Calculations of scattering of N2 molecules from Ru(0001)
Hailemariam Ambaye, J. R. Manson
Journal of Chemical Physics
As a part of an extensive study by the Odense group of N 2 interactions with the Ru͑0001͒ surface Mortensen et al. have reported detailed measurements for state resolved inelastic scattering. 1 This system is of current interest in debates concerning the applicability of the Born-Oppenheimer approximation in the interaction of molecules with metal surfaces. Calculations of N 2 dissociation based on density functional theory predict very efficient energy loss to electronic excitations in
... , 2 while classical trajectory calculations indicate that multidimensional effects associated with translational and rotational motions are much more important than nonadiabatic effects. 3 Here, these scattering data are compared to calculations using a theoretical model that has been useful in explaining surface collisions in other systems involving small molecular projectiles. This theory, which is presented in detail elsewhere, 4-6 is a mixed classical-quantum treatment of surface scattering in which the translational and rotational degrees of freedom are treated with classical mechanics while the excitation of internal molecular vibrational modes is treated quantum mechanically. The interaction potential is chosen to be a strongly repulsive barrier whose corrugation vibrates under the influence of the underlying target atoms. The most important and accurate measurements made were for the average final translational energy normal to the surface ͗E fn T ͘ as a function of final rotational energy E f R . These are shown in Fig. 1͑a͒ for two different energies and incident beam angles, E i T = 1.5 eV with i = 19°and E i T = 2.4 eV with i = 0°and the surface temperature is 610 K for all data shown here. These are compared with two sets of calculations, one using the mass Ru as the surface mass and the other with an effective surface mass 2.3 times that of a single Ru atom. For all calculations the value of the velocity parameter is 1000 m / s. Only qualitative agreement with the negative correlation between ͗E fn T ͘ and E f R is obtained using the smaller mass. However, with the larger effective surface mass quantitative agreement is obtained, and this holds true for essentially all of the comparisons presented here. Figure 1͑b͒ shows a different way of presenting the negative correlation of Fig. 1͑a͒ that includes the effects of energy transfer to the other degrees of freedom of the scattered molecules. Plotted in Fig. 1͑b͒ as a function The quantities ͗⌬E ʈ T ͘, ͗⌬E R ͘, and ͗⌬E ͘ are the average transfer of energy to parallel translational, rotational, and vibrational degrees of freedom, respectively. Again, the calculations with the larger effective surface mass give reasonable quantitative agreement with experiment. In the calculations ͗⌬E ͘ was negligible, in agreement with experimental observations. It should be noted that Ref. 1 also reported two data points taken at E i T = 2.7 eV and i = 19°with which our calculations also agree but for clarity are not shown. The incident energy dependence of the average final translational energy is shown in Fig. 2 where the normalized energy difference 1 − ͗E fn T ͘ / E in T is plotted for several incident beam angles as marked. The data for i = 40°denoted by asterisks and those for i = 50°denoted by cross symbols were extracted from Ref. 7 by the authors of Ref. 1. Calculations are shown for the two masses and reasonable agreement is obtained with the i = 50°data for the higher mass. The data at angles other than 50°are only qualitatively explained, but better agreement is with the larger effective surface mass. The average energy transfer perpendicular to the plane of scattering ͗⌬E x T ͘ is shown in Fig. 3 as a function of incident energy E i with an incident angle i = 19°. The calculations for the larger surface mass show the biggest out-ofplane energy transfers for incident energies greater than 0.4 meV, as expected since a larger surface mass leads to less overall energy transfer and hence higher translational energy in all directions of scattered particles. In this case the better overall agreement with experiment is for an effective mass equal to that of one Ru atom. FIG. 1. ͑a͒ The average normal translational energy ͗E fn T ͘ / E in T as a function of final rotational energy E f R . ͑b͒ Average fractional energy loss to the surface ͗⌬E s ͘ / E in T vs E f R . Incident beam conditions are E i = 2.4 eV and i =0°w ith data shown as circles and E i = 1.5 eV and i = 19°shown as triangles.