Faraday Discuss., 1993,96,297-305 Rotational Rainbows in NO Scattering from Pt(ll1) A. E. Wiskerke, C. A. Taatjes and A. W. Kleyn* FOM-Institutefor Atomic and Molecular Physics, Kruislaan 407, 1098 SJ Amsterdam, The Netherlands R. J. W. E. Lahaye and S. Stolte Laser Centre of the Free University, De Boelelaan 1083, 1081 HV Amsterdam, The Netherlands D. K. Bronnikov Russian National Scientijic Center 'Kurchatov Institute ' 123182, Moscow, Russia B. E. Hayden Department of Chemistry, The University of Southampton, Southampton, UK SO9 5NH The interaction between NO and Pt( 11 1) is dominated by the presence of a deep well corresponding to molecular chemisorption. To study the effect of a deep chemisorption well on the scattering dynamics we have performed measurements of rotational (J) excitation of NO in collisions with Pt( 11 1).The measurements show surprisingly large rotational excitation and a clear rotational rainbow. Classical trajectory calculations were carried out to examine the origin of this rainbow. Using the potential of Haug et al. the observed energy dependence of the rainbow could not be reproduced. We have constructed another model potential, having a shallow well for the 0 end of the molecule. Trajectory calculations with this potential explain the experimental observations qualitatively. We suggest that the rotational exci- tation manifested in the rotational rainbow is a result of the anisotropy in the repulsive part of the interaction potential. Rotational excitation in molecule-surface scattering has been studied for a variety of systems. In many cases the rotational state distributions are closely connected to the surface temperature, indicating that the molecule has accommodated to the Rotational excitation in direct inelastic scattering has also been observed. One of the most characteristic features that can occur in the rotational excitation spectra are the so-called rotational rainbow^.^^^ Rotational rainbows occur when the rotational excita- tion as a function of the initial molecular orientation shows an extremum.This leads classically to a rainbow singularity and in many cases it can be observed as a clear peak in rotational excitation spectra. Rotational rainbows in molecule-surface scattering have been observed in a number of In all these systems the attraction between the molecule and the surface is weak.In such a case rotational excitation resembles that of a rigid ellipsoid scattered from a soft wall. In the scattering of oriented NO from Ag(ll1) such a picture was capable of giving a reasonable explanation of the observed rotational excitation spectra, although certainly many details remain to be clarified. lo In the case of a strong attractive well one expects this picture to change. Molecules that are highly rotationally excited will certainly get trapped in the well. This rotation- ally mediated trapping is suggested in the extensive experimental and theoretical study 297 Rotational Rainbows on NO scattering from Pt( 11 1) by Jacobs and Zare and Jacobs et al.''*' These authors show that chemisorption is indeed very probable and that the scattered molecules have a rotational-state distribution that at the high J end could be approximated by a Bolt- zmann distribution corresponding to the surface temperature.A surprising result of the study of Jacobs and Zare is that the rotational-state distribution does not show any change when the rotational energy becomes equal to and exceeds the initial beam energy (0.2 eV) of the normally incident NO molecules. Clearly energy transfer from the lattice to molecular rotation is a relatively probable event. Jacobs et al. see good agreement between a detailed classical trajectory calculation and the experimental rotational-state distribution. Haug et al.13 have performed quantum-mechanical calculations on the NO/Pt(l11) system.These authors get good agreement with the experimental data of Jacobs and Zare using a simple model potential. The potential shows that rotational rainbows do occur, but are averaged by the surface motion and diluted by trapping in the chemisorption well. Harris and Luntz14 have performed classical trajectory calculations for CO scat- tering from Pt( 11 l), a system which exhibits a similarly strong molecular chemisorption well. These authors observe that most trajectories are very complex and involve strong re-orientation in the attractive well of the potential, chattering or multiple collisions of the rotationally excited molecule and the repulsive wall" and multiple collisions of the entire molecule, traversing the attractive well several times.The latter trajectories have also been found by Jacobs et aE.,12 who use the term 'indirect inelastic scattering' for this case. The origin of these collisions is that the times to accommodate the normal motion and the parallel motion, and the desorption time are very different, depending on the interaction.I6 In view of the complexity of most trajectories one would expect that a rotational rainbow would not be observed in a strongly interacting system such as NO/Pt( 11 1). These rainbows are most likely to survive when the collisions are rather 'sudden' encounters on the anisotropic repulsive wall of the potential-energy surface;' 7*18 the increased influences of corrugation and multiple collisions in a highly attractive potential will tend to average out the rainbow effect^.'^.^' For moderate anisotropies the impulsive limit will be reached at higher translational energies, when the influence of the attractive well, leading to trapping and chemisorption, can be ignored. To get more information on the NO/Pt( 11 1) interaction studies are needed in which the beam energy is increased to be of the order of the well depth. In this case trapping becomes less important and rotational rainbows, if any, might be observed.Therefore we have performed measurement of rotational excitation of NO molecules in collisions with a Pt( 11 1) surface at collision energies between 0.2 and 1.4eV.We will show elsewhere that the angular distributions for NO scattering form Pt( 11 1) are remarkably broad.20 This leads to a loss of scattered intensity with respect to scattering of NO from Ag( 11 1). In addition, the trapping probability of NO on Pt(ll1) at low beam energies is very high, of the order of 90°/~.21-26Therefore, we have decided to first perform experiments on rotational excitation of an unoriented NO beam from Pt(ll1). An additional advantage of unoriented beams is that their energy can be increased easily to 2 eV. At higher energies one expects direct scattering to dominate over trapping, which will simplify the interpretation of the results. Experiments with a molecular beam of oriented NO molecules27 will be carried out at a later stage.We will show that rotational rainbows do indeed occur for NO/Pt( 11 l), and at sur- prisingly low collision energies. We have examined whether the experimental results can be explained with classical trajectory calculations using the interaction potential of Haug et al. Some special features of this potential will be pointed out. Also, calculations using a very simple trial potential with an entirely different topology will be presented in order to reveal some of the features that a more realistic NO/Pt(lll) potential must possess. A. E. Wiskerke et al. Experimental The experimental arrangement has been described before and we will repeat only some important features here. A seeded NO beam can be prepared in a differentially pumped beam line.The orifice of our quartz nozzle has a diameter of 0.1 mm and can be heated to 1000 K. This results in beam energies between 0.3 eV (when seeding 7% NO in He at 300 K) and 1.4 eV (5% NO in H, at 1000 K). The beam is collimated and chopped mechanically using a rotating chopper and impinges on the Pt(l11) in a UHV chamber at a distance of 35 cm from the orifice. A resonance-enhanced multiphoton ionization (REMPI) detector can be rotated about the crystal." Using a mixture of tunable light of around 225 nm and fixed frequency radiation of 308 nm, NO molecules are state selec- tively ionized in a two-step process. Possible effects of alignment or polarization should be small in the present experimental arrangement, since the resonant laser is linearly polarized near the 'magic angle' (45" vs.54.7") with respect to the surface normal, and since the Earth's magnetic field considerably reduces the detectable alignment. We see no evidence (e.g. different rotational branch intensities) for polarization effects in the present study. The REMPI signals are corrected for Honl-London factors and for partial saturation effects, where necessary, using the expressions of Jacobs, Madix, and Zare,28 and are proportional to the number density of NO molecules in the various levels. The Pt(ll1) crystal has been prepared in the usual way. A detailed description of the experimental arrangement will be published elsewhere.29 Results and Discussion A measured rotational excitation spectrum is shown in Fig.1. The initial energy Eiis 0.3 eV, and the initial and final angles are Oi = 45" and 0,= 70", both measured with respect to the surface normal. The spectrum features a very distinct peak at J = 25.5. Both the peak position and the half-height point of the fall-off at high J exhibit a very clear Ei dependence. Measurements of the energy transfer carried out using a mass spec- trometer show an energy loss of ca. 50%, a percentage which does not show a strong Ei 0.5 2 0.4 +-.-c 3 d b 0.3 v -(D G= 0.1 0 0-5 10.5 20.5 30.5 40.5 J Fig. 1 Rotational-state distribution for NO scattering from Pt(ll1) at Ei = 0.3 eV, Oi = 45"' 0,= 70". A rotational rainbow is clearly visible in the spectrum as a peak around J = 25.5.m, P21Qll; 0, Q22R12. Rotational Rainbows dependence.,' Therefore, we conclude that the peak shown in Fig. 1 is due to direct inelastic scattering. Comparing Fig. 1 with the rotational excitation spectrum for NO scattered from Ag(ll1) with the 0 end of the NO molecule preferentially oriented towards the surface shows a striking similarity." Thus it seems very natural to assign the peak observed in Fig. 1 to a rotational rainbow. Measurements of the steric effect of direct inelastic scattering of NO from Pt(ll1) have shown that, under the conditions of the experiments summarized in Fig. 1, 0-end scattering is dominant.21*22 This is attrib- uted to enhanced sticking of the molecules with the N end towards the surface.There- fore, following the assignment for NO-Ag( 11 1),l0 the rotational rainbow peak shown in Fig. 1 might be predominantly due to 0-end scattering. It is well known that NO is strongly bound to Pt(111).2'-26 Following the discussion of Harris and Luntz concerning the interaction of CO with Pt( 11 1) it is very surprising that a rotational rainbow is observed at all at these low energie~.'~ If all molecules feel the very strong chemisorption well, most will be trapped. Those molecules that are not trapped will undergo a complicated scattering pattern, which very likely includes multi- ple hops in the chemisorption well and chattering of the two ends of the molecule against the surface. These complicated collisions occur less frequently for NO scattering from Ag(lll), because the well is less deep and most of the anisotropy appears to be in the repulsive part of the potential.' 731 Under these conditions the rotational excitation is due to a short, impulsive collision at the repulsive wall, which is indicated by the fact that the sudden approximation (which ignores molecular rotation during the collisions) works very well for NO scattering from Ag(11l).17 To resolve the question why a rotational rainbow is observed at all for NO scat-tering from Pt( 11 1) we carried out very simple classical trajectory calculations in which we describe the system by the soft-cube model.Obviously, this is an oversimplification, but it might serve as a starting point for a better understanding of the collision dynamics. Classical trajectory calculations for NO scattering from Pt( 1 1 1) have been previously carried out by Jacobs et al.,' and semi-classical and quantum calculations by Haug et and Lemoine and C~rey.~' Jacobs et aE.have carried out a full three- dimensional classical trajectory study, taking surface motion and vibrational energy into account. The potential used is a complicated expression mainly involving pair poten- tials, which cannot easily be cast into a form suitable for the present calculations. Haug et al. have formulated a much simpler potential. Using this potential they were able to reproduce well the rotational excitation spectrum measured by Jacobs and Zare and the steric effect in adsorption measured by Kuipers et al.and Tenner et a1.21v22 We have used this potential as a starting point for our calculations. The potential-energy surface representing the potential as a function of molecular orientation and distance to the surface is plotted in Fig. 2(a). The functional form of the potential is : V(z,y) = D([R, + R,P,(cos y) + R, P,(cos y)]exp( -2az) -[A0 + AIPl(cos y) + A, P,(cos y)]exp( -az) where z represents the distance between the centre of mass of the molecule and y the molecular orientation with respect to the normal to the cube surface. The parameters R,are: D = 1.2 eV, a = 1.5 k', = 1.0, R, = 0.075, R, = 0.075, A, = 2.0, Al = 0.1125, A, = 0.15. For y = 0 the molecule is bound through the N end. The potential has a deep chemisorption well exhibited fairly small anisotropy. It favours the NO standing up, as observed, but has only a small preference for the N end down.The repulsive wall of the potential is weakly anisotropic. Using the potential by Haug et al. we have performed trajectory calculations. The computational methods have been described bef~re.~'-~ In these calculations we rep- resent the surface by a soft cube which is initially at rest. Unlike the more detailed A. E. Wiskerke et al. 301 0.7 0.35 5 0.0 .................. ............................. ..... . ._.-1. .-............ ................. ..... ........................ .................... ....... ............. .......................... 0.4 .-...........- 0.6......................................................... - .. ......................................... ..................... - 0-- - - 0.4 0.8 -1.2 I I I I I J I I I I I J I I I I I 0.0 60.0 120.0 180.0 yldegrees Fig. 2 Potential-energy surface as a function of the molecular orientation angle y and molecular surface distance z. y = 0" corresponds to the N end towards the surface and y = 180" to the 0 end towards the surface. Upper panel: potential-energy surface of the NO/Pt( 111) interaction as pro- posed by Haug et d.[ref. 131. Lower panel: Model potential-energy surface showing two well separated potential minima. Representative trajectories for the rotational rainbows are shown for both potentials. The dashed lines are for an initial translational energy of 0.6 eV, and the solid lines for 0.3 eV.Rotational Rainbows calculations of Haug et al., we have not coupled the cube to an oscillator to simulate excitation of the lattice. This can be an oversimplification, as shown for instance by Polanyi and The effect of this simplification on the conclusions of this paper is minimal, since it will change the trapping behaviour, but not the rotational excitation. The cube mass was taken to be 600 amu (about three times the mass of a Pt atom), but appeared not to be critical. The computed dependence of AJ on initial orientation angle yi is plotted in Fig. 3(a) for two energies, 0.3 and 0.6 eV. As expected AJ = 0 for yi = 0" and 180". Around yi = 90" again no rotational excitation is seen.In between these angles, maxima in the excitation function are seen around AJ = 15, which classically lead to rotational rainbows. In the calculations no evidence of multiple hops nor chat- tering is seen. The results for 0.3 eV resemble the results published by Haug et al.13 but are not the same, even for the same initial energy. In Fig. 2(a) we also plot the trajectory leading to the rotational rainbow for yi = 45". It is seen that the rotational excitation is induced by the angular anisotropy of the attractive part of the potential. In the collision with the repulsive wall reflection occurs, but with little additional rotational excitation. The rotational excitation is almost entirely due to the attractive part of the potential.As mentioned above our computed rotational excitation functions differ from the ones computed by Haug et al. This we attribute to the fact that Haug et al. have used the sudden approximation. In the sudden approximation the molecule does not re-orient and samples a stronger anisotropy than for a 'real' trajectory. In the latter trajectory the molecular reorientation leads to a decrease of the effective anisotropy. Calculations that we performed using a very large moment of inertia of the molecule, to reduce the re-orientation during the collision, yield rotational excitation functions that match the original calculations by Haug et al. almost exactly. We therefore conclude that the difference between our calculations and those by Haug et al.are entirely due to the fact that we do not use the sudden approximation. The sudden approximation over-estimates the rotational excitation by up to 50%. This approximation also explicitly excludes chattering and multiple hops. The fact that these effects are also not seen in our calculations indicates that scattering on this potential is principally direct. Because the rotational excitation is almost entirely due to the attractive part of the potential the excitation depends on the time spent in the region of the anisotropy. This leads to a decrease of rotational excitation with increasing Ei. This is shown in Fig. 3(a) by the curve computed for Ei = 0.6 eV. This is at variance with the experimentally observed increase of the J value of the rotational rainbow with increasing incoming energy.It is extremely interesting that the scattering from the Haug et al. surface shows evidence of rotational rainbows even with attraction-dominated rotational excitation.13 However, from the experimentally observed shift of the rainbow with increasing Ei,29 we conclude that another type of potential has to be responsible for the rotational rainbow in this case. We have tried to construct a potential that on the one hand leads to the presence of an 0-end rainbow and mimics 0-end scattering for NO from Ag(ll1). On the other hand, the potential should have a very deep well, leading to chemisorption and NO molecules binding through the N end to Pt. In addition, we require rotational excitation to increase with Ei, which implies that the excitation should be due predominantly to anisotropy in the repulsive wall of the system.We thus need to construct a potential with a shallow well for the 0 end, a deep well for the N end and a strong anisotropy of the repulsive wall. Such a potential is shown in Fig. 2(b).The functional form is the same as the one introduced by Haug et al. The parameters are: D = 0.56 eV, a = 3.0 k',Po.= 2.0, R, = 0.0, R, = -0.8, A, = 2.4, A, = 0.5, A, = 0.0. The required character- istics are clearly visible in Fig. 2(b).We have computed the rotational excitation function using this potential and it is reproduced in Fig. 3(b) for Ei = 0.3 and 0.6 eV. For yi between 120" and 180" a simple excitation curve is visible.It leads to a rotational A. E. Wiskerke et al. I I I I20 16 12 d 8 4 0 -1 -0.6 -0.2 0.2 0.6 1 50 40 30 d 20 10 0 -1 -0.6 -0.2 0.2 0.6 1 cos yi Fig. 3 Rotational excitation as a function of the cosine of the initial orientation angle. Cos(yi)= 1 corresponds to the N end towards the surface and cos(yi) = -1 to the 0 end towards the surface. In the upper panel results are shown of classical trajectory calculations using the potential by Haug et al. [ref. 13). In the lower panel results obtained with our present model potential are shown. Results for two energies are shown: Ei = 0.3 eV (----) and 0.6 eV (---). rainbow. The rotational excitation increases with Ei, as observed experimentally.For smaller values of yi (120" yi 0') a very complicated rotational excitation spectrum is seen. This is indicative of multiple hops in the deep attractive well of the potential and of chattering collisions. Similar rotational excitation curves have been obtained by Brunner for NO scattering from Ag using a very deep well.35 In our calculation trapping is impossible because no dissipation of the energy imparted to the cube is taken into Rotational Rainbows account. One can safely assume that most of the complicated trajectories shown for the N end in Fig. 3(b)will lead to trapping, as has been seen by Harris and Luntz.14 From the results presented in this paper we conclude that it is likely that the two ends of a molecule exhibit very different interactions with the surface.The chemisorption observed for NO impinging on Pt(ll1) is due to the deep well that the molecule exhibits at its N end. The anisotropy of the attractive well does not re-orient all incoming mol- ecules so that their N end is towards the surface, which would be followed by trapping in the deep well. We propose that the rotational rainbow observed is due to 0-end scattering, for which the well is shallow and impulsive scattering is seen. This is sup- ported by our earlier observation that most of the signal measured under the conditions of Fig. 1 is due to molecules oriented with their 0 end towards the surface (steric effects of 0.5).21922The potential shown in Fig. 2(b) has not yet been tested in calculations in which trapping is taken into account, for instance by dissipating the energy imparted to the cube.It is very likely that when performing such calculations it will be found that the details of the potential need to be adjusted. However, the major features of this potential, that the NO molecule has two ends interacting entirely differently with the Pt surface and that there is a strong anisotropy in the repulsive wall at the energies of these experiments, appear unavoidable. It should be remarked that the potential used by Lemoine and C~rey,~' which was based on the NO-Ag( 111) potential of Mulhausen et also shows a deep directional well on the N end, although the anisotropy of the wall is less pronounced than in our test potential.More detailed calculations are cur- rently underway. This project is part of the research program of the Stichting voor Fundamenteel Onder- zoek der Materie (FOM), with financial support from the Nederlands Organisatie voor Wetenschappelijk Onderzoek (NWO). Support for B.E.H. from the European Science Foundation is gratefully acknowledged. References 1 J. A. Barker and D. J. Auerbach, Surf.Sci. Rep., 1984,4, 1. 2 J. Hager and H. Walther, Annu. Rev. Muter. Sci., 1989, 19, 265. 3 A. W. Kleyn, A. C. Luntz and D. J. Auerbach, Phys. Rev. Lett., 1981,47,1169; Sure Sci., 1982,117,33. 4 A. W. Kleyn and T. C. M. Horn, Phys. Rep., 1991,199,191. 5 A. C. Kummel, G. 0.Sitz, R. N. Zare and J. C. Tully, J. Chem. 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