Adsorption sites and migration of a carbon monoxide molecule on stepped vicinal surfaces of Cu(211) and Cu(511)

Surface Science 415 (1998) 131–147

Adsorption sites and migration of a carbon monoxide molecule on stepped vicinal surfaces of Cu(211) and Cu(511) Herve´ Le Rouzo, Pascal Parneix, Georges Ras¸eev *, Konstantin S. Smirnov 1 Laboratoire de Photophysique Mole´culaire du CNRS, Baˆt. 213, Universite´ Paris-Sud, 91405 Orsay, Cedex, France Received 3 April 1998; accepted for publication 22 June 1998

Abstract Motivated by recent scanning tunneling microscopy (STM ) and helium-atom scattering experiments, the adsorption of a carbon monoxide molecule on Cu(211) and Cu(511) stepped vicinal surfaces is studied by analyzing the interaction potential and performing classical dynamics simulations both in the canonical and microcanonical ensembles. For both (211) and (511) surfaces we found two adsorption sites, nearly equivalent energetically, located nearly on top above the border-row atoms of a terrace. These sites, favored by a large available phase space, have the highest adsorption probability in agreement with STM results on the CO/Cu(211) system. At low temperatures hindered translation of CO is anisotropic along the different crystallographic directions. For both surfaces, the migration is favored along rows but there are significant differences between Cu(211) and Cu(511). © 1998 Elsevier Science B.V. All rights reserved. Keywords: Adsorption sites of molecules; Carbon monoxide; Computer simulations; Copper; Single-crystal stepped or vicinal surfaces

1. Introduction High crystallographic indices, vicinal or surfaces with steps, as well as surfaces with defects, play an important catalytic role in reactions taking place at gas/solid interfaces. The process responsible for reactivity can be related to adsorption site, surface roughness, reconstruction of the surface before or at adsorption, low or high coverage and coadsorption (see, e.g., Somorjai [1,2]). It can also be related to electron dynamics (charge transfer and excitation of hot electrons [3,4]) or to particularly anharmonic vibrational motion [5], coupling * Corresponding author. Fax: +33-1-6915-6777; E-mail: [email protected] 1 Permanent address: Institute of Physics, St. Petersburg State University, St. Petersburg 198904, Russia.

between the vibrational modes and migration on the surface. It has specifically been demonstrated [1] that several chemical reactions, like dissociation of H molecules or H /D exchange, have a larger 2 2 2 reaction yield when performed on vicinal Pt(332) than on defect-free flat Pt(111) surfaces. Recently, two experimental investigations were reported concerning carbon monoxide (CO) adsorbed on stepped vicinal Cu(211) and Cu(511) surfaces. These studies made use of the scanning tunneling microscopy (STM ) [6 ] (for the CO/Cu(211) system only) and helium-atom scattering (HAS ) [7] experimental techniques. By using a copper atom as a marker for the position of CO adsorbed on a Cu(211) surface, the first study showed that the molecule is adsorbed on a border row of a terrace, probably on top of a copper atom. The HAS experiment mainly studied

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the hindered translation motion of CO on both Cu(211) and Cu(511) stepped vicinal surfaces at 120 K. The results showed no anisotropy of these vibrational modes in different crystallographic directions. The same vibrational modes were also studied by electron-stimulated desorption/ionangular distribution ( ESDIAD) for CO on Cu(110) surface at 32 K and low (0.02 monolayers (ML)) [8,9] and high (0.5 ML) coverages [10]. Probably because of the low temperature, an anisotropy in hindered translation frequency was revealed for this last surface. With these different experimental techniques one can build a model of the adsorption and migration of CO on stepped vicinal surfaces, and this image is a starting point in studying adsorbate reactivity. CO on a copper surface is a system that has been extensively studied by theoretical methods, particularly within the cluster approach [11–15]. For the most involved calculations of CO on a Cu(100) surface, Bauschlicher [15] obtained a reasonable agreement with experimental values for the adsorption energy and vibrational frequencies. However, in this approach a single copper atom, corresponding to the on-top position, is treated very accurately whereas the other atoms are calculated in a relatively approximated way by using a pseudo-potential. Consequently, only the local environment of the surface can be reproduced accurately. A dynamic study necessitates a large number of surface atoms and an analytical representation of the interactions. Therefore cluster modeling of the surface is of limited use for studying the dynamics on the present stepped vicinal surfaces, which have several adsorption sites that are close in energy. Other methods have modeled the diffusion of constituent atoms and the growth of clean, metallic, vicinal surfaces and surfaces with steps, kinks or defects. These studies either used static methods to calculate the total electronic energy and nuclear static properties [16–19] or combined them with classical dynamics where, in canonical ensemble, it is also possible to deduce the thermodynamic properties of the system [20–23]. One can mention early studies using the tight binding ( TB) method by Tersoff and Falicov [16 ] on Cu(111) and Ni(111) surfaces having steps and defects. These

authors determined that the distribution of delectrons of the metal is different at normal adsorption sites and at defects. If the elementary cell is not too large (e.g., for Ag(100)), a diffusion study based on the evaluation of total energy can be performed by using first-principles methods like density-functional theory [17]. Otherwise, manybody model potentials are still currently used [18– 23]. These phenomenological potentials are a sum of a nonlinear function of a local quantity characterizing the environment of an atom plus an atom–atom pair potential. For example, they can be used to find the diffusion barriers along a step and of exchange between diffusing and surface atoms. Inclusion of classical dynamics allows study of the surface and bulk properties of, for example, platinum and rhodium [20–22] metallic stepped surfaces, particularly the step roughening transition temperature. The corresponding transition is continuous and step meandering and kinks appear, for example, above 380 K for Cu(511). On vicinal copper, silver and Ni(119) surfaces [23] these combined methods permit the analysis of different diffusion mechanisms of atoms. Diffusion of CO on a flat Ni(111) surface was studied by Dubbs and Doren [24] by using model empirical potentials and a classical stochastic trajectory method. These authors calculated the diffusion coefficients and also showed that long jumps take place during diffusion. Static properties associated with the adsorption of argon, CO and CO on vicinal oxide surfaces of MgO(001) [25] 2 and discrete-row growth of xenon adsorbed on the vicinal Pt(997) surface [26,27] have also been modeled recently. For the first systems, the molecules are physisorbed and the behavior of the MgO ionic substrate is related to the electrical nature of the adsorbed molecule. Each adsorbate feels differently the local, possibly asymmetric, inhomogeneous environment at the surface step. For the second system it was shown that growth of the adsorbate layer starts at the step by the sequential attachment of xenon atoms. These recent theoretical studies show that adsorption takes place differently on flat and stepped surfaces. The data are in line with experimental studies on CO/vicinal Ni(100) surfaces that show different adsorption probabilities on steps and terraces [28]. Only

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Monte Carlo simulations have been performed on certain of the above-mentioned systems. In this paper we study the adsorption sites, lowfrequency vibrational modes and migration of a carbon monoxide molecule on stepped vicinal Cu(211) and Cu(511) surfaces by: (1) using the analysis of a potential-energy surface (PES) for sorbate molecules and (2) performing classical dynamics simulations. As discussed above, the phenomena related to the dynamics of the self atoms on flat and stepped metallic surfaces have largely been studied. However, treatment of the dynamics of molecular adsorbates on surfaces has been considered only recently. The choice of CO, one of the most commonly adsorbed molecular species studied, and of vicinal metallic surfaces (i.e., with steps) like copper is ideal for permitting simple modeling. The CO molecule does not dissociate on copper and its bond with the metal is relatively weak. The metal is known to have small fcc elementary cells and, for the present crystallographic cuts, reasonably large surface elementary cells. This permits simplification of the theoretical model. The weakness of the bond in this system corresponds to the requirements of a catalytic reaction. The present study is complementary to experimental work, particularly with STM, confirming in an unambiguous way the most probable adsorption site and the dynamic behavior of CO on Cu(211) and Cu(511) surfaces.

2. Model and results of the calculations Let us first present the geometrical structures of the stepped vicinal (211) and (511) surfaces, structures discussed in detail by Witte et al. [29] and Hofmann et al. [30]. In Figs. 1 and 2 we present two cuts of such surfaces (Figs. 1(a) and 2(a) parallel and Figs. 1(c) and 2(c) perpendicular to the surface plane). In these figures the geometrical structure is made with copper atoms represented ˚, as tangent spheres with radius 2−3/2a=1.276 A ˚ is the lattice constant. Note that where a=3.61 A in the rest of the paper we shall use either the crystallographic conventions or, more simply, the usual X, Y and Z notations indistinctly to denote the axes of coordinate systems. For Cu(211) and

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Cu(511) surfaces respectively, [01: 1] and [011: ] directions are called X, [1: 11] and [25: 5: ] directions are called Y, and [211] and [511] directions correspond to Z. Figs. 1(a) and 2(a) represent the surface from above looking along the Z axis. Figs. 1(c) and 2(c) are side views along the direction [011: ] or [01: 1], where we represent the plane formed by the directions [211] and [1: 11] or [511] and [25: 5: ] for (211) and (511) surfaces, respectively. More precisely, the Z direction is defined in Figs. 1(c) and 2(c) as the normal to the plane (referred to as Z=0) passing through the centers of the topmost atoms (white spheres). The Cu(211) and Cu(511) surfaces are formed by terraces of three rows of atoms separated by steps of single atom height. The Cu(211) surface is composed of terraces with the local hexagonal (111) symmetry separated by monoatomic steps with (100) orientation, whereas the Cu(511) surface has terraces with local square (100) symmetry and monoatomic steps with (111) orientation. The present study was performed with slabs of about 200 copper atoms having a depth of three ˚ in thickness. The copper atoms layers, about 7 A were located at their crystallographic equilibrium positions and no relaxation of the surface layers was permitted. For Cu(211) and Cu(511) crystal faces the elementary surface cells X×Y are found ˚ ×6.253 A ˚ ) and to be 2−1/2a×31/2a (=2.553 A ˚ ×6.632 A ˚ ), respect2−1/2a×(3/2)3/2a (=2.553 A ively. A single CO molecule was adsorbed above the copper surface, permitting simulations at low coverage. Figs. 1(c) and 2(c) also show a CO molecule in the on-top position above the terrace edge (on top of a copper atom and not exactly at a site position). Its carbon and oxygen atoms are represented as spheres with covalent radius of 0.77 and ˚ , reduced by a scaling factor of 0.8 to fit the 0.73 A ˚ ) of the adsorbed CO. This bond length (1.126 A pictorial representation shows that the carbon monoxide forms a prolate ellipsoid having diameter of its equatorial circle nearly two times smaller than the diameter of a copper atom. In Figs. 1(b) and 2(b) we present isopotential maps obtained with the atom–atom potential of Tully et al. [31], which will be discussed in detail below. We performed two types of simulation corre-

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Fig. 1. Top view, isopotential map and side view of the Cu(211) surface. The dashed line delimits the elementary cell. (a) Geometrical representation of the surface from above in the [011: ] and [1: 11] or X and Y plane, where Z=0 corresponds to the center of the topmost atoms. The deeper the row of atoms, the more darkly are they shaded. The adsorption sites are labeled A, B, C and D. (b) Iso-potential map of PES for surface–CO interaction starting at −0.57 eV spaced by 0.05 eV. (c) Side view in the Y and Z or [1: 11] and [211] plane for a cut corresponding to X or [01: 1] equal to zero. The surface steps and a single CO molecule located at the step edge are shown.

Fig. 2. Top view, isopotential map and side view of the Cu(511) surface. Same as the case in Fig. 1, where X, Y and Z are now [01: 1], [25: 5: ] and [511], respectively.

sponding to the experimental conditions of Meyer et al.’s [6 ] work by STM at very low coverage. First, we investigated the potential itself by displacing the carbon and oxygem atoms above the surface and searching for the position of the adsorption sites corresponding to the minimum of the PES. According to the rough surface–rigid

lattice model [1], no displacement of copper atoms was allowed. The analysis of the potential surface permits calculation of the vibrational frequencies in the harmonic approximation; i.e., by diagonalization of the matrix of the second derivatives of the potential energy at a local minimum. Note that, close to the surface, the molecular transla-

H. Le Rouzo et al. / Surface Science 415 (1998) 131–147

tional and rotational degrees of freedom are hindered and give rise to low-frequency vibrations. With the present rigid surface, no vibration of copper atoms and therefore neither surface nor bulk phonons were explicitly taken into account. Second, we performed classical molecular dynamics (MD) simulations for the same system consisting of one CO molecule adsorbed on the copper surfaces. The latter were modeled with the slabs described at the beginning of this section. During MD simulations, the internal C–O distance ˚ , which is the mean equilibwas frozen at 1.126 A rium value of the CO bond length obtained in potential-energy analysis. Therefore, the CO molecule had five degrees of freedom: three translational and two rotational, one less than in the potential analysis. Two types of classical simulation were performed, as described below. The first type of calculation using a simulated quenching procedure was employed for searching the energy minima of the PES. In this procedure a friction force is added, acting on atoms to cool the system down. This enables one to locate all local minima (corresponding to specific adsorption sites) in the PES. To generate different initial conditions for the quenching trajectories, a microcanonical trajectory was first created that corresponds to a high rotational and translational energy of the CO molecule. In the microcanonical calculation, the time evolution of the physical system in the phase space was simulated by integrating Hamilton’s classical mechanics equations with a fourth and fifth predictor–corrector algorithm, respectively, for rotation and translation. The quaternions’s formalism of Evans and Murad [32,33] was used to describe the CO rigid-body rotation. The time step used for numerical propagation was 0.2 fs and the corresponding total energy conservation was equal to about 0.001%. Consequently, the system could explore a large region in the phase space and all of the most probable sites could be found during the simulation. At a given energy 1000 quenching trajectories were generated, spaced by 5 ps. A characteristic duration of quenching trajectories to reach a local minimum in the PES was equal to 4 ps. As the cooling time is very short, statistics on the local minima in the PES reflects in fact the time spent by the molecule

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in the corresponding adsorption site during the microcanonical trajectory. At typical experimental conditions, adsorbate molecules interact with a large atomic system (the copper surface) which can be seen as a heat bath. Consequently the CO molecule can exchange energy with the surface. The most appropriate statistical ensemble to describe such a dynamics is obviously the canonical ensemble in which the fluctuations of energy are related to the temperature of the heat bath by the well-known Boltzmann law. Therefore, in order to simulate equilibrium properties of the CO molecule, we performed calculations in the canonical ensemble using the Nose´ algorithm [34]. In this method the physical system is coupled to a heat bath (reservoir) at a given temperature, T , via a fictitious degree bath of freedom. Note that this does not introduce any real vibrational motion (phonon bath) of the substrate atoms. Only an implicit coupling between the adsorbate and substrate degrees of freedom can occur through the additional external degree of freedom. This leads to the kinetic temperature, deduced from the mean kinetic energy along the trajectory, equal to the fixed temperature T . bath The strength of the coupling between the system and the heat bath is governed by a parameter Q, which affects the time evolution of the rovibrational energy of CO. The value of Q was chosen so that a characteristic period associated with the fluctuations of energy as a function of time was of the same order of magnitude as the vibrational period for the phonon modes (0–30 meV; see Witte et al. [29]). The equations of motion were integrated with a time step of 0.2 fs for 10 ns following an equilibration period equal to 10 ps. The initial conditions for the molecule were chosen randomly around the local minimum-energy configuration. We used an atom–atom potential optimized by Tully et al. [31] for a single CO molecule adsorbed on a flat Cu(100) surface. This potential reads V=∑ V (r , r , r )+V (|r −r |) i C O i CO C O i

(1)

where r , r and r denote the position vectors of C O i the carbon, oxygen and ith copper atoms, respectively. The first term in Eq. (1) represents the

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interaction of the CO molecule with the ith copper atom: V (r , r , r )=A exp(−a|r −r |) i C O i i O +B{exp(−2b|r −r |−r ) (2) i C e −2 cos2 g exp(−b|r −r |−r )} i i C e where g is the angle between the Cu C and CO i i vectors: (r −r ) (r −r ) (3) g= C i O C i |r −r ||r −r | C i O C and r is the equilibrium distance of CO. C The above potential equation ( Eq. (2)) includes a repulsive term for surface–oxygen atom interaction and a nearly Morse-type function for surface–carbon atom interaction. The additional angular dependence is modeled by a cosine function favoring the configuration where the carbon, oxygen and ith copper atoms are aligned. The second term in Eq. (1) is a gas-phase Morse function for the internal potential of the CO molecule: V (|r −r |)=F{exp[−2c(|r −r |−r )] CO C O C O CO −2 exp[−c(|r −r |−r )]}. (4) C O CO The values of the parameters can be found in the original paper by Tully et al. [31]. If one takes this potential and performs a vibrational analysis with a rigid Cu(100) surface, then one obtains a result that is close to the vibrational frequencies given by Tully et al. for the CO/Cu(100) system except for the CO–substrate vibrational mode, n . With a rigid surface this 2 vibration is computed as 310 cm−1 instead of 357 cm−1 given by Tully et al. Recently this potential has been used in a quantum-mechanical calculation of the vibrational frequencies of the CO/Cu(100) system [35,36 ] with a result of 349.3 cm−1 for the n vibration, a value which is 2 close to the frequency given by Tully et al. This discrepancy originates from the surface–rigid lattice model used in freezing the copper atoms. Indeed, a simple analysis in harmonic approximation shows that substitution of the CO mass (m ) by a reduced mass (m) of the CO–Cu triCO atomic system will result in a high-frequency shift

of the initially calculated n0 vibrational frequency 2 to the following value: n =n0 앀m /m#370 cm−1. 2 2 CO This rough estimation proves that the origin of the discrepancy is related directly to the model of the rigid copper surface assumed here and that the CO–Cu potential parameterized by Tully et al. [31] is compatible with the experimental data. An explicit calculation with a single moving copper atom in the substrate, first done by Bauschlicher [15] and then by other authors [35,37], confirms the above analysis. Except for this adsorbate–substrate frequency, the other vibrational modes were tested as follows. First we reproduced the observables of the CO/Cu(100) system presented in the papers by Tully et al. [31] and Park et al. [35] in the harmonic approximation. Then we obtained the experimental frequencies of CO on Cu(111) and compared them with the results of Ge et al. [38]. These two flat surfaces were chosen because they correspond to the terraces of the Cu(511) and Cu(211) surfaces, respectively. After testing the potential for flat surfaces, we calculated adsorption site positions, vibrational frequencies and adsorption energies for CO on Cu(211) and Cu(511) stepped surfaces. The atom– atom potential of Tully et al. [31] discussed above reproduces in a fair way the known experimental data on these vicinal surfaces. In Figs. 1(a), 2(a) and 3 we show the positions of the adsorption sites, labeled A, B, C and D. Note that the locations correspond to the vertical projection of the position of the carbon atom, not of the center of mass of the CO molecule. In Table 1 we give the precise location of the adsorption sites of the carbon atom of CO and in Table 2 the vibrational frequencies of the adsorbate. For these different sites, the desorption energy of the CO molecule, including or excluding its internal energy, is listed in Table 1. The isopotential maps (see Figs. 1(b) and 2(b)) and all the figures displaying a representation in the X×Y plane, together with the data in Table 3, correspond to the optimization of four degrees of freedom; i.e., fixing only X and Y coordinates of the carbon atom of the CO molecule.

H. Le Rouzo et al. / Surface Science 415 (1998) 131–147

Fig. 3. Three-dimensional representations of the potentialenergy surfaces presented in Fig. 1(b) and Fig. 2(b).

We analyze separately the first three adsorption sites A, B and C, whose energies are very close to one another, and site D. Site A, located on the middle row of a terrace, is energetically the most stable for both Cu(211) and Cu(511) surfaces. The sites B and C, very close geometrically and energetically to each other, are located on both sides of the on-top position on the border terrace row. The existence of these two sites is facilitated by the small size of the CO molecule compared with the copper atoms (see the beginning of this section). Using Table 1 one can compare the adsorption or binding energy on surfaces (211) and (511). One sees that the energy differences between the lowest three sites is smaller for the Cu(511) surface than for the Cu(211) one. The tridimensional representation of the potential for the Cu(211) and Cu(511) surfaces (Fig. 3) shows

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a flat potential between sites B and C on both surfaces. However, as can be seen from the isopotential curve corresponding to −0.57 eV around sites B and C (see Figs. 1(b) and 2(b)), these sites are actually separated by a small potential barrier. The relative barriers together with their absolute values, collected in Table 3, will help us to understand the behavior of the system during the classical dynamics simulations. Analysis of this table shows the following trends: $ on Cu(211) site B is favored and on Cu(511) both B and C sites are close in energy; $ the barriers between sites B and C on both surfaces are shallow; $ qualitatively from Fig. 3 and quantitatively from Table 3, the barriers between A and B and C sites are higher on the Cu(511) surface; $ the barrier in the X direction between replicas of similar adsorption sites is again higher for AA∞ and BB∞ on Cu(511). However, the reverse is true for CC∞ and DD∞ barriers; and $ finally, on both surfaces site D is the least stable and the internuclear distance of the CO molecule is larger at this site. Moreover, from Fig. 3, one can see that on both surfaces site D site is surrounded by large barriers. Undoubtedly the large available configuration space (see isopotential curve at −0.52 eV on Figs. 1(b) and 2(b)) is a common trend for sites B and C on these surface and will play a role in the MD calculation. The analysis of the potential minima and barriers presented above gives us only an idea of the position of the CO molecule near the potential minimum. When a molecule sticks on the surface, one can wonder about its orientation on the surface. For flat metallic surfaces, the experimental and theoretical (see Eq. (2) for the model potential above) answer is that the CO molecule is nearly normal to those surfaces. For stepped surfaces this question has no unique answer because of surface corrugation and the presence of several adsorption sites. In Fig. 4, the CO molecule is represented as an arrow that feels the local potential of the stepped surface. By using the optimization procedure in the XY plane discussed above, we obtain, for a single CO molecule, the position of carbon

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Table 1 Adsorption-site geometry of the CO molecule on vicinal copper surfaces. Binding energies in configuration spaces 6D and 5D (fixed ˚ ; internal energy about −11.1 eV ). Adsorption probability in 5D (see text for details) CO internuclear distance, R =1.126 A CO CO on Cu(211) Site

A B C D

CO geometrya

Energy

X C [01: 1]

Y C [1: 11]

Z C [211]

R

CO

h CO

Q

1.276 2.553 2.553 2.553

3.809 5.239 1.152 2.405

1.137 1.620 1.521 0.458

1.126 1.126 1.126 1.128

12.2 29.2 36.1 6.4

270 270 90 9

CO

Probability (%)

6D

5D

−11.6801 −11.6715 −11.6610 −11.5786

−0.59035 −0.58181 −0.57132 −0.48875

34 36 25 4

CO on Cu(511) Site

A B C D

CO geometrya

Energy

X C [011: ]

Y C [25: 5: ]

Z C [511]

R

CO

h CO

Q

1.276 1.276 2.553 1.276

3.873 5.797 1.244 2.058

1.189 1.718 1.447 0.539

1.126 1.126 1.126 1.128

9.9 24.3 39.2 13.0

270 270 90 90

CO

Probability (%)

6D

5D

−11.6690 −11.6641 −11.6650 −11.5797

−0.57928 −0.57440 −0.57530 −0.48986

34 31 31 4

˚ , angles are in degrees. aR , h and Q are the spherical coordinates of the CO axis. Lengths are in A CO CO CO Table 2 Vibrational frequencies (in cm−1) of a CO molecule adsorbed on vicinal copper surfaces. The CO internuclear distance is optimized (6D optimization) CO on Cu(211) Site

A B C D

CO internal

CO surface

CO hindered rotation

CO hindered translation

n 1

n 2

n (X ) 3

n∞ (Y ) 3

n (X ) 4

n∞ (Y ) 4

2178.5 2177.8 2179.2 2158.2

309.6 306.7 308.4 255.4

357.3 354.7 365.9 333.4

354.5 351.6 360.2 272.5

8.7 13.6 4.4 51.8

16.8 23.5 14.5 122.1

CO internal

CO surface

CO hindered rotation

n 1

n 2

n (X ) 3

n∞ (Y ) 3

n (X ) 4

n∞ (Y ) 4

2179.0 2178.7 2179.0 2158.3

309.0 307.5 308.7 255.5

361.8 360.8 364.1 333.4

359.4 358.4 358.1 272.7

4.9 5.3 5.3 52.1

13.8 19.1 19.3 121.4

CO on Cu(511) Site

A B C D

and oxygen atoms on an X×Y grid of points. The –A resulting C O vectors, represented as arrows (scaled by a factor of about 1/5) that feel the local

CO hindered translation

potential of the stepped surface, are displayed in Fig. 4. Inspection of this figure first shows that the position of the carbon atom (origin of the arrows)

H. Le Rouzo et al. / Surface Science 415 (1998) 131–147

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Table 3 Energetical barrier heights between the different adsorption sites. E corresponds to 5D optimization but the barriers max change only for the last digit when calculated in 6D. All energies are in eV CO on Cu(211) Paths

DE

E max

A–B −0.4527 B–C −0.5693 A–D −0.4055 C–D −0.3684 A–A∞ −0.4513 B–B∞ −0.4391 C–C∞ −0.4133 D–D∞ −0.3182 CO on Cu(511) Paths

E max

A–B B–C A–D C–D A–A∞ B–B∞ C–C∞ D–D∞

−0.4234 −0.5693 −0.3680 −0.4020 −0.4221 −0.4149 −0.4315 −0.3299

AB BC AD CD AA∞ BB∞ CC∞ DD∞

0.1376 0.0125 0.1848 0.2029 0.1390 0.1427 0.1580 0.1706

DE BA CB DA DC

DE AB BC AD CD AA∞ BB∞ CC∞ DD∞

0.1559 0.0051 0.2113 0.1732 0.1572 0.1595 0.1438 0.1600

0.1291 0.0020 0.0832 0.1203

DE BA CB DA DC

0.1510 0.0060 0.1219 0.0879

˚ from the topmost copper is located at about 2 A atoms. This set of points mimics the terraces and steps of the surface just below. As expected, the CO molecular axis is no longer normal to the (211) or (511) plane. To gain some more insight concerning the orientation of the CO axis, let us project it onto ZX and ZY planes. Let us consider first the projection onto the plane ZY corresponding to [211] and [1: 11] or [511] and [25: 5: ] for (211) or (511), respectively. This projection corresponds to the visualization in Figs. 1(c) and 2(c). The molecular axis is normal to the local surface plane that follows the terraces and steps and this is true for any ZY plane corresponding to a definite value of X. Now, for the projection of the internuclear axis in the ZX plane ([211] and [011: ] or [511] and [01: 1] directions for (211) or (511) surfaces, respectively), the angle is much closer to the normal to the surface. First, for the (211) surface, let us analyze the behavior of a ZX plane located at Y ˚ . The position of the internuclear axis of about 6 A changes continuously from a small positive to a

Fig. 4. Orientation of a single CO molecule adsorbed on Cu(211) and Cu(511) surfaces. For a grid in X ([011: ] or [01: 1]) and Y ([1: 11] or [25: 5: ]) of fixed coordinates of the carbon atom, the four other degrees of freedom of the CO molecule were determined by minimization of the PES. Z is the optimized height of the carbon atom. Arrows start at the carbon atom and indicate the orientation of CO. They mimic the copper ˚ below. The location of the adsorption sites surface located 2 A is not shown.

˚ , the molecule negative angle and, at about X=1 A has its closest position to the surface and is normal to it. Now for the CO/Cu(511) system the situation is inverted: the angle between the molecular axis and ZX plane is first negative and then positive ˚ , at the with the molecule being at about X=1 A largest distance from the surface. Therefore one finds that there is a small angle with the normal to the ZX plane that should follow the barrier heights between the replicas of adsorption sites along X. Consider now the analysis of frequencies in the harmonic approximation. For the three sites A, B and C, the optimized CO internuclear distance is nearly the same and the internal vibrational frequency (n ) close to the value obtained for the 1 flat Cu(100) surface (2179.3 cm−1). As discussed above, the CO–surface vibrational frequency (n ) 2

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is different from the one found by Tully et al. [31] or Park et al. [35]; the difference is due to the rough surface–rigid lattice model [1]. Except for the hindered translation, which is in fact the most sensitive to the corrugation of the surface, no particular experimental values of the vibrational frequencies for CO on Cu(211) and Cu(511) surfaces are reported in the literature. On flat surfaces the CO molecule is adsorbed in the on-top position and therefore one observes only four frequencies, since the hindered rotation or libration (n ) and 3 the hindered translation (n ) are doubly degener4 ated. On the stepped vicinal surfaces these frequencies are split out: the hindered rotation remains nearly degenerate (n and n∞ ), whereas the two 3 3 hindered translation frequencies (n and n∞ ) are 4 4 very different. Analyzing Table 2 for the three sites A, B and C, one sees that – except for hindered translation – the frequencies vary only slightly from site to site. For example, it will be difficult to distinguish the adsorption sites using the infrared spectrum of the internal vibration of CO. This means that, at least with the present potential which is not optimized specifically for each adsorption site, the electron-density distribution for all sites is similar; i.e., the back-donation of delectrons occurs to the same extent for all sites (see the arguments for electronic ab initio calculations in, e.g., Bauschlicher [15]). The hindered translation is different in the two directions X and Y, varies considerably from site to site for CO on Cu(211) and is nearly insensitive to the site for Cu(511). Unfortunately, as we discuss later, one cannot directly compare the present results with the results of HAS experiments [7]. The last site, D, behaves very differently from the other sites. The CO internal vibrational frequency is 20 cm−1 lower than on the other sites and the other frequencies differ also by 30 to 100 cm−1. In particular we note the large values of the vibration quantum for hindered translation and a difference of 60 cm−1 for the hindered rotation frequencies in the two directions X and Y. This can be understood by looking at Fig. 3 and Table 3 which show that, even if this site is the less stable, it is surrounded by a high potential wall. As mentioned, only the hindered translation is different on these stepped surfaces compared

with flat ones, and therefore we refer to the experimental data given for Cu(100) surfaces [39–44]. These vibrational frequencies, n =2086 cm−1, 1 n =345 cm−1 and n =285 cm−1, are in fair 2 3 agreement with the theoretical values except for the hindered rotation which is about 100 cm−1 too high. But the same discrepancy appears for Cu(100) and it is probably due to the potential parameterization of Tully et al. [31]. The hindered translation frequencies were measured using HAS by Braun et al. [7]. In that experiment the coverage was low (h=0.04) and the temperature of 120 K relatively high. Our single-molecule simulations can be compared with these results at low coverage. On a flat Cu(100) surface, Braun et al. [7] measured a single hindered translation frequency n of 32 cm−1. On vicinal 4 Cu(211) and Cu(511) surfaces, and on other corrugated surfaces described in that paper, a single frequency of 25.6 cm−1 was observed. Our hindered translation frequencies of the adsorbate system, calculated from the second derivative of the potential at the minimum of the adsorption sites (see Table 2), correspond to a zero-temperature limit. These vibrational frequencies are very different from site to site and therefore are sensitive to the local environment. For a given site they are also different in the X and Y directions and this anisotropy is not observed by Braun et al. [7] at 120 K. However, such anisotropy was observed by Yates’ group using ESDIAD [8–10] for CO on Cu(110) at a low temperature of 32 K. The Cu(110) surface has terraces of one row instead of three rows for Cu(211) and Cu(511) surfaces. The increase of the coverage of CO on Cu(110) [10] generates repulsion between CO molecules and tilts the CO molecular axis about the surface normal. At low coverage the measured hindered translation quantum (called libration by the authors) is 4.9 and 3.1 meV respectively in the [11: 0] and [001] directions. As a conclusion of the vibration analysis presented in the Table 2, we may note that, except for the hindered translation, the vibrational modes are nearly insensitive to the corrugation of the stepped vicinal surfaces. In analyzing the PES we have obtained some preliminary information on adsorption sites related to their energy and vibration spectrum. To confirm

H. Le Rouzo et al. / Surface Science 415 (1998) 131–147

these results we performed classical MD calculations (see details at the beginning of this section). In a first simulation we generated 1000 quenching trajectories, the initial conditions of which were selected from a microcanonical trajectory run at high energy (rotation and translation of CO). The corresponding kinetic energy for the CO molecule along these MD initial trajectories was about equal to 800 K. Calculations were done at two and three different energies, respectively, for the Cu(511) and Cu(211) surfaces. In the range of initial energies considered in this work (1000 to 2000 cm−1), the statistics were not altered noticeably by the initial energy value chosen. In Table 1 (see below), we report the statistics averaged on the different initial energies for each surface. As discussed at the beginning of the section, the cooling time is relatively short (about 4 ps). Consequently probabilities of adsorption in the different sites reflect the time spent around the adsorption sites during the microcanonical trajectories at high energy. From a statistical point of view, this is linked directly to the local density of rovibrational states associated to each site (indeed, the phase space can be separated into different regions by sharing it with criteria based only on the configuration space). These classical dynamics calculations, including the kinetic energy of the particles, confirm the results obtained from the search of the minima of the potential. As it should be, the adsorption energy is the same using the energy minimization and classical dynamics approaches. The adsorption probability is much higher on site B for Cu(211) and site C for Cu(511) than on site A, and the sum of the sticking probabilities on these two B and C sites, which are geometrically and energetically close, is about 61% for CO/Cu(211) and 62% for CO/Cu(511) (see Table 1). From this study, an entropic effect due to the PES shape is clearly shown. Indeed the most stable adsorption site (site A) is not found to be the most probable owing certainly to a larger anisotropy of the PES around the less stable sites B and C. In the dynamical calculations, the motion of the center of mass is significant and the associated coordinates X, Y and Z refer to this point. In Fig. 5 we present the density of probability of

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Fig. 5. Probability of occupation of different sites in the X×Y ([011: ]×[1: 11] or [01: 1]×[25: 5: ]) plane at a temperature of 125 K for CO/Cu(211) and CO/Cu(511) systems. Here X and Y are the coordinates of the center of mass of the CO molecule. The simulations corresponding to sites A, B and C displayed on the same figure are independent.

adsorption (in terms of these coordinates) corresponding to states of energies associated with a canonical distribution at T=125 K for CO adsorbed on Cu(211) and Cu(511) surfaces. The initial conditions randomly place a CO molecule above an A, a B or a C site. A canonical simulation of 10 ns starts after an equilibration time of 10 ps. The canonical simulation confirms the analysis of the PES and microcanonical simulations show a wider configuration space region for the combined sites B and C (at this temperature these two sites are in communication) than for the lower in energy adsorption site A. At this temperature, the available energy is not high enough to permit diffusion between sites A and B and C. Indeed, for the Cu(211) and Cu(511) surfaces (see Table 3), the

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corresponding barriers are respectively DE= 0.1376 eV and DE=0.1559 eV. In the canonical simulation at T=125 K the mean energy (5k T=0.09 eV ) is always smaller than the barrier B height starting from site A, which is about equal to 0.14 eV and 0.13 eV. This explains why diffusion from these sites was not observed in our calculations. From Fig. 5 the density of probability is more than doubled (0.007 compared with 0.003) and sharper on the Cu(211) surface than on the Cu(511) one. We also see that this probability is nearly uniformly distributed on sites B and C for a Cu(511) surface, whereas for Cu(211) the probability is much higher on site B. This is in agreement with the isopotential maps presented in Figs. 1(b) and 2(b), the tridimensional plots of Fig. 3 and Table 3. Now, looking along the X direction, the sticking probability has a larger geometrical domain for Cu(511) than for Cu(211). A complementary analysis of the canonical simulation at 125 K is presented in Fig. 6, where the density of probability of the position of the center of mass of a CO molecule along the Z direction ([211] and [511]) is plotted for our two surfaces. Here the probability along the Z axis is obtained after integration over the other coordinates (density of probability), not shown in Fig. 6. From this figure site A appears to be closer to the surface than sites B and C. For the adsorption on site A, the closest copper atom is actually below the surface plane (defined by the topmost copper atoms; white spheres on Figs. 1(c) and 2(c)) by ˚ . Therefore it appears that for the three about 0.7 A sites A, B and C, the CO molecule is located nearly at the same distance from the nearest copper ˚ ; i.e., the sum of the atom and close to about 2 A radius of the copper and carbon atoms ˚ , R =0.77 A ˚ ). However, above the (R =1.278 A Cu C B and C sites the distribution in Z of CO molecules is wider because these sites are on both sides of the on-top position of the terrace-edge copper atom and correspond to a flat region of the PES. This explains the large probability of migration between sites B and C. Comparing the Z dependence of the CO center-of-mass position for Cu(211) and Cu(511) surfaces, one sees that on average the CO is located at a larger Z distance from the surface on Cu(511) ( Fig. 6).

Fig. 6. Probability of occupation of different sites as function of the Z coordinate of the center of mass that is along either the [211] or the [511] direction for CO/Cu(211) and CO/Cu(511) surfaces. The result is integrated over the other coordinates. The solid line corresponds to the initial conditions for site A, whereas the dashed line corresponds to those for site B.

Finally, we performed studies of migration of CO molecules by using canonical classical dynamics at a constant temperature of 250 K. These results are presented in Figs. 7 and 8 for Cu(211) and Cu(511) surfaces, respectively. Calculations showed that, with the used potential, CO migration starts at 175 K. At 250 K, one immediately sees that for both Cu(211) and Cu(511) the migration is undoubtedly stronger along the X than along the Y direction. One can interpret the results presented in Figs. 7 and 8 on the basis of the heights of the barriers of the interaction potential. The barrier between the replicas of site A on Cu(511) are higher than on Cu(211) (see Table 3). We see this immediately in Figs. 7 and 8 when comparing the graphs for migration starting from sites A. To migrate on

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Fig. 7. Migration of the CO molecule on the Cu(211) surface (X×Y or [011: ]×[1: 11]) at 250 K. The initial conditions correspond either to A ( labeled site A) or to B ( labeled site B) adsorption sites.

Fig. 8. Migration of the CO molecule on the Cu(511) surface (X×Y or [01: 1]×[25: 5: ]) at 250 K. The initial conditions correspond either to A ( labeled site A) or to B ( labeled site B) adsorption sites.

Cu(511) starting from this site, the CO molecule should jump over the barrier between sites A and B or between replicas of site A. Both barriers are higher than on Cu(211). To migrate starting from B it is as easy as on Cu(211) as on Cu(511) but the whole available phase space is not accessible because of high potential barriers between A and B. On the Cu(211) surface the barrier between the replicas of site A is only DE=0.1390 eV, compared with DE=0.1427 eV between sites B. The difference is smaller at this temperature and one observes nearly the same migration starting from the initial conditions corresponding to site A or B. More quantitative analysis should be correlated with the diffusion coefficients D or D , which are X Y proportional to the mean square displacement (MSD) of the molecules along the X or Y coordinate. At a given temperature, the MSD values were calculated from five Nose´ trajectories each

propagated during 2 ns. In canonical ensemble, the time evolution of the system depends on both the PES and the chosen value of constant Q which governs the coupling between the physical system and the heat bath (see details of Nose´ dynamics at the beginning of this section). In Table 4 we first compare, at three distinct temperatures (200, 250 and 300 K ), the X2, Y2 and X2/ Y2 values for the two surfaces, Cu(211) and Cu(511). To confirm the results obtained from canonical simulations, the second part of Table 4 presents the diffusion coefficients D and D obtained at X Y two energies in a microcanonical simulation for both Cu(211) and Cu(511) surfaces. These energies were chosen in the upper domain of the available energies in the canonical simulations at T=200 K. Because of the barrier heights (see Table 3), only energies in this range permit migration on the two surfaces. All of the canonical and

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Table 4 ˚ 2) and diffusion coefficients D and D (in A ˚ 2/ps) for migration of a CO molecule in the X and Y directions Mean square values (in A X Y on the Cu(211) and Cu(511) surfaces Canonical ensemble Temperature ( K )

200 250 300

Cu(211)

Cu(511)

X2

Y2

X2/ Y2

X2

Y2

X2/Y2

3 44 51

2 5 6

1.5 8.8 8.5

2 8 49

1 4 29

2 2 1.7

Microcanonical ensemble Energy (eV )

0.18 0.21

Cu(211)

Cu(511)

D X

D Y

D X

D Y

0.01 0.03

0.0 0.0

0.001 0.02

0 0

microcanonical simulations were obtained starting from the initial conditions corresponding to site A. One can summarize the results presented in Table 4 in the following way: $ for Cu(211) and Cu(511), in the range of temperature studied, X2 is always larger than

Y2; $ the anisotropy of the diffusion is different on Cu(211) and Cu(511) surfaces. X2 is larger for Cu(211) than for Cu(511). Approaching 300 K, the value of Y2 becomes larger on Cu(511). This behavior is in agreement with the potential barriers displayed in Table 3; $ analysis of microcanonical MD simulations shows that the migration occurs only along X and the motion in Y is confined in the Y direction (D =0). The non-zero Y2 values Y ˚ 2) (around 6 A in the microcanonical simulations (and also in the canonical simulations) reflect, in fact, the amplitude of the CO vibration along the Y axis. From the MD simulations, it also appears that at same internal energy, D is X larger for the Cu(211) than for the Cu(511) surface, thereby confirming the results obtained in the canonical simulations; and $ detailed analysis of the trajectory leading to the diffusion coefficient D in a microcanonical simulation shows that migration takes place not only

through near-neighbor jumps but also through second-neighbor jumps (see a similar diffusion mechanism advocated by Dobbs and Doren [24]).

3. Conclusions The results of the preceding section presented a complete analysis of the stability and migration of CO on stepped vicinal surfaces. The simulations by means of two calculation techniques, potential analysis and classical dynamics, present complementary aspects of the adsorption and migration phenomena. In the potential analysis the CO internuclear distance was left free, whereas in the classical MD ˚ , a mean value simulations it was frozen at 1.126 A obtained from the full optimization of the potential. The internal vibration of CO has a large quantum of energy compared with other vibrational motions of the adsorbate. However, this constraint should not influence qualitatively the results of the present simulations which were concerned mainly with the stability of the adsorption sites and migration on the surface. In the classical dynamics simulation no surface

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or volume phonons were introduced. Nevertheless, we simulated the temperature in the framework of a canonical statistical ensemble by using the Nose´ thermostat [34]. In other words, the phonons of the surface and solid were introduced as a phonon bath corresponding to a thermodynamic temperature that influences the motion of the CO molecule. Recently Merikoski et al. [23] used a Nose´–Hoover thermostat to study the diffusion, mass transport and growth of copper on stepped Cu(119) surfaces. In their simulations the number of degrees of freedom is much larger than in ours. Here, the number of these degrees is restricted to five and consequently the energy exchange between the CO molecule and the heat bath could be overestimated. The vibrational frequencies presented in Table 2 are nearly insensitive to the potential corrugation except for the hindered translation. As mentioned in the preceding section, our results of hindered translation cannot actually be compared with the HAS experiment by Braun et al. [7] because of a difference in the temperature (calculated zero-temperature limit and measured 120 K ). Our translation frequencies are different in the X and Y directions, and this anisotropy was only observed for CO on Cu(110) at a low temperature of 32 K by Yates’ group using ESDIAD [8–10]. We think that at low temperature such an anisotropy should be seen also for CO on Cu(211) and Cu(511) surfaces by any experiment including HAS. From the present potential analysis one cannot infer the modification of the diffusion barriers due to substrate relaxation. However, following Merikoski et al. [23] who studied adsorption, diffusion and growth of copper on stepped copper surfaces, the coupling to the phonon bath tends to lower the effective barrier at high temperatures. Our results confirm the experimental findings of Meyer et al. [6 ] which suggest for Cu(211) an adsorption of CO on the border of a terrace. But the interpretation of experimental results is not straightforward because the resolution is not really atomic. Our microcanonical and canonical (at different temperatures) simulations show that simulations in the phase space (coordinate and momenta) are essential to reach a conclusion similar to the STM result by Meyer et al. [6 ]. This is

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justified on the basis of a larger availability of the phase space for adsorption sites B and C as compared with site A. However, it should be noted that our conclusions are based on quenching trajectories characterized by a very high gradient of temperature (of about 200 K/ps) which is much larger than the experimental characteristic adsorption time. On these stepped vicinal surfaces, migration starts at about 175 K and rises with temperature. This migration, or equivalently the diffusion, has not been measured on these systems to date. Our theoretical simulation shows that it is stronger on Cu(211) than on Cu(511) and that it originates from a difference in the potential barriers on the two systems. Starting from a microcanonical simulation, one can calculate a diffusion coefficient in the X direction whereas the motion in the Y direction is confined up to 300 K. The present simulation can be extended relatively easily, for example by taking into account the phonons of the surface within the harmonic approximation by using the first- and secondneighbor harmonic constants from Tully et al.’s [31] atom–atom potential. It may be that this approximation is insufficient and one may have to use many-body potentials appropriate for stepped surfaces (see, e.g., Todd and Lynden-Bell [21], Chen [22] and Merikoski et al. [23] and references therein). Here the hindered translation frequency of the adsorbate (a few cm−1) is much smaller than that of the surface phonons (greater than 100 cm−1 [29]) and therefore, following Cucchetti and Ying [45], the memory and nonlinear effects are negligible. We have already started simple preliminary calculations allowing the motion of one copper atom in harmonic approximation [37]. But, because of the corrugation originating from stepped surface and potential barriers, this will definitely not be sufficient and one should consider simultaneously the motion of several atoms including relaxation and reconstruction of the surface. Following Hammonds and Lynden-Bell [20], below the step roughening transition temperature the clean metallic surface is relatively stable and there are not too many meanders and kinks. For the Cu(511) having (100) terraces the roughening transition temperature is 380 K [20] and for

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Cu(211) this temperature should be higher as its terraces have closed-packed (111) structure. At the temperatures of up to 300 K chosen for our simulations, the surfaces should be mainly stable and without defects. For an Au(511) surface [46 ], a simulation of quenching of the system by classical dynamics shows a threefold symmetry of the terraces (instead of fourfold for (100) terraces) but no faceting was reported [46 ]. Adsorption will have a stabilizing effect on the initial structure of the surface or recovering partly modified structure back to its initial form [2]. Therefore our very simple model should be a reasonable first approximation for the adsorption of CO molecules on stepped vicinal copper surfaces. To simulate coverage of the surface, several simultaneously adsorbed molecules should be considered. Pouthier et al. [27] have studied the growth of a monolayer of xenon atoms on vicinal Pt(997) surface. For the Xe–Xe interaction they used a Lennard–Jones potential with results in fair agreement with the experiment. In particular, their results agree with the experiment for the sequential attachment of rows of xenon atoms at the bottom of steps of platinum on the surface. On the present CO/Cu chemical system, but for a flat Cu(100) surface, Springer and Head-Gordon [5] have calculated the adsorption as function of CO coverage. Unfortunately they used a CO–CO interaction potential taken from simple CO–CO dimer calculations in the gas phase. Because for the present system there are exchanges of electrons between the adsorbate and the substrate, one should calculate a realistic intermolecular potential in the presence of a metallic surface. Then this exchange of electrons will be explicitly taken into account and the CO–CO interaction potential reliable for the present purpose. Finally, if one is interested in the reactivity of adsorbates, one should study all adsorption sites and consider other geometrical and dynamic factors which should play a role in the reaction. As an example let us consider the catalytic oxidation of CO on vicinal Pt(335) surfaces [47]. The lowest adsorption site for CO and oxygen is on a step, whereas the largest probability of reaction is between CO adsorbed on terrace and an oxygen atom adsorbed on a step.

Acknowledgements One of the authors ( K.S.S.) is grateful to the French Government for a Fellowship. We acknowledge a computing time grant on the CRAY C98 from the Institut du De´veloppement et des Resources en Information Scientifique ( IDRIS) under project number 960554.

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