Vibrational transition rule during a through-bond electron transfer process

The transition rule governing the inelastic excitations of molecular vibrations occurring during a molecular through-state electron transfer process is presented. Using an effective Hamiltonian model, it is shown that the quantum time oscillation of the intermediate electronic state population triggers this transition. Its corresponding quantum oscillation frequency has to be equal to a quantum of vibration. This transition rule is extended to the full spectrum of a quantum vibrator. This new transition rule is expected to be robust when electronically coupling the molecule to the metallic pads of a voltage-biased tunnel junction.