We have investigated the electron-attached states in Watson-Crick guanine-cytosine and adenine-thymine base pairs using the highly accurate equation-of-motion coupled-cluster (EOM-CC) method and extended basis sets. Both base pairs have two bound anionic states. The dipole-bound state is stable even at the neutral geometry, but the valence-bound state is only adiabatically bound. The initial electron attachment results in the formation of a dipole-bound state that acts as a doorway to the valence-bound anionic state. The adiabatic potential energy surface of ground and first excited states of an anion shows an avoided crossing, indicating mixing of the electronic and nuclear degrees of freedom. We have calculated the coupling strength between the valence- and dipole-bound states by fitting a simple diabatic model potential to a cut through the two adiabatic surfaces of the anions obtained from the EOM-CC calculations. The transfer of the electron from the initial dipole-bound to the final valence-bound state has been found to happen at an ultrafast time scale.