Dynamics of quantum tunneling: Effects on the rate and transition path of OH on Cu(110)

Recent low-temperature scanning-tunneling microscopy experiments [T. Kumagai et al., Phys. Rev. B 79, 035423 (2009)] observed the possible quantum tunneling of hydroxyl groups between two equivalent adsorption configurations on Cu(110). Here we analyze the quantum nuclear tunneling dynamics of hydroxyl on Cu(110) using density-functional theory based techniques. We calculate classical, semiclassical, and quantum-mechanical transition rates for the flipping of OH between two degenerate energy minima. The classical transition rate is essentially zero at the temperatures used in experiment and the tunneling rate along the minimum-energy path is also much too low compared to experimental observations. When tunneling is taken into account along a direct path connecting the initial and final states with only a minimum amount of the oxygen movement the transition rate obtained is in much better agreement with experiment, suggesting quantum tunneling effects cause a deviation of the reaction coordinate from the classical transition path.

Figure 1

(Color online) The adsorption geometry of OH on Cu(110) shown from above (top) and from the side (bottom). Two equivalent structures are possible due to symmetry. In our discussion we will refer to the image on the left as the IS and the image on the right as the FS.

Figure 2

(Color online) MEP obtained from a 15-image NEB calculation for the hydroxyl flip process on Cu(110). The red (dashed) and green (solid) curves correspond to the converged MEP with the top two layers of the surface relaxed or fixed in their bulk truncated configuration, respectively. The relaxed and fixed models predict transition barriers of 166 and 187 meV, respectively. The cartoons at the top of the graph are schematic illustrations of how the molecule moves during the flipping process, with the arrows indicating how the molecule moves from one step to the next. Although the difference in position between the O atom in the initial and final states is very small along the MEP the oxygen undergoes a large displacement before passing through the transition state. It is this supplementary oxygen movement which greatly suppresses the tunneling rate along the MEP.

Figure 3

(Color online) Potential energy surface in electron volt for the hydroxyl flip process on the bulk truncated Cu(110) surface as a function of oxygen and hydrogen displacement. This was generated by constraining the angle of the OH to surface normal ($\theta$ in the inset) and fixing the oxygen position at each displacement in the Cartesian $x$ and $y$ axes, both parallel to the surface. At each displacement $\left(r_{\text{O}}={\Delta }_{\text{O-Cu}}\right)$ the hydroxyl was free to relax both by moving in the $z$ direction (normal to the surface plane) and by varying the OH bond length. A total of 90 DFT calculations were performed and the results interpolated by means of a cubic spline to a finer mesh. The MEP is shown as a black curve and each image (except for the initial and final states) is numbered. Bead number eight is the transition state. The white solid line is the direct path joining the initial and final configurations with minimal movement of the oxygen. The dashed red line with no oxygen movement represents the WKB tunneling path used by Kumagai et al.

Figure 4

(Color online) Probability densities of (a) OH and (b) OD position on Cu(110) at 6 K. Both graphs show a double-peaked structure, with a small probability at the transition state (the transition state is where oxygen and hydrogen displacements are both zero). A logarithmic scale is used to emphasize the probability at the barrier region.