Theory of vibrationally assisted tunneling for hydroxyl monomer flipping on Cu(110)
To describe vibrationally mediated configuration changes of adsorbates on surfaces we have developed a new theory to calculate both reaction rates and pathways. The method uses the T-matrix to describe excitations of vibrational states by the electrons of the substrate, adsorbate and tunneling electrons from a scanning tunneling probe. In addition to reaction rates, the theory also provides the reaction pathways by going beyond the harmonic approximation and using the full potential energy surface of the adsorbate which contains local minima corresponding to the adsorbates different configurations. To describe the theory, we reproduce the experimental results in [T. Kumagai \textit{et al.}, Phys. Rev. B \textbf{79}, 035423 (2009)], where the hydrogen/deuterium atom of an adsorbed hydroxyl (OH/OD) exhibits back and forth flipping between two equivalent configurations on a Cu(110) surface at $T = 6$ K. We estimate the potential energy surface and the reaction barrier, $\sim$160 meV, from DFT calculations. The calculated flipping processes arise from i) at low bias, tunneling of the hydrogen through the barrier, ii) intermediate bias, tunneling electrons excite the vibrations increasing the reaction rate although over the barrier processes are rare, and iii) higher bias, overtone excitations increase the reaction rate further.