₁, λ, and ΔS° for the LCuOH/[LCuOH]⁻ couple (formally Cu^III/II) that is central to the proton-coupled electron transfer chemistry related to the thermodynamic square scheme shown in Figure 1. Analysis of these results provides fundamental new insights into formal Cu^III,II redox processes important in oxidation catalysis.

RESULTS

We aimed to use the Marcus relation eq 1 to determine λ. A key constraint is the inherent difficulties in isolating and handling LCuOH that made the use of NMR line broadening methods to directly determine k₁₁ untenable. Instead, we targeted the rate- and equilibrium-constants (k₁₂ and K₁₂ respectively) for the cross reaction between [LCuOH]⁻ and ferrocenium ([Fc]⁺), for use in the appropriately modified form of the Marcus cross-reaction expression to determine k₁₁ (Scheme 1, eq 2).²⁰

$$k_{11}=Z\text{exp}\left(\frac{-\lambda }{4RT}\right)$$ (1)

$$k_{12}=\sqrt{k_{11}{k}_{22}{K}_{12}{f}_{12}}{W}_{12}$$ (2)

Scheme 1. ET Reactions and Associated Rate and Equilibrium Constants Considered in This Work.

To measure K₁₂, we generated LCuOH by treatment of a solution of [Bu₄N][LCuOH] (0.1 mM) at −88 °C with [Fc][BAr₄^F] (BAr₄^F = tetrakis[3,5-bis(trifluoromethyl)phenyl]-borate). All of the experiments in this report were done in CH₂Cl₂; the optical experiments were all at −88 °C. Complete conversion was observed with a slight excess of oxidant (Figure S1). Comparison of the UV–vis spectra of LCuOH (ε_{560 nm} = 11000 (±400) M⁻¹ cm⁻¹) to those of independent preparations using a stronger oxidant, [AcFc][BAr₄^F] confirmed the measured ε_{560 nm} value (Figure S1). A back-titration was then performed by adding aliquots of a solution of ferrocene (50 μL, 4.0 mM stock solution, 1 equiv) to LCuOH generated from the reaction of [LCuOH]⁻ with [Fc]⁺. From the absorbance changes at 560 nm, the concentrations of the compounds in the cross reaction were deduced and K₁₂ was determined to be 400 ± 50 (see Supporting Information for details; Table 1).

Table 1.

Relevant Kinetic and Thermodynamic Parameters

parametera	value
k12	6 (±2) × 107 M−1 s−1
k22b	5.6 × 105 M−1 s−1
K12	400 (±50)
k11	3 (±8) × 104 M−1 s−1
k11′ (25 °C)c	9 × 106 M−1 s−1
λ	0.95 (±0.17) eV
λo	0.50 eV
λi	0.45 eV
S°(Cu) (I = 1.0 M [NBu4][PF6])	−3.1 (±0.4) cal mol−1 K−1
S°(Cu) (I = 0.2 M [NBu4][PF6])	−23 (±0.5) cal mol−1 K−1
S°(Fc*)d (I = 0.1 M [NBu4][PF6])	3.1 (±0.2) cal mol−1 K−1

^aAll rate and equilibrium constants determined at −88 °C, except where noted.

^bReference 21.

^cExtrapolated from −88 °C using λ in eq 1.

^dReference 22.

The cross-reaction rate constant k₁₂ was measured by stopped-flow kinetics performed at −88 °C in CH₂Cl₂. The reaction was followed by UV–vis spectroscopy in the range 400–800 nm at 1.7 ms intervals. Mixing 0.1 mM solutions of [Bu₄N][LCuOH] and [Fc][BAr₄^F] resulted in rapid conversion to LCuOH. Indeed, even under these dilute conditions the reaction was already >70% complete on the mixing time scale (~1–2 ms), complicating efforts to calculate an accurate rate constant. Nonetheless, global analysis of the data using ReactLab KINETICS²³ provided a good fit to a simple, second order reaction mechanism (Figure 2), yielding k₁₂ = 6 (±2) × 10⁷ M⁻¹ s⁻¹ (average of four measurements).²⁴

Figure 2.

(a) Stopped-flow spectra collected every 1.7 ms during the reaction of 0.1 mM [Bu₄N][LCuOH] with 0.1 mM [Fc][BAr₄^F] in CH₂Cl₂ at −88.0 °C. Black curve is the spectrum of 0.1 mM [Bu₄N][LCuOH]. (b) Experimental and modeled single wavelength profiles at 560 nm.

Use of eq 2 also required determination of the “work term” W₁₂, which was estimated to be 23.3 ± 1.2 (unitless) from individual work terms associated with formation of the precursor/successor complexes of the cross- (w₁₂ and w₂₁) and self- (w₁₁ and w₂₂) exchange reactions (see Supporting Information, eqs S5–S7). The measured equilibrium constant K₁₂ was used directly in eq 2 and the [Fc]⁺/Fc self-exchange rate constant (k₂₂ at −88 °C) was taken as 5.6 × 10⁵ M⁻¹ s⁻¹ (error analysis provided in Supporting Information).²¹ Together, the measured values of K₁₂, k₂₂, W₁₂ and f₁₂ (1.0; see Supporting Information) lead to a LCuOH/[LCuOH]⁻ self-exchange rate constant (k₁₁) of 3 (±8) × 10⁴ M⁻¹ s⁻¹ at −88 °C in CH₂Cl₂. Substituting this value of k₁₁ (which due to uncertainties in k₁₂ is given to only one significant figure) into eq 1, using Z = 10¹¹ M⁻¹ s⁻¹ and the relevant values of R and T, yields a reorganization energy λ of 0.95 (±0.17) eV for the LCuOH/[LCuOH]⁻ electron exchange reaction. To facilitate comparisons to self-exchange rates reported for other systems (see Discussion), k₁₁ = 9 × 10⁶ M⁻¹ s⁻¹ at 25 °C was estimated using this λ in eq 1.

The measured reorganization energy (λ) is the sum of the outer-sphere and inner-sphere contributions, λ_o and λ_i, respectively (eq 3).²⁰ The outer sphere reorganization energy can be estimated by eq 4, where Δe is the elementary charge transferred during the self-exchange reaction (1), a₁ and a₂ are the radii of LCuOH and [LCuOH]⁻, r is the center-to-center separation distance (a₁ + a₂), and D_stat and D_opt are the static- and optical-dielectric constants of CH₂Cl₂ (at −88 °C). Substituting the relevant values for each of these parameters into eq 4 leads to an approximate estimate λ_o = 0.50 eV (see Supporting Information), thus giving λ_i = 0.45 eV.

$$\lambda ={\lambda }_{\text{i}}+{\lambda }_{\text{o}}$$ (3)

$${\lambda }_{\text{o}}={(\Delta \text{e})}^2\left[\frac{1}{2a_1}+\frac{1}{2a_2}-\frac{1}{r}\right]\left[\frac{1}{D_{\text{opt}}}-\frac{1}{D_{\text{stat}}}\right]$$ (4)

The reaction entropy (ΔS°) associated with the LCuOH/[LCuOH]⁻ self-exchange was determined from the temperature dependence of the redox potentials of the [LCuOH]^0/− couple (E°(Cu)) and an internal standard (E°(standard)) using an isothermal electrochemical cell (eq 5). The experimental procedure for these measurements has been described.²⁵ Decamethylferrocene (Fc*) was selected as the internal reference (“standard”) because its redox potential is well resolved from the copper couple and ΔS°(Fc*) had been measured previously in CH₂Cl₂ (3.1 cal mol⁻¹ K⁻¹).²² The half-wave potential E_1/2 determined by cyclic voltammetry in CH₂Cl₂ was used as an approximation for E° after this assumption was validated for both redox couples (see Supporting Information). The voltammetry is shown in Figure 3A with 0.2 M [Bu₄N][PF₆].

Figure 3.

(a) Temperature-dependent cyclic voltammograms of [Bu₄N][LCuOH] (1.0 mM) + Fc* (0.5 mM) in CH₂Cl₂, at 1.0 M (blue) and 0.2 M (red) electrolyte (TBAP = [NBu₄][PF₆]). 0.2 M [Bu₄N][PF₆] as electrolyte; sweep rate = 50 mV s⁻¹. (b) Plot of ΔE_1/2 vs T, where ΔE_1/2 = E_1/2(Cu) − E_1/2(Fc*).

As the temperature is raised, E_1/2(Cu) undergoes a perceptible shift to more negative potentials while E_1/2(Fc*) concomitantly undergoes a slight positive shift (Figure 3A). A plot of the differences between E_1/2(Cu) and E_1/2(Fc*), as a function of temperature, is shown in Figure 3B. Fitting this data to a linear function (eq 5) yields a line with a slope of 1.16 × 10⁻³ V K⁻¹. From the known value of ΔS°(Fc*) (3.1 cal mol⁻¹ K⁻¹) and the slope, ΔS°(Cu) is calculated to be −23 (±0.5) cal mol⁻¹ K⁻¹. The opposite signs of ΔS°(Fc*) and ΔS°(Cu) relate to the differences in charge (vida infra). More striking are the different magnitudes of ΔS° which indicate that reduction of LCuOH is accompanied by more significant complex/solvent rearrangement. Suspecting that the larger magnitude of ΔS°(Cu) was due to ion-pairing effects, the voltammetry was remeasured with a higher (1.0 M) concentration of electrolyte (Figure S6). A much smaller temperature-dependent difference between E_1/2(Cu) and E_1/2(Fc*) was observed (slope = −2.7 × 10⁻⁴ V K⁻¹) leading to ΔS°(Cu) = −3.1 ± 2 cal mol⁻¹ K⁻¹. The implications of this significant sensitivity of ΔS°_Cu to ionic strength are discussed below.

$$\frac{\text{d}(E°(\text{Cu})-E°(\text{ standard })}{\text{d}T}=-nF\left[\Delta S°(\text{Cu})-\Delta S°(\text{ standard })\right]$$ (5)

DISCUSSION

Since the results reported herein apparently represent the first determination of λ for a formally Cu^III,II couple, comparisons to other copper systems are important to draw in order to put the findings into context. We compile a selection of such systems comprising Cu^II,I couples in Table 2 and Figure 4, which includes representative compounds and copper protein active sites that exhibit a range of λ values. Also shown are some examples of compounds for which self-exchange rate data are known but for which λ values are not, including data for the Cu^III,II couples [Cu^III,II(H₋₂Aib₃)]^0/− and [Cu^III,IIHLⁿ]^2+/+; in the former and a few other cases, values of λ are estimated using eq 1 and are included in Table 2. Values of λ are estimated using eq 1 and are included in Table 2.

Table 2.

Comparison of Published Copper Self-Exchange Rate Constants (k₁₁) and Reorganization Energies (λ) for Species Depicted in Figure 4

		λ (eV)	k11 (M−1 s−1)	conditions	reference
type I proteins	azurin (CuII,I)	0.82	7.94 × 105 to 1.26 × 106	H2O, 25 °C	30–32
	plastocyanin (CuII,I)	0.72	3.16 × 105 to 6.31 × 105	H2O, 25 °C	33, 34
	nitrite reductase (CuII,I)	0.77	–	H2O, 25 °C	41
“classical” copper(II,I) complexes	[CuII,I(phen)2]2+/+	2.4	50	H2O, 22 °C	26–28
			0.2	CH3CN, 25 °C
	[CuII,I(bipy)2]2+/+	1.88	4.4 × 103	H2O, 25 °C	27
	[CuII,I(bib)2]	2.8c	0.16	CH3CN, 25 °C	53
constrained copper(II,I) complexes	[CuII,I(dmp)2]2+/+	2.28c	23	CH3CN, 25 °C	54
	[CuII,I(SC6F5)(iprtpz)]0/+	1.58c	1.76 × 104	acetone-d6, −20 °C	55
			3.14 × 105	acetone-d6, 25 °C
	[CuII,I(H2TpyNMes)Cl]+/0	1.33c	2.4 × 105	THF, 25 °C	46
	[CuII,I(TMGqu)2]2+/+	0.77	1.2 × 104	CH3CH2CN, 20 °C	36, 37
			4.2 × 10−3	CH2Cl2, −90 °C
	[CuII,I(DMEGqu)2]2+/+	0.89	5.4 × 102	CH3CH2CN, 20 °C	36
	[CuII(UN-O−)(O2•−/O22−)]2+/+	0.81a	–	CH2Cl2, −80 °C	42
copper(III,II) complexes	[LCuIII,II(OH)]0/−	0.95	3 × 104	CH2Cl2, −88 °C	this work
			9 × 106	CH2Cl2, 25 °C	this work
	[CuIII,IIHLn]2+/+	b	5 × 105	H2O, 25 °C	13
	[CuIII,II(H−2Aib3)]0/−	1.48c	5.5 × 104	H2O, 25 °C	12

^aThe reorganization energy of the [Cu^II(ON-O⁻)(O₂^•−/O₂²⁻)]^2+/+ self-exchange was determined by calculating λ_o for the complex in CH₂Cl₂ at −80 °C (using eq 4 and the information in the Supporting Information of ref 42) and adding this value to the computed value of λ_in.

^bThe reported k₁₁ for this complex may have been derived incorrectly using parameters from PCET steps.¹³ Therefore, no λ was estimated for this complex.

^cCalculated from eq 1 using the measured k₁₁.

Figure 4.

Schematic representation of electron-transfer self-exchange properties of copper centers in proteins and model complexes (all experimentally determined, except those italicized with asterisks^36,37). Reorganization energies (eV) are given in blue, and self-exchange rate constants (M⁻¹ s⁻¹, at 25 °C) are given in parentheses. Complexes in black are coordination number invariant during redox-cycling; complexes in navy change coordination number. Complexes are depicted in their reduced forms.

Large reorganization energies (>1.5 eV) accompany Cu^II,I self-exchange (ET) reactions with “classical” copper compounds bearing, for example, phenanthroline (phen) or bipyridine (bipy) ligands.^15,26–28 Cuprous complexes bearing such N-donor ligands are characteristically 4-coordinate, while oxidation is typically accompanied by an increase in coordination number.²⁹ The geometries are also significantly different, with Cu(I) adopting a tetrahedral or “seesaw” geometry while the preferred geometry of copper(II) is either trigonal bipyramidal or square pyramidal. These changes in coordination number and geometry which accompany electron transfer work synergistically to yield large reorganization energies and sluggish rates of electron transfer, typically characterized by rate constants of 10⁰–10² M⁻¹ s⁻¹.¹⁵

The electron self-exchange rate constant we measured for the LCuOH/[LCuOH]⁻ couple is much larger: k₁₁ = 3 × 10⁴ M⁻¹ s⁻¹ at −88 °C and estimated to be ~ 9 × 10⁶ M⁻¹ s⁻¹ at 25 °C. This latter value is similar to that reported for type 1 Cu proteins (10⁵ – 10⁶ M⁻¹ s⁻¹).^16b,30–34 Also, the value we measured at −88 °C is 7 orders of magnitude larger than that measured at −90 °C in CH₂Cl₂ for [Cu^II(TMGqu)₂]²⁺/[Cu^I (TMGqu)₂]⁺ self-exchange (10⁻³ M⁻¹ s⁻¹) (Figure 4),³⁵ which has been touted as a definitive example of a complex held in an entatic state (in a geometry poised between the extremes typical for Cu^I and Cu^II species and thus expected to undergo fast ET reactions).^36–40 Finally, the estimated k₁₁ value for LCuOH/[LCuOH]⁻ ET at 25 °C (in CH₂Cl₂) is ~10 or 100 times larger than those for the known Cu^III,II couples supported by imine–oxime or tetramide (H₋₂Aib₃) ligands (in H₂O), respectively (Figure 4).^12,13 In separate work, it was shown for the latter system that the Cu^III congener is strictly four-coordinate but the Cu^II complex is axially coordinated by one or two solvent water molecules.¹⁴ Thus, slower electron exchange may be rationalized by coupling of ET with a chemical reaction (ligand coordination/decoordination). On the basis of the much faster rates of electron transfer observed in our study, we postulate that ligand exchange does not accompany LCuOH/[LCuOH]⁻ ET in CH₂Cl₂; this postulate is further substantiated by the electrochemistry data (vide infra).

Consistent with the fast electron self-exchange kinetics, a low λ value of 0.95 eV was determined for the LCuOH/[LCuOH]⁻ couple that is only slightly larger than those reported for type 1 Cu proteins^30–34,41 and calculated for the Cu/(TMGqu)₂ and Cu/(DMEGqu)₂ complexes.^36–40 The inner sphere reorganization energy derived from our measurements for the LCuOH/[LCuOH]⁻ system is very small (0.45 eV), indicating that almost half of the total energetic cost is due to reorganization of the solvent in the outer coordination sphere (λ_o = 0.50 eV). By comparison, λ_o values of 0.5–0.6 eV have been reported for redox couples of other systems measured in DMF or CH₂Cl₂.^42,43 The low λ_i is consistent with minimal structural change upon electron self-exchange, as indicated by a small difference in the Cu–N and Cu–X bonds (by ~0.1 Å), but no other significant reorganization of the coordination sphere for LCuX/[LCuX]⁻ pairs (X = OH or Cl).^9a,44 Interestingly, the λ_i we measured is comparable to that measured for electron exchange involving superoxide/peroxide ligands in the [Cu^II(ON–O⁻)(O₂^•−)/(O₂²⁻)]^2+/+ complexes (λ_i = 0.4 eV).⁴² The superoxide/peroxide exchange is ligand-rather than metal-centered and is accompanied by a small change in the solid-state structures. Indeed, all the examples reported to have λ < 1 eV appear to have such structural similarities between their redox states (small differences in metal–ligand bond distances and angles).

A related copper system supported by a mesitylene-substituted terpyridine ligand, “H₂Tpy^NMes” is also a valuable comparator. When prepared with chloride as the auxiliary ligand, the resulting Cu^II and Cu^I complexes are both square planar (Figure 4) and fast Cu^II,I self-exchange kinetics were observed (k₁₁ = 2.4 × 10⁵ M⁻¹ s⁻¹).⁴⁵ This system provides a particularly interesting comparison to LCuOH/[LCuOH]⁻ because the charges and reduction potentials are very different, yet the structural similarities are striking and, in both cases, redox exchange involves a persistent square-planar geometry that correlates with fast kinetics. Lastly, we note that the low λ is a bit surprising in light of the importance of ion pairing in this system (vide infra). As noted by Savéant,⁴⁶ the occurrence of ion pairing can add an additional free energy term to the intrinsic barrier, or can add mechanistic complexity. Both effects should slow the reactions, so the very rapid reaction reported here is particularly remarkable.

We next compare ΔS° associated with reduction for the [Cu^III,II(H₋₂Aib₃)]^0/− and [LCuOH]^0/− systems. For the former, ΔS° was reported to be −17.0 and −13.1 cal mol⁻¹ K⁻¹ in 1.0 and 0.1 M aqueous solutions of [Na][ClO₄], respectively.¹⁴ For the latter, we found ΔS° to be −3.1 and −19 cal mol⁻¹ K⁻¹ in CH₂Cl₂ with 1.0 and 0.2 M concentrations of [Bu₄N][PF₆], respectively. Thermodynamic relationships that underpin solvent- and complex-dependent reaction entropies are sophisticated and often involve a range of parameters, thus complicating comparison of specific values between systems.^47,48 Nonetheless, we can attribute the differences in the dependencies of the ΔS° values on ionic strength for the two systems to ion pairing effects. In water, ion-pairing between [Cu(H₋₂Aib₃)]⁻ and the electrolyte counterion is minimal because of the high polarity of the solvent.⁴⁹ Thus, a 10-fold increase in ionic strength does not appreciably alter the effective dielectric constant (ε_eff) of the medium. Since ΔS° is inversely proportional to ε_eff (albeit with exceptions),⁴⁹ this small change in ε_eff results in a minimal dependence of ΔS° on ionic strength for the [Cu^III,II(H₋₂Aib₃)]^0/− system. In contrast, ion pairing is significant in CH₂Cl₂.^{50, 51} Reduction of LCuOH is therefore expected to be accompanied by formation of the [LCuOH]-[Bu₄N] ion pair complex, and at higher electrolyte concentrations the [Bu₄N]⁺ cation is more readily available and less outer-sphere reorganization is required en route to formation of the ion pair. A 5-fold increase in the concentration of [Bu₄N][PF₆] also significantly increases ε_eff because of the lower polarity of the CH₂Cl₂ solvent.⁵⁰ The net result is a significant dependence of ΔS° on the electrolyte concentration for the [LCuOH]^0/− system.

The low value of ΔS° for [LCuOH]^0/− (−3.1 cal mol⁻¹ K⁻¹), which is similar to ΔS° for [Fc*]^+/0 (3.1 cal mol K⁻¹), is strong evidence that solvent is not coordinated to the copper complex in either oxidation state. One of the reasons decamethylferrocene is considered the “gold standard” internal reference for electrochemistry is because its redox potential is essentially constant in a variety of solvents.²² This behavior is attributed to small structural differences between [Fc*]⁺ and Fc*, and weak solute–solvent interactions. These characteristics are correlated with small values of ΔS°, especially in nonpolar, or slightly polar solvents like CH₂Cl₂. The similar magnitudes of ΔS° for the [Fc*]^+/0 and [LCuOH]^0/− half reactions therefore indicate that in both cases electron transfer is accompanied by minimal reorganization within the inner- and outer-coordination spheres (i.e., solvent is not exchanged). The opposite signs of ΔS° for the two reactions clearly relate to the differences in charge; LCuOH reduction leads to the acquisition of a negative charge and minor organization of the solvent around the charged ion (a small loss of entropy), while [Fc*]⁺ reduction leads to charge neutralization and dissipation of the preorganized solvent cage (a small gain in entropy).

CONCLUSIONS

We analyzed low temperature stopped-flow kinetics, electro-chemical, and UV–vis spectroscopic data using the Marcus relations to determine key parameters for electron self-exchange between the complexes LCuOH and [LCuOH]⁻ (Table 1). Key findings were a fast ET rate, low reorganization energy, and a ΔS° associated with reduction of LCuOH that is sensitive to ionic strength but is small at high concentrations of electrolyte. Comparisons to the few other Cu^III,II systems and the more extensive data for Cu^II,I couples, including biological type 1 copper sites (Table 2, Figure 4), highlights the LCuOH/[LCuOH]⁻ system as having among the fastest ET rates and lowest λ values. These results, in particular the low λ_i of 0.45 eV, are consistent with minimal structural differences between the complexes. By analogy, we propose that a low ET reorganization energy at least partially underlies the previously reported fast rates of PCET by LCuOH. While PCET intrinsic barriers do not always correlate with ET ones in the same system, the inner-sphere rearrangements are often similar.⁵² For example, large changes in V–O distances in a vanadiumdioxo system gave a large PCET intrinsic barrier.^53d Thus, the rigidity of the LCuOH system should facilitate PCET as well as ET. These factors might also be important in catalysis by Cu(III) centers proposed as intermediates in oxidase and oxygenase enzymes.^1,5

Finally, we note that the low reorganization energy for the LCuOH/[LCuOH]⁻ system has potential implications for adoption of these or similar species as redox mediators. Notably, the similarities between the properties of Cu^II,I complexes used as highly efficient redox mediators and hole transport materials in dye sensitized solar cells (DSCs) with those of LCuX/[LCuX]⁻ systems we have described herein suggests that explorations of the latter for potential DSC applications might be worthwhile.