Quaternary Ammonium Salts as Supporting Electrolytes in Cathodic Reductions: An Analysis of Their Electrochemical Stability

We present a study of the thermodynamic and kinetic electrochemical stability of a test set of more than 5000 singly charged and doubly charged cations containing a quaternary ammonium group. The redox potentials and the inner-sphere reorganization energies are calculated using density functional theory employing an implicit solvent model for the solvation. We find three different categories of cations regarding their behavior under one-electron reduction. One category fragmentizes upon reduction, in another category the nitrogen atom is part of a ring which opens upon electron addition and, finally, the systems of the third category containing multiple bonds undergo only minor structural changes. An important class of quaternary ammonium ions belonging to the first category is provided by the tetraalkylammonium ions that fragmentize into a tertiary amine and an alkyl radical. We observe that systems undergoing ring-opening appear to be somewhat more stable electrochemically than the other two categories on average. Experimentally, we, for example, find this behavior for a system containing the quaternary nitrogen atom as a member of a ring. We suggest that in addition to the routinely employed tetraalkylammonium ions also such systems are well suited for use as supporting electrolyte in electrochemical reductions. For all systems investigated, the adiabatic values for the electron affinities and the ionization potentials show strong linear correlations with the reduction potential and the oxidation potential, respectively. This, however, is not the case for the quantities computed from the frontier orbital energies of density functional theory. The inner-sphere reorganization energies are important quantities determining the activation energy of heterogeneous electron transfer and we find that the values calculated for the oxidized state and the reduced state are quite similar for all three categories of ions. For the cations containing multiple bonds the inner-sphere reorganization energies show a strong prevalence for very small values due to the strong structural similarity of equilibrium conformations in the oxidized and the reduced state. This finding is in accord with the known instability of systems containing a carbon-carbon double bond next to a charged nitrogen under acidic conditions. A simple model relating a single Huang-Rhys factor and an effective vibration frequency given by the sum of all mode frequencies to the inner-sphere reorganization energy works very well. The effective curvatures of the potential energy curves for the oxidized and the reduced cations are found to be almost identical, which we interpret as a hint toward the applicability of Marcus theory in the harmonic approximation to the electron transfer processes in quaternary ammonium cations.