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Grazing incidence scattering of vibrationally excited H2 molecules from metal surfaces
Surface Science 604 (2010) 2031–2035
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Surface Science j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / s u s c
Grazing incidence scattering of vibrationally excited H2 molecules from metal surfaces D. Stradi a,b, C. Díaz a,⁎, F. Martín a,b a b
Departamento de Química Módulo 13, Universidad Autónoma de Madrid, 28049 Madrid, Spain Instituto Madrileño de Estudios Avanzados en Nanociencias (IMDEA-nanociencia), Cantoblanco 28049 Madrid, Spain
a r t i c l e
i n f o
Article history: Received 14 June 2010 Accepted 11 August 2010 Available online 19 August 2010 Keywords: Grazing incidence Quasi-classical dynamics Vibrationally excitation Reflectivity
a b s t r a c t We have studied the scattering of vibrationally excited H2 molecules from metal surfaces under fast grazing incidence conditions, by means of quasi-classical calculations based on six-dimensional potential energy surfaces. We show that, in spite of the fast parallel motion, the reorientation of the molecule along the trajectory plays a fundamental role on the scattering, being responsible for the nonmonotonic behavior observed as a function of the normal incidence energy, similar to that observed under slow normal incidence conditions. The present study has allowed us to further prove that the interaction between a H2 molecule and an ordered metal surface under fast grazing incidence conditions is, in general, governed by the normal momentum of the molecule. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Diffraction of fast (E = 0.1–2 keV) atoms and molecules from surfaces under grazing (θ = 0.1°–4.0° — see Fig. 1) incidence conditions has been recently proposed as a very promising tool to determine surface properties with unprecedented accuracy [1–8]. The observation of diffraction under these extreme conditions is possible thanks to the strong decoupling between the fast motion parallel to the surface along the incidence direction and the slow motion perpendicular to the surface [9]. The interaction between the projectile and the surface under these conditions is governed by the perpendicular motion (perpendicular energy). The de Broglie wavelength associated to this perpendicular motion is of the order of the surface lattice constant, which explains why diffraction can be observed experimentally, despite the huge total momentum of the projectile. If the de Broglie wavelength were much smaller than the typical surface constant, most like the thermal displacement of surface atoms would introduce decoherence thus hiding diffraction. Recently [10] it has been shown, theoretically, that scattering of fast H2 molecules at grazing incidence could also be useful to determine sticking probabilities corresponding to thermal energies and normal incidence. In Ref. [10] it was shown that total molecular reflectivity probabilities, as a function of the normal energy, computed at fast grazing incidence reproduce for several systems, those in which dissociative adsorption at low normal incidence is a direct process, i.e., those approximately following normal energy scaling, the total
⁎ Corresponding author. E-mail address: [email protected] (C. Díaz). 0039-6028/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.susc.2010.08.017
molecular reflectivity probabilities obtained at slow normal incidence. At low incidence energies (up to ≈1 eV) molecular reflectivity and dissociative adsorption are almost complementary, i. e., dissociative adsorption is equal to 1 − reflectivity. Thus, molecular reflectivity at fast grazing incidence can be used to estimate dissociative adsorption at slow normal incidence. This striking result, found for both activated (H2/NiAl(110)) and non-activated (H2/Pd(111)) systems, has been proved for H2 molecules in their rovibrational ground state [10]. For activated systems, it has been recently shown [11] that the dissociative adsorption probabilities of vibrationally excited molecules colliding with metal surfaces, at low energy and normal incidence, exhibits a nonmonotonic behavior as a function of the incidence energy (which is at variance with the monotonic behavior obtained for molecules on their rovibrational ground state [12]). Dissociative adsorption first decreases with the incidence energy until it reaches a minimum after which it increases with the incidence energy. The excited state ν at which the nonmonotonic behavior shows up depends on the system, but, in all cases, it is observed whenever the translational energy plus the fraction of the initial vibrational energy transferred to the reaction coordinate is higher than the minimum reaction barrier. This phenomenon has been attributed to an efficient (inefficient) reorientation of the molecule at low (medium and high) incidence energies. At low incidence energies (typically b0.1 eV) the molecules are very efficiently reoriented along their trajectories in such a way that the probability of finding one of the few barrierless reaction paths is very high and, consequently, the dissociation probability is high. When the energy increases the reorientation becomes less efficient, thus decreasing the dissociation probability. For high energies (typically N0.4 eV), although the reorientation is very inefficient, the increasing number of barrierless
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D. Stradi et al. / Surface Science 604 (2010) 2031–2035
Fig. 1. Schematic representation of a grazing incidence collision of H2 with a metal surface. The coordinate system used in the dynamics is also shown. The inset represents the six degrees of freedom of a diatomic molecule.
reaction paths ensures the enhancement of the dissociative adsorption probability. This phenomenon has been observed for three different kinds of activated systems [11], two pure surfaces, Pt(111) and Cu(110), one bimetallic alloy surface NiAl(110), and two bimetallic pseudomorphic surfaces Pd/Ru(0001) and Cu/Ru(0001). Here we investigate whether the dissociative adsorption nonmonotonic behavior, for vibrationally excited H2 molecules on metal surfaces, can also be observed under fast grazing incidence conditions, i.e., whether the reorientation mechanism is still active under fast grazing incidence conditions. To answer this question we have studied the scattering of vibrationally excited H2 molecules from several metal surfaces under fast grazing incidence conditions. Specifically, we have studied four activated systems: H2/Pd/Ru(0001), H2/Cu/Ru(0001), H2/ Cu(111) and H2/NiAl(110), for which a nonmonotonic behavior of the dissociative adsorption probability has been observed for vibrationally excited H2 at low normal incidence energy. This paper is organized as follows. In Section 2 we describe briefly the methodology employed. Results on scattering as well as their discussion are presented in Section 3. We summarize the main conclusions in Section 4.
[19] for H2/Pd/Ru(0001) and H2/Cu/Ru(0001), and in Ref. [20] for H2/ Cu(111). In performing the dynamics calculations we have used the socalled quasi-classical trajectory (QCT) method [21], in which the zero point energy (ZPE) of the molecule is included in the calculation. Our choice of the QCT method is based on previous studies comparing quantum and quasi-classical methods, which show that the QCT method can successfully describe diatomic molecule/metal surface processes such as dissociative adsorption [22] and even diffraction [23]. The QCT method is a useful tool to perform this kind of studies, not only because is computationally cheap, but also because it allows one to follow the molecule through the Cartesian and the momentum space. In our dynamic study under fast grazing incidence conditions we have fixed the total incidence energy to 400 eV, and to cover the whole normal incidence energy range [0.05 eV–0.8 eV] the incidence angle, θ (see Fig. 1), has been varied from 0.64° to 2.56°. The molecule is considered to be reflected whenever the distance molecule-surface, Z, becomes equal to initial distance, Zi, with the molecule's velocity vector pointing towards the vacuum and the atomic distance H–H being smaller than 2.25 Å. In order to ensure low statistical errors for each translational energy and rovibrational state, we have considered around 104 trajectories. 3. Results We have studied scattering under fast grazing incidence for four selected systems that have been widely studied previously under normal incidence and thermal energy conditions: H2/Cu/Ru(0001) and H2/Pd/Ru(0001) [19], H2/Cu(111) [17,24], and H2/NiAl(110) [25,26]. For the first two systems, the nonmonotonic behavior for dissociative adsorption (1 − reflectivity) at slow normal incidence is already observed for the lowest vibrational excited state ν = 1, whereas for the other two systems it is found at higher ν values [11]. We show below that the same pattern is reproduced at fast grazing incidence. In Fig. 2 we have plotted 1 − reflectivity (which corresponds to dissociative adsorption at slow normal incidence) as a function of the normal energy, for H2 (ν = 1,2, J = 0)/Cu/Ru(0001), H2 (ν = 1,2, J = 0)/Pd/Ru(0001), H2 (ν = 4,5, J = 0)/NiAl(110), and H2
2. Theory
1 0.8
A H2(ν,J=0)/Cu/Ru(0001) B H2(ν,J=0)/Pd/Ru(0001) v=2
v=2 Graz. Nor.
0.6
Graz. Nor.
0.4
1-Reflectivity
To carry out our molecule/surface study we have worked within the Born–Oppenheiner Static Surface (BO–SS) approximation, i.e., neither electron–hole pair excitation processes nor the motion of the surface atoms is taken into account. Surface phonons induce decoherence, and can influence the intensity of the diffraction peaks [7,13], but they are not expected to modify significantly the total reflectivity [14]. The BO approximation could be considered too restrictive taking into account the high energy of the projectile, but recent experiments showing diffraction of fast grazing He atoms from metal surfaces [4,5] prove that the role of electronic excitations is not as dramatic as could be expected, and, therefore, that the BO approximation can be safely used. In our study we have included the six degrees of freedom (DOFs) of the molecule (see inset Fig. 1). Thus, we have carried out six-dimensional (6D) dynamics calculations based on 6D potential energy surfaces (PESs). The 6D PESs used in the present work to describe the electronic interaction between a H2 molecule and a surface were developed previously to study molecule/surface interactions at low collision energy (b2 eV). In all cases, the PESs were obtained by applying the corrugation reducing procedure [15] to a set of DFT (density functional theory) data. This state-of-the-art interpolation method has been proved to yield very accurate PESs, and have been used to study H2/metal dynamic interactions (see, for example, [16,17]). Details of the PESs can be found in Ref. [18] for H2/NiAl(110), in Ref.
0.2 0 1 0.8
v=1 [101] Cu
Pd
C H2(ν,J=0)/NiAl(110)
D H2(ν,J=0)/Cu(111)
v=5
v=4
0.6
Graz. Nor.
Graz. Nor.
0.4 0.2 0 0
[101]
v=1
0.2
v=3
[001]
v=4
[101] Al Ni
0.4
0.6
0.8
0
Cu
0.2
0.4
0.6
0.8
1
Normal energy (eV) Fig. 2. 1 − reflectivity as a function of the normal incidence energy for: (A) H2 (ν = 1,2, J = 0)/Cu/Ru(0001); (B) H2 (ν = 1,2, J = 0)/Pd/Ru(0001); (C) H2 (ν = 4,5, J = 0)/NiAl (110); (D) H2 (ν = 3,4, J = 0)/Cu(111). Both slow normal and fast grazing incidence results are shown.
D. Stradi et al. / Surface Science 604 (2010) 2031–2035
(ν = 3,4, J = 0/Cu(111)), under both slow normal and fast grazing incidence conditions. In this latter case we have considered that the molecules collide with the surface along well defined crystallographic directions (shown in the insets of Fig. 2), i.e., we consider that the collision proceeds in channeling regime. From this figure we can see that fast grazing incidence scattering results reproduce the nonmonotonic behavior found at slow normal incidence. Specifically, for each system and each rovibrational state (ν, J = 0), the 1 − reflectivity minimum for both slow normal and fast grazing incidence is located at approximately the same normal energy value. One can see that, for H2 (ν, J = 0)/Pd/Ru(0001) and H2 (ν, J = 0)/Cu/Pd(0001), the resemblance between slow normal and fast grazing incidence probabilities is larger for the lower ν values, i.e., it is larger for ν = 1 than for ν = 2, whereas, for H2 (ν, J = 0)/NiAl(110) and H2 (ν, J = 0)/Cu(111), the resemblance is larger for the higher ν values, i.e., it is better for ν = 3 and ν = 4 than for ν = 4 and ν = 5, respectively. At this point we should point out that the ν value at which the nonmonotonic behavior is observed depends on both the minimum reaction barrier height and the efficiency of the energy transfer from the vibrational motion to the reaction coordinate (which is more efficient for late barrier systems than for early barrier systems). These are the reasons why the nonmonotonic behavior is observed for lower ν values in the case of H2/Cu/Ru(0001) and H2/Pd/Ru(0001) (late barrier systems with low minimum reaction barriers) than in the case of H2/NiAl(110) and H2/ Cu(111). Nevertheless it can be observed (Fig. 2) that the nonmonotonic behavior of the 1 − reflectivity curve is less pronounced as ν increases, because when ν increases the 1 − reflectivity probability tends to the saturation value over the whole normal energy range. To ensure that the results discussed above are not affected by reflected molecules moving through the region of the configuration space where the PESs are not appropriately described by our spin unpolarized DFT calculations, i.e., the regions where both H–H and molecule-surface distances are large, we have analyzed the vibrational distribution of the reflected molecules under the incidence conditions considered in Fig. 2. From Table 1 we can see that vibrational excitation (large H–H distance) is negligible. On the contrary, vibrational de-excitation (small H–H distances) is substantial, higher at high normal incidence energies. We analyze now that the nonmonotonic behavior of the 1 − reflectivity probability found at fast grazing incidence has the same origin as the nonmonotonic behavior found for dissociative adsorption at thermal normal incidence. At low normal incidence energies, the nonmonotonic behavior has been shown to be due to molecular reorientation along the trajectory [11]. Here, we have analyzed the orientation of the molecules along their trajectories at fast grazing incidence. In Fig. 3 we have plotted the distribution of the initial orientation (Θ — see Fig. 1) of the molecules whose trajectories end up in dissociation, i.e., whose trajectories do not end up in scattering, for H2 (ν = 1,2, J = 0)/Cu/Ru(0001) and H2 (ν = 3,4, J = 0)/Cu(111). From this figure, it can be seen that, at low normal incidence energies (energies below the 1 − reflectivity minimum — see Fig. 2), the Θ angular distributions are rather broad, in some cases (see Fig. 3 B) very similar to
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the initial angular distribution of the whole ensemble of molecules. Since at such low energies there are few accessible reaction paths, the behavior observed in Fig. 3 can only be attributed to a very efficient reorientation of the molecules, which allows them to find the few accessible reaction paths. Molecular reorientation becomes less efficient when the normal incidence energy increases. This effect can be straightforwardly inferred from the angular distributions shown in Fig. 3, corresponding to the incidence energies at which the minimum of the 1 − reflectivity curves is observed (see Fig. 2). These angular distributions are far narrower than those corresponding to low and high normal incidence energies, which means that only molecules with an initially appropriate orientation can dissociate. In the case of Cu(111), Pd/Ru(0001) and Cu/Ru(0001) the angular distribution at the 1 − R minimum clearly peaks around Θ = 90°, while for NiAl(110) it peaks around Θ = 45°. In this latter case, the lack of molecular reorientation at the minimum is less pronounced, which is consistent with the fact that the nonmonotonic behavior of the 1 − reflectivity curve is also less pronounced, as shown in Fig. 2. When the normal energy further increases, the number of accessible reaction paths becomes so large that the number of molecular orientations leading to dissociation necessarily increases. From Fig. 3 it can be also observed that the higher the vibrational state the less crucial the reorientation of the molecule: the Θdistribution at the minimum of the 1 − reflectivity curve exhibits a less pronounced peak around Θ = 90° or 45° for the higher vibrational states. This is so because the higher the vibrational energy the higher the energy transfer to translation and, therefore, the higher the number of accessible barrierless reaction paths. Similar results (not shown here) have been obtained for H2 (ν = 1,2, J = 0)/Pd/Ru(0001). Although this molecular reorientation mechanism is basically the same as for vibrationally excited molecules under slow normal incidence conditions [11], the striking finding here is its high efficiency at fast grazing incidence, despite the fast parallel motion. To further investigate the role of molecular reorientation on the nonmonotonic behavior discussed above, we have analyzed the behavior of rotationally excited molecules in a particular vibrational state. Fig. 4 shows 1 − reflectivity as a function of the normal energy for H2 (ν = 1, J = 0,1)/Cu/Ru(0001) (Fig. 4 A), H2 (ν = 3, J = 0,1,2)/Cu (111) (Fig. 4 B) and H2 (ν = 5, J = 0,2)/NiAl(110) (Fig. 4 C). In this figure it can be seen that the more rotational excitation the less nonmonotonic behavior of the 1 − reflectivity curve. At high enough rotational excitation the nonmonotonic behavior disappears. We attribute this behavior to the fact that the initial rotational motion helps the molecule to change its orientation along the trajectory, thus being more likely for the molecule to find a barrierless path for dissociation over the whole energy range. This hypothesis is confirmed by the initial angular distributions of the molecules that dissociate at energies corresponding to the minimum of the 1 −reflectivity curve observed for H2 (ν, J = 0) (see Fig. 4 D, E and F). One can see that the peaks around 90° or 45° are far wider (if not disappear) than those observed for H2 (ν, J = 0) (see Fig. 3). Although this behavior might, in principle, be attributed to the increase of the number of barrierless reaction paths due to an energy transfer from the rotational to the
Table 1 Vibrational distribution of reflected H2 molecules for the 4 systems investigated here. Pνf being the percentage of reflected molecules on the final vibrational state νf and En the normal incidence energy. In all the cases the initial rotational state is J = 0. System
En (eV)
Pνf = 0
Pνf = 1
Pνf = 2
Pνf = 3
H2 H2 H2 H2 H2 H2 H2 H2
0.4 0.1 0.4 0.12 0.6 0.2 0.4 0.05
28% 15% 52% 41% 31% 29% 18% 7%
27% 25% 36% 25% 24% 21% 19% 8%
33% 57% 22% 34% 17% 19% 17% 8%
10% 3%
1%
1%
13% 20% 12% 10%
10% 11% 15% 12%
5%
(ν = 2)/Pd/Ru(0001) (ν = 2)/Pd/Ru(0001) (ν = 2)/Cu/Ru(0001) (ν = 2)/Cu/Ru(0001) (ν = 3)/Cu(111) (ν = 3)/Cu(111) (ν = 5)/NiAl(110) (ν = 5)/NiAl(110)
Numbers in bold refer to vibrationally elastic reflection.
Pνf = 4
Pνf = 5
17% 55%
Pνf = 6
2%
D. Stradi et al. / Surface Science 604 (2010) 2031–2035
1
A H2(ν=1,J=0)/Cu/Ru(0001) B H2(ν=2,J=0)/Pd/Ru(0001) Initial
Initial
0.6
0.12 eV
1
Initial
Initial
0.1 eV
[101] Pd
D H2(ν=4,J=0)/Cu(111)
B H2(ν=3,J)/Cu(111)
E H2(ν=3,J=2)/Cu(111) Initial
0.8
0.4 eV
0.4 eV 0.2 eV
0.2 eV
1-Reflectivity
No. of molecules (arb. units)
0.2
0.04 eV
C H2(ν=3,J=0)/Cu(111)
Nor. J=0 Graz. J=0 Nor. J=1 Graz. J=1
0.4
0.12 eV 0.04 eV
Initial
0.8
0.4 eV
0.4 eV
A H2(ν=1,J)/Pd/Ru(0001) D H2(ν=1,J=1)/Pd/Ru(0001)
0.6 Nor. J=0 Graz. J=0 Nor. J=1 Graz. J=1 Nor. J=2 Nor. J=2
0.4 0.2 [101]
E
0.1 eV H2(ν=4,J=0)/NiAl(110)
0.1 eV
F H2(ν=5,J=0)/NiAl(110)
Cu
1
Initial
Initial
0.2 eV
C H2(ν=5,J)/NiAl(110)
F H2(ν=5,J=2)/NiAl(110) Initial
0.8
0.4 eV
0.4 eV
0.6
Nor. J=0 Graz. J=0 Nor. J=2 Graz. J=2
0.05 eV 0.02 eV
0.4
0.01 eV
45
90
135
0 45 Θ (deg.)
90
0.05 eV
[001]
0.01 eV
Al Ni
0.2
0
No. of molecules (arb. units)
2034
135 0
0.2
0.4
0.6
0.8
Normal energy (eV) Fig. 3. Initial molecular angular distribution for 1 − reflectivity: (A) H2 (ν = 1,J = 0)/Cu/ Ru(0001); (B) H2 (v = 2,J = 0)/Cu/Ru(0001); (C) H2 (ν = 3,J = 0)/Cu(111); (D) H2 (ν = 4,J = 0)/Cu(111); (E) H2 (ν = 4, J = 0)/NiAl(110); (F) H2 (ν = 5, J = 0)/NiAl(110). Black curves: initial angular distribution of the total ensemble of molecules; blue, green and red curves: initial angular distribution of the molecules that end up in dissociation, for several normal incidence energies, En, including the energy at which the minimum for the 1 − reflectivity probability is reached (green curves).
translational motion, this should be discarded for low J values, because the available rotational energies for J = 1 and J = 2 are only 14 and 42 meV, respectively. In contrast, such an energy transfer from rotation to translation might play a major role, opening reaction channels, for highly rotationally excited molecules (J N 5). Therefore, for highly rotationally excited molecules, in addition to a monotonic behavior, an overall increase of the 1 − reflectivity probability is expected. Finally, it is worth pointing out that the J value at which the nonmonotonic behavior for the 1 − reflectivity curve disappears is higher for the higher vibrational states. This means that the vibrational motion quenches somehow the effect of the rotational motion on molecular dissociation, i.e., on the 1 − reflectivity probability. 4. Conclusions We have used quasi-classical dynamics, based on six-dimensional DFT (density functional theory) potential energy surfaces (PESs), to analyze the behavior of vibrationally excited molecules scattered from metal surfaces under fast grazing incidence conditions. Our results
0
45
90
Θ (deg.)
135
180
Fig. 4. Left panels: 1 − reflectivity as a function of the normal incidence energy for H2 (ν = 1, J = 0,1)/Pd/Ru(0001) (A), H2 (ν = 3, J = 0,1,2)/Cu(111) (B) and H2 (ν = 5, J = 0,2/NiAl(110) (C). Right panels: initial molecular angular distribution for 1 − reflectivity for H2 (ν = 1, J = 1)/Pd/Ru(0001) (D), H2/(ν = 3, J = 2)/Cu(111) (E) and H2 (ν = 5, J = 2)/NiAl(110) (F). Black curves: initial angular distribution of the total ensemble of molecules; green curves: initial angular distribution of the molecules that end up in dissociation, for the normal incidence energies, En, at which the minimum of the 1 − reflectivity probability is reached.
show that the nonmonotonic behavior of dissociative adsorption (1 − reflectivity) as a function of the normal incidence energy previously found for vibrationally excited H2 molecules at low normal incidence energy (b1.0 eV) is also observed at fast grazing incidence. As in the case of slow normal incidence, the nonmonotonic behavior is due to molecular reorientation, in spite of the fast parallel motion of the molecule. This finding strongly supports the idea that, for activated systems, the interaction between a H2 molecule and a metal surface under fast grazing incidence conditions is mainly governed by the motion of the molecule perpendicular to the surface. Finally we remark that, although present experimental setups do not allow one to perform scattering of state-resolved H2 molecules under fast grazing incidence conditions, we expect that a new generation of experimental devices, combining a molecular fast grazing incidence scattering stage with an appropriate state-resolved H2 selection stage (using, for instance, pulsed narrow bandwidth laser Raman excitation [27]), will be useful to test the predictions reported in this manuscript.
D. Stradi et al. / Surface Science 604 (2010) 2031–2035
Acknowledgements We thank the Red Española de Supercomputatión (BSC-RES) and CCC-UAM (Spain) for allocation of computer time. This work has been financially supported by the DGI through projects FIS2007-60064 and CSD 2007-00010, and the CAM project S2009/MAT1726. References [1] A. Schüller, S. Wethekam, H. Winter, Phys. Rev. Lett. 98 (2007) 016103-1. [2] P. Rousseau, K. Khemliche, A.G. Borisov, P. Roncin, Phys. Rev. Lett. 98 (2007) 016104-1. [3] A. Schüller, H. Winter, Phys. Rev. Lett. 100 (2008) 097602-1. [4] N. Bundaleski, H. Khemliche, P. Soulisse, P. Roncin, Phys. Rev. Lett. 101 (2008) 177601. [5] A. Schüller, M. Busch, S. Wethekam, H. Winter, Phys. Rev. Lett. 102 (2009) 017602-1. [6] M. Busch, A. Schüller, S. Wethekam, H. Winter, Surf. Sci. 603 (2009) L23. [7] F. Aigner, N. Simonović, B. Solleder, L. Wirtz, J. Burgdörfer, Phys. Rev. Lett. 101 (2008) 253201. [8] M.S. Gravielle, J.E. Miraglia, Phys. Rev. A 78 (2008) 022901. [9] D. Farías, C. Díaz, P. Nieto, A. Salin, F. Martín, Chem. Phys. Lett. 390 (2004) 250.
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[10] C. Díaz, P. Rivière, F. Martín, Phys. Rev. Lett. 103 (2009) 013201. [11] G. Laurent, C. Díaz, H.F. Busnengo, F. Martín, Phys. Rev. B 81 (2010) 161404. [12] H.A. Michelsen, C.T. Rettner, D.J. Auerbach, in: R.J. Madix (Ed.), Springer Series in Surface Science, Vol. 34, Springer-Verlag, 1994arXiv. [13] D. Farías, K.H. Rieder, Rep. Prog. Phys. 61 (1998) 1575. [14] G.J. Kroes, Prog. Surf. Sci. 60 (1999) 1. [15] H.F. Busnengo, A. Salin, W. Dong, J. Chem. Phys. 112 (2000) 7641. [16] P. Nieto, E. Pijper, D. Barredo, G. Laurent, R.A. Olsen, E.J. Baerends, G.J. Kroes, D. Farías, Science 312 (2006) 86. [17] C. Díaz, E. Pijper, R.A. Olsen, H.F. Busnengo, D.J. Auerbach, G.J. Kroes, Science 326 (2009) 832. [18] P. Rivière, H.F. Busnengo, F. Martín, J. Chem. Phys. 121 (2004) 751. [19] G. Laurent, Martín, H.F. Busnengo, Phys. Chem. Chem. Phys. 11 (2009) 7303. [20] C. Díaz, R.A. Olsen, H.F. Busnengo, G.J. Kroes, J. Phys. Chem. C. 114 (2010) 11192. [21] M. Karplus, R.N. Porter, R.D. Sharma, J. Chem. Phys. 43 (1965) 3259. [22] G.J. Kroes, M.F. Somers, J. Theor. Comp. Chem. 4 (2005) 493. [23] D. Farías, C. Díaz, P. Rivière, H.F. Busnengo, P. Nieto, M.F. Somers, G.J. Kroes, A. Salin, F. Martín, Phys. Rev. Lett. 93 (2004) 246104. [24] C. Díaz, R.A. Olsen, D.J. Auerbach, G.J. Kroes, Phys. Chem. Chem. Phys. 12 (2010) 6499. [25] P. Rivière, H.F. Busnengo, F. Martín, J. Chem. Phys. 123 (2005) 074705. [26] P. Rivière, M.F. Somers, G.J. Kroes, F. Martín, Phys. Rev. B 73 (2006) 205417. [27] P. Maroni, D. Papageorgopoulos, A. Ruf, R.D. Beck, T.R. Rizzo, Rev. Sci. Instrum. 77 (2006) 054103.
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Grazing incidence scattering of vibrationally excited H2 molecules from metal surfaces D. Stradi a,b, C. Díaz a,⁎, F. Martín a,b a b
Departamento de Química Módulo 13, Universidad Autónoma de Madrid, 28049 Madrid, Spain Instituto Madrileño de Estudios Avanzados en Nanociencias (IMDEA-nanociencia), Cantoblanco 28049 Madrid, Spain
a r t i c l e
i n f o
Article history: Received 14 June 2010 Accepted 11 August 2010 Available online 19 August 2010 Keywords: Grazing incidence Quasi-classical dynamics Vibrationally excitation Reflectivity
a b s t r a c t We have studied the scattering of vibrationally excited H2 molecules from metal surfaces under fast grazing incidence conditions, by means of quasi-classical calculations based on six-dimensional potential energy surfaces. We show that, in spite of the fast parallel motion, the reorientation of the molecule along the trajectory plays a fundamental role on the scattering, being responsible for the nonmonotonic behavior observed as a function of the normal incidence energy, similar to that observed under slow normal incidence conditions. The present study has allowed us to further prove that the interaction between a H2 molecule and an ordered metal surface under fast grazing incidence conditions is, in general, governed by the normal momentum of the molecule. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Diffraction of fast (E = 0.1–2 keV) atoms and molecules from surfaces under grazing (θ = 0.1°–4.0° — see Fig. 1) incidence conditions has been recently proposed as a very promising tool to determine surface properties with unprecedented accuracy [1–8]. The observation of diffraction under these extreme conditions is possible thanks to the strong decoupling between the fast motion parallel to the surface along the incidence direction and the slow motion perpendicular to the surface [9]. The interaction between the projectile and the surface under these conditions is governed by the perpendicular motion (perpendicular energy). The de Broglie wavelength associated to this perpendicular motion is of the order of the surface lattice constant, which explains why diffraction can be observed experimentally, despite the huge total momentum of the projectile. If the de Broglie wavelength were much smaller than the typical surface constant, most like the thermal displacement of surface atoms would introduce decoherence thus hiding diffraction. Recently [10] it has been shown, theoretically, that scattering of fast H2 molecules at grazing incidence could also be useful to determine sticking probabilities corresponding to thermal energies and normal incidence. In Ref. [10] it was shown that total molecular reflectivity probabilities, as a function of the normal energy, computed at fast grazing incidence reproduce for several systems, those in which dissociative adsorption at low normal incidence is a direct process, i.e., those approximately following normal energy scaling, the total
⁎ Corresponding author. E-mail address: [email protected] (C. Díaz). 0039-6028/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.susc.2010.08.017
molecular reflectivity probabilities obtained at slow normal incidence. At low incidence energies (up to ≈1 eV) molecular reflectivity and dissociative adsorption are almost complementary, i. e., dissociative adsorption is equal to 1 − reflectivity. Thus, molecular reflectivity at fast grazing incidence can be used to estimate dissociative adsorption at slow normal incidence. This striking result, found for both activated (H2/NiAl(110)) and non-activated (H2/Pd(111)) systems, has been proved for H2 molecules in their rovibrational ground state [10]. For activated systems, it has been recently shown [11] that the dissociative adsorption probabilities of vibrationally excited molecules colliding with metal surfaces, at low energy and normal incidence, exhibits a nonmonotonic behavior as a function of the incidence energy (which is at variance with the monotonic behavior obtained for molecules on their rovibrational ground state [12]). Dissociative adsorption first decreases with the incidence energy until it reaches a minimum after which it increases with the incidence energy. The excited state ν at which the nonmonotonic behavior shows up depends on the system, but, in all cases, it is observed whenever the translational energy plus the fraction of the initial vibrational energy transferred to the reaction coordinate is higher than the minimum reaction barrier. This phenomenon has been attributed to an efficient (inefficient) reorientation of the molecule at low (medium and high) incidence energies. At low incidence energies (typically b0.1 eV) the molecules are very efficiently reoriented along their trajectories in such a way that the probability of finding one of the few barrierless reaction paths is very high and, consequently, the dissociation probability is high. When the energy increases the reorientation becomes less efficient, thus decreasing the dissociation probability. For high energies (typically N0.4 eV), although the reorientation is very inefficient, the increasing number of barrierless
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D. Stradi et al. / Surface Science 604 (2010) 2031–2035
Fig. 1. Schematic representation of a grazing incidence collision of H2 with a metal surface. The coordinate system used in the dynamics is also shown. The inset represents the six degrees of freedom of a diatomic molecule.
reaction paths ensures the enhancement of the dissociative adsorption probability. This phenomenon has been observed for three different kinds of activated systems [11], two pure surfaces, Pt(111) and Cu(110), one bimetallic alloy surface NiAl(110), and two bimetallic pseudomorphic surfaces Pd/Ru(0001) and Cu/Ru(0001). Here we investigate whether the dissociative adsorption nonmonotonic behavior, for vibrationally excited H2 molecules on metal surfaces, can also be observed under fast grazing incidence conditions, i.e., whether the reorientation mechanism is still active under fast grazing incidence conditions. To answer this question we have studied the scattering of vibrationally excited H2 molecules from several metal surfaces under fast grazing incidence conditions. Specifically, we have studied four activated systems: H2/Pd/Ru(0001), H2/Cu/Ru(0001), H2/ Cu(111) and H2/NiAl(110), for which a nonmonotonic behavior of the dissociative adsorption probability has been observed for vibrationally excited H2 at low normal incidence energy. This paper is organized as follows. In Section 2 we describe briefly the methodology employed. Results on scattering as well as their discussion are presented in Section 3. We summarize the main conclusions in Section 4.
[19] for H2/Pd/Ru(0001) and H2/Cu/Ru(0001), and in Ref. [20] for H2/ Cu(111). In performing the dynamics calculations we have used the socalled quasi-classical trajectory (QCT) method [21], in which the zero point energy (ZPE) of the molecule is included in the calculation. Our choice of the QCT method is based on previous studies comparing quantum and quasi-classical methods, which show that the QCT method can successfully describe diatomic molecule/metal surface processes such as dissociative adsorption [22] and even diffraction [23]. The QCT method is a useful tool to perform this kind of studies, not only because is computationally cheap, but also because it allows one to follow the molecule through the Cartesian and the momentum space. In our dynamic study under fast grazing incidence conditions we have fixed the total incidence energy to 400 eV, and to cover the whole normal incidence energy range [0.05 eV–0.8 eV] the incidence angle, θ (see Fig. 1), has been varied from 0.64° to 2.56°. The molecule is considered to be reflected whenever the distance molecule-surface, Z, becomes equal to initial distance, Zi, with the molecule's velocity vector pointing towards the vacuum and the atomic distance H–H being smaller than 2.25 Å. In order to ensure low statistical errors for each translational energy and rovibrational state, we have considered around 104 trajectories. 3. Results We have studied scattering under fast grazing incidence for four selected systems that have been widely studied previously under normal incidence and thermal energy conditions: H2/Cu/Ru(0001) and H2/Pd/Ru(0001) [19], H2/Cu(111) [17,24], and H2/NiAl(110) [25,26]. For the first two systems, the nonmonotonic behavior for dissociative adsorption (1 − reflectivity) at slow normal incidence is already observed for the lowest vibrational excited state ν = 1, whereas for the other two systems it is found at higher ν values [11]. We show below that the same pattern is reproduced at fast grazing incidence. In Fig. 2 we have plotted 1 − reflectivity (which corresponds to dissociative adsorption at slow normal incidence) as a function of the normal energy, for H2 (ν = 1,2, J = 0)/Cu/Ru(0001), H2 (ν = 1,2, J = 0)/Pd/Ru(0001), H2 (ν = 4,5, J = 0)/NiAl(110), and H2
2. Theory
1 0.8
A H2(ν,J=0)/Cu/Ru(0001) B H2(ν,J=0)/Pd/Ru(0001) v=2
v=2 Graz. Nor.
0.6
Graz. Nor.
0.4
1-Reflectivity
To carry out our molecule/surface study we have worked within the Born–Oppenheiner Static Surface (BO–SS) approximation, i.e., neither electron–hole pair excitation processes nor the motion of the surface atoms is taken into account. Surface phonons induce decoherence, and can influence the intensity of the diffraction peaks [7,13], but they are not expected to modify significantly the total reflectivity [14]. The BO approximation could be considered too restrictive taking into account the high energy of the projectile, but recent experiments showing diffraction of fast grazing He atoms from metal surfaces [4,5] prove that the role of electronic excitations is not as dramatic as could be expected, and, therefore, that the BO approximation can be safely used. In our study we have included the six degrees of freedom (DOFs) of the molecule (see inset Fig. 1). Thus, we have carried out six-dimensional (6D) dynamics calculations based on 6D potential energy surfaces (PESs). The 6D PESs used in the present work to describe the electronic interaction between a H2 molecule and a surface were developed previously to study molecule/surface interactions at low collision energy (b2 eV). In all cases, the PESs were obtained by applying the corrugation reducing procedure [15] to a set of DFT (density functional theory) data. This state-of-the-art interpolation method has been proved to yield very accurate PESs, and have been used to study H2/metal dynamic interactions (see, for example, [16,17]). Details of the PESs can be found in Ref. [18] for H2/NiAl(110), in Ref.
0.2 0 1 0.8
v=1 [101] Cu
Pd
C H2(ν,J=0)/NiAl(110)
D H2(ν,J=0)/Cu(111)
v=5
v=4
0.6
Graz. Nor.
Graz. Nor.
0.4 0.2 0 0
[101]
v=1
0.2
v=3
[001]
v=4
[101] Al Ni
0.4
0.6
0.8
0
Cu
0.2
0.4
0.6
0.8
1
Normal energy (eV) Fig. 2. 1 − reflectivity as a function of the normal incidence energy for: (A) H2 (ν = 1,2, J = 0)/Cu/Ru(0001); (B) H2 (ν = 1,2, J = 0)/Pd/Ru(0001); (C) H2 (ν = 4,5, J = 0)/NiAl (110); (D) H2 (ν = 3,4, J = 0)/Cu(111). Both slow normal and fast grazing incidence results are shown.
D. Stradi et al. / Surface Science 604 (2010) 2031–2035
(ν = 3,4, J = 0/Cu(111)), under both slow normal and fast grazing incidence conditions. In this latter case we have considered that the molecules collide with the surface along well defined crystallographic directions (shown in the insets of Fig. 2), i.e., we consider that the collision proceeds in channeling regime. From this figure we can see that fast grazing incidence scattering results reproduce the nonmonotonic behavior found at slow normal incidence. Specifically, for each system and each rovibrational state (ν, J = 0), the 1 − reflectivity minimum for both slow normal and fast grazing incidence is located at approximately the same normal energy value. One can see that, for H2 (ν, J = 0)/Pd/Ru(0001) and H2 (ν, J = 0)/Cu/Pd(0001), the resemblance between slow normal and fast grazing incidence probabilities is larger for the lower ν values, i.e., it is larger for ν = 1 than for ν = 2, whereas, for H2 (ν, J = 0)/NiAl(110) and H2 (ν, J = 0)/Cu(111), the resemblance is larger for the higher ν values, i.e., it is better for ν = 3 and ν = 4 than for ν = 4 and ν = 5, respectively. At this point we should point out that the ν value at which the nonmonotonic behavior is observed depends on both the minimum reaction barrier height and the efficiency of the energy transfer from the vibrational motion to the reaction coordinate (which is more efficient for late barrier systems than for early barrier systems). These are the reasons why the nonmonotonic behavior is observed for lower ν values in the case of H2/Cu/Ru(0001) and H2/Pd/Ru(0001) (late barrier systems with low minimum reaction barriers) than in the case of H2/NiAl(110) and H2/ Cu(111). Nevertheless it can be observed (Fig. 2) that the nonmonotonic behavior of the 1 − reflectivity curve is less pronounced as ν increases, because when ν increases the 1 − reflectivity probability tends to the saturation value over the whole normal energy range. To ensure that the results discussed above are not affected by reflected molecules moving through the region of the configuration space where the PESs are not appropriately described by our spin unpolarized DFT calculations, i.e., the regions where both H–H and molecule-surface distances are large, we have analyzed the vibrational distribution of the reflected molecules under the incidence conditions considered in Fig. 2. From Table 1 we can see that vibrational excitation (large H–H distance) is negligible. On the contrary, vibrational de-excitation (small H–H distances) is substantial, higher at high normal incidence energies. We analyze now that the nonmonotonic behavior of the 1 − reflectivity probability found at fast grazing incidence has the same origin as the nonmonotonic behavior found for dissociative adsorption at thermal normal incidence. At low normal incidence energies, the nonmonotonic behavior has been shown to be due to molecular reorientation along the trajectory [11]. Here, we have analyzed the orientation of the molecules along their trajectories at fast grazing incidence. In Fig. 3 we have plotted the distribution of the initial orientation (Θ — see Fig. 1) of the molecules whose trajectories end up in dissociation, i.e., whose trajectories do not end up in scattering, for H2 (ν = 1,2, J = 0)/Cu/Ru(0001) and H2 (ν = 3,4, J = 0)/Cu(111). From this figure, it can be seen that, at low normal incidence energies (energies below the 1 − reflectivity minimum — see Fig. 2), the Θ angular distributions are rather broad, in some cases (see Fig. 3 B) very similar to
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the initial angular distribution of the whole ensemble of molecules. Since at such low energies there are few accessible reaction paths, the behavior observed in Fig. 3 can only be attributed to a very efficient reorientation of the molecules, which allows them to find the few accessible reaction paths. Molecular reorientation becomes less efficient when the normal incidence energy increases. This effect can be straightforwardly inferred from the angular distributions shown in Fig. 3, corresponding to the incidence energies at which the minimum of the 1 − reflectivity curves is observed (see Fig. 2). These angular distributions are far narrower than those corresponding to low and high normal incidence energies, which means that only molecules with an initially appropriate orientation can dissociate. In the case of Cu(111), Pd/Ru(0001) and Cu/Ru(0001) the angular distribution at the 1 − R minimum clearly peaks around Θ = 90°, while for NiAl(110) it peaks around Θ = 45°. In this latter case, the lack of molecular reorientation at the minimum is less pronounced, which is consistent with the fact that the nonmonotonic behavior of the 1 − reflectivity curve is also less pronounced, as shown in Fig. 2. When the normal energy further increases, the number of accessible reaction paths becomes so large that the number of molecular orientations leading to dissociation necessarily increases. From Fig. 3 it can be also observed that the higher the vibrational state the less crucial the reorientation of the molecule: the Θdistribution at the minimum of the 1 − reflectivity curve exhibits a less pronounced peak around Θ = 90° or 45° for the higher vibrational states. This is so because the higher the vibrational energy the higher the energy transfer to translation and, therefore, the higher the number of accessible barrierless reaction paths. Similar results (not shown here) have been obtained for H2 (ν = 1,2, J = 0)/Pd/Ru(0001). Although this molecular reorientation mechanism is basically the same as for vibrationally excited molecules under slow normal incidence conditions [11], the striking finding here is its high efficiency at fast grazing incidence, despite the fast parallel motion. To further investigate the role of molecular reorientation on the nonmonotonic behavior discussed above, we have analyzed the behavior of rotationally excited molecules in a particular vibrational state. Fig. 4 shows 1 − reflectivity as a function of the normal energy for H2 (ν = 1, J = 0,1)/Cu/Ru(0001) (Fig. 4 A), H2 (ν = 3, J = 0,1,2)/Cu (111) (Fig. 4 B) and H2 (ν = 5, J = 0,2)/NiAl(110) (Fig. 4 C). In this figure it can be seen that the more rotational excitation the less nonmonotonic behavior of the 1 − reflectivity curve. At high enough rotational excitation the nonmonotonic behavior disappears. We attribute this behavior to the fact that the initial rotational motion helps the molecule to change its orientation along the trajectory, thus being more likely for the molecule to find a barrierless path for dissociation over the whole energy range. This hypothesis is confirmed by the initial angular distributions of the molecules that dissociate at energies corresponding to the minimum of the 1 −reflectivity curve observed for H2 (ν, J = 0) (see Fig. 4 D, E and F). One can see that the peaks around 90° or 45° are far wider (if not disappear) than those observed for H2 (ν, J = 0) (see Fig. 3). Although this behavior might, in principle, be attributed to the increase of the number of barrierless reaction paths due to an energy transfer from the rotational to the
Table 1 Vibrational distribution of reflected H2 molecules for the 4 systems investigated here. Pνf being the percentage of reflected molecules on the final vibrational state νf and En the normal incidence energy. In all the cases the initial rotational state is J = 0. System
En (eV)
Pνf = 0
Pνf = 1
Pνf = 2
Pνf = 3
H2 H2 H2 H2 H2 H2 H2 H2
0.4 0.1 0.4 0.12 0.6 0.2 0.4 0.05
28% 15% 52% 41% 31% 29% 18% 7%
27% 25% 36% 25% 24% 21% 19% 8%
33% 57% 22% 34% 17% 19% 17% 8%
10% 3%
1%
1%
13% 20% 12% 10%
10% 11% 15% 12%
5%
(ν = 2)/Pd/Ru(0001) (ν = 2)/Pd/Ru(0001) (ν = 2)/Cu/Ru(0001) (ν = 2)/Cu/Ru(0001) (ν = 3)/Cu(111) (ν = 3)/Cu(111) (ν = 5)/NiAl(110) (ν = 5)/NiAl(110)
Numbers in bold refer to vibrationally elastic reflection.
Pνf = 4
Pνf = 5
17% 55%
Pνf = 6
2%
D. Stradi et al. / Surface Science 604 (2010) 2031–2035
1
A H2(ν=1,J=0)/Cu/Ru(0001) B H2(ν=2,J=0)/Pd/Ru(0001) Initial
Initial
0.6
0.12 eV
1
Initial
Initial
0.1 eV
[101] Pd
D H2(ν=4,J=0)/Cu(111)
B H2(ν=3,J)/Cu(111)
E H2(ν=3,J=2)/Cu(111) Initial
0.8
0.4 eV
0.4 eV 0.2 eV
0.2 eV
1-Reflectivity
No. of molecules (arb. units)
0.2
0.04 eV
C H2(ν=3,J=0)/Cu(111)
Nor. J=0 Graz. J=0 Nor. J=1 Graz. J=1
0.4
0.12 eV 0.04 eV
Initial
0.8
0.4 eV
0.4 eV
A H2(ν=1,J)/Pd/Ru(0001) D H2(ν=1,J=1)/Pd/Ru(0001)
0.6 Nor. J=0 Graz. J=0 Nor. J=1 Graz. J=1 Nor. J=2 Nor. J=2
0.4 0.2 [101]
E
0.1 eV H2(ν=4,J=0)/NiAl(110)
0.1 eV
F H2(ν=5,J=0)/NiAl(110)
Cu
1
Initial
Initial
0.2 eV
C H2(ν=5,J)/NiAl(110)
F H2(ν=5,J=2)/NiAl(110) Initial
0.8
0.4 eV
0.4 eV
0.6
Nor. J=0 Graz. J=0 Nor. J=2 Graz. J=2
0.05 eV 0.02 eV
0.4
0.01 eV
45
90
135
0 45 Θ (deg.)
90
0.05 eV
[001]
0.01 eV
Al Ni
0.2
0
No. of molecules (arb. units)
2034
135 0
0.2
0.4
0.6
0.8
Normal energy (eV) Fig. 3. Initial molecular angular distribution for 1 − reflectivity: (A) H2 (ν = 1,J = 0)/Cu/ Ru(0001); (B) H2 (v = 2,J = 0)/Cu/Ru(0001); (C) H2 (ν = 3,J = 0)/Cu(111); (D) H2 (ν = 4,J = 0)/Cu(111); (E) H2 (ν = 4, J = 0)/NiAl(110); (F) H2 (ν = 5, J = 0)/NiAl(110). Black curves: initial angular distribution of the total ensemble of molecules; blue, green and red curves: initial angular distribution of the molecules that end up in dissociation, for several normal incidence energies, En, including the energy at which the minimum for the 1 − reflectivity probability is reached (green curves).
translational motion, this should be discarded for low J values, because the available rotational energies for J = 1 and J = 2 are only 14 and 42 meV, respectively. In contrast, such an energy transfer from rotation to translation might play a major role, opening reaction channels, for highly rotationally excited molecules (J N 5). Therefore, for highly rotationally excited molecules, in addition to a monotonic behavior, an overall increase of the 1 − reflectivity probability is expected. Finally, it is worth pointing out that the J value at which the nonmonotonic behavior for the 1 − reflectivity curve disappears is higher for the higher vibrational states. This means that the vibrational motion quenches somehow the effect of the rotational motion on molecular dissociation, i.e., on the 1 − reflectivity probability. 4. Conclusions We have used quasi-classical dynamics, based on six-dimensional DFT (density functional theory) potential energy surfaces (PESs), to analyze the behavior of vibrationally excited molecules scattered from metal surfaces under fast grazing incidence conditions. Our results
0
45
90
Θ (deg.)
135
180
Fig. 4. Left panels: 1 − reflectivity as a function of the normal incidence energy for H2 (ν = 1, J = 0,1)/Pd/Ru(0001) (A), H2 (ν = 3, J = 0,1,2)/Cu(111) (B) and H2 (ν = 5, J = 0,2/NiAl(110) (C). Right panels: initial molecular angular distribution for 1 − reflectivity for H2 (ν = 1, J = 1)/Pd/Ru(0001) (D), H2/(ν = 3, J = 2)/Cu(111) (E) and H2 (ν = 5, J = 2)/NiAl(110) (F). Black curves: initial angular distribution of the total ensemble of molecules; green curves: initial angular distribution of the molecules that end up in dissociation, for the normal incidence energies, En, at which the minimum of the 1 − reflectivity probability is reached.
show that the nonmonotonic behavior of dissociative adsorption (1 − reflectivity) as a function of the normal incidence energy previously found for vibrationally excited H2 molecules at low normal incidence energy (b1.0 eV) is also observed at fast grazing incidence. As in the case of slow normal incidence, the nonmonotonic behavior is due to molecular reorientation, in spite of the fast parallel motion of the molecule. This finding strongly supports the idea that, for activated systems, the interaction between a H2 molecule and a metal surface under fast grazing incidence conditions is mainly governed by the motion of the molecule perpendicular to the surface. Finally we remark that, although present experimental setups do not allow one to perform scattering of state-resolved H2 molecules under fast grazing incidence conditions, we expect that a new generation of experimental devices, combining a molecular fast grazing incidence scattering stage with an appropriate state-resolved H2 selection stage (using, for instance, pulsed narrow bandwidth laser Raman excitation [27]), will be useful to test the predictions reported in this manuscript.
D. Stradi et al. / Surface Science 604 (2010) 2031–2035
Acknowledgements We thank the Red Española de Supercomputatión (BSC-RES) and CCC-UAM (Spain) for allocation of computer time. This work has been financially supported by the DGI through projects FIS2007-60064 and CSD 2007-00010, and the CAM project S2009/MAT1726. References [1] A. Schüller, S. Wethekam, H. Winter, Phys. Rev. Lett. 98 (2007) 016103-1. [2] P. Rousseau, K. Khemliche, A.G. Borisov, P. Roncin, Phys. Rev. Lett. 98 (2007) 016104-1. [3] A. Schüller, H. Winter, Phys. Rev. Lett. 100 (2008) 097602-1. [4] N. Bundaleski, H. Khemliche, P. Soulisse, P. Roncin, Phys. Rev. Lett. 101 (2008) 177601. [5] A. Schüller, M. Busch, S. Wethekam, H. Winter, Phys. Rev. Lett. 102 (2009) 017602-1. [6] M. Busch, A. Schüller, S. Wethekam, H. Winter, Surf. Sci. 603 (2009) L23. [7] F. Aigner, N. Simonović, B. Solleder, L. Wirtz, J. Burgdörfer, Phys. Rev. Lett. 101 (2008) 253201. [8] M.S. Gravielle, J.E. Miraglia, Phys. Rev. A 78 (2008) 022901. [9] D. Farías, C. Díaz, P. Nieto, A. Salin, F. Martín, Chem. Phys. Lett. 390 (2004) 250.
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