Predicting Redox Behavior of Methyl Viologen and Analogues in Water using Density Functional Theory

Redox flow batteries (RFBs) are gaining attraction as promising energy storage devices.¹ While aqueous RFBs (ARFBs) exhibit lower voltages due to the limited potential window of water, they offer advantages in terms of safety. Despite some commercialization of ARFBs, ongoing research endeavors strive to improve their performance. Alkyl viologens, structurally similar to a1 in Figure 1 have been widely investigated as ARFB anolytes.²

To enhance their performance, modifications have been explored in two key directions: 1. Improving solubility: Alkyl groups at the 1,1' positions were substituted with charged functional groups such as 3-(trimethylammonio) propyl, 3-sulfonatopropyl, and 3-carboxypropyl. This strategy effectively increases solubility, crucial for high concentration electrolytes and enhanced energy density.^3,4 2. Suppressing dimerization: Upon single-electron reduction, viologen radical cations can form dimers, hindering battery performance. Introducing conjugated ring systems like phenylene, furandiyl, or thiophenediyl between the pyridinium rings of viologen (compounds a2, a3, and a4 in Fig. 1) hinders dimerization. Notably, these extended molecules exhibit lower reduction potentials (RPs) compared to their parent compound. This suggests potentially higher cell voltages, improved reversibility of redox reactions, and ultimately, enhanced battery performance.⁵

Seeking further performance enhancements, the author investigated modifications beyond altering the viologen backbone. This strategy involved changing the connection position of the pyridine rings in molecules a1-a4, resulting in the isomeric compounds b1-b4 (Fig. 1). Notably, while sharing the same chemical formula as their counterparts, these isomers possess distinct arrangements of atoms. To evaluate the impact of this structural variation, density functional theory (DFT) calculations were employed to determine the reduction potentials (RPs) of both the original compounds (a1-a4) and their newly generated isomers (b1-b4) in water.

Figure1.

The molecular structures of methyl viologen (a1) and its extended molecules (a2, a3 and a4) and their isomers obtained by changing the linking positions of pyridines.

All calculations were performed using the Gaussian 09 software.⁶ The RPs were determined employing the thermodynamic cycle represented in Scheme 1. In the cycle, “Ox” and “Red” denoted oxidized and reduced species, respectively. Gas and solution states are indicated using “(g)” and “(s)”, respectively. The Gibbs free energy of the gas-phase electron, following the electron convention with Fermi-Dirac statistics, was set to −3.632 kJ/mol.⁷ The solution-phase Gibbs free energy difference, Δ G s o , is determined by two factors: Gas-phase Gibbs free energy difference, Δ G g o and the solvation-free energy difference, ΔΔ G s o l o = Δ G s o l o Red − Δ G s o l o Ox . The RP relative to the standard hydrogen electrode (SHE) can be evaluated using the equation, E 1 / 2   v s   S H E = Δ G s o / n F − 4.281 , where n is the number of electrons transferred in the reduction reaction and F is Faraday’s constant. This equation was first reported by Isse and Gennaro.⁸

Scheme1.

Born-Haber cycle.

All DFT calculations employed the M06-2X functional, which is recognized as one of the most accurate hybrid functionals for organic compounds.⁹ Geometry optimization for both dicationic and radical cationic forms of the studied molecules was performed using the 6-311++G(d,p) basis set. The unrestricted method was employed for open-shell species. Frequency calculations at the same theoretical level ensured that optimized structures corresponded to true minima on the potential energy surface. Solvation-free energies were computed using the SMD model,¹⁰ a universal continuum solvation model based on the solute electron density, to incorporate solvent effects on energetics. The accuracy of the proposed method was assessed using compounds a1-a4. The mean absolute deviation (MAD) between calculated and experimental RPs in acetonitrile was 0.003 V, with the root mean square (RMS) deviation of 0.036V (see Table S1 in supporting information). This excellent agreement shows that the method is reliable, at least for predicting RPs for molecules studied in this work.

Table 1 summarizes the calculated adiabatic electron affinities (AEAs) corrected with zero-point energies and the RPs of the studied compounds. The calculated RP of methyl viologen (−0.40 V) closely matches with the experimental value¹¹ (−0.45 V), demonstrating the high accuracy of the employed computational method. Replacing the a1-a4 compounds with their corresponding structural isomers, b1-b4, leads to a significant decrease in their RPs. Specifically, the RPs drop by −0.46 V, −0.45 V, −0.34 V, and −0.45 V, averaging a reduction of −0.42 V. This suggest that the b1-b4 isomers hold great premise as superior anolytes in ARFB, due to their enhanced ease of oxidation, potentially leading to higher energy output. Furthermore, b1-b4 isomers exhibit lower AEAs compared to a1-a4 (−0.06, −0.08, 0.01, and −0.17 eV; average of −0.08 eV). This along with the corresponding decrease in RPs gives the resulting reductions in ΔΔ G s o l o for b1-b4 isomers (−0.40, −0.37, −0.35, and −0.27 eV, average of −0.35 eV). The decrease in ΔΔ G s o l o contributes four times as much to the reduction of RPs of b1-b4 isomers as the decrease in AEAs compared to a1-a4 isomers. This indicates that optimizing solvation properties could be a viable strategy for further enhancing the performance of ARFB anolytes.