Pre-Equilibrium Reaction Mechanism as a Strategy to Enhance Rate and Lower Overpotential in Electrocatalysis

Abstract

Pre-equilibrium reaction kinetics enable the overall rate of a catalytic reaction to be orders of magnitude faster than the rate-determining step. Herein, we demonstrate how pre-equilibrium kinetics can be applied to breaking the linear free-energy relationship (LFER) for electrocatalysis, leading to rate enhancement 5 orders of magnitude and lowering of overpotential to approximately thermoneutral. This approach is applied to pre-equilibrium formation of a metal-hydride intermediate to achieve fast formate formation rates from CO₂ reduction without loss of selectivity (i.e., H₂ evolution). Fast pre-equilibrium metal-hydride formation, at 10⁸ M^–1 s^–1, boosts the CO₂ electroreduction to formate rate up to 296 s^–1. Compared with molecular catalysts that have similar overpotential, this rate is enhanced by 5 orders of magnitude. As an alternative comparison, overpotential is lowered by ∼50 mV compared to catalysts with a similar rate. The principles elucidated here to obtain pre-equilibrium reaction kinetics via catalyst design are general. Design and development that builds on these principles should be possible in both molecular homogeneous and heterogeneous electrocatalysis.

Introduction

Metal-hydrides are key intermediates in a broad scope of chemistries including solar fuels and organic transformations for commodity and fine chemical synthesis. However, electrocatalytic approaches involving metal-hydride intermediates are universally plagued by a competition between desired product formation (hydride transfer to substrate), and competitive reaction of the hydride intermediate with the protons that are needed in solution to generate the hydride intermediate [via electron-transfer (ET) and proton-transfer (PT) steps, Scheme 1].

Scheme 1. Three Common Pathways for the Metal–Hydride Reaction.

An example situation where these competing reactions have been studied is in C–H bond formation with CO₂ and the interest in that chemistry derives from its potential applications in solar fuel chemistry.¹⁻⁸ Desired products include formate, methanol, ethanol, or ethylene which all contain C–H bonds; but H₂ formation is an ongoing challenge. Contributions from a number of research groups have demonstrated that we can use catalyst design for thermochemical control of reaction chemistry to achieve selectivity for C–H bond formation over H₂ evolution.⁹⁻¹⁶ However, that approach does not necessarily produce fast rates for C–H bond formation with CO₂.¹⁷ Approaches to enhancing the reaction rate for C–H bond formation with CO₂ are needed, and have primarily used reaction conditions, rather than catalyst design to achieve improvements: successful examples of this approach include stabilization of transition states for hydride transfer to CO₂ by choice of the solvent,¹⁸⁻²⁵ use of hydride-transfer mediators,²⁶ or additions of base or alcohol.^27,28

We have previously demonstrated that the large metal carbonyl clusters promote hydride formation with rate 10⁸ M^–1 s^–1.²⁹⁻³¹ We believe that this fast rate has two possible origins. The multiple metal–metal bonds in the clusters serve as multiple sites for protonation, and this should provide a kinetic boost to the rate of cluster-hydride formation.^30,31 In addition, the high anionic charges, 3– or 4–, on the clusters promote PT: while the delocalized structures of the clusters enable access to modest reduction potentials relative to single-metal site electrocatalysts, at a given formal oxidation state or overall charge.³²

A remaining challenge is to design a complete catalytic cycle competent for solar fuel chemistry or chemical synthesis which has fast hydride formation without H₂ production. Pre-equilibrium kinetic schemes have been reported as a tool for optimizing rates in O₂ reduction,³³ in hydride formation chemistries,³⁴ and in CO₂ reduction to CO.³⁵ Pre-equilibrium dynamics of intermediate formation in a catalytic cycle often impact a subsequent rate. As an example, PT transfer rates to two-electron reduced [CoCp(dxpe)(NCCH₃)]²⁺ complexes [Cp = cyclopentadienyl, dxpe = 1,2-bis(di(aryl/alkyl)phosphino)ethane] can be controlled by the equilibrium constant for dissociation of MeCN from Co prior to PT,³⁴ and pre-equilibrium kinetics of CO₂ binding to iron(0) porphyrin enhance the observed apparent rate constant for CO formation, under reaction conditions where the thermodynamics for C–O bond-breaking are favorable.³⁵ Fast H₂ evolution by iron porphyrin also proceeds with a pre-equilibrium kinetic scheme involving fast Fe-hydride formation.^36,37

When conceiving of the work reported herein, we reasoned that fast formation of (H-1)^3– at significant concentrations will boost the formate formation rate by orders of magnitude if (H-1)^3– is formed with very fast rate to enable a pre-equilibrium reaction mechanism. According to the pre-equilibrium approximation, which can be used in the case of a fast initial chemical step in a catalytic cycle, the observed rate of a possible formate formation reaction should scale with the equilibrium constant (K₁) for pre-equilibrium hydride formation (Scheme 2), according to eq 1

1

where k_obs (s^–1) is the observed rate of reaction, K₁ is the equilibrium constant for formation of (H-1)^3–, k₂ (M^–1 s^–1) is the rate for hydride transfer to CO₂, and [CO₂] (M) is the concentration of CO₂. We further noted during this experimental design that the fast pre-equilibrium chemical step should offer a kinetically derived lowering of the overpotential for the reaction because a fast chemical step following ET results in the anodic shift of the reduction peak potential of any electrocatalyst.

Scheme 2. Proposed CO₂ Reduction Mechanism by 1^3–

Herein, we demonstrate that formate is generated at an overpotential of 10 mV and with the rate of 1.2 × 10³ M^–1 s^–1 using 1^3– in 0.1 M Bu₄NBF₄ MeCN/H₂O (95:5) (Calculation S1). We can also use stronger acids than water to enhance K₁, and with anisidinium tetrafluoro borate, it is generated at an overpotential of 64 mV with the rate of 5.07 × 10² M^–1 s^–1. The well-understood mechanistic origin of this result from the pre-equilibrium mechanism provides a roadmap for future catalyst design. In principle, any electrocatalytic reaction can be designed with a view to achieving pre-equilibrium intermediate formation to overcome slow rates that might be associated with thermochemically controlled rates for selectivity in subsequent chemical steps using heterogeneous or homogeneous electrocatalysis.

Results and Discussion

To study catalysis by 1^3–, we prepared samples of (PhCH₂NMe₃)₂[Co₁₁C₂(CO)₂₃] (1^2–) following a previously published method (PhCH₂NMe₃⁺ = benzyl ammonium cation).³⁸ The CV of 0.05 mM 1^2– recorded in 0.1 M Bu₄NBF₄ MeCN solution under 1 atm N₂ shows three reversible redox couples with E_1/2 = −0.2, −0.57, and −0.95 V versus SCE which were assigned as the 1^1–/2–, 1^2–/3–, and 1^3–/4– couples, respectively (Figure S1).^31,38 For experiments probing the catalytic activity of 1^3–, this species is generated in the CV measurement in all discussions below starting from 1^2–. When solutions of 0.05 mM 1^2– in 0.1 M Bu₄NBF₄ MeCN were titrated with water, the current density, j_p, at −1.054 V increased linearly up to 4% (2.2 M) H₂O after which the changes in j_p were very small (Figure 1 left). This increase in j_p suggests that a catalytic reaction is occurring. CV of 0.05 mM 1^2– collected under 1 atm CO₂ in 0.1 M Bu₄NBF₄ MeCN/H₂O (95:5) showed a further increase in j_p at −1.054 V, relative to the CV collected under 1 atm N₂, and this suggests that a catalytic reaction has occurred where hydride is transferred to CO₂ to afford formate (Figure 1 left). Current enhancements consistent with catalytic formate formation were also observed using anisidinium tetrafluoroborate (AnsdH⁺) as the source of H⁺ (Figure 1 right).

Figure 1.

CV of 0.05 mM 1^2– in 0.1 M Bu₄NBF₄ MeCN solution (black): (left) in 0.1 M Bu₄NBF₄ MeCN/H₂O (95:5) under 1 atm N₂ (red); in 0.1 M Bu₄NBF₄ MeCN/H₂O (95:5) under 1 atm CO₂ (blue). (right) with 5.1 mM AnsdH⁺ under 1 atm N₂ (red) and with 0.25 mM AnsdH⁺ under 1 atm CO₂ (blue). Inset: Plot of j versus [H₂O] under 1 atm CO₂.

The most acidic proton source in solutions of CO₂-saturated 0.1 M Bu₄NBF₄ MeCN/H₂O (95:5) is carbonic acid produced from 0.24 M CO₂ in MeCN/H₂O and that has pK_a = 17.03.^39,40 The pK_a of AnsdH⁺ in MeCN is 11.86.⁴¹ The waveforms obtained with MeCN/H₂O (95:5) or with AnsdH⁺ are different. Catalysis with water is observed at similar potential as the reduction potential for 1^3–/4–, whereas catalysis using AnsdH⁺ as the proton source is observed at a potential more anodic than the reduction of 1^3–. A possible mechanistic origin of these waveforms is discussed later, along with the determination of k_obs.

Characterization of Formate

Controlled potential electrolysis (CPE) experiments carried out under both 1 atm N₂ and 1 atm CO₂ were performed to identify the product in the CV experiments. CPE experiments −1.13 V over 40 min were followed by analysis of the head space using gas chromatography with thermal conductivity detector (GC-TCD) and analysis of the solution using proton NMR spectroscopy. Using 5% H₂O as the proton source in MeCN solutions, we determined that the Faradaic efficiency (FE) for formate and H₂ production are 75(5) and 15(2) %, respectively (Table S1, Figures S2–S4, see the Supporting Information for experimental details). CPE experiments performed using AnsdH⁺ as the source of protons under 1 atm CO₂ were run at −0.9 V, and those yielded formate and H₂ with FE of 70(8) and 25(3)%, respectively (Table S1, Figures S2 and S3). No CO₂-reduced products were detected by proton NMR when the CPE experiments were carried out under 1 atm N₂ or in the absence of 1^2– under 1 atm CO₂. To confirm the carbon source, isotopically labelled ¹³CO₂ was used for CPE experiments, and the ¹³C{¹H} NMR spectrum collected of the CPE solution showed a peak at 172.9 ppm which conclusively indicates that formate was produced from CO₂ during electrocatalysis (Figure S3D). CPE experiments run with the used electrodes from CPE experiments containing 1^2–, and those also produced no carbon-containing products. SEM–EDX measurements performed on used electrodes revealed no deposited Co on the glassy carbon (Figure S5).

Mechanistic Studies of Hydride Formation

Our first step toward understanding the mechanism for formate formation by 1^3– was to measure the rate for catalyst-hydride, (H-1)^3–, formation (k₁, Scheme 2) in MeCN/H₂O (95:5) under both N₂ and CO₂ atmospheres, where clusters of H₂O–MeCN (under N₂ and CO₂) and/or carbonic acid (under CO₂), respectively, are the proton sources for (H-1)^3– formation. Use of low [H⁺] in CV experiments accesses a kinetic region where the (H-1)^3– formation rate is measured based on the shift in peak potential: with low [H⁺], the follow-up chemical steps in the catalytic cycle are suppressed, and a small return wave is observed in the CV at ∼−0.72 V (Figure 2).

Figure 2.

CVs of 0.1 mM 1^2– in 0.1 M Bu₄NBF₄ MeCN/H₂O (99.3:0.7). (left) Under 1 atm N₂ at variable scan rates (starting from bright green 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.2, 1.4, and 1.6 V s^–1); CV in black is for 1^2– without added H₂O. (right) Under 1 atm CO₂ at variable scan rates (starting from red trace 0.8, 1.2, 1.6, 2, 3, 4, 5, and 6 V s^–1). Insets: plots of (E_p – E_1/2) (F/RT) vs ln(υ). The red line is a linear fit with slope fixed at −0.5.

Accordingly, we collected CVs of 0.1 mM 1^2– with 0.7% (0.38 mM) H₂O in 0.1 M Bu₄NBF₄ MeCN under N₂ and under CO₂ at 100 mV/s (Figure 2). Under N₂, the reductive peak potential E_p,c shifted from E_1/2 anodically by 100 mV relative to CVs lacking H₂O, which suggests a fast rate for PT following the ET. The 1^3–/4– redox couple is also observed at a consistent potential in these CVs, which suggests that some of the 1^2– is regenerated from (H-1)^3– in a reaction with protons during the CV experiment, and some of the (H-1)^3– remains and is oxidized at −0.72 V on the return scan.

For a chemical reaction that proceeds ET, the peak potentials (E_p) shift anodically relative to the formal potential of 1^3–/4– (E_1/2). The kinetic information is contained in the “peak shift”, ΔE_p (where ΔE_p = E_p – E_1/2) according to 2(42,43)

2

where R is ideal gas constant (8.314 J mol^–1K^–1), T is temperature (K), F is Faraday’s constant (C mol^–1), k₁ is the second-order rate constant of the PT reaction (s^–1), and other symbols were defined earlier. Due to the fast catalysis following the formation of (H-1)^3– (vide infra), eq 2 is potentially a little inaccurate in this situation, and therefore, we also determined a value for k₁ using a foot-of-the wave analysis (FOWA),^44,45 so that the two measurements can be compared.

Experimentally, k₁ can be obtained by recording E_p – E_1/2 as a function of υ, and we performed this experiment with a ratio of [H⁺]/[1^2–] = 3800, where E_p – E_1/2 is already ∼150 mV due to the fast PT step. A plot of (E_p – E_1/2)F/RT vs ln(υ) according to eq 2 gave k₁ = 3.9 × 10⁵ M^–1 s^–1 under 1 atm N₂ (Table 1, Figure 2 left, Calculation S2). The same experiment was repeated under 1 atm CO₂, and a higher rate of 1.2 × 10⁷ M^–1 s^–1 was observed for k₁ (Table 1, Figure 2 right, Calculation S2). This higher rate for k₁ is consistent with carbonic acid as the proton source, which has lower pK_a than H₂O as the proton source in MeCN. The value of k₁ measured using AnsdH⁺ as the proton source was the same (within error) under 1 atm of N₂ or CO₂ and is 3 × 10⁸ M^–1 s^–1 (Table 1, Figures 2, S6, Calculation S2). FOWA of CV traces collected under catalytic conditions yielded values for k₁ that are in good agreement with the peak-shift analysis (Calculation S2, Table 1, Figure S7).

Table 1. Thermodynamic and Kinetic Data for (H-1)^3– Formation by 1^3–a.

[H+]/mM	pKa	Epc/V	Epc/2/V	k1b/M–1 s–1
H2O, N2 (380)		–0.85	0.80	3.9 × 105(1.9 × 105)c
H2O, CO2 (380)	17.03	–0.83	–0.78	1.2 × 107(1 × 107)c
AnsdH+, N2 (0.15)	11.8	–0.81	–0.76	3 × 108d,e
AnsdH+, CO2 (0.25)	11.8	–0.81	–0.76	4.6 × 108e

^aMeasured in 0.1 mM Bu₄NBF₄ MeCN with H₂O or AnsdH⁺ under 1 atm CO₂ or N₂.

^bk₁ calculated using peak shift analysis (Calculation S2).

^cCalculated using FOWA analysis (Calculation S2).

^dValue from ref (31).

^eOverlap of peak with 1^2–/3– couple precluded FOWA.

Catalytic Formate Formation Rate and Mechanism

Our next effort toward understanding the effects of pre-equilibrium kinetics on formate production by 1^2– was to characterize the chemistry under reaction conditions that promote turnover in the catalytic cycle. CV experiments were performed with varied [1^2–] in 0.1 M Bu₄NBF₄ MeCN under CO₂, and the acid source was either 5% (2.77 M) H₂O or 2 mM AnsdH⁺ (Figure 3). In each case, a linear correlation between j_c versus [1^2–] was observed, and this indicates that formate production is of first order in [1^2–]. Similarly, the reaction is of first order with respect to [H⁺] under 1 atm CO₂ when either H₂O or AnsdH⁺ is the source of H⁺ (Figure S8).

Figure 3.

CVs of 1^2– with (0.05, 0.06, 0.77, 0.09, 0.11-, and 0.12 mM H⁺, colors) in 0.1 M Bu₄NBF₄ MeCN under CO₂, at 100 mV/s and using the GC electrode. (left) with 5% H₂O as the source of H⁺. Inset: plot of j_c versus [1^2–], at −1.054 V. (right) with 2 mM AnsdH⁺ as the source of H⁺. Inset: plot of j_c vs [1^2–], at −0.82 V. Red lines are linear fit to the data, and black CV trace has no added H⁺.

The rate of formate formation by 1^2– (k_obs, s^–1) can be obtained using a fast scan CV measurement of the limiting current (i_lim).^46,47 The experiment is performed with excess substrate relative to the catalyst to achieve i_lim, which is independent of the scan rate due to mutual compensation of substrate depletion during catalysis and diffusion. These reaction conditions also lead to the form of eq 1, where neither [1^3–] or [H⁺] influences k_obs. Analysis of i_lim to measure the rate of formate formation under 1 atm CO₂ was performed using the same two sources of protons as mentioned above: CO₂-saturated H₂O and AnsdH⁺, in 0.1 M Bu₄NBF₄ MeCN solution (Calculation S4, Figure 4). In addition, the k_obs values obtained were corrected for the measured FE which are 75 and 70% for formate under 1 atm CO₂, in MeCN/H₂O (95:5) and MeCN with added AnsdH⁺, respectively. Therefore, the values for k_obs are 296 and 142 s^–1, respectively, in MeCN/H₂O (95:5) and MeCN with added AnsdH⁺, under 1 atm CO₂ (Table 1).

Figure 4.

Forward CV traces of (top left) 0.06 mM 1^2– in 0.1 M Bu₄NBF₄ MeCN/H₂O (95:5) under 1 atm CO₂ at the scan rate = 0.1, 0.2, 0.4, 0.6, 0.9, 1.2, 1.5, 2, 3, 4, 6, 8, 12, 14, 18, 21, and 22 V/s; and (bottom left) 3.5 mM AnsdH⁺ and 0.2 mM 1^2– in 0.1 M Bu₄NBF₄ MeCN under CO₂ at various scan rates: 0.3, 0.5. 0.7, 0.8, 1.2, 1.8, 2.5, 3, 4, 5, 5.5, 6, 7, and 8 V/s. (Right) Plots of j_max vs υ at potentials negative to −1.08 V (top) and −0.82 (bottom), after subtraction of the background current value.

A comparison of the data collected with low [H⁺] (Figure 2) and with high [H⁺] for catalytic conditions (Figure 4) provides some information about the mechanism for formate formation with either H₂O or AnsdH⁺ and how those mechanisms may differ slightly as a function of the proton source. As described earlier, under reaction conditions with low [H⁺], there is an anodic shift in E_p,c(1^3–/4–) due to the folfast PT reaction which affords (H-1)^3– from 1^4–. The anodic shift in E_p,c(1^3–/4–) from E_1/2 is 140 and 100 mV with H₂O or AnsdH⁺, respectively, under 1 atm CO₂ (Table 1). As the [H⁺] increases, the catalytic current response with H₂O gradually shifts cathodically, whereas the response under AnsdH⁺ remains at E_cat/2 = −0.78 V (Table 2). Both of these behaviors are common in molecular electrocatalysis and indicate nuances in the reaction mechanism. With AnsdH⁺, the constant value of E_cat/2 over a wide range for [H⁺] simply suggests that the mechanism for formate formation (or background H₂ evolution) is unchanged even as the concentration of (H-1)^3– available in solution increases with increased [H⁺] (Scheme 2). When H₂O/carbonic acid is the proton source, then at higher [H⁺], E_cat/2 for 1^2– shifts cathodically so that E_cat/2 ∼ E_1/2 at [H⁺]_max. Water (or carbonic acid) is a weaker acid than AnsdH⁺ by 5 pK_a units. The cathodic shift in E_cat/2 with increased [H⁺] may therefore arise from a competing bimolecular evolution of H₂ as has been described in prior reports by us³¹ and by others (Scheme 1).⁴⁸ It is also possible that more negative potentials are needed to drive hydride transfer from (H-1)^3– to CO₂ under the solution conditions containing 5% H₂O; perhaps due to lower solubility of CO₂, CO₂ equilibria with H₂CO₃ and HCO₃^–, or relative solvation of the substrate in solution.

Table 2. Thermodynamic and Kinetic Data for Formate Formation by 1^3–a.

[H+]/mM	Ecat/2/V	K1b	kobsc/s–1	kcatc/M–1 s–1
H2O, CO2 (2800)	–1.01	15.8	296	1.2 × 103
AnsdH+, CO2 (3.8)	–0.78	5.5 × 1012	142	5.1 × 102

^aMeasured in 0.1 mM Bu₄NBF₄ MeCN with excess H₂O (carbonic acid) or AnsdH⁺, under 1 atm CO₂. E_1/2 (1^3–/4–) = −0.95 V versus SCE.

^bSee Calculation S3 for K₁.

^ck_obs obtained from the fast scan method (Calculation S4); values are corrected for the FE of formate (Table S1).

Pre-equilibrium Effects on Catalysis

The formate formation rate catalyzed by 1^2– (k_obs) is orders of magnitude slower than the rate for formation of the intermediate (H-1)^3– (k₁) (vide supra). Therefore, the formation of (H-1)^3– can be considered as a pre-equilibrium step with both a forward and reverse rate constant, k₁ and k_–1, and an equilibrium constant, K₁ = k₁/k_–1 (Scheme 2). A key feature of the pre-equilibrium mechanism is that k_obs is enhanced linearly according to the magnitude of K₁: that is a “normal” mechanism would have k_obs = k₂[CO₂], but the pre-equilibrium mechanism has k_obs = K₁k₂[CO₂] (eq 1, and the terms and units were defined earlier).

Even at very low ratios of [H⁺]/[1^2–] under 1 atm CO₂, the 1^3–/4– redox couple is irreversible, and therefore, we cannot determine K₁ using an electrochemical measurement (Figure 3 right).⁴⁹ However, we can estimate a value for K₁ if we know the pK_a value for (H-1)^3– and the pK_a values for the proton sources used for catalysis, which are CO₂ saturated H₂O and AnsdH⁺. We determined the pK_a value for (H-1)^3– as 24.6 using infra-red spectroelectrochemical titrations of 1^4– with acid sources (Calculation S5, Figure S9). We then used thermochemical cycles to determine the values for K₁ from the pK_a values of (H-1)^3–, CO₂ saturated water, and AnsdH⁺ (Calculation S3). The values of K₁ were determined as 15.8 and 5.5 × 10¹², when CO₂ saturated water or AnsdH⁺ are used as the proton source, respectively.⁵⁰⁻⁵² Using the experimentally determined value for k₁, this calculation further provides an estimate of k_–1 as 1.2 × 10⁴ and 5.4 × 10^–5 M^–1 s^–1, when CO₂ saturated water or AnsdH⁺ are used as the proton source, respectively, since K₁ = k₁/k_–1. According to these estimates, K₁ > 1, and we should expect that the pre-equilibrium formation of (H-1)^3– enhances k_obs relative to k₂ (eq 1, Scheme 2).

Catalyst Benchmarking

As mentioned in the introduction, we predicted that two features of the catalyst performance (rate and overpotential) will be enhanced by the pre-equilibrium reaction kinetics, relative to reports of formate formation by other molecular catalysts. These two effects are nicely illustrated using a Tafel style plot where the TOF (which is equivalent to k_obs above) is plotted as log₁₀(TOF/s^–1) versus overpotential (V). On this plot, formate formation by 1^3– is illustrated using both AnsdH⁺ and H₂O as the source of protons (Figure 5). Overpotential is defined as

3

where η is overpotential (mV), E_CO2 is the thermodynamic potential for reduction of CO₂ into formate under standard conditions (mV), and E_cat/2 is the potential at which the catalytic current density reaches half of its maximum current (i_cat/2 and see Calculation S1).⁵³

Figure 5.

Tafel-style plot: Log₁₀[(TOF/s^–1) (EF)²] vs overpotential (η) at E_cat/2, for selected molecular CO₂ to HCO₂^– reduction catalysts. Details of calculations and parameters used to construct the plot are shown in Table S2 and references therein. η = E_CO2/HCOO^– – E_cat/2.

Kinetic enhancements to k₁ result in a low overpotential for the catalytic reaction at 64 mV using 1^3– in MeCN/AnsdH⁺. Specifically, E_1/2 for 1^3– is −0.95 V, but E_cat/2 is −0.78 V, and the 170 mV anodic shift in E_cat/2 has a kinetic origin in the extremely fast PT rate and formation of (H-1)^3–, at 3 × 10⁸ M^–1 s^–1. Another example of a very fast formate forming catalyst is [(bipy)Co(PyS)₂]⁺ which has TOF similar to 1^3– while the overpotential remains pinned to the value of E_1/2 so that the overpotential for formate formation is 110 mV.⁵⁴

A plot of Log₁₀(TOF/s^–1) versus E_cat/2 for molecular catalysis of CO₂ to formate shows a linear correlation (Figure 6). Absent kinetic effects, a linear free-energy relationship (LFER) should exist between Log(TOF/s^–1) and hydricity (free energy for loss of hydride, ΔG_H^–) over a series of catalysts.⁵⁵ It is also known that ΔG_H^– scales roughly with E_cat/2 and pK_a of the catalytic hydride intermediate over a series of catalysts having similar mechanism, and this relationship underlies a rough correlation between Log₁₀(TOF/s^–1) and E_cat/2. Given that the structure of 1^3– is different than the structure of the single-site metal catalysts that comprise most of the catalysts in Figures 5 and 6, it is possible that 1^3– does not fall on the ΔG_H^– versus E_cat/2 correlation line for those compounds. Therefore, we include a brief discussion using ΔG_H^– as a benchmark against related catalysts to complement the observations in Figure 6.

Figure 6.

LFER between Log(TOF/s^–1) and E_cat/2 for selected molecular electrocatalysts {1^2–, [Fe₄N(CO)₁₂]^1–,^20,25 [Fe₄N(CO)₁₁(PPh₃)]⁻,⁵⁶ [FeN₅Cl₂]⁺,⁵⁷ [FeP₄N₂]²⁺,⁵⁸ [Co(imino-bpy)]²⁺,⁵⁹ [(bipy)Co(PyS)₂]⁺,⁵⁴ CpCoP^Cy₂N^Bn₂I₂,¹⁸ [Ni(qpdt)₂]⁻,⁶⁰ [Pt(depe)₂]⁺,^15,16 Ir(POCOP),²² and [Mn(bipy)(CO)₃]/Fe–S}.²⁶ Data for this plot, see Table S2. The blue shadow highlights correlation of Log₁₀[(TOF/s^–1)(FE_HCOO^–)²] with E_cat/2.

To assess the driving force for hydride transfer from (H-1)^3– to CO₂, we first determined ΔG_H^– for (H-1)^3–. The ΔG_H- was obtained from the pK_a for (H-1)^3– using a thermochemical cycle, and it is 41.1 ± 2.6 kcal mol^–1 in MeCN when using an organic acid as the source of protons (Calculation S5, Figure S9).⁶¹⁻⁶⁴ The ΔG_H^– for formate in MeCN is 44 kcal mol^–1,¹¹ and that suggests that reaction of (H-1)^3– with CO₂ to give 1^2– and HCOO^– is favorable by 2.9 kcal mol^–1 which is relatively close to thermoneutral. Other example catalysts which have hydricity close to thermoneutral for C–H bond formation with CO₂ include [Fe₄N(CO)₁₁(PPh₃)]⁻,⁵⁶ Pt(dmpe)₂,¹⁴ and [(bipy)Co(PyS)₂]⁺,⁵² which have ΔG_H^– estimated at 45, 41.4, and 38 kcal mol^–1, respectively. We note that the hydricity for [H-Fe₄N(CO)₁₁(PPh₃)]⁻ and [H–Pt(dmpe)₂] was determined experimentally, and for [(bipy)Co(PyS)₂]⁺, a theoretical estimate was made.^14,54,56 The catalysts 1^3– and [Pt(dmpe)₂]²⁺ have near-identical hydricity in MeCN but 1^3– produces formate with a rate that is 5 orders of magnitude faster as a result of the pre-equilibrium reaction mechanism. Another direct comparison involves [(bipy)Co(PyS)₂]⁺, which has hydricity 3.1 kcal mol^–1 stronger than 1^3–, and yet, the two catalyst exhibit inverted rates: 1.2 × 10³ M^–1 s^–1 for 1^3–(65,66) and 98.2 M^–1 s^–1 for [(bipy)Co(PyS)₂]⁺ in MeCN, which we also attribute to the pre-equilibrium kinetics of (H-1)^3– formation.

Catalyst Design for a Pre-Equilibrium Mechanism

These findings illustrate how clusters, or more generally nano-sized materials with delocalized electronic structure, can be employed to enhance the reaction rate of the first chemical step in the catalytic cycle to achieve the pre-equilibrium mechanism. The active catalyst, 1^3–, has 3- charge while retaining a very modest reduction potential of −0.95 V. The low potential, despite the high anionic molecular charge, likely arises from low reorganization energy associated with the delocalized bonding in the metal–metal bonded cluster; the fast PT to afford (H-1)^3– may be promoted by the high anionic charge on intermediate 1^4–, by the large array of almost-identical surface sites that are available to react with the proton, and by a low reorganization energy for the PT. In any electrochemically driven catalytic cycle, a fast chemical step following ET will lower the overpotential for catalysis, as defined in eq 3, since E_cat/2 is kinetically shifted by the fast chemical step.

Using the cluster structure to achieve a pre-equilibrium mechanism has further advantages beyond the lowered overpotential described in the preceding paragraph. Following generation of the intermediate, in this case (H-1)^3–, there is now just one reactive site on the catalytic intermediate, and thus, the selectivity of the second chemical step remains under thermochemical control with a rate that is enhanced by the pre-equilibrium value of K₁ according to eq 1.

Regarding future applications of the pre-equilibrium mechanism to enhance the electrocatalyst performance, there are a few obvious scenarios that come to mind. The establishment of the pre-equilibrium depends on the reactivity of both the catalyst (more precisely, the catalyst following a redox event) and the substrate that is required for intermediate formation. These will be discussed separately. Regarding the catalyst: heterogeneous and nano-scale catalysts possess delocalized structures and multiple reactive surface sites similar to the clusters described herein and should be amenable to design of pre-equilibrium mechanisms for solar fuel chemistry. Molecular catalysts, likewise, are promising candidates, and proton relays are a structure type in this category that is well-known to be effective in fast and low overpotential H2 evolution from protons. Beyond, proton reduction, new strategies in molecular chemistry must provide multiple sites for specific substrate binding or site specificity, and possible ideas in this area include incorporation of H-bond accepting or -donating functional groups that are chosen with a pK_a value that is not suitable for proton relay behavior. A nucleophilic molecular catalyst is another obvious approach, but that is not a good one since it also results in high energy (very cathodic potentials in the case of reduction) for the catalytic turnover.

Regarding the substrate: in this work, the substrate needed for intermediate formation was a proton, and the proton activity is easily changed (and benchmarked according to the pK_a scale) to promote a large equilibrium constant (K₁: see eq 1, Scheme 2). The tuning of substrates such as CO₂, CO, or N₂ may be a little more challenging, but strategies are known which can drive fast catalyst/substrate interactions that have high equilibrium constants. As examples, Lewis acid co-catalysts are known to polarize overall non-polar molecules including N₂ and CO₂, just like the anion associated with a proton changes its pK_a value and activity. Other mechanisms for tuning the reactivity of substrates include use of heterogeneous or homogeneous electrocatalysts with chemically inequivalent bind sites to polarize incoming substrates, to serve as ET sites, and to stabilize intermediates and enhance K₁.

It is apparent from the foregoing discussion that many of the catalyst design strategies reported by researchers in the heterogeneous and homogeneous electrocatalysis and solar fuel communities may already be drawing on pre-equilibrium reaction mechanisms to achieve high performance through tuning of the catalyst, substrate, or both. Recognition of those pre-equilibrium mechanisms will result in better control and further enhanced performance because it can guide tuning of elementary steps in the catalytic cycles. Alternatively, minor adjustments to the substrate choice or catalyst design may induce pre-equilibrium mechanisms from existing catalytic cycles that involve successive ET and chemical reaction steps.

Conclusions

In this report, we described a general strategy for use of the pre-equilibrium reaction mechanism to enhance the reaction rate. This was illustrated for formate formation from CO₂ and catalyzed by [Co₁₁C₂(CO)₂₃]^3– (1^3–). Relative to the known LFER for Log₁₀(TOF/s^–1) versus E_cat/2 for reported catalysts, the reaction rate to form formate was enhanced by 5 orders of magnitude, and the overpotential was lowered by 100 mV. Specific to the example demonstrated herein, pre-equilibrium metal-hydride formation led to the enhanced catalyst performance. Selectivity for formate formation (over H₂ formation or other CO₂ reduction products) arises from the thermoneutral hydride transfer elementary chemical step, whereas pre-equilibrium kinetic effects originate in the hydride formation at 3 × 10⁸ M^–1 s^–1. A rationale for the observed rates and selectivity were discussed in this report, in relation to the nano-scale structure of 1^3– and the choice of the proton source which both promote the pre-equilibrium reaction mechanism. In addition, the generality and clearly understood origin of the effects presented herein can be applied broadly to the design of homogeneous and heterogeneous catalysts, and possible strategies to achieve this in future efforts were discussed.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/jacs.2c10942.

• Experimental methods, calculations, CPE results, CV measurements, and details of electrochemical analysis (PDF)

The authors declare no competing financial interest.