Directing the reactivity of metal hydrides for selective CO₂ reduction

Significance

Electrocatalytic CO₂ reduction to fuels using renewable electricity provides an entry into sustainable carbon-neutral fuels. Most reactions require proton equivalents, but direct proton reduction to H₂ leads to low product selectivity, a significant challenge in the field. The issue of product selectivity arises from shared catalytic intermediates for both CO₂ reduction and H₂ evolution. We describe how thermodynamic relationships regarding the reactivity of H⁺ and CO₂ with one of these shared intermediates, homogeneous metal hydrides, can be applied to identify catalyst candidates and conditions where H₂ evolution is suppressed in favor of highly selective CO₂ reduction. The conceptual framework is used to outline operational conditions for electrocatalytic reduction of CO₂ to formate (HCO₂⁻) by [Pt(dmpe)₂](PF₆)₂ with negligible H₂ production.

Abstract

A critical challenge in electrocatalytic CO₂ reduction to renewable fuels is product selectivity. Desirable products of CO₂ reduction require proton equivalents, but key catalytic intermediates can also be competent for direct proton reduction to H₂. Understanding how to manage divergent reaction pathways at these shared intermediates is essential to achieving high selectivity. Both proton reduction to hydrogen and CO₂ reduction to formate generally proceed through a metal hydride intermediate. We apply thermodynamic relationships that describe the reactivity of metal hydrides with H⁺ and CO₂ to generate a thermodynamic product diagram, which outlines the free energy of product formation as a function of proton activity and hydricity (∆G_H−), or hydride donor strength. The diagram outlines a region of metal hydricity and proton activity in which CO₂ reduction is favorable and H⁺ reduction is suppressed. We apply our diagram to inform our selection of [Pt(dmpe)₂](PF₆)₂ as a potential catalyst, because the corresponding hydride [HPt(dmpe)₂]⁺ has the correct hydricity to access the region where selective CO₂ reduction is possible. We validate our choice experimentally; [Pt(dmpe)₂](PF₆)₂ is a highly selective electrocatalyst for CO₂ reduction to formate (>90% Faradaic efficiency) at an overpotential of less than 100 mV in acetonitrile with no evidence of catalyst degradation after electrolysis. Our report of a selective catalyst for CO₂ reduction illustrates how our thermodynamic diagrams can guide selective and efficient catalyst discovery.

The emerging availability of inexpensive renewable electricity has motivated interest in using electrolytic methods to generate sustainable fuels. Electrocatalytic CO₂ reduction provides an entry to carbon-neutral fuels, but product selectivity remains a significant challenge (1, 2). Nearly all reductive reactions of interest involve protons as well as electrons, introducing the complication of direct proton reduction to H₂ under electrolytic conditions. Diversion of electron equivalents into proton reduction results in lower Faradaic efficiency for the desired CO₂ reduction reaction. Various strategies to inhibit or suppress H₂ evolution for heterogeneous (3–7) and homogeneous (8, 9) catalysts have been explored.

To understand the factors that determine selectivity between CO₂ and H⁺ reduction, we have been investigating the reactivity of metal hydrides. Selectivity for formate production is particularly challenging because metal hydride intermediates are common to both reaction pathways (Fig. 1). As a result, very few heterogeneous (10–13) or homogeneous (14–16) catalysts have been reported with high (>90%) Faradaic efficiency for formate production. Understanding the reactivity of metal hydrides is key to controlling the bifurcating reaction pathways that ultimately determine selectivity. Most selective catalysts for CO₂ reduction utilize kinetic inhibition (or a high-transition state barrier) to minimize H₂ evolution.

Fig. 1.

Proposed catalytic cycles for H⁺ and CO₂ reduction.

In this report, we utilize a thermodynamic approach to describe the reactivity of metal hydrides with H⁺ and CO₂ by applying known free energy relationships (14, 17–28). We depict our findings in a diagram (Fig. 2) that describes the thermodynamic products as a function of hydricity (∆G_H−) (Eq. 1) of the metal hydride intermediate vs. proton activity (pK_a). Notably, a region is delineated in which select combinations of hydricity and pK_a lead to thermodynamic favorability for selective CO₂ reduction to formate over hydrogen evolution. Since hydricity values have been measured for many classes of compounds and can be predictably tuned through metal and ligand design (29), we believe that the diagrams provide instructive guidelines for targeting the discovery of selective reduction catalysts.

Fig. 2.

Free energy calculations for H₂ and HCO₂⁻ generation from metal hydrides and aqueous thermodynamic product diagrams (A and B).

We establish the utility of our diagram by using it to select a known metal hydride [HPt(dmpe)₂]⁺ with an appropriate hydricity in acetonitrile to access conditions in which selective CO₂ reduction to formate is favorable. We demonstrate that the resting state catalyst [Pt(dmpe)₂](PF₆)₂ reduces CO₂ to formate with high Faradaic efficiency and low overpotential.

Results and Discussion

Thermodynamic Product Diagrams.

We first describe the construction of the thermodynamic product diagram in acetonitrile (CH₃CN), but the relationships hold in other solvents provided that the correct constants are used (vide infra). The thermodynamic cycle describing the free energy for the reaction of a metal hydride toward H⁺ to evolve H₂ is shown in Fig. 2. The free energy of H₂ evolution (Eq. 4) is dependent on the hydricity, pK_a of the acid, and the heterolytic bond forming energy of H₂, which is 77 kcal/mol in acetonitrile (30). Eq. 4 has successfully been applied to identify and optimize electrocatalysts for H₂ evolution (26, 31–38) and H₂ oxidation (31–34, 39–42), and to achieve reversible reactivity (43, 44).

The relationship between pK_a, hydricity, and H₂ evolution in acetonitrile is quantitatively depicted in Fig. 2A. The black line differentiates the boundary in which the free energy of Eq. 4 in Fig. 2 (ΔG_H2) equals zero and MH/H⁺/H₂ exist in equilibrium, analogous to lines in a Pourbaix diagram. Protonation to evolve hydrogen is exergonic for hydride complexes of a given hydricity under conditions below the black line (green zone) and endergonic above the line (blue zone).

The thermodynamic requirement for reduction of CO₂ to formate, a net hydride transfer, is also dictated by the hydricity (∆G_H−) of the donor as shown in Eq. 6 (Fig. 2). Eq. 6 has been applied to rationalize or predict the activity of the iron-based CO₂ reduction electrocatalyst by Berben and coworkers (20) and CO₂ hydrogenation catalysts (45–50) as well as formate oxidation electrocatalysts (51). Transition metal hydricity values lower than that of formate will result in exergonic hydride transfer to CO₂. This information can be mapped onto the thermodynamic product diagram illustrating metal hydride reactivity with protons (Fig. 2B). The thermodynamic product distribution that results from stoichiometric mixtures of metal hydride and acid of specific pK_a values under 1 atm of CO₂ is described in this diagram. The pK_a of formic acid is estimated to be ∼20.9 in acetonitrile (52); therefore, it is expected to be protonated at lower pK_a values.

In Fig. 2B, a region is defined where specific metal hydricity and pK_a combinations will result in selective reduction of CO₂ to formate without concomitant H₂ evolution (near the bottom right of Fig 2B). The challenge of selective CO₂ reduction is often introduced by comparing the thermodynamic potentials for H⁺ reduction with CO₂ reduction to formate [−0.028 V (53) vs. −0.150 V (22) vs. Fe(C₅H₅)₂^+/0 in CH₃CN]. Since the former is more positive than the latter, hydrogen is assumed to be the more favorable thermodynamic product upon reduction. However, these potentials are listed at the standard state (1 M H⁺). A full Pourbaix diagram that spans a larger range of proton activity (pK_a) provides a more complete picture (SI Appendix, Fig. S1).The thermodynamic potential for proton reduction shifts with the pK_a of the solution by 59 mV per unit according to the Nernst equation for a 2 e⁻, 2H⁺ process. Similarly, CO₂ reduction to formic acid follows the same relationship until the solution pK_a matches that of formic acid to generate formate. For CO₂ reduction to formate, the thermodynamic potential shifts will deviate in accordance with a 2 e⁻, 1H⁺ process or 29.5 (59/2) mV per pK_a unit. The smaller decline in thermodynamic potential vs. pK_a compared with H⁺ reduction results in a crossing of potentials, where CO₂ reduction to formate occurs at a more positive potential at higher pK_a values and can thus be the more favorable thermodynamic product. The crossing point in the Pourbaix diagram (SI Appendix, Fig. S1) matches the pK_a (25.1), which defines the initial point in which selective CO₂ reduction can be achieved in our diagram. A similar crossing in the 2H⁺/H₂ and CO₂/HCO₂⁻ is observed in Pourbaix diagrams in water (54), although it is complicated by CO₂ equilibria with hydroxide at high pH (55). We believe that our redrawn thermodynamic product diagram, where potential is replaced by hydricity, provides a more instructive guide for targeting catalysts to access the region where selective CO₂ reduction is possible, which we demonstrate experimentally herein.

A recently published perspective by Kubiak and coworkers (22) described a primarily linear relationship between hydricity and the one-electron reduction potentials of the parent complex for previously reported groups 8–10 metal hydrides. The perspective provides valuable insight into the relationship between hydricity and reversible redox properties as they pertain to H₂ evolution and CO₂ reduction. However, the authors note that their correlation is qualitative and dependent on similar hydrogen atom transfer bond dissociation free energies among their complexes. Additionally, the authors detail why some metal hydrides deviate significantly from their observed trend and were excluded from the linear fit. We note that the diagrams shown in Fig. 2 are based directly on thermodynamic hydricity values and are thus applicable to all metal hydrides, regardless of metal identity, oxidation state, or ligand environment. The thermodynamic hydricity can also be accurately measured for complexes without reversible redox potentials using methods that have previously been described (19).

Application in other solvents.

The diagrams shown in Fig. 2 can be drawn for any solvent provided that the appropriate constants (ΔG_H2 and ΔG_HCO2−) are known in the respective solvent. For example, the diagram illustrating the relationships between metal hydricity and proton activity (similar to Fig. 2A) in dimethylsulfoxide (DMSO) is shown in SI Appendix, Fig. S2 (ΔG_H2 = 60.7 kcal/mol in DMSO) (30). The hydricity of formate (ΔG_HCO2−) in DMSO is estimated to be 42 kcal/mol (56). The equivalent diagram shown in Fig. 2B for DMSO is shown in SI Appendix, Fig. S3. We note that we were unable to find a published value for the pK_a of formic acid in DMSO, and therefore, the line between CO₂/HCO₂⁻ is drawn across the whole range of pK_a values shown. Applying thermodynamic relationships with metal hydricity is most useful in organic solvents with self-consistent data on acid pK_a values. Most measurements of this type have been made in CH₃CN (57–61) and to a lesser extent DMSO (62), but additional values in various solvents are continually being reported.

ΔG_H2 and ΔG_HCO2− have also been reported in aqueous solution (34.2 and 24.1 kcal/mol, respectively) (17). The analogous diagrams in Fig. 2 A and B are shown in SI Appendix, Figs. S4 and S5, respectively. However, the diagrams do not account for the equilibria between CO₂ and OH⁻ to form HCO₃⁻ and CO₃²⁻, which become more significant at higher pH values.

The hydricity value (∆G_H−) for metal hydrides also has a solvent dependence. Multiple studies have measured how solvent affects the hydricity values (14, 18, 19, 23–25, 27, 35). Hydricity values for transition metal hydrides tend to be lower and span a narrower range in solvents with higher dielectric constants, but their absolute values do not change in a predictable fashion by solvent. However, a notable trend is that hydricity values for transition metal hydrides in organic solvents tend to decline to a greater magnitude (become better donors) in water compared to HCO₂⁻ (∆G_HCO2−). As a result, there are a few examples where CO₂ reduction to HCO₂⁻ is exergonic in water but endergonic in organic solvents (14, 27, 48). Additionally, detailed studies by Miller and coworkers (63) determined that aqueous hydricity can also be dependent on anions commonly found in aqueous buffers as well as hydroxide at higher pH values.

Kinetic vs. thermodynamic selectivity.

The diagrams depicted in this study delineate how to achieve thermodynamic selectivity for CO₂ reduction. In CH₃CN, DMSO, and H₂O, thermodynamic selectivity can only be achieved at modest or low proton activity (pK_a > 25.9 in CH₃CN, pK_a > 13.6 in DMSO, and pH > 8.1 in H₂O). However, kinetic barriers for protonation can be applied to achieve selectivity for CO₂ reduction under more acidic conditions. The difference in kinetic selectivity will still have to compensate for larger free energies of protonation of the metal hydride to form hydrogen at lower pK_a/pH values. Consistent with the free energy associated with H₂ and HCO₂⁻ formation (Eqs. 4 and 7, respectively) the only two molecular catalysts with >90% selectivity for formate generation function optimally at modest to high pK_a/pH conditions, with decreasing selectivity at lower proton activities (16, 20). Yet, both maintain fairly high selectivity under more acidic conditions, indicating that the product distribution is also under kinetic control (64).

Application of Thermodynamic Product Diagrams for Catalyst Discovery.

To target the region in Fig. 2B where selective CO₂ reduction to HCO₂⁻ in CH₃CN is dictated by the thermodynamic Eqs. 4 and 6, we selected [Pt(dmpe)₂](PF₆)₂ (3) as a possible catalyst. The corresponding hydride [HPt(dmpe)₂](PF₆) (2) has an experimentally measured hydricity (∆G_H−) (Eq. 1) of 41.4 kcal/mol (Fig. 2) (19, 65). Consistent with Eq. 6, [HPt(dmpe)₂](PF₆) reacts stoichiometrically with CO₂ to give HCO₂⁻ and [Pt(dmpe)₂](PF₆)₂ (3) (21). The preparation and characterization of the hydride precursor Pt(dmpe)₂ (1) along with 2 and 3 have been previously reported (65, 66). Complexes 1, 2, and 3 are diamagnetic with easily distinguishable ³¹P{¹H}NMR spectral signatures.

According to Eq. 4 and Fig. 2, the threshold for H₂ evolution with [HPt(dmpe)₂](PF₆) (2) is at a pK_a of 25. Acids with pK_a values lower than 25 will be exergonic for H₂ evolution. As expected, stoichiometric reaction of [HPt(dmpe)₂](PF₆) (2) with acids, such as anilinium tetrafluoroborate (pK_a = 10.62) and protonated 1,8-diazabicyclo[5.4.0]undec-7-ene (pK_a = 24.34) in CH₃CN (60), results in protonation to give H₂ and [Pt(dmpe)₂](PF₆)₂ (3) (SI Appendix, Figs. S6 and S7). In contrast, [HPt(dmpe)₂](PF₆) (2) is stable to protonation using acids with higher pK_a values (ΔG_H2 > 0), which we demonstrate experimentally. No reaction is observed with [HPt(dmpe)₂](PF₆) (2) upon addition of phenol (pK_a = 29.1) (SI Appendix, Fig. S8) (62). According to Eq. 4, H₂ evolution with [HPt(dmpe)₂](PF₆) (2) and phenol has an endergonic free energy of 5.5 kcal/mol.

The pK_a (31.1) (65) of the metal hydride provides an upper bound on acids that can be used for metal hydride generation. As a result, [HPt(dmpe)₂](PF₆) (2) can be selectively generated at an electrode using proton sources with pK_a values between 31.1 and 25. Therefore, phenol (pK_a = 29.1) is sufficiently acidic to generate [HPt(dmpe)₂](PF₆) (2) without additional protonation to evolve H₂.

Selective electrocatalytic reduction of CO₂ to formate.

[Pt(dmpe)₂](PF₆)₂ (3) exhibits a 2 e⁻ reduction to [Pt(dmpe)₂] (1) at −1.73 V vs. Fe(C₅H₅)₂^+/0 in acetonitrile (Fig. 3, black trace). Electrochemical reduction of 3 to 1 in the presence of phenol results in a loss of reversibility (blue trace in Fig. 3), which we attribute to formation of the hydride 2 [electron transfer (E) followed by a chemical step (C), protonation, or an EC step]. Higher concentrations of phenol do not result in an increase in current (green trace in Fig. 3).

Fig. 3.

Cyclic voltammetry under 1 atm of N₂ of 0.5 mM solution of [Pt(dmpe)₂](PF₆)₂ (3) (black); after addition of 1 equivalent of phenol (blue); and 5 equivalents of phenol (green); and under 1 atm of CO₂ with 5 equivalents of phenol (red); and 10 equivalents of phenol (orange). Conditions: 0.1 M Et₄NPF₆, 1 mM Fe(C₅H₅)₂ present as an internal reference, glassy carbon working and auxiliary electrode, Ag/AgCl pseudoreference electrode, 10 mV/s scan rate.

According to Eq. 5, [HPt(dmpe)₂](PF₆) (2) is sufficiently hydritic to react with CO₂ to generate formate (ΔG° in Eq. 6 = −2.6 kcal/mol). The cyclic voltammogram on addition of 1 atm of CO₂ to 3 with phenol is shown by the red trace in Fig. 3. Titration with increasing concentrations of phenol results in an increase in current (Fig. 3), which is indicative of electrocatalysis. The current reaches a maximum at 10 equivalents.

A proposed catalytic cycle for CO₂ reduction to formate with thermodynamic parameters (E_1/2 for e⁻ transfer and pK_a for protonation reactions) for each step is depicted in Fig. 4.

Fig. 4.

Proposed catalytic cycle and thermodynamic properties. ^aFree energy for H₂ evolution (kilocalories per mole) calculated from Eq. 4 with an equivalent of phenol. ^bFree energy of hydride transfer (kilocalories per mole) to form formate under 1 atm of CO₂ calculated using Eq. 6.

Electrolysis was performed at −2.4 V vs. Fe(C₅H₅)₂^+/0 under 1 atm of CO₂ (1 mM 3 in 10 mM phenol) for 1 h (SI Appendix, Figs. S9 and S10). The concentration of formate in solution after electrolysis was measured using two different methods. The first method used an internal dimethylforamide (DMF) standard to quantify formate by ¹H NMR spectroscopy (SI Appendix, Fig. S11). The second method required acidifying the postelectrolysis solution with HCl and quantifying the formic acid with a DMF internal standard using ¹H NMR spectroscopy (SI Appendix, Fig. S12). The Faradaic efficiency for formate production from either method was greater than 90%. The headspace of the cell was analyzed by GC to detect and quantify H₂ and CO production. A small amount of H₂ (<0.1%) was sometimes observed, but CO was never detected. ³¹P{¹H} NMR spectra of the pre- and postelectrolysis solution display a single resonance that corresponds to 3. Quantification by integration relative to the PF₆⁻ anion (SI Appendix, Figs. S13 and S14) confirms retention of the catalyst after electrolysis.

The maximum catalytic current observed in the cyclic voltammetry (Fig. 3, orange trace) and the peak current under noncatalytic conditions (Fig. 3, black trace) was used to estimate an observed rate constant (k_obs) of 0.5 s⁻¹ (SI Appendix, Eq. S4) (67, 68) for CO₂ reduction to formate. The standard potential for CO₂ reduction to formate in acetonitrile was recently estimated (22). The thermodynamic potential under our conditions (pK_a of 29.1) is E° = −1.64 V. Using the half-wave potential E°_1/2 = −1.73 V (69), the overpotential for catalysis is 90 mV.

To quantify any potential H₂ or formate generated directly at the electrode, an equivalent electrolysis in the absence of any Pt compound was performed (SI Appendix, Fig. S15). Analysis of the headspace by GC detected the presence of <0.1% mL H₂, no CO, and no formate in solution by ¹H NMR spectroscopy. Calibration curves for H₂ and formate quantification are shown in SI Appendix, Figs. S16 and S17, respectively.

General considerations.

The diagrams in Fig. 2 informed our choice of [Pt(dmpe)₂](PF₆)₂ (3) as a good catalyst candidate for selective CO₂ reduction to formate. The hydricity of the corresponding hydride [HPt(dmpe)₂](PF₆) (2) is sufficient to reduce CO₂, and there are appropriate acids to access the region of selective reduction. Although the thermodynamic framework described herein proved effective for [Pt(dmpe)₂]²⁺ (3), some considerations on its application to other potential catalysts are discussed.

Although nearly all molecular hydrogen evolution reaction (HER) catalysts involve a metal hydride intermediate, H–H bond formation can occur through two distinct mechanisms: bimolecular (homolytic) or heterolytic (protonation; as described here). There are cases where both homolytic and heterolytic H₂-forming pathways are viable, such as in the well-studied cobaloxime HER catalysts (70–72), with the predominant operating mechanism dependent on the specific reaction conditions (73–80). The free energy of homolytic H–H bond formation is dependent on the homolytic bond energy of the metal hydride and H₂ and is not expected to have a dependence on the proton activity.

Consequently, the thermodynamic framework described in Fig. 2 is most useful for metal hydrides that are stable to homolytic H₂ bond formation. This is generally true for many classes of transition metal hydrides, including those in the [Ni(P₂N₂)₂]²⁺ class of catalysts (70, 71, 78–91), the water soluble [HNi(DHMPE)₂]²⁺, and the subject of these studies [HPt(dmpe)₂](PF₆)₂ (2). [The ³¹P{¹H}NMR spectra of [HPt(dmpe)₂](PF₆)₂ (2) in acetonitrile show no change over 23 h, confirming that there is no appreciable homolytic pathway for H₂ generation (SI Appendix, Fig. S18).] Application of these guidelines to metal hydrides prone to homocoupling to form H₂ would be expected to impact the pH-dependent H₂ evolution activity, present challenges to isolating the metal hydride under electrolytic conditions without generating H₂, and lead to lower overall selectivity.

The reduction potential required to generate [HPt(dmpe)₂](PF₆) (2) from the resting-state catalyst [Pt(dmpe)₂](PF₆)₂ (3) (shown as E_red1 in Eq. 7) is positive of the reduction potential for 2 (E_red2 in Eq. 7):

$${\left[\text{LM}\right]}^{\text{n}+1}\underset{{\text{E}}_{\text{red}1}}{\overset{2{\text{e}}^{-},{\text{H}}^{+}}{\to }}{\left[\text{LMH}\right]}^{\text{n}}\underset{{\text{E}}_{\text{red}2}}{\overset{{\text{e}}^{-}}{\to }}{\left[\text{LMH}\right]}^{\text{n}-1}.$$ [7]

Facile electrolytic generation of [HPt(dmpe)₂](PF₆) (2) is possible, because E_red1 is greater than E_red2 (−1.7 vs. −2.8 V vs. Fe(C₅H₅)₂^+/0) (shown in SI Appendix, Fig. S19). As a result, additional reduction of [HPt(dmpe)₂](PF₆) (2) to another intermediate is not possible at the electrochemical potential required to reduce 3. Several other group 10 metal hydride complexes (26) along with multiple cobalt hydride complexes (84, 88, 92–94) have the same property; reduction of the hydride complex ([LMH]ⁿ in Eq. 7) is more challenging than reduction of the parent complex ([LM]ⁿ⁺¹ in Eq. 7) to generate the hydride (or E_red1 > E_red2). In cases where this property does not hold [i.e., the reduction potential of the hydride intermediate (E_red2) is positive of the parent complex], it will likely be reduced under electrolytic conditions to generate a stronger hydride donor. For example, cobaloxime hydride complexes will generally be reduced further at potentials necessary to generate the hydride [LMH]ⁿ in Eq. 7 (or E_red2 > E_red1). In these cases, the hydricity of the reduced complex ([LMH]ⁿ⁻¹ in Eq. 7) can be applied to understand the pK_a-dependent hydrogen evolution catalysis, as [LMH]ⁿ⁻¹ will likely be generated under electrolytic conditions.

Conclusion

Despite immense interest in electrolytic fuel generation, there are few guidelines for the rational design of catalysts for selective CO₂ reduction. We use thermodynamic relationships to understand the reactivity of metal hydrides, a branch point in the reactivity for formation of either H₂ or HCO₂⁻. We applied our analysis to construct a diagram that defines catalyst parameters for achieving selective CO₂ reduction by targeting an appropriate hydricity. Hydricity is akin to an activity descriptor for H₂ and HCO₂⁻ generation—a thermodynamic quantity that describes the bond energy of a key intermediate. Like an activity descriptor, hydricity is general across many classes of compounds, expanding its utility. Identifying descriptors in molecular systems is particularly advantageous, as bond energies are easily tuned through metal–ligand design.

We applied our thermodynamic product diagram to identify a metal hydride with appropriate hydricity to reduce CO₂ to formate under conditions that minimized concomitant H₂ evolution. We expect that the thermodynamic framework described herein will continue to stimulate the discovery of more selective and efficient catalysts necessary for a carbon-neutral energy economy.

Methods

Experimental details, cyclic voltammograms, NMR spectra, data from electrolysis, H₂ (GC) and HCO₂⁻ (NMR) calibration curves, and additional thermodynamic product diagrams in DMSO and H₂O are provided in SI Appendix. SI Appendix includes synthetic methods and materials, physical methods, electrochemical methods (including controlled potential electrolysis and product analysis), additional thermodynamic product diagrams, and NMR spectra.