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We present a method based on graph theory for evaluation of the inelasticpropensity rules for molecules exhibiting complete destructive quantuminterference in their elastic transmission. The method uses an extendedadjacency matrix corresponding to the structural graph of the molecule forcalculating the Green function between the sites with attached electrodes andconsequently states the corresponding conditions the electron-vibrationcoupling matrix must meet for the observation of an inelastic signal betweenthe terminals. The method can be fully automated and we provide a functionalwebsite running a code using Wolfram Mathematica, which returns a graphicaldepiction of destructive quantum interference configurations together with theassociated inelastic propensity rules for a wide class of molecules.

Graph-theoretical evaluation of the inelastic propensity rules for molecules with destructive quantum interference