| In this thesis, we present the first-principle calculations of inelastic electron tunneling spectroscopy(IETS) in single molecular break junctions. In a two-probe electrode-molecule-electrode setup, density functional theory(DFT) is used for the construction of the Hamiltonian and the Keldysh non-equilibrium Green's function(NEGF) technique will be employed for determining the electron density in non-equilibrium system conditions. Total energy functional, atomic forces and Hessian matrix can be obtained in the DFT-NEGF formalism and self-consistent Born approximation(SCBA) is used to integrate the molecular vibrations (phonons) into the framework once the phonon spectra and eigenvectors are calculated from the dynamic matrix. Geometry optimization schemes will also be discussed as an indispensable part of the formalism as the equilibrium condition is crucial to correctly calculate the phonon properties of the system.;As the application of the DFT-NEGF-SCBA formalism, we calculate the IETS of the gold-octanedithiol(ODT) molecular junction. The I-V curve, conductance and IETS from ab-inito calculations are compared directly to experiments. A microscopic understanding of the electron-phonon coupling mechanism in the molecular tunneling junctions is explained in this example. In addition, comparisons of the hydrogen-dissociative and hydrogen-non-dissociative ODT junctions as well as the different charge transfer behaviors are presented to show the effects of thiol formation in the ODT molecular junction.;To overcome the numerical difficulties, especially the large computational time demand of the electron-phonon coupling problem, we develop a numerical approximation for the electron self-energy due to phonons and the error is controlled within numerical precision. Besides, a direct IETS second order I-V derivative expression is derived to reduce the error of numerical differentiation under reasonable assumptions. These two approximations greatly reduce the computation requirement and make the calculation feasible within current numerical capability. |
