Theoretical Framework. Standard ET models have been established based on the electrostatic Hamiltonian (Coulomb interactions) because electrodynamic effects and vacuum fluctuations (fluctuations between zero-photon and one-photon states) are considered small enough to be neglected. By contrast, to explore cavity-free QED effects on ET in a molecule, we consider a molecule to be a neutral system of charges coupled with infinite one-photon states (electromagnetic modes) in a homogeneous dielectric environment. To incorporate all of the degrees of freedom of nuclei, electrons, and photons into the QED-ET theory, we begin with the minimal coupling Hamiltonian (i.e., spinless) under the electric dipole approximation, make the several approximations (including the Condon approximation, the steepest-descent approximation, the low-vibrational-frequency limit), and derive an explicit expression for the total ET rate kET as