Theory of single molecule vibrational spectroscopy and microscopy.

We have carried out a density functional study of vibrationally inelastic tunneling in the scanning tunneling microscope of acetylene on copper. Our approach is based on a many-body generalization of the Tersoff-Hamann theory. We explain why only the carbon-hydrogen stretch modes are observed in terms of inelastic and elastic contributions to the tunneling conductance. The inelastic tunneling is found to be efficient and highly localized in space without any resonant interaction and to be governed by a vibration-induced change in tunneling amplitude.