Unified description of inelastic propensity rules for electron transport through nanoscale junctions

We present a method to analyze the results of first-principles based calculations of electronic currents including inelastic electron-phonon effects. This method allows us to determine the electronic and vibrational symmetries in play, and hence to obtain the so-called propensity rules for the studied systems. We show that only a few scattering states--namely those belonging to the most transmitting eigenchannels--need to be considered for a complete description of the electron transport. We apply the method on first-principles calculations of four different systems and obtain the propensity rules in each case.