Multidimensional Effects on Dissociation of ${\mathrm{N}}_2$ on Ru(0001)

The applicability of the Born-Oppenheimer approximation to molecule-metal surface reactions is presently a topic of intense debate. We have performed classical trajectory calculations on a prototype activated dissociation reaction, of ${\mathrm{N}}_2$ on Ru(0001), using a potential energy surface based on density functional theory. The computed reaction probabilities are in good agreement with molecular beam experiments. Comparison to previous calculations shows that the rotation of ${\mathrm{N}}_2$ and its motion along the surface affect the reactivity of ${\mathrm{N}}_2$ much more than nonadiabatic effects.

Figure 1

(a) Coordinate system used. (b) High symmetry points of the Ru(0001) surface. White (gray) spheres denote atoms in the first (second) layer. Atoms in the third (fourth) layer are directly below the atoms in the first (second) layer.

Figure 2

The log of the probability of ${\mathrm{N}}_2$ dissociation on Ru(0001) is plotted vs normal translational energy $E_i$. Continuous lines with full symbols represent 6D adiabatic calculations, the dashed line with full symbols represents $2+1\mathrm{D}$ adiabatic calculations from 11, and the dashed line with open symbols $2+2\mathrm{D}$ nonadiabatic calculations from 11. Experimental measurements: full circles from 10; full green diamonds from 10; full red squares from 14. The inset shows $S_0$ times ${10}^2$ vs normal translational energy. Results are shown for different nozzle temperatures ($T_n$).

Figure 3

Two-dimensional cuts through the potential energy surface for (a) the molecule approaching the top site with the N-N bond parallel to the surface (${\theta }_i=90°$) and (b) the molecule approaching a site halfway between the top and fcc sites with ${\theta }_i=90°$. The potential is for the molecule oriented as indicated by the inset. The spacing between contour levels is 0.8 eV. The anisotropy and corrugation of the ${\mathrm{N}}_2/\mathrm{Ru}(0001)$ (solid line) and ${\mathrm{H}}_2/\mathrm{Cu}(100)$ [19] (dashed line) potentials near the minimum barrier is illustrated by plotting their dependence on $\theta$ (c) and $u$ (d), keeping all other coordinates fixed to the barrier geometry $Q^{*}$. Here, $u$ is the coordinate for motion along a straight line parallel to the surface, such that $V$ varies the least.

Figure 4

Computed dissociation probability vs incidence energy for several initial vibrational states $v_i$ and $J_i=0$.