We have analyzed the low-energy electron attachment to wobble base pairs using the equation of motion coupled cluster method and extended basis sets. A doorway mechanism exists for the attachment of the additional electron to the base pairs, where the initially formed dipole-bound anion captures the incoming electron. The doorway dipole-bound anionic state subsequently leads to the formation of a valence-bound state, and the transfer of extra electron occurs by mixing of electronic and nuclear degrees of freedom. The formation of the valence-bound anion is associated with proton transfer in hypoxanthine-cytosine and hypoxanthine-adenine base pairs, which happens through a concerted electron-proton transfer process. The calculated rate constant for the dipole-bound to valence-bound transition in wobble base pairs is slower than that observed in the Watson-Crick guanine-cytosine base pair.