Symmetry Selection Rules for Vibrationally Inelastic Tunneling

A combined experimental and theoretical study is presented for the C-D stretch mode excitation of acetylene isotopes, ${\mathrm{C}}_2\mathrm{HD}$ and ${\mathrm{C}}_2{\mathrm{D}}_2$, on Cu(100) via inelastic electron tunneling (IET) in a scanning tunneling microscope junction. The calculated IET images using density functional theory show that the measured signal from ${\mathrm{C}}_2{\mathrm{D}}_2$ derives from the antisymmetric stretch mode. Selection rules are derived and involve the constraint imposed by the IET image on the symmetry characters of the vibrational mode and the adsorbate-induced electron states at the Fermi level.