Molecular transport junctions: Propensity rules for inelastic electron tunneling spectra

We develop a series of propensity rules for interpreting inelastic electron tunneling (IET) spectra of single-molecule transport junctions. IETS has no selection rules, such as those seen in optical, infrared, and Raman spectra, because IETS features arise not from the field-dipole interaction characterizing these other spectroscopies but from vibronic modification of the electronic levels. Expansion of the Landauer-Imry formula in Taylor series in molecular normal coordinates gives a convenient, accurate perturbation-type formula for calculating both frequency and intensity of the IETS spectrum. Expansion in a Dyson-like form permits derivation of propensity rules, both symmetry-based and pathway-deduced, allowing correlation of structure and coupling geometry with the IETS spectrum. These propensity rules work very well for the calculated spectrum of five typical molecular bridges.