  In this article we present a novel semi-analytical approach to calculate
first-order electron-vibration coupling constants within the framework of
density functional theory. It combines analytical expressions for the
first-order derivative of the Kohn-Sham operator with respect to nuclear
displacements with coupled-perturbed Kohn-Sham theory to determine the
derivative of the electronic density matrix. This allows us to efficiently
compute accurate electron-vibration coupling constants. We apply our approach
to describe inelastic electron tunneling spectra of metallic and molecular
junctions. A gold junction bridged by an atomic chain is used to validate the
developed method, reproducing established experimental and theoretical results.
For octane-dithiol and octane-diamine single-molecule junctions we discuss the
influence of the anchoring group and mechanical stretching on the inelastic
electron tunneling spectra.
