Tafel slopes from first principles

Tafel slopes for multistep electrochemical reactions are derived from first principles. The derivation takes place in two stages. First, Dirac’s perturbation theory is used to solve the Schrödinger equation. Second, current–voltage curves are obtained by integrating the single-state results over the full density of states in electrolyte solutions. Thermal equilibrium is assumed throughout. Somewhat surprisingly, it is found that the symmetry factor that appears in the Butler–Volmer equation is different from the symmetry factor that appears in electron transfer theory, and a conversion formula is given. Finally, the Tafel slopes are compiled in a convenient look-up table.