J. Phys. Chem. 1991,95, 8409-8421
8409
have been measured by time-delayed laser reionization time-offlight measurements, and confirm that a substantial fraction of the incident translational energy is lost in most collisions. This work will be reported separately.28
apparent contradiction to our results. However, three points should be considered: (i) the doubly charged ion is probably a little less stable to begin with (Coulomb repulsion of 1-2 eV across the molecular framework); (ii) neutralization itself imparts an energy up to the second ionization potential (9.7eV)IZinto the molecule; and (iii) the Cwz+is formed by high-energy electron-impact ionization of vapor sublimed from a hot source (up to 800 OC), likely imparting a large amount of electronic energy into some fraction of the nascent ions. Therefore, we feel that there is no necessary contradiction with our results obtained using jet-cooled singly charged molecules. [Extensive fragmentation of Cwz+has also been observed in Xe CID experiments under multiplesollision conditions.] Second, our subsequent work includes the following: (i) we have succeeded in laser reionization experiments to detect the scattered neutrals and found under lowest fluence conditions that only Cw(0)is returned (no definitive evidence for neutral fragments); (ii) photofragmentation of scattered ions (under single-photon conditions) show definitively that a large amount of energy is deposited into impact-heated Ca+ by the higher energy collisions: and (iii) velocity distributions of the scattered neutrals
Acknowledgment. This research was funded by the Office of Naval Research. We acknowledge crucial discussions of surface scattering with (the late) R. B. Bernstein. The surface materials used in this work were provided by R. S.Williams. Assistance in preparation of the molecular carbon samples was obtained from S. Anz, R. Ettl, and F. Ettl. For providing information prior to publication, special thanks goes to Mark Ross, Steven McElvany, and John Callahan, and to B. Dunlap and R. Mowrey of the Naval Research Laboratory for providing results on impact simulations, including permission to quote their results and to reprint Figure 11. Registry NO. Cw, 99685-96-8; C ~ O115383-22-7; , Cu, 134841-08-8. (28)Beck, R. D.;Yeretzian, C.; St. John, P.; Whetten, R. L., to be published.
Frank H. Ceuzebroek, Arjan E. Wiskerke, Manfred G. Tenner, Aart W. Kleyn, FOM Institute for Atomic and Molecular Physics, Kruislaan 407, 1098 SJ Amsterdam, The Netherlands
Steven Stoke,* Laser Centre, Vrije Universiteit. P.O. Box 7161, 1007 MC Amsterdam, The Netherlands
and Akira Namiki Department of Electric and Electronic Engineering, Toyohashi University of Technology, Tempaku, Toyohashi 440, Japan (Received: April 29, 1991)
Final rotational state J distributions of oriented NO molecules scattered with a translational energy Ei of 0.1and 0.34eV from Ag( 1 1 1) are directly measured. When the 0 end is preferentially directed to the surface, the average rotational excitation is more than 50% higher than when the N end is preferentially directed to the surface, at Ei = 0.34 eV. For scattering closer to the surface than specular, a rotational rainbow is observed around J = 23.5. The corresponding average initial orientation angle y, of these molecules is determined to be (47 8 ) O . This value is in accordance with that found in theoretical studies by Voges and Schinke, who suppose that the rotational excitation is related to orientational anisotropy in the repulsive part of the potential. In the N-end distribution a single peak is found with its maximum around J = 8.5,which is also observed in the 0-end distribution. For angles closer to the normal than specular, the rotational rainbow disappears in the 0-end distribution. The N-end distribution, however, does not change. The shift between the angular density distributions for the 0 end and N end can be only partially explained by the difference in rotational excitation between the two ends of the molecule. Other mechanisms result in transfer of parallel momentum to other degrees of freedom, especially for N-end collisions. Some of these mechanisms, such as corrugation of the surface and multiple bounces, are discussed.
*
Introduction In scattering experiments the main objective is to obtain insight into the interaction between the scattered particle and the collision partner. In the case of a two- or three-body collision, knowledge of only a few initial and final variables is necessary to fix the entire kinematics of the collision, i.e., all final momenta can be determined as a function of the initial ones. From this the collision dynamics can be recovered. However, a molecule-surface interaction is a multiple-particle system and is usually underdetermined, Le., not all final momenta can be computed on the basis of the experimental results. From these experiments the full collision dynamics cannot be reconstructed, see, e.g., Horn et al.' If one assumes the Bom-oppenheimer approximation to be valid, the collision proceeds along a multidimensional potential energy hypersurface (PES). At present a full ab initio determination of (1) (a) Horn, T. C. M.; Kleyn, A. W.; Gislason, E. A. J . Chem. Phys. 1986,85, 7388; (b) Chcm. Phys. 1988, 127, 81.
such a PES is out of the question. It is the aim of scattering experiments to indicate which parts of the PES are particularly important to explain certain dynamical phenomena. Given a PES, a full quantum calculation of the scattering dynamics is also impossible at present and approximations must be made. The highest dimensionality in scattering calculations can be obtained in classical trajectory calculations. It is again the purpose of experiments to indicate which kind of dynamical calculation can be used. Ultimately, the experimental results should serve as a test of the dynamical calculation and the PES. This situation however, is still far from being realized, a t least in the case of gas-surface scattering. As an example, the detailed description of the interaction potential of even relatively simple systems such as Ar and Xe/Pt( 1 1 1) is under debatenZq3 The potentials used (2) Arumainayagam, C. R.; Madix, R. J.; McMaster, M. C.; Suzawa, V. M.; Tully,J. C. Surf. Sci. 1990, 226, 180. (3) Head-Gordon, M.; Tully, J. C.; Rettner, C. T.; Mullins, C. B.; Auerbach, D. J . J . Chem. Phys. 1991, 94, 1516.
0022-3654191 12095-8409%02.50/0 0 1991 American Chemical Society
8410 The Journal of Physical Chemistry, Vol. 95, No. 21, I99'1
in most scattering calculations are constructed empirically, using Morse or Lennard-Jones potentials. Many parameters such as the bond distance, the steepness, and the well depth can be varied. On the other hand, to describe some gross features of the measured angular and velocity distributions rather simple models of the surface, such as cubelike models or extensions involving corrugation,' are employed with some success. In this way some insight into heavy atom-surface interaction has been obtained. In the case of heavy molecule-surface scattering the state of the system becomes much more compli~ated.~The internal states of the molecule, i.e., the rotational, vibrational, and electronic degrees of freedom, come into play. Besides, for a molecule stereodynamical properties are important. The orientation and alignment of various vector properties such as the angular momentum J and the symmetry axis of the molecule are essential parameters to describe the interaction.6 In rotationally inelastic scattering of heteronuclear molecules under gas-phase conditions it has been possible to reveal the dependence on the orientation of the internuclear axis by using angular and velocity distribution, due to the limited dimensionality of the problem.' As an example, in the work by Schepper et a1.8 and Andres et ale9double differential cross sections could be obtained. In the case of K scattering from CO a double-peak structure was observedS8The spectra were interpreted in terms of rotational rainbows.1° This analogy with the atmospheric rainbow is used when a local maximum in rotational excitation as a function of the orientation angle y is found having a local maximum in intensity. Using isotope labeling, the assignment of the rainbow peaks to a certain orientation of the internuclear axis of the CO molecule was made. In gassurface scattering this type of assignment can not be made on the basis of angular and velocity distributions alone. The reason for this situation is the much more complex nature of the gassurface interaction as compared to gas-phase scattering. This complexity occurs despite the fact that a surface possesses a high degree of spatial symmetry. The interaction with the phonon bath, the possibility of multiple collisions eventually leading to trapping of the molecules, the corrugation of the surface (structural or thermal), and possibly friction all serve as sources of smearing and broadening of the angular and velocity distributions. Final-state resolved measurements are needed to obtain more insight. Rotationally state-resolved measurements of direct inelastic scattered molecules such as NO, N,, HCI, I,, CO, NH3, etc., from various surfaces (Ag, Pt, Au, Pd, Ir, LiF, Ge, GeO, graphite, diamond, etc.) have been obtained during the past decade." In some cases the measurement of the final rotational state J distributions was combined with the determination of the alignment and orientation of the J vector.I2 From this type of measurements a detailed understanding of the gassurface interaction has arisen, especially in the case of N2 scattered from Ag( 11 l).13 For the heteronuclear NO molecule ambiguity about rather elementary aspects of the interaction potential exists. To be able to obtain more insight into the dynamics of heavy molecule-surface in-
Geuzebroek et al. teraction it is necessary to perform even better defined state-tostate experiments. One possible approach is the use of oriented molecule beams, as pioneered by Kramer and Bernstein.'' In gas-phase inelastic and reactive scattering these beams have already been in use for more than 2 decades to determine the role of the orientation of the internuclear axis.I5 The main stream of experiments was devoted to the search for orientational dependencies or steric effects in the reactive cross section. Some work was done on interaction potentials of inelastic scattering events as we11.I6 In our case the fortunate situation exists that the molecule most heavily studied in gassurface rotational excitation experiments, namely, NO, can also be oriented by making use of the first-order Stark effect." So-oriented molecule beams have been introduced in gassurface scatteringI8and adsorption studiesI9 of NO, and indeed steric effects have been found. Furthermore a large amount of work has been performed on the interaction of polyatomic molecules and surfaces in the Bernstein group. This work involved the determination of orientational effects in sticking probability, angular distributions, and velocity distribution of a large amount of symmetric top molecules such as CH3X, t-BuC1, etc., scattered from graphite.20 The results were understood in terms of different theoretical models based on optical potentials, hard cube analysis, simple cluster calculations, and an image charge model.*' To introduce the system studied in this paper, NO/Ag(l 1 l), a brief review of its properties pertinent to the present study will be given. In adsorption experiments it has been shown that the interaction of this system is rather weak: the binding energy is only -0.2 eV with a desorption temperature of 100 K as shown by Behm and Brundle.22 The binding configuration is assumed to be bridge bonded, possibly bent. To measure the static orientation of the NO molecules adsorbed at the Ag(ll1) surface, Edamato et al. performed angularly resolved photoelectron spectroscopy (ARPES).23 It was found that the NO molecules are standing upright with the N-end down. However the T, used in their experiments, 150 K, makes interpretation of the results ambiguous. Since this T,is well above the desorption temperature, a large dose had to be used to adsorb a considerable amount of molecules (30000langmuirs; 1 langmuir = lo4 Torr s)). Which adsorption states are actually involved is uncertain. It is interesting to note that according to Behm and Brundle at 150 K the only stable NO species is stabilized by nearly adsorbed 0 atoms. So and Ho employed electron energy loss spectroscopy (EELS) and thermal desorption spectroscopy (TDS), doing measurements as a function of coverage." Their TDS measurements are similar to those of Behm and Brundle.22 In the EELS spectra several loss peaks are found that are not all fully assigned. Loss peaks at 143 and 159 meV are assigned to upright or tilted NO in bridge position. Not assigned is a feature located at 80 meV, although some remarks are made that this peak can be attributed to NO molecules lying flat at the surface. A similar conclusion was drawn for a peak at 110 meV in the NO/Ni(100) system.z On the basis ~~
(4) (a) Grimmelmann, E.K.; Tully, J . C.; Cardillo, M. J. J . Chem. Phys. 1980, 72, 1039. (b) Tully, J. C. J . Chem. Phys. 1990, 92, 681. ( 5 ) (a) Barker, J. A.; Auerbach, D. J. Surf. Sci. Rept. 1984, 4, 1. (b) Gerber, R. B. Chem. Rev. 1987,87, 29. (6) a r e , R.N . Angular Momentum; John Wiley and Sons: New York, Singapore, 1988. (7) Buck, U.In Atomic and Molecular Beams Methods; Scoles,G., Ed.; Oxford University Press: New York, Oxford, 1988; Chapter 21 and references therein. (8) (a) Schepper. W.; Ross,U.; Beck, D.2.Phys. A 1979,290, 131. (b) Beck, D.;Raps, U.; Scheppcr, W. Phys. Reu. A 1990, 19,2173. (9) Andres, J.; Buck, U.;Meyer, H.; Launay, J. M. 1.Chem. Phys. 1982, 76, 895. (IO) Schinke, R.; Bowman, J. M. In Molecular Collision Dynumics; Bowman, J. M., Ed.;Springer-Verlag: Berlin, 1983; Chapter 4. (1 1) (a) Lin, M. C.; Ertl. G. Annu. Reu. Phys. Chem. 1986,37, 587. (b) HBget, J.; Walther, H.Annu. Reo. Mater. Sci. 1989, 19, 265. (c) Kleyn, A. W.; Horn, T. C. M. Phys. Rep. 1991, 199, 191. (12) (a) Luntz. A. C.; Kleyn, A. W.; Aucrbach, D. J. Phys. Reu. B 1982, 25,4273. (b) Sitz, G.0.; Kummel, A. C.; Zare, R. N. 1.Chem. Phys. 1987, 87, 3247. (13) Sitz, G. 0.; Kummel, A. C.; a r e , R. N. J . Chem. Phys. 1988,89, 2559.
~~
~~
(14) Kramer, K. H.; Bernstein, R. B. J. Chem. Phys. 1965, 42, 767. (IS) Parker, D.H.;Bernstein, R. B. Annu. Reu. Phys. Chem. 1989,40,
561. (16) Stolte, S.In Atomic and Molecular Beams Methods; Scoles, G., Ed.; Oxford University Press: New York, Oxford, 1988; Chapter 25 and reference? therein __._._ __..
(17) (a) van der Ende, D.; Stolte, S.Chem. Phys. Lett. 1980,45, 55; (b) Chem. Phys. 1984,89, 121. (18) Kuiccrs. E. W.; Tenner, M. G.; Kleyn, A. W.; Stolte, S.Nature 1988, 334, 420. (19) Fecher, G.;Bcwering. N.; Vollmer, M.; Pawlitzky, B.; Heinzmann, U.Sur/. Sci. Lett. 1990, 230, L169. (20) (a) Curtis, T.J.; Bcrnstein, R. B. Chem. Phys. Lett. 1989,161,212. (b) Mackay, R. S.;Curtis, T. J.; Bernstein, R. B. Chem. Phys. Lett. 1989, 164, 341. (c) Ionov, S.I.; LaVilla, M. E.; Bernstein, R. B. J . Chem. Phys. 1990.93, 7416. (21) (a) Lcvine. R. D. Chem. Phys. Lett. 1990, 174, 1. (b) Ionov, S.I.; Bernstein, R. B. J . Chem. Phys. 1991.94, 1564. (c) Ionova, I. V.; lonov, S. I.; Bernstein, R. B. To be published. (22) Behm, R.J.; Brundle, C. R. J . VUC.Sci. Technol. A 1984,2, 1040. (23) Edamoto, K.;Maehama, S.;Miyazaki, E.; Miyahara, T.; Kato, H. Sur/. Sci. Lett. 1988, 204, L739. (24) So, S. K.; Franchy, R.; Ho, W. J . Chem. Phys. 1989, 91, 5701.
Rotational Excitation of Oriented Molecules
The Journal of Physical Chemistry, Vol. 95, NO.21, 1991 8411
of the loss peak at 43 meV attributed to adsorbed N atoms, So and Ho assume that dissociation does occur. The TDS peak at approximately 400 K is assumed to be due to associatively desorbed NO. A small amount of associatively desorbing O2is found in TDS as well. However no clear feature due to 0 atoms is observed in the EELS spectra. JBnsch et al. employed TDS and metastable quenching spectroscopy (MQS)on NO at Ag grown on Ru(lll).% They state that this system behaves similar to NO/Ag(111). Considerable N 2 0 formation is found and no NO dissociation is assumed to occur. From the discussion above it is clear that the static adsorption of NO on Ag( 1 11) is not completely resolved. For instance, the orientation of the equilibrium configuration is not known. The usual assumption is that NO is bonded via the N atom, similar to the case of CO where the C atom is the bonding atom. The latter molecule is assumed to be oriented with its axis perpendicular to the surface, where the general picture is that in the upright configuration the degeneracy of the 2u* orbital of the free molecule is maintained. However in the case of free NO the 2u* orbital is already partially filled, leading generally to a bent bonding ~rientation.~’Experimentally the orientation of NO on several surfaces has been determined using techniques such as near-edge X-ray absorption fine structure spectroscopy (NEXAFS), ultraviolet photoelectron spectroscopy (UPS), XPS, and EELS. Configurations in which NO is perpendicular, bent, tilted, and recently even parallel to the surface have all been results which depend on coverage. Theoretical work by Bauschlicher and Bagus emphasizes the fact that Ag has a closed d she1L2* They show that when a 4s-2p bond is formed in the case of an Ni-NO molecule, the configuration is bent. When d-type binding is taken into account, a linear configuration is expected. The d band is not expected to play a large role in the binding with an Ag surface, which suggests a bent configuration. The dynamics of the NO/Ag( 111) interaction was studied by several groups. Asada measured angular distributions at an incident translational energy Ei = 0.10-0.20 eV without resolution of the rotational states.29 The NO molecules are scattered in a lobe peaked more or less in the specular direction with a fwhm of about 30-40°, for in-plane scattering. Kuipers et al. extended the measurements to higher The angular distribution of the direct inelastically scattered molecules can be understood to some extent with simple models: at low Ei the distributions are broadened by excitation and deexcitation of surface phonons, while at higher energies phonon excitation and surface corrugation come into play. In further work by Asada and Matsui velocity distributions of the scattered molecules were obtained.” These results showed that the noble gases and homonuclear molecules exhibit a behavior that can be described quite well by the cube models.4 Particles scattered into the direction of the surface normal gain considerable translational energy. For the heteronuclear molecules NO and CO this gain is considerably less. The main assumption of cube models, namely, parallel momentum conservation, is fulfilled to a lesser extent by these heteronuclear molecules. Besides, the angular distributions of the heteronuclear molecules are slightly broader than for the more symmetric atoms and molecules. One possible explanation for the differences is an additional coupling between the translational and rotational degrees of freedom caused by the asymmetry of the heteronuclear molecules, leading to a larger spread in the scattering distribution and smearing of the angular dependence of the final energy.
Direct measurements of rotational excitation of initially rotationally cold NO molecules scattered from Ag(ll1) have been obtained by several authors, using laser techniques. Large rotational excitation was measured by Kleyn et al. for Ei = O.lCk1.7 eV.32 The main observation of this work is the bimodal behavior of the rotational state distributions at high Ei. A careful study showed a scaling with the translational energy corresponding to the component of the momentum perpendicular to the surface E, = Ei(cos2Oi), with Oi the incident angle (measured with respect to the surface normal). The bimodal structure occurs when E, is increased above about 0.2 eV. At low J a Boltzmann-like feature is observed, a deviation from which appears at high J in the form of a shoulder. The shoulder was assumed to be due to a rotational rainbow, similar to those observed in gas-phase scattering. The dependence on E, of the two parts of the bimodal distribution is quite different: the high-J shoulder increases quickly with E,, while the appearance of the low-J part is remarkably constant. From similar rotational distributions measured for Ei = 0.03-0.20 eV Kubiak et al. inferred a bilinear relation between the amount of rotational excitation with Ei and Ts.33 Their model is an extension of simple cube models with Ei increased by a term corresponding to the binding energy. The well depth of 0.28 eV resulting from a fit to the measurements is consistent with those measured from static results. Kimman et al. measured the final translational energy as a function of the final rotational state.34 An anticorrelation was found between the rotational excitation and phonon excitation, which is also seen in other systems.3s This effect can in part be understood on the basis of a very simple kinematic model. Angular distributions for individual J states have been obtained by Kleyn et a1.32and recently by Rettner et aLX In general higher rotational states are scattered with a high probability in the direction of the surface. At Ei = 0.10 eV the angular distribution of the different rotational states are almost identical, and also the final translational energy is constant. The uncoupling between rotational and translational degree of freedom seems to be almost perfect in that case, as is also seen for the NO/Ge system.” At higher Ei the coupling becomes stronger. Trapping has been studied in several scattering experiments. From those it is concluded that at E. = 0.1 eV about 3040% of the molecules trap at the surface.”l3* At higher Ei the trapping probability decreases rapidly to about 1% at 1 eV. Changing Bi does not change trapping probabilities, at least at high surface temperatures. A scaling with the total translational energy is assumed. Although the definition of trapping used in these studies based on angular distribution is under debate,’ a well depth of 0.2 eV is more or less consistent with the data. In addition Auerbach and Rettner performed residence time measurements at 100 K. From the measured desorption time of 2.4 ms at 100 K and with the assumption of a prefactor of lo”, a well depth of 0.2 eV is found as well.39 To explain the scattering experiments, a large amount of theoretical work has been done, especially to understand the rotational excitation. The complexity of the approaches taken differs enormously in the way the equations of motion are solved, the treatment of the N O degrees of freedom, the way the interaction with the surface is taken into account, etc. One of the major
(25) (a) Sandell, A.; Nilsson, A.; Martenson, N. Surf.Sci. Lcrr. 1991,241, LI and references therein. (b) Zhou, R.-H.; Cao, P.-L. Surf.Sci. Lcrr. 1991, 243, L49. (26) Jinsch, H. J.; Huang, C.; L u d v i b n , A,; Rocker, G.; Redding, J. D.; Metiu, H.; Martin, R. M. Surf. Sci. Lett. 1989, 214, 377. (27) Ibach, H.; Mills, D. L. Electron Energy Loss Spectroscopy and Surface Vibrations; Academic Press: New York, 1982; pp 184, 293-296. (28) Bauschlicher, C. W.; Bagus, P. S.J . Chem. Phys. 1984, 80, 944. (29) Asada, H. Jpn. J. Appl. Phys. 1981, 20, 527. (30) Kuipers, E. W.; Tenner, M.G.;Spruit, M. E. M.; Klep, A. W. Surf. Sci. 1987, 189, 669. (31) Asada, H.; Matsui, T. Jpn. J. Appl. Phys. 1982, 21, 259.
C. Phys. Reu. Lett. 1986.57, 2053.
(32) (a) Kleyn, A. W.; Luntz, A. C.; Auerbach, D. J. Phys. Reo. Lett. 1981. 47. 1169: Ib) Sur/. Sci. 1982. 117. 33. (33) Kubiak; G.‘D.; Hurst, Jr., J. E.; Rcnnagel, H. G.; McClelland, G. M.; &re, R. N. J. Chem. Phys. 1983, 79, 5163.
(34) Kimman, J.; Rettner, C. T.; Auerbach, D.J.; Barker, J. A.; Tully, J.
(35) MMI, A.; Gritsch, T.; Budde, F.; Chuang, T. J.; Ertl, G. Phys. Rev. Lett. 1986,57, 384. (36) Rettner, C. T.; Kimman, J.; Auerbach, D.J. J. Chem. Phys. 1991, 94, 734. (37) Budde, F.; MMI,A.; Hamza, A. V.; Ferm, P. M.; Ertl, G. Surf. Sci. 1987, 192, 507. (38) Kuipen, E. W.; Tenner, M. G.; Spruit, M. E. M.; Klep, A. W. Surf. Sci. 1988, 205, 241. (39) Auerbach, D.J.; Rettner, C. T. In Kinetics of Surface Reactions; Grunze, M., Kreuzer, H. J., Eds.; Springer-Verlag: Berlin, Heidelberg, 1987; p 125.
8412 The Journal of Physical Chemistry, Vol. 95, No. 21, 1991
distinctions is whether the problem is treated from a basically dynamical or statistical point of view. The latter treatment has been taken by several authors.40 In the dynamical studies the problem has been treated both classically and quantum mechanically. The latter approach predicts highly oscillating rotational state distributions,IO which have never been observed in experiment. In some studies the 211 nature of the N O molecule is taken into account, leading to a pair of PES!' The degeneracy of the *-orbital when directed parallel or perpendicular to the surface is lifted. Another important factor is how to treat the different degrees of freedom of the surface, such as the phonon system and the lateral position where the molecule collides. This can be done in several ways by cubelike interaction, by harmonic oscillators, by generalized Langevin treatment, etc. Several empirical PES have been constructed for use in scattering calculations. One of the essential points is where to locate the anisotropy with respect to the orientation of the molecule. The potential due to Voges and Schinke assumes that the N O molecule is anisotropic with respect to the two ends of the molecule, especially in the repulsive part of the interaction potential.42 The equilibrium configuration is with N O lying flat on the surface with a well depth of 0.09 eV, which is rather low for NO/Ag(lll). The potential is constructed by fitting it to the rotational state distributions measured by Kleyn et al. for 0.2 eV < Ei < 1 .O eV. Another approach was taken by Tully and @workers, who assume a large anisotropy in the attractive part of the intera~tion:~with the largest attractive well (0.75 eV) with N end down. A molecule with the 0 end in front is spun around while approaching the surface, which results in rotational excitation. In addition the molecules are rotationally excited on the way out. The large well depth used by Tully and co-workers is based on observations by Goddard et alauusing TDS and Kleyn et al. using an extrapolation of the apparent temperature of the Boltzmann-like part of the rotational state distributions to zero Ei.32However, later work showed that these determinations of the well depth are respectively i n c ~ m p l e t e ~and ~ - *i ~n c o r r e ~ t . ~ In ~ , a~ ~second version of the potential by Tully and co-workers, among some other changes made to the potential, the well depth is decreased by a factor of 3 to match the experimental value for NO/Ag(l 11).34347 In Brenig's group several Morse potentials have been tried with anisotropy both in the repulsive and in the attractive terms4 In the final version rotational excitation is due to both the attractive and repulsive regions of the PES. The well depth is chosen to match the experimental value. With all PES, consistency with a t least part of the experimental data can be obtained. The use of rather different assumptions to construct the interaction potential can lead to similar results. The problem is that although there is a wealth of experimental data, the number of parameters to vary in the system is rather large. The only independent theoretical work on the shape of the interaction potential has been performed very recently by DePristo and Alexander, who use corrected effective medium (CEM) theory to determine the NO/Ag( 11 1) interaction.& In the calculation N O is found lying almost flat at the surface. Some dependence on the lateral position has been found in their results. The PES for the two directions of the *-orbital are quite different. To obtain even more detailed experimental information to improve the description of the NO/Ag( 111) interaction, orien(40) (a) Zamir, E.; Levine, R. D. Chem. Phys. Len. 1984,104, 143. (b) Nyman, G.;Holmlid, L.; Pettersson, J. B. C. J . Chem. Phys. 1990,93,845. (41) (a) Alexander, M. H. J . Chem. Phys. 1984,80,3485. (b) Corey, G. C.; Liu. W.-K. Surf. Sci. 1984, 148, 675. (42) (a) Schinke, R. J . Chem. Phys. 1982, 76, 235. (b) Voges, H.; Schinke, R. Chem. Phys. Lerr. 1983, 100, 245. (c) Schinke, R.; Gerber, R. B. J . Chem. Phvs. 1985.82. 1567. -(43) Muhlhiusen, C. W.; Williams, L. R.; Tully, J. C. J . Chem. Phys. 1
1
1985. 83. 2594. (44) Goddard, P. J.; West, J.; Lambert, R. M. Surf. Sci. 1978, 71, 447. (45) Tanaka, S.;Sugano, S.Sur/. Sci. 1984, 136, 488. (46) (a) Brenig, W.; Kasai, H.; MUllcr, H. Surf. Sci. 1985, 161.608. (b) Kasai, H.; Brenig. W.; Muller, H. 2.Phys. B 1985, 60, 489. (47) Tully, J. C. In Kinerics ofburface Reactions; Grunze, M., Kreuzer, H. J., Eds.; Springer Verlag: Berlin, Heidelberg, 1987; p 37. (48) DePristo, A. E.; Alexander, M. H. J . Chem. Phys. 1991, 94, 8454.
Geuzebroek et al. tation-dependent measurements have been performed for gassurface scattering. The NO molecules are oriented by using the linear Stark effect. The orientational distributions are such that either the 0 end or the N end is preferentially directed to the surface just before the collision. Angular distributions of direct inelastically scattered N O from Ag( 111) were obtained as a function of ~ r i e n t a t i o n . ~The ~ scattering lobes of the two orientational distributions are shifted with respect to each other in such a way that the 0-end distribution leads to a lobe peaked closer to the surface than does the N-end distribution. To explain this result, the simplifying assumption of parallel momentum conservation from cube models was taken. It was inferred that in an 0-end collision more energy is transferred from the initial translational energy to other degrees of freedom than in N-end 'collisions. Consistency with the interaction potential by Voges and Schinke is found if it is assumed that this extra excitation for 0-end collisions can be attributed to additional rotational e x ~ i t a t i o n . ~ ~The ~ ~ measured ' higher trapping probability for 0-end collisions was explained on the basis of the difference in rotational e x c i t a t i ~ n .The ~ ~ additional energy loss in the rotational degree of freedom will increase the chance of a molecule losing its initial translational energy and thus increase its probability of getting trapped a t the surface. The subject of this paper is the direct measurement of the final rotational state of the scattered molecules as a function of orientation. In this way the interpretation of the former results can be tested, and new more direct information about the anisotropy of the interaction potential can be obtained. Some preliminary results were shown before.53 For low Ei (=O.lO eV) it was shown that for scattering in the direction of the surface the probability to excite high final J states is somewhat larger for 0-end than for N-end collisions. In this paper results will be presented mainly for Ei = 0.34 eV that show that the steric effect depends both on the final J state as well as on the final scattering angle Or (defined with respect to surface normal) of the scattered N O molecules.
Experimental Section The basic setup of the experiment consists of a oriented molecule beam line, a metal surface mounted in a ultrahigh-vacuum chamber, and two detectors that can be rotated around the surface independently. In the oriented beam line the initial state of the molecules is prepared in a three-step process. In a supersonic expansion the rotational and spin-orbit degrees of freedom are cooled in such a way that approximately 50% of the molecules are in the lowest rotational (J = 0.5) and spin-orbit state (Q = 0.5). Hexapole focusing is employed to select out one of the A-doublets available for J = Q = 0.5. To be able to orient the molecules, an electric field is applied just before the surface. In the selection process in the hexapole as well as in the orientation process itself we make use of the fact that a molecule like NO with a projection of the electronic angular momentum on the internuclear axis A # 0 possesses a first-order Stark effect when an electric field of significant strength is applied to it. After the scattering event total density measurements are performed using electron impact combined with a quadrupole mass spectrometer (QMS). Alternatively the scattered particles can be detected internal state specific by using resonance-enhanced multiphoton ionization (REMPI). With the exception of the REMPI detector the apparatus and experimental procedures have been described in detail b e f ~ r e . ~Only ~ , ~matters ~ concerning this detector and (49) Tenner, M. G.;Kuipers, E. W.; Kleyn, A. W.; Stolte, S. J . Chem. Phys. 1991, 94, 5191. (50) Tenner, M. G.;Kuipers, E. W.; Kleyn, A. W.; Stolte, S.Surf. Sci. 1991, 242, 376. ,c,
(51) Hand, M. R.; Chang, X. Y.; Holloway, S.Chem. Phys. 1990, 147,
JJl.
(52) Kuipers, E. W.; Tenner, M. G.; Kleyn, A. W.; Stolte, S. Sur/. Sci. 1989, 2111212, 819.
( 5 3 ) Tenner, M. G.;Geuzebroek, F. H.; Kuipen, E. W.; Wiskerke, A. E.; Kleyn, A. W.; Stolte, S.; Namiki, A. Chem. Phys. Lerr. 1990, 168.45. (54) Spruit, M. E. M.; Kuipers, E. W.; Tenner, M. G.;Kimman, J.; Kleyn, A. W. J . Vac. Sci. Technol. A 1987, 5, 496.
The Journal of Physical Chemistry, Vol. 95, No. 21, 1991 8413
Rotational Excitation of Oriented Molecules
beam shortly before it hits the surface. The laser is fired before a NO background gas pressure is built up in the detector. An additional advantage of chopping the beam is the suppression of the rising edge of the NO beam pulse, which is not stated selected very well (see Figure 5 of ref 55). The molecules scattered from the crystal (K)are ionized by using REMPI, accelerated, and deflected into a particle multipler M (by ETP, type AEM 1OOO). The signal is collected by measuring the current in the ion pulse by using a gated integrator (Stanford Research Systems SR250). Subsequent data processing is performed using a CAMAC crate and a p-PDP 11 computer. Rotational-state distributions are obtained by making a wavelength scan.56 The measured spectra are transferred into relative populations of the different rotational states J. The results are corrected for Honl-London factors. A spectrum of a background gas at 300 K was reduced to a population over the rotational states. The rotational temperature deduced by fitting the result with a Boltzmann distribution were accurate within 20 K. It was possible to obtain the rotational-state distribution for isotropic or unoriented beams. To obtain the dependence on orientation with a reasonable accuracy, a different method had to be used. One rotational transition was chosen at a time and the steric effect R,,(J,ef) for a certain Of defined as
m-Q
Rb Tb
Figure 1. Setup of REMPI detector: Q,quartz window; R and T, feedthroughs for rotation and translation of REMPI detector; Rb and Tb, transmissions for rotation and translation; P, pair of prisms for translating laser beam; E, ionization volume shielded for orientation field; K, crystal in mount; M, particle multiplier.
the evaluation of the data obtained with it will be discussed in detail here. In contrast to earlier experiments, the chopper in the molecular beam line has been moved to 67.5 cm from the surface (>2 m previously), in order to avoid NO gas buildup in the detector and to be able to perform time-of-flight experiments. Furthermore, the modified Bosch fuel injection valve employed earlierSShas been replaced by a pulsed solenoid valve (General Valve Series 9 with an aperture of 0.5 mm). Internal state resolved measurements of the scattered molecules have been performed by 1+1 REMPI via the A22 X211 transition using photons at 225 nm.% A Lambda Physik excimer (EMG 201 MSC) pumped dye laser (FL 3002) combined with second harmonic generation using a BBO crystal is employed to generate the necessary 225-nm light. The energy is about 2 mJ/pulse with a bandwidth of 0.2 cm-l. It is weakly focused using a lens with f = 1 m, producing ionization at about 80 cm after the lens at an laser intensity of =l MW/cm2. As is shown in Figure 1 the laser beam is sent into the scattering chamber and directed along the axis of rotation of both detectors in the UHV chamber. In vacuum the beam is translated parallel to this axis by two prisms P at a variable distance between 2 and 10 cm from the surface. By rotation of the prisms and the detector as a whole, the final scattering angle can be varied. The laser ions are created in a heavily shielded region E to minimize the influence of the orientation field, which is without shielding about 3 kV/cm at the position where the ions are generated. Two sets of grids are needed to shield the field. The detector has to satisfy two essentially conflicting requirements. First, the Orientation field and the laser beam with its stray light have to be efficiently shielded. Second, the structure should be very open to avoid buildup of residual gas in the detector, produced by scattered molecules. These conflicting requirements could be met (without invoking differential pumping of the detector) by using a rather closed structure for the detector box combined with chopping the NO
-
~
(55) Tenner, M.G.;Kuipers, E. W.;Langhout, W.Y.;Kleyn, A. W.; Nicolasen. G.: Stolte. S.Surf.Sci. 1990, 236, 151. (56) Jacobs, D.C.; Madix. R. J.; &re, R. N. J. Chem. Phys. 1986,85, 5469.
was determined for the corresponding J state. Here L(J,Of)and Z+(J,e,) are defmed as the densities measured for the two situations corresponding to negative and positive polarity of the orientation pole and thus to orientational distributions with the 0 end or the N end preferentially directed to the surface. After every 100 shots the direction of the orientation field was switched to eliminate the influence of long time drift, especially of the laser intensity. Depending on the intensity of the rotational line between 600 and 2000 shots were needed for a single measurement. The steric effect was measured only for a selection of rotational states. The rotational state distribution for the isotropic beam was combined with the steric effects for the different J states to determine the rotational state distributions for 0-end and N-end collisions. It has been shown that the probability distribution for a beam D= M,D = 1/4) state selected in the X211 (u = 0,J = and subsequently oriented in an homogeneous electric field in front of the surface iss5 1
W-(COSys) = -(1 + K 2 1 W+(COSys) = 5'1 - K
COS
ys)
COS
yI)
(2)
Here W-and W+corresponds respectively to probability distributions for negative and positive pole voltages and y, is defined as the angle between the internuclear axis, pointing from 0 to N, and the surface normal. For clarity, negative (positive) polarity corresponds to the 0 end (N end) preferentially directed to the surface. The factor K = (1 + a l / E ) - 1 / 2takes into account the deviation that occurs when the high-field limit of the orientation process has not been reached yet. For the X211 (u = 0,J = 52 = MJD = state t l = 6.64 kV/cm. In a practical situation with E = 15 kV/cm the correction factor K is determined to be 0.914. Equation 2 is valid only when the beam consist purely of the wanted state. In practice this condition is not entirely met. It is not possible to work under ideal focusing conditions of the hexapole if Eiexceeds 0.2 eV and the state selector does not produce a pure beam. Most experiments described in this paper were performed at Ei= 0.34 eV. The population of the selected beam in that case was determined by using the REMPI detector. An integration over the entire angular width of the beam was made, because the composition of the selected beam is not constant over the beam profile due to the focusing properties of the hexapole. It appeared that the state selected beam consists out of 25 (*5)% of molecules in a rotational state higher than J = 0.5. These molecules do not orient and give rise to an isotropic
Geuzebroek et al.
8414 The Journal of Physical Chemistry, Vol. 95, No. 21, 199
background. The orientation distribution of these molecules is yJ = 0.5 (1 - PJds), with PJe5 the probability simply WJ,,~(COS of finding a molecule initially in J = 0.5. If one assumes that rotational excitation does not depend on the initial J state of the molecule, a simple calculation shows that
Since the sum of the two orientation distribution W-(y,) and W+(y,) is isotropic with respect to ys the correction factor is independent of ys. In our case the correction CJ,o.s= (PJ-o.s)-' on the measured steric effects is 1.34 f 0.08. Of the molecules selected in J = 0.5 about (7 f 1)% are determined to be in the state (lower component of the A doublet). undesired MjQ = The latter state can be probed by the Qzl + RI1branch of the spectrum and can be easily separated from the wanted MjQ = +I/., state (upper component of the A doublet), probed by the Q l l Pzland R21branches. The molecules in the lower A doublet orient in the opposite way. The correction factor in this case, C, is derived in a similar way as eq 3 to be (2pA.u~- l)-', with PA," the part of the molecules in J = 0.5 in the upper component of the A doublet. In our case CA= 1.15 f 0.03. As stated before the electric field of 15 kV/cm is not high enough to reach the high-field limit of eq 2. An additional correction of Co = 1/K = 1 . 1 f 0.03 has to be made. The steric effect for an ideal situation is given by Rideal(J,flf)= CJ+o.sCAC&mear(J,Of) = (1.7 f 0.1 8)R,(J,0f), which refers to the orientational distributions given by eq 2 with K = 1 . In the following we will denote the ideal orientational distribution W- and W+ with K = 1 as rewith as corresponding corrected densities spectively WONand WNo, IONand INo.
+
.-m E 8
1.0
0.3
9 2 0.2 wr, v
0.1
0
0
20
40
60
80
0,("1 F i i 2. (a) Total density distribution of an isotropic (nonoriented) NO beam scattered from Ag( 11 1) at T, = 570 K, as a function of Of and normalized at peak value. Incident conditions are Ei = 0.34 eV, 0, = 45' (indicated by arrow). Solid line is drawn to guide the eye. (b) Average final translational energy ( E l ) as a function of Of at similar incident condition (indicated by arrows) as in Figure 2a. Line shows result in case of parallel momentum conservation. At low Of a large amount of parallel momentum is transferred.
Rettner et al.% There is a small but significant discrepancy with the ( E f )distributions of Kuipers et alaMand Tenner et al.'9 These errors might be due to the use of a cooler NO beam or systematic Results errors in the time-of-flight analysis. For the results in this paper In this section results of measurements are reported for NO the differences have no influence on the interpretation of the scattering from Ag( 1 1 1) at a fixed surface temperature T, = 570 measurements. The results obtained at the maximum of the K. Most experiments have been performed at Ei = 0.34 eV, for angular distribution can be described relatively well assuming a which translational energy stable operation of the hexapole lens flat surface or cubelike models, since parallel momentum is for long periods of time turned out to be possible. (In earlier conserved quite well.36 However, in the flank of the distribution experiments a slightly higher Ei (0.44eV) could be a ~ h i e v e d ~ ~ ) . in the direction of the surface normal, one observes an appreciable At Ei = 0.34eV and Oi = 45" (E, = 0.17 eV) the bimodal structure amount of parallel momentum transfer. At Of = 35", for instance, and the rotational rainbow become clearly observable. At Oi = the final energy corresponding to the momentum parallel to the 45" scans can be made over a wide range of final angles, in the surface E,, = El sin2 (Of) is about 0.07 eV compared to an initial direction of the normal as well as toward the surface, measuring E,,j = Ei sin2 (ei) = 0.17 eV. In the next subsections results will the total density as well as the final internal state distribution. be given for Of = 52", 35" and 70°, respectively representative To observe the initial translational energy dependence experiments of scattering in the direction of maximum density, closer to the were also performed at a lower and at a higher E,. normal than specular, and closer to the surface than specular. Angular and Translational Energy Distributions. The angular Rotational-State Distributions. Rotational-state density disdensity distributions measured at Ei = 0.34 eV and Oi = 45" are tributions Zo(J,Of)for Ei = 0.34 eV and Oi = 45" are shown in displayed in Figure 2a. The average final translational energy Figure 3. No correction for J or orientational dependencies of (Ef)of the scattered particles is determined in the way described the final velocities has been applied, so Io(J,Of)is a density disbefores7 and shown as a function of Of in Figure 2b. These tribution. Under the present experimental conditions the corremeasurements have been performed using unoriented beams from sponding flux distributions will be very similar.'JT The J states our state-selected beam line: the hexapole was on and the orihave been probed by the Q21+ RI1and the Qll + Pzl lines (Le., entation field off. The scattering distribution shows the usual Q = 0.5). The final rotational-state distributions for final D lobular peak characteristic of direct inelastic scattering with the 1.5 show behavior similar to that observed bef~re.'~.)~ No orimaximum of the distributions shifted about 7" toward the surface. entation field is applied, so the results are obtained by using an The angular density distribution is similar to earlier work36from isotropic orientational distribution. The data has been fitted to which the trapping probability at Ei = 0.34 eV and Ts= 500 K Boltzmann distributions for J < 17.5, and the results are norwas determined to be about 108, independent of Oi. Consequently malized to the maximum of the Boltzmann distribution observed the amount of trapped particles emerging at the specular will be at each 0,. The spectra at Or = 52" and 70" show a bimodal low (14% at the angle of maximum intensity, assuming a cosine structure, i.e., at low-J a BoltPnann-like distribution appears, whde distribution for the desorbed flux). Since the absolute value of at high J a rotational rainbow appears in the form of a shoulder. the steric effect measured in the trapping desorption channel is The shoulder disappears at lower O1. For comparison, results also low (54%), the influence of this channel on direct inelastic obtained by Kleyn et al. for a similar condition (E,, = 0.19 eV, scattering can be neglected (see also ref 49). The mean final but Ei = 0.32,Oi = Of = 40") are given in the Of = 52" translational energy ( E l ) increases gradually with decreasing O1. The agreement is good. The results of Figure 2 are in good agreement with the data from Several theoretical studies show quantum oscillations in the rotational-state d i s t r i b u t i ~ n s . ~The ~ ~ 'absence ~ ~ ~ of those in the experimental distributions has been attributed to averaging due (57) Geuzebroek, F. H.; Wiskerke, A. E.; Kleyn, A. W.; Stolte, S.Nucl. to the high rotational temperature of the incident beam used by, Instrum. Meth. B 1991, 58, 354.
The Journal of Physical Chemistry, Vol. 95, No. 21, 1991 8415
Rotational Excitation of Oriented Molecules
1.O
0.5
0.0 0.5
2.
1.0
5.5 10.5 15.5 20.5 25.5 30.5 35.5
Final rotational state J
'8 8
U
8
4
0.5
€
s
1
Q 0.0 1.O
0
0.5
20
40
60
EO
8,(") Figure 4. (a) Rotationally resolved steric effects R u ( J , B f )given for El = 0.34 eV and Bi = 4 5 O and three values of 0,: open diamonds, 70'; open
0.0 0.5
5.5 10.5 15.5 20.5 25.5 30.5 35.5
Final rotational state J Figure 3. Final rotational state distributionsIo(J,Bf)for an isotropic NO
beam scattered from Ag( 1 1 1) for different B1. Initial conditions similar as in Figure 2. The results are extracted from the REMPI spectra and corrected by using H6nl-London factors. Two rotational branches are used both probing the D = 0.5 state of the scattered N O open squares, Q21+ RII line; open diamonds, Q l l + P2,line. The solid lines are fits to a Boltzmann distribution for J 5 17.5 with a temperature TrI. (a) 81 = 35O, Tfil= 410 K; (b) Of = 52O, Tfit= 360 K, also shown are results by Kleyn et al.32 for E, = 0.19 eV (asterisks); (c) 81 = 7O0, Tfi,= 320 K. for instance, Meyn et Since 75% of our present beam consists out of one J state, it is rotationally extremely cold. Nevertheless no quantum oscillations are observed in Figure 3, which is in agreement with the study by Rettner et Steric Effect MeasuremenQ. Rotationally resolved steric effects are given for Ei = 0.34 eV and Oi = 45' and two values of Of in Figure 4a. The ideal steric effects Ridml(J,ef) are given, so the data are corrected in the way described before. The J values are carefully chosen such that the rotational transitions used do not coincide with other transitions. The results are obtained using the QZ1 R II branch, except for the lowest J point, which is taken a t the Q I I+ PZIband head. This lowest point is actually built up of contributions from J = 1.5, 2.5, and 3.5. At low J, corresponding to the part of the rotational distribution showing Boltzmann-like behavior, the steric effect is rather low and negative with a minimum around J = 8.5 (minimum Ridtrl(J,Of) -0.3). So generally the low-J states are produced more efficiently by N-end collisions. When J is increased, the steric effect changes sign and obtains a high positive value ((maximum Ridul(J,df) +1.35). High rotational excitation is more probable for 0-end collisions. Two trends as a function of Of can be observed in the data. First, at low rotational states f?id-l(J,@f)flattens out and becomes slightly more negative if Of is decreased. Second, the J state where the steric effect passes zero shifts to higher J states with decreasing Or. At Of = 70° the steric effect passes zero at about J 11.5 while at Of = 3 5 O the x axis is crossed only at J = 18.5. To state this differently: for a fixed J the steric effect is not constant as a function of Of, as is explicitly shown in Figure 4b. The variation of RiM(J,Of) with 0, is very different for different J states. While, for instance, a t J = 8.5Ridml(J,0f)is nearly
+
-
-
-
squares, 5 2 O ; open circles, 35O. Results are obtained by using transitions of the Q2, + R,,branch, except the lowest point, which is obtained at the Qll + P,, band head which is built up from signal of the J = 1.5,2.5, and 3.5. (b) Steric effect RM(J,Bf)as a function of Of for different final J states: closed diamonds, J = 8.5; open squares, J = 18.5; open circles, J = 27.5. Solid line is a linear fit to the steric effects RwQm(B,) obtained for the total density using the QMS. All the steric effects are corrected for nonideal selection and orientation. Error bars are given for J = 27.5, in other case errors are indicated by symbol size. The angular dependence of Ridnl(J,Bf)is strongly dependent on the specific final J state.
independent of the final angle, for J = 18.5Rw(J,0J runs from about 0 at low to 1 at high 8 Previous results on the same system were shown by Tenner et ;!al In that case the translational energy was much lower (Ei = 0.1 eV), with Oi = 45' and Of = 60°. Despite the fact that a rotational rainbow was not observed a t this Ei, a nonzero steric effect was observed. The J dependence of those results is similar to that of the present study, shown in Figure 4. We will come back to this point later. OrienCatiorrDepenaentRotatioaal Excitation. At the transitions where both Zo(J,Of)and Ridal(J,Of) are measured, the orientation-dependent intensities INO(J,Of) and zoN(J,df) can be determined. If Zo(J,Of)has been measured for a given scattered J state but not Rid&,ef), an interpolation for Ridd(J,Of)is taken. The resulting distributions are shown in Figure 5. The data are again fitted to Boltzmann distributions for J < 17.5. The intensities for each Of are normalized to the same value as the corresponding result in Figure 3, for the same OF A remarkable dependence on both orientation and Of is seen. At Of = 70' the most striking difference between the distributions for both orientations is observed. The high-J shoulder is present exclusively in the WON distribution. Although the population of the low-J peak is higher in the case of the WNodistribution, there is still a low-J Boltzmann-like peak present in the other distribution. When the final angle is decreased, the difference in shape of the two orientational distributions becomes smaller. For scattering closer to the normal than specular the high-J peak in the WONdistribution has almost disappeared. On the other hand, the WN0 result hardly changes shape as a function of Or. The average amount of rotational excitation (Erot)is quite different for the two orientational distributions. While (E,) varies between 45 and 55 meV for WON when Of is changed from 35' to 70°, for WNoa constant value of about 30 meV is found. The rotational excitation averaged
8416 The Journal of Physical Chemistry, Vol. 95, No. 21, 1991
Geuzebroek et al.
~.
Figure 5. (a) Final rotational state distributions for the two orientation distributions WNo(upper panel) and WON(lower panel) for Of = 35". Incident condition as in Figure 2. The data are normalized to the same value as the corresponding result in Figure 3 for the same O1. Symbol definition similar to Figure 3, except that closed squares refer to J states for which the steric effect is directly measured (see Figure 4). The results are constructed from the results in Figures 3 and 4 as described in the text. Again Bolzmann fits with temperature Tfitare made for J I17.5. WNo:Tfit= 370 K; WoN: Tfi, 470 K. (b) As in Figure 5a, but Of = 52"; WN0; Trt = 316 K; WON:Tfit= 420 K. (c) As in Figure 5a, but Of = 70'; WN0: Tfit= 258 K; WON:Tfit 320 K. I n the WONresult the high rotational rainbow is very clearly observable around J = 23.5.
-
1::
0.2 -
0.2
0.4
l 0.0 I
d'
-0.2 -0.4
-0.6
-
0
0 20
/
L
I
40
60
-0.60.5
80
Of 0 Figure 6. Steric effects R,,(t+) (solid squares) averaged over the measured rotational state distributions as defined in eq 4. Incident conditions similar to those in Figure 2. As a comparison Riu,QMS(Of)obtained for total density using the QMS are shown (open squares). The solid line is a linear fit to Rwl,QMs(Of).Good agreement is found between R,, and showing the consistency of data set. the Ridal,QMS(~f). over all angles is more than 50% higher for the 0-end orientational distribution than when the N end is preferentially directed to the surface. Using the isotropic rotational state distributions, Zo(J,Or),and Ridcrl(J,Bf) the total steric effect for a certain final angle Rav(Of) can be obtained by averaging:
The results are shown in Figure 6. The quantity Ra,(Of) should be compared to the steric effect Rida],QMS(ef) obtained with the quadrupole mass spectrometer." Comparison shows a reasonable agreement, indicating the consistency of the experimental data set. It should be noted that the rotational distribution is given only for the lowest final spin-orbit state, Le., the XI, state. In state in fact about 40% of the molecules are excited to the the scattering process. The rotational excitation of the molecules state, excited to the 113/2state is somewhat higher than in the llIl2 while the steric effect has essentially the same dependence on the rotational state. So RaV(Of)obtained by only taking the XI,,, state will be somewhat lower than the real value. Translational Energy Dependence. From previous work it has been concluded that the rotational excitation scales with En.32*33 To investigate the influence of this parameter on the rotationally
d3/2
5.5
10.5 15.5 20.5 25.5 30.5
Final rotational state J Figure 7. Steric effects Rw(J,Bf) for E,, = 0.05 eV; Ei = 0.10 eV and Oi = 45". Rotational transitions used in the measurements are similar Of = 70" to those used for Figure 4. Two Or are shown: Of = 30" (0); (0).
resolved steric effect, additional measurements were performed at a considerable higher E, = 0.28 eV (Ei = 0.34 eV, Bi = 2 5 O ) . In this case the results of Rideal(J,Of) are essentially the same as in Figure 4. The minimum value is obtained at the same J, and also the high-/ behavior is remarkably the same. The angular dependence of Rw(J,Of) is also similar to the E, = 0.17 eV results. The main difference occurs in the rotational state distributions: the high-1 rainbow shifts to higher J values, as is consistent with the findings of Kleyn et Furthermore, the shift of the angular distributions of higher rotational states toward the surface is more pronounced. Finally, experiments were performed a t E, = 0.05 eV (Ei = 0.10 eV, Oi = 45O) for which conditions the results of the Rm(J,Of) are shown in Figure 7 for Or = 30° and 70°. The results at Bf = 70' are taken under conditions similar to those obtained by Tenner et al.53 It should be noted that the new results are corrected (ideal) steric effects, while the Tenner results are raw data. The latter were obtained at a orientation voltage of 7 kV/cm, leading to a correction factor CO = 1.38 (C, = 1.1 in the present results). Because of the lower translational energy of the beam, the hexapole selection is much more efficient, so much smaller corrections CJ,o., and C, are needed. We assume both to be 1. Taking the different corrections for both experiments into account, there is good agreement between the data of Figure 7 and those obtained p r e v i o u ~ l y .Orientation-dependent ~~ rotational distributions are obtained in a way similar to that for E, = 0.17 eV. As expected, the high-J rainbow disappears almost completely, as can be seen in Figure 8. Only in the WONdistribution at Or = 70° a small
-
Rotational Excitation of Oriented Molecules
ai
Ee
0.5 0.0
Ll?L!J
0.5
5.5
10.5 15.5 20.5 25.5 30.5
Final rotational state J Figure 8. Orientation-dependent final rotation state distribution for Ei = 0.10 eV and 0, = 4 5 O . Results are constructed in a similar way as Figure 5. 0 end preferentially directed to the surface, closed triangles; N end to the surface, open triangles. (a) 4 = 30'; Tr, = 290 K; (b) Of = 70'; Tn, 320 K. deviation from a Boltzmann distribution can be observed, around J = 18.5. Compared to the WNodistribution there is a small shift to higher Jcomponding to a slightly higher rotational excitation. The rotational state distributions are only weakly dependpt on Of, in shape as well as in average rotational excitation. Over the angular distribution (E,) varies between 23 and 27 meV for WNo and from 24 and 32 meV for the WONdistribution. The shape of the rotational state distributions for the two orientations is very similar at Of = 35O, the difference being only in intensity. N-end collisions are more highly populated except at the highest J. This means that again there is a large angular dependence of R(J,Of) on the final angle, especially for J = 18.5 (see Figure 7). One important conclusion can be drawn from the translational energy-dependent results: the inference drawn from unoriented rotational state distributions that the energy dependence of the high- and low-J part of the distribution can be attributed to N-end and 0-end collisions appear to be valid. Increasing E, from 0.05 to 0.28 eV does not shift the minimum in the steric effect measurements: for all situations it can be found at J = 8.5. Although we have not determined the orientation-dependent rotational distributions at E, = 0.28 eV, it is a safe conclusion that increasing E, does hardly influence (E,,,) for N-end collisions: it remains almost constant at a value of about 30 meV. A similar conclusion was drawn by Kleyn et al. using the low-J Boltzmann-like part of the isotropic distribution^.'^ The rotational excitation of 0-end collisions increases much faster with E,. We determine an increase in (E,,,,) of about 20 meV when E, is increased from 0.05 to 0.17 eV. Discussion The interaction between a diatomic molecule and a solid surface is extremely complex due to the multiparticle nature of the collision. At present a full theoretical treatment of all degrees of freedom is possible only in extensive classical trajectory calcu* However, to obtain insight into the dominant lation~.~~*"* features of the interaction, simplified treatments are badly needed. The largest exchange of energy occurs between the translational motion of the diatomic and the lattice vibrations. This exchange is treated with some degree of accuracy by the cube models. Experimentally, however, more information is obtained on rotational excitation than on lattice vibrational excitation. Therefore many simplified theoretical treatments of the NO-Ag( 11 1) interaction have focused on rotational excitation, often entirely ignoring the degrees of freedom of the lattice. These models have (58)
Jacobs, D.C.; Zare, R. N. J . Chem. Phys. 1989, 91, 3196.
The Journal of Physical Chemistry, Vol. 95, No. 21, 1991 8417 explained the non-Boltzmann-like behavior of rotational excitation in terms of rotational rainbows, the most striking observation of these studies. Therefore we will start the discussion with the rotational excitation at structureless surfaces, explored for NOAg( 1 11) by Voges and Schinke (VS) in a seminal To explain the rotational-state distributions measured by Kleyn et al.,32 VS found it necessary to introduce a potential that is anisotropic with respect to the two ends of the molecules, in analogy with earlier work on gas-phase scattering!2 The main feature of their model is the existence of rotational rainbows, one for each end of the molecule. The term "rotational rainbow" is used when an extremum in the rotational excitation as a function of the orientation angle occurs, Le., when the rainbow condition dJ/dy, = 0 is fulfilled. In a classical sense such a rainbow leads to a singularity in intensity (in quantum mechanics the singularity does not exist). Of course, this singularity is lifted in the experimental situation, because of the finite opening of the detector. Classical trajectory calculations taking this into account still show quite sharp local maxima in intensity as a function of J, with a very fast decrease above the rotational rainbow; see,e.g., Holloway and H a l ~ t e a d . ~In~the VS model local maxima in rotational excitation occurs for ys = 4 5 O and 1 3 5 O . Since the attractive well used in the VS potential is rather small, the VS model can be viewed as a more elaborate version of a rigid ellipsoid scattered of a flat nonvibrating surface. The rotational excitation occur at the turning point on the repulsive wall and is proportional to the gradient dV/drs at that position. The very different E, dependence of the low- and high-1 parts of the measured rotational state distributions led VS to assume that the torques exerted at the rainbow orientation angles for the two ends of the molecules are very different (a similar conclusion was also drawn by Tanaka and S u g a n ~ ~The ~ ) . high-J rainbow at one end of the molecule is strongly dependent on E,. The low-J rainbow is almost completely fixed, to resemble the invariance of the low-J Boltzmann like part of the spectrum. VS could not assign the rainbows to a certain end of the molecule. If we want to compare the experimental data with the VS the angular spread in the data has to be taken into account. For the moment the discussion will be restricted to the data taken a t Of = 70°. At that Of the parallel momentum is conserved rather well (see Figure 2b and Figure 20 of ref 36). From the fact that this condition is fulfilled at this angle, we infer that these molecules are scattered from a rather flat surface. In the VS results no surface structure is incorporated, so for a valid comparison parallel momentum conservation is essential. Later the results obtained at other Or will be discussed. The rotational-state distributions obtained at Or = 70° for the two orientational distribution are very different. In the WON(0-end preferentially directed to surface) result a clear rotational rainbow is observed a t high J , with a clear cutoff above J = 23.5. From this result the conclusion can be drawn once and for all that the high-J rainbow is due to 0-end collision. The assignment made by Kuipers et a1.'* on the basis of angular distribution measurements is correct. On the other hand, no convincing evidence for a N-end rainbow can be found a t first sight in the "N-end" distribution. The shape of the curve resembles more a Boltzmann distribution instead of a clear classical rainbow structure. The maximum intensity is achieved at a Jvalue close to the predicted low rainbow position by VS, but this is not surprising since VS used the experimental results as a fit. The main question now is whether the low-J rainbow really exists, perhaps smeared or blurred. In the past several factors have been proposed that might be responsible for the absence of a clear low-J rainbow. The first factor is rather obvious: in a quantum mechanical calculation the rainbows are far less sharp than classically expected, especially ~ @ factor is the nonzero the N-end (low J) r a i n b o ~ . ~ ~A* ~second rotational temperature of the beam, which was assumed to be responsible for the smearing of the low-J rainbow by VS.42q46In ( 5 9 ) Holloway, S.; Halstead, D. Chem. Phys. Lett. 1989, 154, 181. (60) Barker, J. A.; Kleyn, A. W.; Auerbach, D.J. Chem. Phys. f e l t . 1983, 97, 9.
8418 The Journal of Physical Chemistry, Vol. 95. No. 21, 199'1
Geuzebroek et al.
,-
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our case, due to the focusing of the hexapole, about 75% of the molecules in the incident beam are in the J = 0.5 ground state, which corresponds with a very low rotational temperature. Calculations have shown that at this rotational temperature supernumerary rainbows survive in a calculation using noncorrugated surfaces.46 So we believe that the nonzero rotational temperature is a minor smearing factor in our results. Several other factors have been introduced to explain the relatively smooth behaviour of the rotational state distributions. Surface vibrations6' and especially surface corrugation62 probably serve as smoothing factors, while the occurrence of multiple boun~es~**~~,64 might result in blurring of the rotational rainbows. To decide whether a low-J rainbow exists from the rotational-state distribution alone is a rather difficult task. We will try to show what new insight can be obtained from orientation-dependent measurements. In doing this it is important to realize that the orientational measurements described in this paper make use of preferential orientational distribution^.^^ This means that in a certain orientational distribution, where one of the ends of the molecule is preferentially directed towards the surface, there is always some dilution by molecules with the "wrong" end directed toward the surface. At first sight this may appear as a large limitation of the application of oriented molecule beams. However, it is possible to make use of the preferential nature of the orientational distributions. To illustrate this, in Figure 9 we plotted the ratio of the probabilities to find a molecule with a certain orientation angle in the two orientational distributions WON/ Wyo = (1 + cos yJ/( 1 - cos ys). It is immediately clear that the ratio becomes large only for molecules with cos Y~ = 1 (end-on collisions). Molecule with broadside orientation (cos ys = 0) are equally populated in both orientational distributions. The maximum steric effect that can be measured is limited by the ratio WON/ WNo. When a certain final rotational state J is produced by a narrow range of cos ysalone, a simple calculation shows that Rideal(J)can never become higher than 2 cos ysfor this particular J state. More generally, if there exists a excitation function c(Jo;ys) such that every ys leads to a single final Jo state the following equation holds: 1
S_,cos 7s C(J0,COS 7s) d cos Ya
=2
5.5 10.5 15.5 20.5 25.5 30.5 35.5
Final rotational state J
Figure 9. Probability ratio of the two orientational distributions WON/ WNo = 0.5(1 cos y,)/OS(I - cos y,) as a function of orientation angle y,. The maximum population ratio ION/INO of a factor 6 for E, = 0.17 eV measured at high final J states corresponds to a orientational angle y, = 450.
Rideal(J0)
t
= 2(cos Ys) ( 5 )
~ ; c ~ J o ~ Ys) c o sd cos Ya This expression is just the expectation value of cos ys of the molecules leading to the final state Joe So the measured Rkl!J) reflects the average orientation angle of the molecules producing ~
(61) Hurst, Jr., J. E.; Kubiak, G. D.; a r e , R. N. Chem. Phys. Le??.1982, 93, 235. (62) Brunner, T.; Brcnig, W. Surf. Sci. 1988, 201, 321.
(63) (a) Polanyi, J. C.; Wolf, R.J. Ber. Bumen-Ges. Phys. Chem. 1982, 86, 356; (b) J . Chem. Phys. 1985.82, 1555. (64) Harris, J.; Luntz, A. C. J . Chem. Phys. 1989, 91, 6421.
Figure 10. Difference of the rotational state distributions measured for the two orientational distributions ION(J,ef) - IN&,@f) for two final angles Or: 70° (open diamonds) and 3 5 O (open circles). Incident condition: see Figure 2. The result corresponds to a orientation distribution where broadside molecules are eliminated. In the 8, = 70° result, apart from the clear high J , 0-end rainbow, some sign of an N-end rainbow is present around J = 8.5.
a certain final J state or in general any final state. The maximum Rid&) measured in the experiments is about 1.35 f 0.2 (ZON/ZNO = 5), reached a t J = 23.5 in the result for Or = 70°,corresponding to the rotational state where the 0-end rainbow is located. Above the rainbow Ridspl(J)remains constant. Applying eq 5 we find that the maximum value of Rihl corresponds to an average orientation angle of (yI) (47 f .')8 This value is in excellent agreement with the prediction by VS.42 Applying the same arguments to the low-J peak leads to a completely different result. The steric effect in the l o w 4 peak does not become larger than about -0.25, corresponding to a average orientation angle of about looo. Part of the explanation why this value is so close to the broadside orientation angle can be found by assuming that a tail of 0-end collisions will contribute to the rotational state distribution around the N-end rainbow. The result by VS shows that the rotational state of the N-end rainbow a t cos ys -0.7 (J = 8 . 5 ) is also accessible for molecules with cos ys c 0 and 0.8. The molecules with cos y, 0 have a high abundance in the orientational distribution. The probability to find such a molecule will be equal for the WON and the WNo d i ~ t r i b u t i o nso , ~ ~this process gives rise to Ripal(J) = 0. This contribution will of course reduce the total stem effect measured at J around the assumed N-end rainbow. However, we believe that this is only part of the explanation. As can be seen in Figure 5 the low-J peak is still clearly observed in the WON distribution. Calculations by Tenner et aLM and Hand et aL5' based on the VS potential show that this observation is inconsistent with the VS potential. If the low-J peak is related to a large extent to a N-end rainbow around cos ya= -0.7 (135'), the low-J peak should essentially show up only in the WNodistribution: the residual of this peak in the WONdistribution should be quite small due to the large probability ratio to find molecules with ya= 135' in the two orientational distributions. The fact that there is a clear low-J peak in the WONdistribution shows that the VS model is not describing the situation completely. Now assume that the N-end rainbow is hidden by one of the mechanism discussed above: 0-end collisions with low cos y,, surface corrugations, or multiple bounces. In all of these cases the highly abundant broadside molecules constitute the major part of the disturbers of the N-end rainbow. So we need a way to put additional weight on the molecules with end-on orientation. This can be done by taking the difference between the rotational state distributions of the WONand the WNodistributions. The resulting distributions are shown in Figure 10. In the = 70' distribution a remarkable structure is observed around J = 8.5, apart from the clear highJ rainbow at J = 23.5. The maximum, with a fast dropoff when J is increased slightly above J = 8.5 indicates clear non-Boltzmann character of the low-J peak and has some rcsemblance with a rotational rainbow. The shape of the curve is partly due to the coincidence of two extremes: the maximum in the rotational distribution and the minimum in the steric effect measurement are both at J = 8.5. So we conclude that an in-
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dication of the N-end rainbow is observed,though heavily blurred and smeared. Of course one of the main points neglected so far is the fact that the shape of the interaction potential used by VS might be incorrect. Several other PES have been introduced. The potential used by Tully and co-workers assumes a strong anisotropy in the attractive part of the ~ t e n t i a l . 4Using ~ the first version of the potential very good agreement with the results of K l e p et al. was found.32 The important difference with the VS model is that only an 0-end rainbow at high J is assumed to exist. The N-end of the molecule does not give rise to a rotational rainbow, but instead a Boltzmann-like behavior is observed. On first sight good agreement with our data is found, the main problem being the much too large well depth used in their first study. A similar problem exists with the results by Corey and Lemoind5 who use a potential based on the first version by Tully and co-workers. The PES has been modified in a later version such that the resulting well depth obtains a reasonable Agreement with the isotropic rotational state distributions is claimed; however, no results are shown, so a comparison with those results is hard to make. Brenig and co-workers construct a PES based on Morse-like potentials with anisotropy in the attractive as well as the repulsive term.46 Although the binding geometry in their final version is upright, the rotational excitation is very similar to the VS result, with a low and a high rotational rainbow for the two ends of the molecules. Brenig et al. propose that the corrugation of the surface serves as the major smearing factor of any structure in the rotational-state distributions.62 Their final result closely resembles the experimental data of Kleyn et al. Orientation-dependent calculations of the final rotational-state distribution are performed using quantum mechanical methods.66 In these results the low4 rainbow is shifted to more broadside orientation angles. Because of the dilution effect the low-J peak is observed both in the WON as well as in the WNo result, in a m d a n c e with experimental result (Figure 5 ) . However, compared to VS the high4 rainbow is shifted to more end-on ys (cos ys = l), due to the existence of the larger and anisotropic well in the Brenig potential. The population ratio IoN/INopredicted by the calculation is much larger than the experimental result, i.e., much higher steric effects are predicted than observed in the experiments. So far we have treated the surface being flat with no interaction with phonons, although some problems resulting from this assumption were already mentioned. If the dependence on final angle is to be discussed, some more realistic model of the interaction with the surface has to be assumed. Tenner et al. have applied one of the simplest ways to extend the model: they use a soft-cube model with the VS interaction potential and take the surface temperature into The results are obtained as a function of final translational and rotational energies, which are coupled to a final angle Of using parallel momentum conservation. Their results for a translational energy of 0.2 eV (about the same as E, = 0.17 eV used in the experiment) show that the high-J rainbow is shifted toward the surface with respect to the lower rotational states. This observation was used to explain the angular dependence of the total intensity measurements: 0-end collisions lead on the average to a higher scattering angle than N-end collisions. The energy needed to rotationally excite the molecules is taken from E,. In part this is compensated by the anticorrelation with phonon excitation, which is taken into account in the calculations. This compensation is not complete,u so higher rotational states possess a lower final translational energy. The result is a bending of higher rotational states toward the surface, an observation made by others as well.32” As can be seen from Figure 3 the experimental results are consistent with this picture. Similar calculations were performed by Hand et al.sl They use classical as well as quantum mechanical calculations, where the interaction with the surface is taken into account by using onedimensional harmonic oscillators, at 0 K at the start of the cal(65) (a) Carey, G. C.; Lrmoine, D.Chem. Phys. Left. 1989,160,324. (b) Lemoine, D.;Corey, G. C. 1. Chem. Phys. 1991, 91, 767.
The Journal of Physical Chemistry, Vol. 95, No. 21, 1991 8419 0.6 0.4
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When the averaged steric effect Rav,l(Of)is calculated, the rotational-state distribution lo(J,Of)is changed, while the steric effect Ridcol(J,Of) is kept constant. In this way a quantitative value is assigned to the shift due to the mechanism proposed by Tenner et al., the rotationally induced angular shift. As a reference, the rotationally resolved steric effects at Of = 50° are taken as representative for the total angle averaged result. Rav,2(Of),on the other hand, is a measure for the angular shift due to the angular dependence of the steric effect Ridcol(J,Of).In this case the rotational-state distribution is kept constant, with again the 81 = 50° results as a reference. The results are shown in Figure 11 together with the steric effect obtained with the QMS. It appears that the change in RaV,*(Of) is much larger than in R,v,I(Of), when changing Br from 3 5 O to 70°. Less than 20% of the difference in steric effect between scattering to low and high Of can be explained by the existing explanation; the rest has to be found in unknown mechanisms. One point should be stressed in this respect: the relative importance of the mechanisms is certainly different at other incident translational energies Ei.At 0.10 eV, Bi = 4 5 O for instance, Rav,l(Of)is almost insensitive to Of, while at higher E, a larger dependence will probably be found. We tentatively assume that the rotationally induced angular shift will be the most important shift mechanism at high E, (>0.3 eV) while
8420 The Journal of Physical Chemistry, Vol. 95, No. 21, 1991
unknown mechanisms are the determining factor at low E,. Another point of inconsistency between the VS model and the experimental data is the rather low well depth used (0.08 eV). In this respect it is interesting to note that the VS model underestimates the rotational excitation and the position of the highJ r a i n b o ~ . ~ ~While J in the calculation J = 17.5 is found, the experimental rainbow is located at J = 23.5. Measured in energy, this is a large difference (68 meV versus 123 meV). This point was already raised by Brenig et ala,&who attribute the discrepancy to the low well depth used in the VS potential. Upon incorporating a deeper well of about 0.24 eV the 0-end rainbow is raised to higher J values. On the other hand other experimental verifiable quantities, such as the energy transfer and the amount of trapping, will also change. Tenner et al. find that the trapping probability increases to much higher than experimental values when the well depth is increased. They compensate for this by increasing the cube mass to 400 amu, which is rather high and unrealistic. However, the definition of trapping used in the experiments does not necessarily have to be the same as in the calculations. In the calculations particles are “trapped” when they lose their “perpendicular” translational energy, to rotational or phonon excitation. However, the calculations are only one-dimensional and do not take into account the parallel momentum. This is a simplifying assumption that is certainly not always valid, especially at higher surface temperatures. (In some theoretical studies the definition for trapping has been modified such that the total energy is negative and lower than a value coupled to the surface temperature, for instance, -2kTs.3*47)That the parallel momentum is clearly playing a role in the NO/Ag( 1 1 1) system can be inferred from the fact that the trapping probability determined by Kuipers et al. shows total incident energy scaling, Le., no dependence on di.3s The experimental procedure used there is based on the angular distributions: the molecules scattered in the direction of the surface normal are assumed to have undergone a trapping/ desorption event. By assuming a cosine distribution for the trapped particles and integrating over the direct inelastic peak, a trapping probability can be extracted by comparing the fluxes in the two channels. For a similar system, Ar/Pt( 1 1 l), it has been concluded that this method fails at high surface temperature ( T , >> desorption temperature). Molecules that lose their perpendicular momentum in the first collision still possess their parallel momentum. This momentum is not transferred easily. If the residence time of the molecule at the surface is short, “desorption” can occur before complete equilibration of the parallel momentum has taken place. The result is a non-cosine distribution of the desorbed particles, still peaked more or less in the specular direction. In the NO/Ag(l11) case the situation is even more complex because of the additional complicating factor, the rotational excitation. The conclusion for the moment is that one has to be extremely careful using trapping probabilities as an argument in determining potential energy surfaces. Without a proper treatment of the parallel degree of freedom we cannot exclude a deeper well depth on the basis of a discrepancy between the experimental trapping probability and a model calculation thereof.3 To obtain insight about the sources of inconsistency between data and theory, one should notice that the largest deviations from the results of the VS soft-cube model calculations occur for scattering in the direction of the normal. In Figure 1 1 this is reflected in the fact that Rav,l(Of)is constant for Of C Oi. The mechanism proposed by Tenner et al.50to explain their orientation-dependent angular distributions, Le., the rotationally induced angular shift, does not seem to be active at these angles. This is not surprising, since the molecules scattered in the direction of the normal have the largest deviations from cube models and parallel energy conservation. It appears that the calculations of Tenner et al. clearly underestimate the intensity of molecules scattered at low Bp Furthermore, contrary to the cube model, molecules scattered in this direction do not gain a large amount of normal momentum but have a considerable loss of parallel momentum instead. It is important to notice that molecules with their N end preferentially in front are scattered with high probability in the direction of the surface normal, while the average
Geuzebroek et al. final translational energy (Ef)of the two orientations is similar to within 2%.57 So we can draw the conclusion that N-end collisions lead on the average to a larger amount of parallel momentum transfer than 0-end collisions. Several mechanism are available to explain parallel to normal momentum transfer, some of which have already been introduced. Surface corrugation serves as a major possibility. Corrugation can have different natures. Examples are static corrugation, the lateral shape of the surface due to the existence of individual atoms; dynamic corrugation, deformation due to the impact at the surface; and thermal corrugation caused by the nonzero surface temperature. Another related possibility to explain the parallel momentum loss is the occurrence of multiple bounces, which are not taken into account by Tenner et al.? particles that lose their initial parallel momentum in the first bounce are assumed to be trapped in the calculation. At the rather low translational energies used in our study a substantial amount of multiple bounces might occur, as have also been suggested to occur from calculations by Polanyi and Wolft3 Harris and Luntz for CO/Pt( 1 1 l),@and Jacobs and Zare for N O / R ( l l l).58 Roughly, two types of collisions can lead to multiple bounces. In the first case, already introduced above, molecules lose their perpendicular momentum in the first bounce but not their parallel momentum. The parallel momentum is not transferred effectively to phonons. So a molecule has to make several collisions before it has equilibrated its parallel momentum at the s ~ r f a c e .When ~ the surface temperature is high, the chance for molecules to escape from the attractive well is significant, still having memory of their initial momentum. The second type of multiple bounces occurs when a molecule is strongly rotationally excited in the first bounce: if the molecule is not able to escape the interaction region fast enough, the molecule might hit the repulsive wall for a second time with its other end (~hattering~~). In that case the rotational energy can be transferred back into translational energy. Classical trajectory calculations with a more realistic description of the surface are needed to determine which of the phenomena described above are playing a role in the parallel momentum transfer. From the orientational measurements we can draw one important conclusion based on the larger parallel momentum transfer for N-end as compared to 0-end collisions: the process explaining the parallel momentum transfer probably has a larger influence on N-end than on 0-end collisions. Two observations support the view that processes like multiple bounces and/or corrugation are important in the scattering of NO from Ag( 1 1 1). The first is related to the difference between the rotational-state distributions for W N and ~ WoN orientational distributions, shown in Figure 10. As discussed before, at Or = 70’ some evidence of a attenuated rainbow structure can be observed at low J. On the other side of the specular angle a different picture appears: at dr = 35O no a trace of a rainbow feature is observed in the difference. Instead it appears as though the result can be described by the difference of two Boltzmann distributions with different temperatures. Some thermalizing (not with the surface temperature!) process seems to occur, possibly involving multiple bounces. A second experimental observation concerns the alignment of the final angular momentum vector. As shown by Luntz et a1.I2 the alignment is found with a preference for the final J vector to be directed parallel to the surface, indicating that the forces are directly preferentially normal to the surface. However this occurs only at high J states, well above the J = 8.5. At low J the alignment is still low, indicating that the molecules populating this state have undergone a much more complicated interaction. A simple VS model combined with a flat surface does indeed fail to describe the measurements properly at low J.67 The situation is also quite different compared to N2 scattering from Ag(ll1). In that case the alignment increases gradually starting from J = 0.13 At the rotational rainbow the alignment is already perfect, contrary to the NO/Ag( 111) case where at J = 8.5 the alignment is still low. An explanation is given (66) T. Brunner, Thesis, Technischen Universitit MOnchen, 1990. (67) Kleyn, A. W.; Luntz, A. C.; Auerbach, D.J. Sur/. Sei. 1985, 152/ 153, 99.
Rotational Excitation of Oriented Molecules by Brunner, who shows in a calculation that surface corrugation serves as an important factor to decrease the angular momentum alignment at low JSaAlternatively, multiple bounces will most probably lead to additional population of the low final rotational states possibly with a decrease of the angular momentum alignment of these states. Conclusion
In this paper it is shown that the rotational state distributions of N O molecules scattered from a Ag( 1 1 1) surface are strongly dependent on the initial orientation of the molecule. With the 0 end preferentially directed to the surface, the rotational excitation energy was measured to be more than 50% higher than with the N end preferentially directed to the surface at the highest translational energy used in this study (Ei = 0.34 eV). A number of conclusions could be drawn on the basis of the experiments, making use of the nature of the orientational distributions: (1) In the rotational-state distributions a clear high-J rainbow is observed that occurs only when the 0 end is preferentially directed to the surface. The molecules in this rainbow are more abundant in the results for high Br, i.e. the molecules with high rotational excitation are scattered with higher probability in the direction of the surface than molecules with low J?6Making use of the nature of the orientation distribution it is shown that the high steric effect Rideal(J)(=1.35 f 0.2) measured at high final J states can only be obtained if the molecules which are excited to this final state have on the average a relatively end-on initial orientation angle (cos ys = 1). A more detailed analysis leads us to the conclusion that the 0-end rainbow is populated by molecules with an average orientation angle ys between 40' and 5 5 O . This is in agreement with the model by Voges and Schinke!* (2) One of the main questions related to the rotational state distributions is the existence of a second rainbow a t low J due to N-end collisions, perhaps heavily smeared and blurred. In the rotational state distributions with the N end preferentially directed to the surface a single peak is observed, which does not show a explicit rainbow character but can instead be described rather well with a Boltzmann distribution. Furthermore the low-J peak is
The Journal of Physical Chemistry, Vol. 95, NO.21, 1991 8421 also clearly observed in the 0-end rotational state distributions, where it still maintains its Boltzmann-like shape. From the relatively low measured steric effect the average orientation angle of the molecules populating the low-J peak is inferred to be close to broadside (ys = 90O). The molecules with a broadside orientation angle can be eliminated by taking the difference of the rotational-state distributions of the two orientational distributions. Upon doing so at 6, = 70°,a feature appears around J = 8.5 that might be attributed to the N-end rotational rainbow. However, in any case this feature is relatively small, so the N-end rainbow is heavily blurred and smeared. (3) To explain the angular dependence of the results a comparison is made with classical trajectory calculation by Tenner et al.50 and Hand et aLS1 In both these cases the Voges and Schinke model is combined with some simple interaction with surface phonons, with the only interaction directed normal to the surface. At the translational energies used in this study (EiI 0.34 eV) the shift between the angular distributions measured for the two ends of the molecule can be only partly explained by the larger rotational excitation of 0-end collision^.^^^^^^^^ Individual J states, especially those between the two rotational rainbows (8.5 < J < 23.5) possess a large angular dependence of the measured steric effects: i.e., angular distributions of individual J states shift drastically if the orientation is changed. This observation is accompanied with a large amount of parallel momentum transfer, indicating the breakdown of the models used in the calculations. The possible phenomena to explain the breakdown of parallel momentum conservation are corrugation of some sort or multiple bounces. Since N-end collisions possess a higher possibility to be scattered to final angles where parallel momentum transfer is found, we conclude that the N-end collisions are more influenced by the process explaining the parallel momentum transfer. Acknowledgment. Craig Taatjes is kindly acknowledged for his careful reading of the manuscript. This work is part of the research program of the Stichting voor Fundamenteel Onderzoek der Materie and was made possible by financial support from the Nederlandse Organisatie voor Wetenschappelijk Onderzoek.
