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The inelastic scattering of electrons which carry current through asingle-molecule junction is modeled by a quantum dot, coupled to electronreservoirs via two leads. When the electron is on the dot, it is coupled to asingle harmonic oscillator of frequency $\omega_0$. At zero temperature, theresonance peak in the linear-response conductance always narrows down due tothe coupling with the vibrational mode. However, this narrowing down is givenby the Franck-Condon factor only for narrow resonances. Contrary to some claimsin the literature, the linear-response conductance does not exhibit anyside-bands at zero temperature. Small side-bands, of order $\exp [-\beta \hbar\omega_0]$, do arise at finite temperatures. The single-particle density ofstates exhibits discontinuities and logarithmic singularities at thefrequencies corresponding to the opening of the inelastic channels, due to theimaginary and real parts of the self-energy. The same singularities alsogenerate discontinuities and logarithmic divergences in the differentialconductance at and around the inelastic thresholds. These discontinuitiesusually involve upwards steps, but these steps become negative within a rathernarrow range of the elastic transparency of the junction. This range shrinksfurther as the the excitation energy exceeds the bare resonance width.

Voltage-induced singularities in transport through molecular junctions