Electrochemical Mechanisms of Copper Bipyridine Complexes in Dichloromethane and Water

Voltammetric mechanisms for copper bipyridine complexes are evaluated for Cu(bpy)3(PF6)2 in dichloromethane (DCM), Cu(bpy)3(ClO4)2 in water, and copper bipyridine complexes formed in situ from a stoichiometric 1:3 mix of Cu(II) and bpy in water. The mechanism for Cu(bpy)3(PF6)2 in aprotic DCM is a simple irreversible (slow) heterogeneous electron transfer, Eirrev , with a standard heterogeneous electron transfer rate of 6 × 10−4 cm s−1. For Cu(bpy)3(ClO4)2 in water near pH 6, the mechanism is a six species square scheme, with multiple chemical and electrochemical steps. Voltammetric morphologies for Cu(bpy)3(PF6)2 in DCM and Cu(bpy)3(ClO4)2 in water were evaluated by established diagnostics and modeled with digital simulations. Established diagnostics underrepresent the complexity of copper bipyridines in water. For the complexes formed in situ, the stoichiometric ratio is insufficient to form only Cu(bpy)3 2+, so an equilibrium model that characterizes speciation at given pH and electrode potentials is used. Solvent, pH, and speciation impact the observed voltammetry of copper bipyridine complexes.

Transition metal complexes form when ligands chelate a metal. The configurations the complex can adopt, or speciations, vary with metal and ligand. For transition metals near the middle of the d-block, 1 speciations of 2,2′-bipyridine (bpy) complexes are well characterized, but complexes of early and late transition metals are studied less thoroughly. The Ru(bpy) 3 2|3 couple is exploited as an outer sphere redox reagent in diverse electrochemical systems because the bipyridine ligands are firmly bound to ruthenium across a large range of pH and oxidation states in a variety of solvents. In contrast, copper bipyridine complexes are more varied and are dependent on solvent, pH, and relative concentrations of metal and ligand in the electrolyte.
Of the copper complexes of 2,2′-bipyridine, copper di-and mono-cations chelated with either two or three bipyridine ligands are most common. 2, 3 Garribba and coworkers 2 characterized numerous complexes formed with various ratios of 2,2′-bipyridine and Cu 2+ across pH from 4 to 11, with EPR, IR spectroscopy, and UV-Vis spectrophotometry. The triscomplex is described as an elongated octahedron, while the biscomplex adopts a tetragonal geometry in water. From distribution diagrams for pH of 4 to 11, Cu(bpy) 3 2+ is the dominant species in solution when more than four equivalents of bpy are available for complexation to copper. Additionally, the formal electron count of copper complexes may help explain the diverse complexation profiles. Cu(bpy) 3 2+ can be assigned 20 electrons using the covalent electron counting method, while the biscomplex of the same oxidation state is more stable with 16 electrons. Speciation and complex stability are central to emergent research on first row transition metal complexes.
Copper bipyridine complexes are of technological interest and are exemplars for the voltammetry and speciation of other first row transition metal complexes of bipyridine such as Cr(bpy) 3 3+ and Co(bpy) 2 + . 4,5 Copper tris-bipyridine complexes have been used to quench the excited state emissions of Ru(bpy) 3 2+ in materials, 6 and as critical components of bridged bimetallic structures for molecular magnets. 7 Cu(bpy) 3 2+ properties of electron energy, redox potential, and speciation contribute to the properties of these advanced materials, all of which can be assessed voltammetrically.
Voltammetry of transition metal complexes captures the intertwining of equilibrium and kinetics through characterization of redox potentials, speciation, and the stability of ligand chelation. Kinetic rates are assessed relative to the voltammetric perturbation rate, the scan rate ν. Voltammetric morphology reflects chemical and electrochemical reactions, where electron transfer processes are denoted  steps and chemical processes are  steps, and combinations of  and  steps are common.
A typical experimental protocol is: qualitative evaluation of voltammetric morphology with scan rate; quantitative evaluation of the apparent mechanism with established mathematical diagnostics; 8 and mechanism modeling by simulation and equilibrium models. Well established diagnostics rely on cyclic voltammetric characteristics that include peak splitting ΔE p , ratio of forward and reverse peak currents i p,f /i p,b , and linearity of i p,f with ν 1/2 . Often, the mechanisms assigned by established diagnostics underestimate the mechanistic complexities identified by simulation.
Two reports of copper bipyridine complex electrochemistry are found in the literature. Polarography is reported by Onstott and Laitinen. 3 From half wave potentials, dissociation or instability constants (K) for Cu(II) bisand tris-bipyridine complexes are reported as (K 2 = 6.3 × 10 −15 ) and tris-(K 3 = 1.4 × 10 −18 ), respectively. Inverse dissociation constants are stability constants. The mechanism posed is reduction of the triscomplex followed by loss of one bipyridine and a second reduction of the biscomplex to form copper amalgam with loss of two bipyridines. Majumdar and coworkers 9 report cyclic voltammetry of Cu(bpy) 3 (ClO 4 ) 2 in acetonitrile at 50 mV s −1 . Half wave potential E 1/2 of 0.04 V vs SCE for a quasireversible, one electron reduction is reported.
Here, voltammetric mechanisms are evaluated for Cu(bpy) 3 (PF 6 ) 2 in dichloromethane (DCM), Cu(bpy) 3 (ClO 4 ) 2 in water, and copper bipyridine complexes formed in situ from a stoichiometric 1:3 mix of Cu(II) and bpy in water. The mechanism for Cu(bpy) 3 (PF 6 ) 2 in aprotic DCM is a simple irreversible (slow) heterogeneous electron transfer,  irrev , consistent with both established diagnostics and simulation. For Cu(bpy) 3 (ClO 4 ) 2 in water near pH 6, the mechanism is more complex, with multiple  and  z E-mail: johna-leddy@uiowa.edu * Electrochemical Society Fellow. steps. Modified synthetic protocols and characterizations by UV-Vis spectrophotometry and X-ray diffraction (single crystal and powder) are provided. The voltammetry in water is well fit by simulation with a six species square scheme mechanism. Based on established diagnostics, the experimental data may be misidentified as a single electron transfer  mechanism with no chemical steps. The simulation fit is not unique, as other mechanisms fit the data equally well. However, the identified mechanism best reflects the voltammetric experiments across various conditions.

Experimental
Syntheses and characterization.-Copper complexes were synthesized based on reference 10 with minor modifications as described in SI.1. The synthesized complex Cu(bpy) 3 (PF 6 ) 2 was evaluated in dichloromethane (DCM). Because the hexafluorophosphate is insoluble in water, the perchlorate complex Cu(bpy) 3 (ClO 4 ) 2 was used in aqueous electrolyte. Also in aqueous electrolyte, copper bipyridine complexes were formed in situ from a 1:3 stoichiometric mixture of CuSO 4 and bipyridine.
The hexafluorophosphate and perchorate complexes were characterized by absorption spectrophotometry and X-ray diffraction. Results are consistent with expected elemental composition, literature reports for UV-vis spectroscopy 2,9 and single crystal and powder X-Ray diffraction. 11 Single crystal X-ray diffraction is consistent with no waters of hydration. Characterizations are reported in the Supplemental Information.
Voltammetric measurements.-Cyclic voltammograms were collected on a CH Instruments 760B Potentiostat. In N 2 sparged DCM, 1 mM Cu(bpy) 3 (PF 6 ) 2 with either 0.2 M TBABF 4 or 0.2 M TBAP was studied at a glassy carbon disk (0.468 cm 2 , Pine Instruments) working electrode, either 10 cm 2 platinum mesh or ∼6.5 cm 2 graphite rod counter electrode, and a Ag|Ag oxide quasireference electrode. To correct voltages to SCE reference, ferrocene was added to the electrolyte solution after data collection to determine the potential vs ferrocene|ferrocenium (Fc|Fc + , −0.4 V vs. SCE). In water, 1.01 mM Cu(bpy) 3 (ClO 4 ) 2 in 0.1 M Na 2 SO 4 was characterized with a glassy carbon disk (0.468 cm 2 , Pine Instruments) working electrode with a graphite rod (∼6.5 cm 2 ) counter electrode and a 1001 Series Gamry Instruments SCE (+0.242 V vs NHE, saturated KCl) reference electrode in degassed and ambient solutions. When necessary, degassed water was sparged and blanketed with N 2 . Three sets of measurements on separate solutions, with three replicate scans at each scan rate (25-350 mV s −1 , random order), were collected for a total of 9 scans at each of seven scan rates in aqueous and aprotic media.
Simulations.-Simulations for the voltammetry of the synthesized complexes in water and DCM used the commercial simulation software DigiSim®. From established diagnostics, an initial mechanism is identified. Data were first fit for CVs at 100 mV s −1 , then those parameters are held constant while scan rate is changed. The"goodness of fit" was assessed by comparison of critical characteristics for the simulated voltammograms against experimental voltammograms. Although a good fit identifies a likely mechanism, this does not confirm a unique mechanism. A more quantitative description for the goodness of fit for Cu(bpy) 3 (PF 6 ) 2 in DCM and Cu(bpy) 3 (ClO 4 ) 2 in water can be found in the SI.
Examples of incomplete and poorly parameterized mechanisms are also shown.

Voltammetry Results
Cyclic voltammetry and attendant data analysis are reported for the two synthesized complexes, Cu(bpy) 3 (PF 6 ) 2 in DCM and Cu(bpy) 3 (ClO 4 ) 2 in water, as well as for copper bipyridine complexes formed in situ in water. Forward peak currents were measured from capacitive background and reverse peak currents were measured from the diffusional tail of the forward wave. Current density (mA cm −2 ) is normalized by the geometeric electrode area. Experimental potentials are reported vs SCE.
Critical cyclic voltammetric characteristics.-Critical characteristics include the peak currents for the forward and reverse voltammetric sweeps i p,f and i p,b and the corresponding peak potentials E p,f and E p,b . The ratio i p,f /i p,b deviates from one where chemical steps (denoted ) are part of the electrochemical mechanism. The peak splitting, ΔE p = |E p,f − E p,b |, estimates the heterogeneous electron transfer rate (k 0 ) for simple electron transfer reactions (denoted ). Where the electron transfer rate is fast (reversible), comparable (quasireversible), and slow (irreversible) compared to the scan rate dependent mass transport rate, the electron transfer steps are denoted  rev ,  q , and  irrev . Where electron transfer is not  rev , ΔE p increases with scan rate. The range of ΔE p is about 65 to 140 mV for  q . 8 The formal potential (E 0′ ) for the reaction is approximated by E ave = 0.5(E p,f + E p,b ).
Cyclic voltammetry of Cu(bpy) 3 (PF 6 ) 2 in dichloromethane.-Cyclic voltammetric data for 1 mM Cu(bpy) 3 (PF 6 ) 2 in N 2 sparged DCM (0.2 M tetrabutylammonium electrolyte) are shown in Fig. 1 across scan rates for a voltage range of 0.6 to −0.6 V vs SCE. Experimental potentials were determined relative to the Fc|Fc + redox couple, and subsequently converted to SCE. Scans across a wider potential window (1.0 V to −1.0 V) found no additional faradaic processes.
Data for Cu(bpy) 3 (PF 6 ) 2 are summarized in Table I. Tabulated parameters include forward and reverse peak currents i p,f and i p,b measured from background (μA), ΔE p (mV), and E ave (V vs SCE).
From the voltammograms in Fig. 1, the charge and peak currents for the forward and reverse sweeps are comparable, consistent with no loss or generation of electroactive species through chemical steps. In Table I, the peak splitting is > 59 mV and increases with scan rate, but E ave is largely invariant across the seven scan rates. The data are consistent with a single electron transfer with no following chemical steps. ΔE p is greater than ∼140 mV for all scan rates, indicative of an irreversible (slow) electron transfer,  irrev for scan rates between 25 and 350 mV s −1 . The symmetry of the voltammograms in Fig. 1 are consistent with a transfer coefficient α of about 0.5 ± 0.2. The average and standard deviation for E ave is 0.077 ± 0.005 V vs SCE and estimates the formal potential for Table I. Tabulated electrochemical data for Cu(bpy) 3 (PF 6 ) 2 in N 2 sparged DCM. Averages and standard deviations are for a total of 9 replicate measurements recorded in three separate solutions. Cu(bpy) 3 2+ in DCM. As discussed in SI.3, the difference in E ave = 0.077 ± 0.005 V vs SCE for the Cu(bpy) 3 2|3 couple and the standard potential E 0 = − 0.082 V vs SCE for the Cu(II)|Cu(I) couple yields the ratio of serial formation constants as 3 . Linear plots of the forward peak current i (p,f) against ν 1/2 generally mark linear diffusion as a component in the electrode processes. For the case of slow electron transfer  irrev , the established diagnostics of Equation 1 plot forward peak current i p,f against ν 1/2 . 8 Parameters are current (A), scan rate (V s −1 ), dimensionless charge transfer coefficient α, A electrode area (here, 0.45 cm 2 ), c * bulk solution concentration of the probe (mol cm −3 ), and D diffusion coefficient (cm 2 s −1 ). Where the voltammetric morphologies are symmetric about E ave , the transfer coefficient is taken as 0.5 because across the range α of 0.5 ± 0.2, the morphologies are largely invariant with α. Preliminary analysis of the voltammetry for Cu(bpy) 3 (PF 6 ) 2 in DCM for a plot of i p,f (ν) vs ν 1/2 (SI Fig. 6) yields the following with R 2 = 0.995.
1.14 0.06 10 6.6 1. The intercept approaches zero, as expected from Equation 1. For α approximated as 0.5, the slope of (1.14 ± 0.06) × 10 −4 A (s V −1 ) 1/2 yields D of 1.3 × 10 −6 cm 2 s −1 in DCM. A spreadsheet built in-house determines k 0 (cm s −1 ) from ΔE p with correction for uncompensated resistance. Standard heterogeneous rate is maximized with minimized standard deviation when fit with uncompensated resistance of 225 Ω for scan rates of 50 to 350 mV s −1 . This fit of the experimental data yields k 0 of (7.0 ± 0.8) × 10 −4 cm s −1 for α of 0.5. Resistance of 225 Ω for DCM is not uncommon for a solvent with a dielectric constant of 8. Established diagnostics 8 for variation of ΔE p with scan rate specific to  irrev yield k 0 of (6.1 ± 0.2) × 10 −4 cm s −1 . Both estimates of k 0 identify irreversible electron transfer kinetics,  irrev . Resistance correction yields a 15 % higher k 0 .
Cyclic voltammetry of Cu(bpy) 3 (ClO 4 ) 2 in water.-Cyclic voltammetry of 1.01 mM Cu(bpy) 3 (ClO 4 ) 2 in 0.1 M Na 2 SO 4 aqueous electrolyte was undertaken between +0.1 and −0.8 V vs SCE for scan rates between 25 and 350 mV s −1 . The electrolyte was not degassed. Scans across a wider potential range showed no additional faradaic processes. The apparent single redox process centered at −0.2 V vs SCE is shown in Fig. 2. Voltammetric characteristics are summarized in Table II.
The morphology of the voltammogram is approximately symmetric with a shallower diffusional tail for the reduction and a sharper wave for the reoxidation. As scan rate increases, ΔE p increases modestly but i p,f /i p,r decreases. E ave is invariant. The change in peak current ratios is consistent with chemical  steps.
From established diagnostics, a plot of i p,f vs ν 1/2 is linear in SI  with R 2 = 0.997. Linear plots of i p,f vs ν 1/2 typically characterize a diffusional component to the voltammetry. Linear plots with zero intercepts are anticipated for simple  rev and  irrev , but not for  q . The regression identifies a diffusional component to the voltammetry of Cu(bpy) 3 (ClO 4 ) 2 but does not confirm a simple reversible (fast) or irreversible (slow) electron transfer. Chemical steps and speciation may also have an impact. If the voltammetric response for Cu(bpy) 3 (ClO 4 ) 2 in water is crudely approximated as simple  irrev , the in-house spreadsheet yields k 0 of (7.8 ± 0.9) × 10 −3 cm s −1 and D of 4.1 × 10 −6 cm 2 s −1 .    Within this approximation, both k 0 and D are higher than those found in DCM. Voltammetric morphology and established dynamics may identify the voltammetry of Cu(bpy) 3 (ClO 4 ) 2 as a single electron transfer  mechanism or perhaps as an  mechanism. Simulation identifies a more complex set of  and  steps.
Cyclic voltammetry of Cu(II) bipyridine complexes generated in situ in water.-Cu(bpy) 3 2+ was synthesized in situ by mixing CuSO 4 with bypyridine in a 1:3 stoichiometric ratio. The electrochemical solution contained 1.2 mM copper and 0.1 M sodium sulfate near neutral pH. The voltammograms are shown in Fig. 3 for a scan range from 0.1 to −0.5 V vs SCE. The faradaic processes are centered around −0.21 V vs SCE, and no additional faradaic waves were observed over a wider potential range of 1.4 V to −0.8 V. The electrochemical charactristics are tabulated in Table III. A preliminary assessment for the voltammograms in Fig. 3 identifies moderately symmetric waves with a shallow diffusional tail on the forward sweep and narrower tail on the return wave, similar to the complex Cu(bpy) 3 (ClO 4 ) 2 dissolved in water. As the scan rate decreases, i p,f /i p,b increases, as consistent with a following chemical reaction, an  mechanism (Table III). The return wave diminishes relative to the forward wave as scan rate slows because the slower scan rates allow longer times for the following reaction to consume the species generated on the forward sweep. The value of ΔE p fall into the range for  rev to  q , but the mechanism is likely more complex than a simple  mechanism. The systematic shift of E ave with scan rate may also mark more complex  mechanisms.
From established diagnostics, a plot of i p,f vs ν 1/2 (SI Fig. 8) is linear with a nonzero intercept, which is consistent with diffusional components in the voltammetric response but not a simple  rev or  irrev mechanisms. The regression is shown with R 2 = 0.991. Crudely approximating a simple  mechanism with the in-house spreadsheet, k 0 and D were estimated as (3.5 ± 0.8) × 10 −3 cm s −1 and 5.8 × 10 −6 cm 2 s −1 . For a simple , k 0 of 0.004 cm s −1 is moderately fast (quasireversible), but not reversible. These values are only rough estimates, especially for the kinetics, because the mechanism is more complex than a simple . Speciation of copper bipyridine complexes formed in situ include chemical equilibria of trisand bisbipyridine complexes of copper cations.

Discussion
Three cases for copper ligated with bipyridine are evaluated voltammetrically, Cu(bpy) 3 (PF 6 ) 2 in DCM, Cu(bpy) 3 (ClO 4 ) 2 in water, and copper bipyridine complexes formed in situ in water. Variations in the voltammetric morphologies are apparent, consistent with increasing mechanistic complexity from an apparent simple  irrev in DCM, to a more complex mechanism for the complex in water, with yet greater complexity for complexes formed in situ. Several factors impact the mechanistic path.
For the three copper bipyridine systems, mechanisms are evaluated by fit of the voltammetric morphologies with DigiSim® for the synthesized complexes. Established voltammetric diagnostics provide an initial assessment that is extended and vetted on simulation. In DCM, the mechanism found by simulation and established diagnostics is the same. In water, the simulation identifies a similar, but more complex, mechanism than that identified by established diagnostics. For the copper species formed in situ, a pH dependent equilibrium model for fractional concentrations characterizes the voltammetry.
Cu(bpy) 3 (PF 6 ) 2 in DCM.-Voltammograms for Cu(bpy) 3 (PF 6 ) 2 in aprotic DCM are shown in Fig. 1 and summarized in Table I. The overall symmetry of the voltammograms, invariant i p,f ≈ i p,b , constant E ave , and ΔE p (mV) >140 mV at all scan rates are consistent with a simple irreversible (slow) electron transfer  irrev . Established diagnostics for  irrev with ΔE p of 151 to 273 mV yield ′ E 0 of 0.077 V vs SCE, D of 0. 1.3 × 10 −6 cm 2 s −1 , and k 0 of (7.0 ± 0.8) x 10 −4 cm s −1 . Transfer coefficient α is taken as 0.5. These provided the initial inputs to the simulation for Cu(bpy) 3 (PF 6 ) 2 in DCM.
The simulation mechanism is  irrev for a single electron transfer, slow compared to mass transport. The diffusion coefficient, standard heterogeneous rate constant, and transfer coefficient found by established diagnostics and simulation for simple  irrev are in good agreement and support identification of an  irrev mechanism. Majumdar et al. 9 report similar voltammetry for Cu(bpy) 3 (ClO 4 ) 2 in aprotic acetonitrile with 0.1 M TBAP at 50 mV s −1 and found E 1/2 of 0.04 V vs SCE and ΔE p of 160 mV, also consistent with  irrev .  Cu(bpy) 3 (ClO 4 ) 2 in water.-Upon initial inspection of Fig. 2, the mechanism appears to be  q . Application of established  q diagnostics yield k 0 of (7.8 ± 0.9) × 10 −3 cm s −1 and D of 4.1 × 10 −6 cm 2 s −1 . However, subtle distinctions in the voltammetric morphology are noted, consistent with additional chemical and electrochemical steps. The cyclic voltammograms have largely symmetric morphologies, but the diffusional tail of the forward sweep is more shallow and the reverse sweep is sharper. The slight asymmetry suggests either α differs from ∼0.5 or, more likely, chemical steps and speciation have a subtle impact on the voltammetric response. Following chemical steps are consistent with the ratio i p,f /i p,b that increases with decrease in scan rate. Slower scan rates allow more time for following chemical reactions. From ΔE p in the range from 70 to 105 mV and a largely symmetric voltammetric morphology, the electron transfer rates are likely in the  q range. The average potential E ave = −(0.207 ± 0.001) V vs SCE.
The nuances in the voltammograms suggest chemical and electrochemical steps of at least , with a proposed mechanims similar to  outlined for polarography by Onstott and Laitinen. 3 However, based on the covalent model of electron counting, experimental data for degassed solutions, and numerous reports in Constable, 1 a more rigorous chemical interpretation of a six species "square scheme" model is adopted. The proposed mechanism is shown in Eqs. 6-16, and is depicted schematically in Fig. 5.
The six species square scheme is composed of four heterogeneous electron transfer steps for the trisand biscomplexes, where the complexes are formally reduced from 2+ to 1+ to zero. Three instability constants K describe loss of ligands for each of the proposed complexes. A species X is present in all aqueous solutions and mediates oxidation of the electrochemically reduced forms of B, H, C, and W to the oxidized forms A, G, B, and H, respectively. The homogeneous electron transfers with X are characterized with equilibrium constants K′. In the model, the forward rate of reaction is pseudo first order in X. Tabulated data for homogeneous and heterogeneous reaction rates can be found in the SI. Figure 6 shows overlays of simulated (dotted line) and experimental (solid red line) voltammograms for seven scan rates of 25-350 mV s −1 . The 100 mVs −1 data were fit first. Inputs to the simulations of the modified square scheme mechanism include diffusion coefficients for the copper bipyridine complexes between 3 and 6 × 10 −6 cm 2 s −1 . The pH dependent instability constants K are drawn from literature reports by Garribba 2 and Onstott and Laitinen. 3 The simulations are run for pH near 6. Simulation inputs for instability constants are K I = 450, K II and K III = 664.07 as calculated by DigiSim® and constrained by formal potentials. For the Cu(II) and Cu(I) complexes, the equilibrium concentrations of the trisand biscomplexes are in a 1:3 ratio. The only source of bpy is from the complexes. Because values of K I and K II are on the order of 10 2 , the analytical concentration of Cu(bpy) 3 (ClO 4 ) 2 added to water equilibrates to form substantial concentrations of Cu(bpy) 2 2+ and bpy before voltammetric perturbation. During and after voltammetric perturbation, the equilibrium speciation model identifies a mix of trisand biscomplexes, with a preponderance of the biscomplex at more negative potentials. Tabulated data for these values can be found in the SI.
The From a chemical perspective, the proposed modified square scheme accounts for some of the observed differences of the in situ complexes and helps explain why the voltammograms are similar in degassed and ambient aqueous conditions. The non-trivial fit suggests an oxidizing agent X in solution that is generating the shown morphologies in aqueous media. The identity of X is less certain, but it is known that X must be present in all aqueous systems. Although originally modeled as a pseudo first order oxygen mechanism, the same fit to nitrogen degassed experimental data rule out the possibility of oxygen being the major species X. Perchlorate was also postulated as X, but the similarities in voltammograms with and without perchlorate (in situ and crystalline compound) eliminate perchlorate. Notably, water, Na 2 SO 4 , species of copper and bpy, and minimal concentrations of proton are the only species common to all aqueous studies.
A notable feature of the voltammograms is the definition of the forward and reverse peak currents. The forward current is broad, whereas the return current is sharp and well defined at all scan rates. One reason is well documented in Constable 1 and elsewhere, 3,12 and is also modeled by the fractional concentration plots in Fig. 7. Upon return oxidation in the voltammetric timescale, the copper bipyridine complex preferentially adopts the four-coordinate bisconfiguration rather than the six-coordinate triscomplex present initially. The following chemical steps for ligand binding and loss captured in K I , K II , and K III can manifest as increased rates of electron transfer in the voltammograms as products on the forward and reverse sweeps are lost to chemical processes. Instability constants are ratios of forward and reverse chemical rates, the rates of which impact the voltammetric morphology, where the rates are not fast as compared to the scan rate perturbation. The slow decay of the diffusional tail on the forward sweep, past E p,f , arises because X mediates regeneration of the more oxidized species. This feedback increases current as more reactants are resupplied. This also contributes to the broadening of the forward wave relative to the reverse wave. Where X is not included in the mechanism, the decay past the forward peak is poorly fit by the simulation.
Based on the high correlation of the simulation and the experiments, the six-species square scheme is a good representation of the voltammetric mechanism for Cu(bpy) 3 (ClO 4 ) 2 in water, although other mechanisms may also be appropriate, as shown in the SI. It is noted that the mechanism is appropriate near pH 6 and for moderate scan rates (0.01 ⩽ ν ⩽ 1 V s −1 ). The instability constants are consistent with literature reports. [1][2][3]12 Because protons in water can protonate bipyridine, speciation of copper and bipyridine is more diverse in water than in aprotic solvents. The modified square scheme mechanism in water is substantially more complex (Fig. 5 than the simple  irrev mechanism found in DCM (Fig. 1). When copper bipyridine complexes are formed in situ from a stoichiometric 1:3 mixture near pH 6-7, a variety of species are formed and the voltammetric morphology is altered further (Fig. 3).
Distribution of in situ species in aqueous systems.-The cyclic voltammograms for the synthesized complex Cu(bpy) 3 (PF 6 ) 2 in aprotic DCM are characteristic of a simple  irrev mechanism. Protons are introduced by the aqueous electrolyte when the synthesized complex Cu(bpy) 3 (ClO 4 ) 2 is evaluated in water. The cyclic voltammetric mechanism is more complex, fit by a simulation of a six species square scheme mechanism. Voltammograms of Cu(bpy) 3 2+ formed from a 3:1 stoichiometric mixture of bpy and Cu(II) were subtly different from the crystalline complex, consistent with greater impact from chemical steps and a more complex speciation. From Garribba 2 and Onstott and Laitinen, 3 the formation constants for the ligated copper dication are large, although not as large as some other transition metal bipyridine complexes. For example, the tris-bipyridine complex of ruthenium, Ru(bpy) 3 2+ is stable in most solvents, including acidic, aqueous electrolytes, indicating the formation constants for Ru(bpy) 3 2+ are stronger than for Cu(bpy) 3

2+
. The binding of bipyridine to copper dications is archetypal of many later transition metal complexes. The magnitude of the instability constants can be partially explained by the formal electron count of each complex. Cu(bpy) 3 2+ can be assigned 20 electrons using the covalent electron counting model, where the metal is neutral and assumed to have the number of electrons corresponding to the position in the d-block. Bipyridine, a strong field, π-acceptor ligand, is assigned four electrons each, and the overall positive 2 charge on the complex removes two electrons from the count. Following this logic, Cu(bpy) 3 z+ (z = 1, 0) has 21 and 22 electrons respectively. Typically, octahedra are considered electronically stable with 18 electrons, whereas tetrahedra are considered electronically stable with 16 electrons. Some of the propensity to form the Cu(bpy) 2 2+ may be due to the formal electron count of 16 (17 and 18 for the 1+ and zero species, respectively).  The copper system is modeled for literature serial formation constants 2,3,12 for Cu(II) with bpy: β 1 = 1.4 × 10 8 ; β 2 = 4.5 × 10 13 ; and β 3 = 8.9 × 10 16 . For Cu(I) complexes, serial formation constants are not reported, but Cu(I) binds two but not three bipyridines. For the model, γ 1 and γ 2 are approximated as β 1 and β 2 , but γ 3 is taken as 10 3 , which is equivalent to negligible binding in the model. The protonation of bpy to form Hbpy + is characterized by an acid dissociation constant, pK a = 4.33. Outputs of the model are shown in Fig. 7 for various ratios of c L /c M at pH of 7.14. The voltammetry in Fig. 3 for copper complexes formed in situ with a stoichiometric ratio is modeled by c L /c M = 3. The stoichiometric mixture did not form Cu(bpy) 3

2+
is formed. When c L /c M > 3, more Cu(bpy) 3 2+ is formed than Cu(bpy) 2 2+ . For c L /c M = 6, the fraction of Cu(bpy) 3 2+ is 0.86; for c L /c M = 8, the fraction is 0.90 (see SI). Similar fractional concentrations in aqueous solutions, 2,3,12 where c L /c M ≈ 4.1, demonstrate bistriscomplexes at equal concentrations. Because the Cu(I) complex binds only two bpy and γ 2 ? γ 1 , the product of the reduction is only Cu(bpy) 2 2+ with release of one bpy. In all cases considered here, the fractional concentrations of the unligated metal cations were negligible. Thus, within the constraints of the model, Cu(bpy) 3 2+ is formed in situ under conditions of a large excess of bpy. For the fraction of Cu(bpy) 3 2+ at 90 % at neutral pH, c L /c M of 11 is needed. See SI.5 for more details that include distributions at other pH values. For c L /c M = 3, with pH about ∼6, the distributions are little changed as the bipyridine is sparsely protonated (pKa = 4.33). The experimental pH is measured at 5.8, so the fraction deprotonated is 97 %. At pH 7.14, the model represents the experimental pH.
From the model (SI.5) for c L /c M = 3, pH also impacts the fractional concentrations (SI Fig. 11). The fractional concentrations are little affected at pH of 8 and higher. As pH decreases below 7, bpy is protonated to form Hbpy + , which cannot bind to metal cations as a bidentate ligand. At pH = pK a , the fraction of biscomplex is 60 % higher than the triscomplex. At pH of 3, the concentration of the biscomplex is almost 12 fold higher than the triscomplex and the fraction of free bpy is <0.05. Cu(bpy) 2 2+ is formed from a stoichiometric mix c L /c M = 3 at pH acidic of pK A .
In situ Cu(bpy) 3 2+ assessment.-As shown in Fig. 3 and Table III, the ratio of i p,f /i p,b increases as scan rate slows, consistent with a following chemical reaction. The slower sweep rate allows more time for the product to react, resulting in a diminished concentration and, thus, peak current, on the return sweep. An increase in ΔE p with scan rate marks slow kinetics. The plot of i p,f vs ν 1/2 is linear (SI Fig. 8) but the intercept is non-zero. The slope marks diffusional processes and the intercept suggests chemical kinetics (). From the equilibrium model, the dependency on pH and − E E M 0 suggests an increase in the complexity of the mechanism. The voltammetric behavior of the in situ complexes is considered in view of the equilibrium model.
In Fig. 7, the conditions of neutral pH and 3:1 stoichiometric mix are represented by pH 7.14 and c L /c M , on the top right. When the Cu (II) salt and bypyridine are mixed, equilibrium establishes the mixture of species shown at − > E E M 0 +0.15 V. For c L /c M = 3 at neutral pH, the system contains equal amounts of Cu(bpy) 3 2+ and Cu(bpy) 2 2+ . At more acidic pH, the concentration of the bisspecies is higher than the concentration of the triscomplexes. Because the solution is formed stoichiometrically and Cu(bpy) 2 2+ lacks the third ligand, the fractional concentration of bpy is the same as the two copper dication complexes. As the applied potential is swept negative to reduce the dicationic complexes, both Cu(bpy) 3 2+ and Cu(bpy) 2 2+ undergo reduction with similar potentials (within a few millivolts) with the tris-complex slightly easier to reduce. As the reduction proceeds, only Cu(bpy) 2 + is formed as the reduced product because Cu(I) complex does not adopt three bpy ligands. As Cu(bpy) 2 + is formed, bpy is lost from the Cu(bpy) 3 + and the fraction concentration of the bpy rises to 1.
These observations based on the equilibrium model apply to copper complexes formed stoichiometrically in situ in water and also apply to Cu(bpy) 3 (ClO 4 ) 2 in water. The distinctions in the voltammograms in Figs. 2 and 3 arise from distinctions in kinetic rates rather than distinctions in equilibrium conditions.

Conclusions
As with many transition metal complexes, voltammetric morphology is impacted by chemical () and electrochemical () reactions, and by the electrolyte environment. Identification of mechanism by established diagnostics such as ΔE p and i p,f /i p,b may tag a simpler reaction mechanism than that found by simulation. For an appropriate simulation fit, the time dependent dynamics of the voltammetry must embed the underlying equilibria. In aprotic DCM, the electrochemical mechanism for Cu(bpy) 3 2+ reduction is a simple slow electron transfer ( irrev , with k 0 = 6 × 10 −4 cm s −1 ), as found by established diagnostics and simulation. In water, established diagnostics identify a simpler, less adequate mechanistic description than simulation because the underlying equilibria of copper with bipyridine has rich speciation. The cyclic voltammetric simulations capture the speciation equilibria that include changes in structure and chelation. Speciation may be driven, in part, by the electronic stability imparted in tetrahedral complexes with 16 electrons, and in octahedral complexes with 18 electrons.
On consideration of the speciation events and distribution of solution species, more complex reaction mechanisms are found for bipyridyl copper complexes in water than identified by established diagnostics for voltammetry. Attention to mechanistic details can impact catalyst optimization and design of advanced materials.