Why halides enhance heterogeneous metal ion charge transfer reactions

The reaction kinetics of many metal redox couples on electrode surfaces are enhanced in the presence of halides (i.e., Cl−, Br−, I−). Using first-principles metadynamics simulations, we show a correlation between calculated desorption barriers of V3+–anion complexes bound to graphite via an inner-sphere anion bridge and experimental V2+/V3+ kinetic measurements on edge plane pyrolytic graphite in H2SO4, HCl, and HI. We extend this analysis to V2+/V3+, Cr2+/Cr3+, and Cd0/Cd2+ reactions on a mercury electrode and demonstrate that reported kinetics in acidic electrolytes for these redox couples also correlate with the predicted desorption barriers of metal–anion complexes. Therefore, the desorption barrier of the metal–anion surface intermediate is a descriptor of kinetics for many metal redox couple/electrode combinations in the presence of halides. Knowledge of the metal–anion surface intermediates can guide the design of electrolytes and electrocatalysts with faster kinetics for redox reactions of relevance to energy and environmental applications.

. The ref is chosen as a perchlorate-or sulfate-based salt solution (instead of acid) for the cases where the rate data in presence of halides is available only in halide-based salt solutions to eliminate the effect of pH on rate constants. Table S1 are calculated at room temperature using various methods. For comparing rate data to desorption barriers in Figure 3, rate constants in hydrohalic and sulfuric acid electrolytes were taken from a single reference for each redox couple to avoid discrepancies in the experimental method used.

S2. Derivation of Rate Law
For deriving the rate law in Scheme 1 of the main text, the conversion between + and +1 was considered to occur through an adsorbed surface intermediate * +1 . * + + ⇄ * +1 + − ⇄ * + +1 + − (S1) Because the concentration of the adsorbed intermediate is much lower than the bulk concentrations of the ions in solution, the overall rate of formation of the surface intermediate ( * +1 ) is assumed to be zero (i.e., the pseudo-steady-state hypothesis). Only the forward rates are considered for this model, given that the exchange current density is proportional to the forward rate at equilibrium. * This gives an expression for the coverage of the surface intermediate ( The forward rate law can be expressed in terms of the coverage of the surface intermediate. The units of  (S10) Eq. S10 was used to generate the plot of the rate in Scheme 1. The derivative of the log of the rate with respect to inverse temperature was used to extract the apparent activation energy and the apparent frequency factor.

S3. Experimental V 2+ /V 3+ Kinetic Measurements in H2SO4, HCl, and HI on EPPG
V 2+ /V 3+ kinetic measurements were conducted on Edge Plane Pyrolytic Graphite (EPPG) (3.81 mm outer diameter × 4 mm thick, Pine Research) using the experimental setup described in prior work. 30,34 The EPPG disk was encapsulated in epoxy for stability, making the total outer diameter of the disk 5 mm. A threeelectrode two-compartment cell, with the two compartments separated by a Nafion 117 membrane (Fuel Cell store), was used. A double junction Ag/AgCl (Pine Research) was used as the reference electrode, and a graphite rod (99.9995 % metals basis, Alfa Aesar) was used as the counter electrode. The reference electrode was calibrated against the reversible hydrogen electrode by comparing to a Pt wire in the supporting electrolyte with 1 bar H2 bubbled into solution. Vanadium(IV) sulfate hydrate (VOSO4•xH2O [x assumed to be 5], ≥ 99.99% trace metals basis, Sigma Aldrich) in sulfuric acid (H2SO4, 99.999%, Sigma Aldrich), vanadium (III) chloride (VCl3, 99% metals basis, Alfa Aesar) in hydrochloric acid (HCl, ACS Reagent 37%, Sigma Aldrich), and vanadium (V) oxide (V2O5, ≥ 99.6% trace metals basis, Sigma Aldrich) in hydriodic acid (HI, 57%, contains no stabilizer, Sigma Aldrich) was used as the starting salt for preparing electrolytes to avoid the presence of any other anions in solution and isolate the effect of the specific anion on reaction kinetics. All solutions were prepared using purified water with 18.2 MΩ cm resistivity obtained from Millipore Sigma Synergy Ultrapure Water Purification System. The concentration of vanadium ions in each prepared electrolyte was 0.2 M and the acid concentration was fixed at 1 M. The electrolytes were prepared by the pre-electrolysis method described in our previous work. 30,34 The prepared solutions were first reduced to V 2+ , followed by oxidation to reach the specific concentration distribution of V 2+ and V 3+ . The concentrations of both V 2+ and V 3+ were confirmed via UV-Vis spectroscopy, using the calibration curves and Gaussian fitting parameters available in our prior work. 30,34 H2SO4 was used as the counter electrolyte solution during pre-electrolysis for measurements in H2SO4. However, for measurements in HCl and HI, perchloric acid (HClO4, 60%, Fisher Chemical) was used as the counter electrolyte solution, which was replaced after pre-electrolysis to prevent the contribution of currents due to formed Cl2 or I2 by the crossover of Cl − /I − anions from the working electrolyte compartment. 30 Further, H2SO4 was not used as the counter electrolyte solution for measurements in HCl and HI because of the inhibiting effect of sulfate on the measured V 2+ /V 3+ kinetics in HI on a glassy carbon electrode. 30,34 ClO4 − being a non-interacting anion ensures that the nature of the intermediate is unaffected in HCl and HI.
All electrochemical experiments were conducted on a cleaned EPPG electrode (cleaning process of EPPG described below) using a VSP potentiostat/galvanostat with a built-in electrochemical impedance spectroscopy (EIS) analyzer (Biologic Science Instruments USA). The exchange current densities ( ) were extracted by conducting steady state ( , ) and EIS ( , ) measurements described below. The two independent techniques were in good agreement, providing additional confidence in the reproducibility of our kinetic measurements. The apparent activation energies ( ) were extracted from the temperature dependence of . Temperature was controlled by a refrigerated/heated bath circulator (Fisher Scientific).
Steady state current measurements at various rotation rates: Steady state measurements were conducted between +300 mV and −100 mV overvoltage for different combinations of V 2+ and V 3+ concentrations at various rotations rates to confirm the measurements are in the kinetic regime. If measurements were not in the kinetic regime for highly oxidative overpotentials, the kinetic currents were evaluated by Koutecky-Levich analysis. 35 These kinetic currents were normalized by the electrochemical active surface area (ECSA) and plotted in the log scale vs. the applied overvoltage to obtain the Tafel plot. The log of oxidative kinetic currents in the region of 117−300 mV were extrapolated to zero overvoltage and the intercept was used to obtain , .
Electrochemical Impedance Spectroscopy: EIS measurements were conducted at open circuit voltage (OCV) with an overlaid 10 mV amplitude sine wave for a frequency range of 500 kHz to 100 mHz (with six points per decade) at each desired combination of V 2+ and V 3+ concentrations. The EIS measurements were taken before beginning each set of steady state measurement at a particular rotation rate. Before each EIS measurement, the OCV was equilibrated for 15 seconds. The measurements were fitted to a modified Randles circuit. 35 The charge transfer resistance ( ) values were used to evaluate , at each rotation rate, which were then averaged and used for analysis. The change in OCV among different electrolytes ( Figure S1) can be potentially caused by the difference in the stability of V 3+ complexes formed in H2SO4, HCl and HI. It has been shown previously that V 3+ complexes differently in each of these electrolytes. 30 Tafel and Nyquist plots from the EIS data, and the measurements to extract the capacitance to estimate the electrochemical active surface area in H2SO4 ( Figure S2, Table S2), HCl ( Figure S3, Table S3), and HI ( Figure S4, Table S4) are given below.
Apparent activation energies: , and , for each combination of V 2+ and V 3+ concentrations were evaluated by using the temperature variation (at 23.3, 30, 35, and 40 °C) of the corresponding , and , values, respectively, and using an Arrhenius relationship, as done in our prior work. 30,34 Scheme S1. Modified Randles circuit used for fitting all the EIS measurements for V 2+ /V 3+ reaction in different electrolytes. is the solution resistance, is the constant phase element, is the charge transfer resistance for V 2+ /V 3+ redox reaction obtained by multiplying fitted 3 with the electrochemically active surface area, and is the Warburg element for convective diffusion to account for the mass transfer at low frequencies.
Impedance from ( ) is a function of resistance 2 and time constant 2 . , , 3 , 2 , and 2 are obtained by the Zfit application of EC-Lab Software V11.18. 36  Tafel plots are constructed from steady-state measurements corrected for solution resistance. Circles in Tafel plots correspond to experimental measured points while the lines are used to guide the eye. The circles in the Nyquist plots are from EIS experimental measurements (b, e, h, k) and the dotted lines represent fits obtained from the EC-Lab software after modelling as a modified Randles circuit. All fitting parameters are available in Table S2. The ECSA (c, f, i, l) was obtained by the cyclic voltammetry capacitance method in H2SO4 for measurements in H2SO4. Note that all these plots are from a single experimental run. Each condition was repeated three times and the average exchange current densities evaluated from the three runs are reported in the main text.  Table S3. The ECSA (c, f, i, l) was obtained by the cyclic voltammetry capacitance method in HClO4 for measurements in HCl. Note that all these plots are from a single experimental run. Each condition was repeated three times and the average exchange current densities evaluated from the three runs are reported in the main text.  Figure S3. Each condition was repeated three times and the average exchange current densities evaluated from the three runs are reported.

HCl (°C) [V 2+ ] (M) (Ω) (F s (a−1) ) (Ω) (s) (Ω) ECSA (cm 2 ) (Ω cm 2 )
23  Table S4. The ECSA (c, f, i, l) was obtained by the cyclic voltammetry capacitance method in HClO4 for measurements in HI. Note that all these plots are from a single experimental run. Each condition was repeated three times and the average exchange current densities evaluated from the three runs are reported in the main text.

S4. Cleaning of EPPG and measurement of ECSA
The EPPG disk insert was first rinsed with Millipore water, followed by polishing for ~ 5 min with ultrafine alumina slurry (0.05 μm diameter particles, Allied Pure) on a Rayon microcloth polishing cloth (Pine Research). Subsequently, the electrode was rinsed with Millipore water multiple times to get rid of any alumina particles suspended on surface, followed by sonication for 45 min. Following sonication, the disk insert was mounted into a Pine Research E5-series ChangeDisk RDE assembly and affixed to a Modulated Speed Rotator. The cyclic voltammetry capacitance method was used to evaluate the ECSA of the EPPG. Cyclic voltammograms, 10 cycles each, at different scan rates (10, 20, 50, 80, 100, 150, and 200 mV/s) were conducted between −0.1 to 0.4 V (vs. Ag/AgCl) in 1 M H2SO4. The difference in the current at 0.15 V (vs. Ag/AgCl) during the increasing and decreasing voltage sweeps from the 10 th cycle was plotted against the scan rate. The slope of the corresponding line passing through the origin is twice the capacitance corresponding to the electrochemical double layer. Using a specific capacitance of 40 μF cm −2 for carbon surfaces in H2SO4, 37,38 the ECSA was determined.
For measurements in HCl and HI, we measured the ECSA in 1 M HClO4 instead of 1 M HCl due to the possibility of specific adsorption of Cl − and I − anions, respectively, on electrode surface during cycling. Additionally, H2SO4 was not used to prevent the introduction of any SO4 2− due to their inhibiting effect on reaction kinetics. 23 To consider the change in specific capacitance with change in electrolyte, the ECSA of EPPG was measured in 1 M H2SO4, followed by 1 M HClO4, and then again in 1 M H2SO4, assuming the same specific capacitance. We observed that the ECSAs in 1 M H2SO4 initially and after measurements in 1 M HClO4 were within ±2%, indicating that the EPPG surface is unchanged after using it for measurements in 1 M HClO4. Further, on comparing the ECSA in 1 M H2SO4 to 1 M HClO4 using the same specific capacitance, ECSAs were observed to be ~15% higher in 1 M HClO4 compared to 1 M H2SO4. As a result, to compensate for this effect, the specific capacitance of 46 μF cm −2 (~15% higher than in 1 M H2SO4) was used to evaluate the ECSA in 1 M HClO4. Spin-polarized density functional theory (DFT) calculations were performed using Vienna Ab Initio Simulation Package (VASP). [39][40][41] The PBE functional was used for all metadynamics simulations. 42 The projector augmented wave method was chosen to describe electron-ion interactions. 43 A 400 eV plane wave kinetic energy cutoff was set for all systems. A Γ-centered 1×1×1 k-point grid was used. The systems modeled were V 3+ -anion complexes on the graphite edge plane (112 ̅ 0), V 3+ -, Cr 3+ -, and Cd 2+ -anion complexes on Hg(111), and Fe 3+ -anion complexes on Au(111).

S5. Computational Methods and Simulation Cell Setup for Metadynamics
Details of the unit cell dimensions and compositions for NVT metadynamics simulations are shown in Figure 2a and Figures S8-S9. Graphite(112 ̅ 0) with lattice constants of a = 2.45 Å and c = 6.77 Å (Figure 2a) was used as a model surface for EPPG. The graphite surface was passivated with 42 adsorbed *H and five adsorbed *OH. In addition to vanadium, 38 explicit water molecules were added to maintain an aqueous environment with a density of 1 g/cm 3 . The middle layer of carbon atoms was fixed to their bulk positions. Spin-polarized DFT was used with a spin density of 2 spin-up electrons to model the V 3+ ion. A three-layer 3×3 Hg(111) surface with an Hg interatomic distance of 3.60 Å (Figure S8) was used to model a mercury drop electrode. In addition to the Cr 3+ ion, 48 explicit water molecules were added to maintain an aqueous environment with a density of 1 g/cm 3 . The middle layer of Hg atoms was fixed to their bulk positions. Spin-polarized DFT was used with a spin density of 3 spin-up electrons to model the Cr 3+ ion. The same procedure was used for the V 3+ and Cd 2+ on Hg(111) with 2 spin-up electrons for V 3+ and 0 spin-up electrons for Cd 2+ . VASP input files and geometries for metadynamics simulations are available in the NOMAD repository at https://dx.doi.org/ 10.17172/NOMAD/2021.07.03-1 A three-layer 4×4 Au(111) surface with lattice constant a = 4.17 Å (Figure S9) was used as a model for a polycrystalline gold electrode. In addition to the [Fe(H2O)5X] 2+ complex, 48 explicit water molecules were added to the simulation cell to maintain an aqueous environment with a density of 1 g/cm 3 . To prevent system translation and maintain a symmetric simulation cell, the middle layer of Au atoms was fixed to their bulk positions during the simulation. Spin-polarized DFT was used with a spin density of five spin-up electrons to model the high-spin Fe 3+ ion. A Nosé-Hoover thermostat was used to equilibrate the system at 300 K. 44,45 Equations of motion were integrated with a time step of 0.5 fs, and all hydrogen atoms were replaced with deuterium to dampen the high frequency OH bond vibrations. To calculate desorption free energy barriers, the distance between the metal ion and the surface (z coordinate) was chosen as the collective variable. Adding an additional collective variable that biases the coordination number between the metal ion and solvent water molecules, which occurs on a longer timescale than desorption, did not affect the desorption barriers and thus was not further considered ( Figure S10). The free energy barrier for [*I-Cr(H2O)5] 2+ desorption on Hg(111) when biasing both the coordination number of Cr 3+ with water and the Cr 3+ distance from the surface is 1.24 eV (Figure S10). The most stable adsorbed [*I-Cr(H2O)5] 2+ configuration occurs at a Cr 3+ -Hg distance of 5.2 Å and a coordination number of five and is described by the dark blue energy well. This prediction is similar to the desorption barrier when only biasing the Cr 3+ distance from the surface, which is 1.21 eV as shown in the free energy profile in Figure 3b. The second collective variable biasing the coordination number of water with the metal ion did not change the desorption barriers by more than three percent.
After at least a 5 ps equilibration period, gaussian bias potentials with height 0.01 eV and width 0.10 Å were deposited every 15 fs to bias the collective variable. The width of the gaussian hills was based on the standard deviation of changes in the collective variable during equilibration. Metadynamics simulations were stopped once the distance of the desorbed metal ion complex exceeded 1.5RS−X + RX−M from the surface for more than 0.3 ps, where RS−X is the surface-anion bond distance in the gas phase and RX−M is the bond distance between the anion-metal ion of the gas-phase complex ( Table S5). The effect of applied potential was not considered in these simulations.   Figure S12. Standard experimental rate constants on EPPG, mercury drop electrodes, and gold vs. the predicted desorption barrier of V 3+ -anion complex on graphite(112 ̅ 0), Hg(111), and Au(111). Colors denote the sulfuric and hydrohalic acid, namely H2SO4 (red), HCl (green), HBr (blue), and HI (purple).