  The microscopic theory of chemical reactions is based on transition state
theory, where atoms or ions transfer classically over an energy barrier, as
electrons maintain their ground state. Electron transfer is fundamentally
different and occurs by tunneling in response to solvent fluctuations. Here, we
develop the theory of coupled ion-electron transfer, in which ions and solvent
molecules fluctuate cooperatively to facilitate electron transfer. We derive a
general formula of the reaction rate that depends on the overpotential, solvent
properties, the electronic structure of the electron donor/acceptor, and the
excess chemical potential of ions in the transition state. For Faradaic
reactions, the theory predicts curved Tafel plots with a
concentration-dependent reaction-limited current. For moderate overpotentials,
our formula reduces to the Butler-Volmer equation and explains its relevance,
not only in the well-known limit of large electron-transfer (solvent
reorganization) energy, but also in the opposite limit of large ion-transfer
energy. The rate formula is applied to Li-ion batteries, where reduction of the
electrode host material couples with ion insertion. In the case of lithium iron
phosphate, the theory accurately predicts the concentration dependence of the
exchange current measured by {\it in operando} X-Ray microscopy without any
adjustable parameters. These results pave the way for interfacial engineering
to enhance ion intercalation rates, not only for batteries, but also for ionic
separations and neuromorphic computing.
