Proficient Computation of Inelastic Pulsation Indicators in Electron Movement

Abstract

The present research widens the effortless and competent lowest order expansion (LOE) for Inelastic Electron Tunneling Spectroscopy (IETS) to comprise difference in the electronic arrangement on the level of the vibration energies. This facilitates first-principles computations of IETS line shapes for molecular junctions close to resonances and band edges. This research exhibits how this is significant for the elucidation of investigational IETS using both a competent model and firstprinciples simulations. The inelastic scattering of electronic current on atomic vibrations is a powerful tool for investigations of conductive atomic-scale junctions. Inelastic electron tunneling spectroscopy (IETS) has been used to probe molecules on surfaces with scanning tunneling microscopy (STM), and for junctions more symmetrically bonded between the electrodes. Typical IETS signals show up as dips or peaks in the second derivative of the current-voltage (I -V) curve. In many cases the bonding geometry is unknown in the experiments. Therefore, first-principles transport calculations at the level of density functional theory (DFT) in combination with non-equilibrium Green’s functions (NEGF) can provide valuable insights into the atomistic structure and IETS. For systems where the electron-vibration (e-vib) coupling is sufficiently weak and the density of states (DOS) varies slowly with energy (compared to typical vibration energies) one can greatly simplify calculations with the lowest order expansion (LOE) in terms of the e-vib coupling together with the wideband approximation (LOE-WBA). The LOE-WBA yields simple expressions for the inelastic signal in terms of quantities readily available in DFT-NEGF calculations. Importantly, the LOE-WBA can be applied to systems of considerable size. However, the use of the WBA cannot account for IETS signals close to electronic resonances or band edges, which often contains crucial information. For example, a change in IETS signal from peak to peak-dip shape was recently reported by Song for single-molecule benzene-dithiol (BDT) junctions, where an external gate enabled tuning of the transport from off-resonance to close-to-resonance. Also, high-frequency vibrations involving hydrogen appear problematic since the LOE-WBA is reported to underestimate the IETS intensity. Here we show how the energy dependence can be included in the LOE description without changing significantly the transparency of the formulas or the computational cost. We describe how the generalized LOE differs from the original LOE-WBA, and demonstrate that it captures the IETS line shape close to a resonance. We apply it to DFT-NEGF calculations on the resonant BDT system and to off-resonant alkane-dithiol junctions, and show how the improved LOE is necessary to explain the experimental data.