CO_{2} sticking on Pt(111); the role of kinetic energy and internal degrees of freedom

D. Kulginov^{†}, M. Persson, C. Åkerlund, I. Zorić, and B. Kasemo

Department of Applied Physics, Chalmers University of Technology and Göteborg University, S-412 96, Göteborg, Sweden

Abstract

CO_{2} adsorbed on Pt(111) is a system that have several attractive features that makes it suitable for studies of the role of internal degrees of freedom on the sticking process. In particular, this relatively long and linear molecule has a low energy vibrational mode. We have carried out measurements of non-dissociative sticking coefficient, S_{0}, of CO_{2} on the Pt(111) surface in the zero coverage limit as a function of incident kinetic energy, E_{i}, at different angles of incidence. A most interesting feature of the measured S_{0} for this physisorption system is its slow decline from 0.6 at E_{i} = 60 meV towards a value of S_{0} ≈ 0.1 at the highest measured energy of 1.2 eV. Our classical trajectory studies suggest that the observed high energy tail of S_{0} is primarily due to translational-rotational (T–R) energy transfer in the initial collision of the molecule with the surface while the effects of the intramolecular vibrations on S_{0} are negligible. The calculated S_{0} depends non-monotonically on the rotational anisotropy of the molecule–surface interaction. This is shown to be an effect of the dramatic influence of the number of bounces made by the two ends of the molecule against the surface in the initial collision on the T–R energy transfer.

I. INTRODUCTION

Recent studies^{1,2} of the energy and angular dependence of the sticking coefficient for non-dissociative chemisorption of simple molecules (CO and NO) on Pt(111) have revealed several interesting common features. On the experimental side the energy dependence of the initial sticking is characterized by a slow decline, with increasing kinetic energy, from an initially high value, to a smaller but still sizable value at the highest energy (∼ 3 eV). Furthermore, the sticking coefficient is practically independent of incident angle being thus determined by the total energy of the incoming particle.

Classical trajectory calculations with reasonable particle–surface potentials have reproduced the experimentally observed features.^{1,2} A qualitative explanation presented to explain the above data involves a strong translation–rotation coupling, caused by the deep, anisotropic, and corrugated potential well. Basically, while the translational to rotational energy conversion causes reduction of the sticking in the low energy region, it helps in keeping it relatively high at higher energies, resulting in an overall slow decrease of the sticking probability versus incident energy.

Non-dissociative adsorption of CO_{2} on Pt(111) is another adsorption system where the above ideas can be tested. This system represents, in contrast to CO or NO on Pt(111), a case of a weak chemisorption (or strong physisorption), with a well depth^{5} ∼ 0.2 eV in contrast to the ∼ 1 eV well depth for the above systems. On the other hand, the closed-shell CO_{2} molecule is rather elongated, but the anisotropy of its polarizability is weak, so the dominant part of the molecule–surface interaction anisotropy is expected to come from its repulsive part. This implies that the mechanism of translation–rotation energy transfer for this system might be different from that for CO or NO on Pt where the chemisorption bond should give rise to a strong anisotropy of the attractive part of the interaction.

An additional novel feature present in the CO_{2}–Pt(111) system is the existence of a low energy (∼ 80 meV) vibrational mode, both in the gas and adsorbed phase. Mieher and Ho^{3,4} have carried out EELS studies for CO_{2} adsorbed at 85 K on Pt(111). The observed EEL spectra include vibrational losses at 82 meV (scissor mode), 165 eV (symmetric stretch), and 291 meV (asymmetric stretch), all only slightly shifted from the known gas phase values. The shape of the observed EEL spectra is consistent with a freely rotating molecule.

Although CO_{2} is a frequent participant in several Pt(111) catalyzed reactions (as a reaction product), static (or dynamic) studies of this particular system are almost non-existent. Segner et al.^{6} have measured the angular distribution for CO_{2} scattered from Pt(111) at ≈ 600 K. Their results indicate the presence of both direct scattering and trapping– desorption channels. The integrated intensities in these two channels are of the same magnitude indicating a sticking coefficient of ∼ 0.5 for low energy molecules.

Thus, CO_{2}–Pt(111) is a possible fertile ground for studies of how translation–rotation and translation–vibration coupling (caused by the anisotropic repulsive interaction with the surface) affect the sticking process. With this in mind we carried out energy and angular dependence studies of the non-dissociative sticking coefficient for CO_{2} on Pt(111) at 85 K. These studies have been complemented with trajectory simulations of the sticking process in order to understand the influence of the anisotropic interaction on the translation–rotation energy transfer and to estimate the vibrational excitation probabilities.

The paper is organized as follows. We present the experimental method and the results of measurements in Sec. II. In Sec. III we introduce the model employed for our classical trajectory studies. The results are presented and discussed qualitatively in Sec. IV. Before summarizing our results in Sec. VI, we also make a comparison of the calculated and measured sticking coefficients in Sec. V.

II. EXPERIMENT AND RESULTS

The experimental apparatus has been described previously.^{7} The sticking coefficient measurements, in the energy range 60 meV < E_{i} < 1200 meV, were done by the method of King and Wells.^{8} (The highest energy of the seeded beam was limited by the onset of CO_{2} dissociation in the heated tungsten nozzle as the temperature was raised above 1000 K). The absence of direct dissociation upon adsorption was tested by searching (after adsorption at 85 K) for a CO_{2} signal in the desorption mode at temperature well above the normal CO_{2} desorption temperature. If CO_{2} had dissociated into CO+O or C+O+O a high temperature desorption signal should be observed due to recombinations reactions. The absence of such a signal implies that no dissociation of CO_{2} took place upon adsorption. Thus, all the data represent the initial sticking coefficient, S_{0}, for nondissociative adsorption of CO_{2} on Pt(111).

The experimental results for S_{0} as a function of incident kinetic energy, at normal incidence, are shown in Fig. 1. The observed features include a high initial sticking coefficient of ∼ 0.6 at 60 meV which declines sharply with increasing kinetic energy down to to S_{0} ≈ 0.2 at 0.4 eV, followed by a slower decline towards a value of S_{0} ≈ 0.1 at the highest measured energy (1.2 eV). Measurements at an incidence angle of 45^{∘} fall exactly on the normal incidence curve, implying that the total translational energy as a primary variable for the sticking process. This is not unexpected, provided that the principle of detailed balancing can be applied, since the measured angular distribution of the desorbing CO_{2} molecules^{6} is well fitted to the cosine form. Although our sticking data resemble previously^{1,2} obtained data for CO and NO sticking on the same surface, there are several noticeable differences. These are: i) a relatively low absolute sticking value at low energy (S_{0} ≈ 0.6 at 65 meV) which is probably due to the proximity of the surface temperature to the desorption temperature, ii) the initial decrease of S_{0} (for E_{i} < 0.5 eV ) is somewhat faster compared to the behavior of the CO and NO–Pt(111) systems.

III. THEORY

We use classical trajectory calculations for the simulation of the sticking process. Classical mechanics is certainly applicable to the translational and rotational motion of the CO_{2} molecule at the incident energies of interest because of its small rotational constant^{9} (∼ 0.05 meV). A simple estimate based on the forced oscillator model suggests that the excitation of intramolecular vibration is negligible so the molecule is treated as a rigid rotor. This finding is also corroborated by the quantum-mechanical calculations by Clary and DePristo^{10} and by the scattering experiments by Mantell et al.^{11} who find small (< 10^{−2}) probability for excitation of the CO_{2} asymmetric stretch mode in the scattering from the hot Pt surface. The energy transfer to the lattice vibration at the incident energies of interest are typically much larger than the phonon energies which justifies a classical treatment of the lattice dynamics of platinum.^{12,13}

The (111) surface of platinum is modelled by one of the triangular faces of a tetrahedral cluster of atoms^{14} with central, harmonic interatomic forces. The atoms at the three lower faces of the tetrahedral cluster are kept fixed. This particular choice of the cluster shape allows us to have a considerable surface area with a moderate number of movable bulk atoms. Nevertheless, this area is too small to obtain a homogeneous static potential in the surface region, so we augment the upper face of the cluster with fixed surface atoms. The cluster has been chosen to be sufficiently large so that there is no dependence of the trajectories on the cluster size. This requires a cluster with 36 movable and 15 fixed surface atoms (the total number of movable atoms is 70). The interatomic forces are limited in range to the nearest-neighbouring atoms with a value for the force constant that reproduces the maximum phonon energy in bulk.^{15}

Since the interaction of the CO_{2} molecule with the Pt surface is not known in detail, we have constructed a rather primitive model that reflects the gross features of the interaction. This model contains a single anisotropy parameter that allows us to study the influence of the anisotropy of the molecule–surface interaction on the sticking. The interaction potential is modelled by a sum of pairwise Morse potentials, V_{M}(r) = D[e^{−2λ(r−r_{eq})} − 2e^{−λ(r−r_{eq})}], acting between each surface atom and three interaction centers representing the CO_{2} molecule. One of the centers is located at the C atom while the other two are placed at a distance of αl_{CO} from the C atom along each C–O bonds, where l_{CO} = 1.16 Å is the C–O bond length^{9}. The parameter 0 ≤ α ≤ 1 controls the anisotropy of the molecule–surface interaction; for α = 1 the centers coincide with the nuclei of the molecule while for α = 0 they are located at the C-atom. The moment of inertia does not depend on α and is kept fixed at the value I = 43.2 amu Å^{2} appropriate for CO_{2}.^{9} An analogous approach has been used to describe the anisotropy of the N_{2}–Ag(111) interaction.^{16} The sum of pair potentials is taken over the first surface layer, but we also add the interaction with the second layer of atoms in the cluster using the repulsive part of V_{M}. The values of the Morse potential parameters, λ = 1.8 Å^{−1} and r_{eq} = 3.6 Å, have been chosen to be in agreement with what is known about the atomic radii and the steepness of the Pauli repulsion for closed shell systems.^{10,17,18} The value of D is then adjusted so that the resulting well depth, 235 meV, of the static surface is close to the experimentally observed value.^{19}

We use the Verlet algorithm^{20} for solving the equations of the translational motion, while the rotation is described by constrained equations of motion^{21} that are solved by the “leapfrog” algorithm.^{22} The time step used is 1.6 fs. The initial scattering conditions that we use for the molecule, normal incidence and no initial rotation, correspond closely to the experimental conditions in the molecular beam. In this work we have not included surface temperature and the cluster atoms are initially at rest, whereas in the experiment the surface has been kept at 85 K.

Some care is needed in determining the sticking criterium in the calculation. We use the term “trapping” for the event in which the translational energy of normal motion of the molecule is negative after the first collision. The molecules that are trapped with positive total energy may leave the surface by conversion of this energy to normal motion after the first round trip in the well. The calculations show that after two round trips in the potential well (i.e., after four turning points of the center of mass of the molecule) this conversion is primarily due to a cluster edge effect (cf the discussion by Harris and Luntz^{1}), because for the corresponding initial conditions a larger cluster leads to sticking after four turning points. The sticking coefficient is therefore determined as the relative number of trajectories with at least four turning points after sampling the impact parameter over the surface elementary lattice cell and the initial orientation of the molecule.

IV. DISCUSSION

We find from our trajectory study that the molecular rotation plays a significant role in the sticking dynamics. This fact is demonstrated in Fig. 2a) where the calculated sticking coefficient, S_{0}, is shown for three different values of the anisotropy parameter, α. The value α = 0 corresponds to a treatment of the CO_{2} molecule as a particle with no rotation and gives a S_{0} that is non-zero only for incident energies, E_{i}, up to ∼ 0.6 eV. This result is in sharp contrast to those where the rotation has been included. The calculations for α = 0.6 and 1.0 give a considerable S_{0} at E_{i} up to more than 1 eV. Such a high-energy tail for S_{0} has also been identified and discussed in a classical trajectory study by Harris and Luntz^{1} for CO on Pt(111). This behaviour is not unexpected for such a chemisorption system with a well depth of ∼ 1 eV and high anisotropy, which results in a strong translational–rotational coupling, while it is less obvious for a physisorption system like CO_{2} on Pt(111). The effects of the anisotropy of the molecule–surface interaction on S_{0} is most interesting. S_{0} varies non-monotonically with anisotropy, α, for essentially all E_{i}, and the maximum S_{0} is attained for α = 0.6.

In order to develop an understanding of the effects of the rotation on the sticking it is useful to view sticking as a two-step process: The first step involves trapping in which the incident translational energy of the normal motion is transferred to rotation, lateral motion and lattice vibration in the initial collison. The second step involves energy equilibration of the trapped molecule with the surface eventually leading to sticking. For molecules trapped with positive total energy the last process competes with the conversion of this energy to translational motion normal to the surface that may lead to desorption. For non-zero surface temperature the trapped molecules may also desorb by gaining translational energy from the surface. This picture makes most sense for a physisorption system where the coupling between the lateral and normal motion is relatively weak, and has been shown to be useful to understand the angular dependence of sticking of hydrogen molecules in the physisorption well on Cu^{23}. A comparison of the calculated trapping probabilities, P_{0}, as shown in Fig. 2b), with the calculated S_{0} in Fig. 2a) demonstrates that most of the behaviour of S_{0} with respect to α is already present in P_{0}. A similiar non-monotonic behaviour of P_{0} was also identified by Engdahl^{16} in his trajectory study of trapping of N_{2} on Ag, but its origin has never been clarified. For α = 0, where the translational–rotational coupling is turned off, P_{0} is essentially equal to S_{0}. This can be understood from the fact that the energy transfer to the lateral motion is small at normal incidence, and most molecules are trapped with negative total energy. The decrease of P_{0} relative to S_{0} for non-zero α is caused by the energy transfer to rotation that makes it possible for the molecule to be trapped with positive total energy.

The dynamics of the initial collision of the linear CO_{2} molecule with the relatively flat close-packed Pt(111) surface show some similiarites with the impulsive multiple “bounces” of the ends of a stick against a hard surface. This similarity is illustrated by two representative trajectories in Fig. 3 and takes its origin in the fact that the main anisotropy is in the repulsive part in our model of the molecule–surface interaction. The molecule only makes one bounce for moderate initial angles, θ_{i}, between the molecular axis and the surface normal. At larger θ_{i} it is possible for the molecule to make a second bounce with its other end, as shown in Fig. 3b). In particular, the trajectories in Fig. 3 reveal that most of the rotational energy gained in the first bounce is transferred back to translational energy in the second bounce, so the rotational excitation is typically much larger after a single-bounce collision than after a double-bounce one. However, when the anisotropy of the interaction decreases, the initial rotational excitation after the first bounce becomes insufficient to produce the second bounce irrespective of the initial orientation of the molecule. In fact, we find that the appearance of a second bounce in the initial collision requires a minimum value of the anisotropy parameter of about 0.6. It is no coincidence that the maximum of P_{0} correlates with this critical value as we will now demonstrate.

The increase of P_{0} with α in the single bounce regime, α < ∼ 0.6, is simply due to the concomitant increase of the energy transfer to rotation in the initial collision. For α = 0 and E_{i} = 0.9 eV the average energy transfer to the lattice is ∼ 0.55eV. As can be seen in Fig. 4a), this is close to the average energy transfer to the lattice vibration, ΔE_{latt}, for α = 0.6 at θ_{i} = 0, where the average energy transfer to rotation, ΔE_{rot}, is small. For larger θ_{i}, ΔE_{rot} increases and attains a maximum at θ_{i} ∼ 40^{∘}. This behaviour just reflects the variation of the torque on the molecule with θ_{i}. An important effect, as can be seen also in Fig. 4b), is the anticorrelation between ΔE_{rot} and ΔE_{latt} for single-bounce collisions; an increase of ΔE_{rot} by varying either α or θ_{i} results in a decrease of ΔE_{latt}. This anticorrelation has been discussed previously and shown to play an important role in the inelastic scattering of NO^{24} and N_{2}^{25} from Ag. The increase of ΔE_{rot} with α is only partially compensated by the anticorrelation of ΔE_{latt}. Since the energy transfer to the lateral motion is negligible at normal incidence, this results in a net increase of energy transfer from the normal motion, as demonstrated by the plot for the average energy, E_{z}, of the normal motion of the molecule after the initial collision with the surface in Fig. 4a).

The decrease of P_{0} for α > ∼ 0.6 is primarily due to the appearence of double-bounce collisions that nearly close the channel of the energy transfer to rotation. This effect is demonstrated by the plots for energy transfers in Fig. 4b) for α = 1.0. For θ_{i} < ∼ 23^{∘}, the molecule makes only single bounces and ΔE_{rot} is larger than for α = 0.6, but for θ_{i} > ∼ 23^{∘}, where the molecule makes double-bounces, ΔE_{rot} decreases dramatically with θ_{i}. Nevertheless, ΔE_{latt} in a double-bounce collision is even smaller than in a single-bounce collision for α = 0.6. This results in a E_{z} that is small only for a narrow range of θ_{i} while for the other values of θ_{i}, E_{z} is even larger than its value ∼ 0.3 eV for α = 0. Hence this behaviour shows that P_{0} decreases for α > ∼ 0.6 and for sufficiently large α it is even smaller than P_{0} for α = 0 at E_{i} below 0.6 eV. Nevertheless, even for large α like α = 1, there still is a high energy tail of P_{0} which is due to a small part of single-bounce collisions that are possible for sufficiently small θ_{i}.^{26}

Finally, we turn to the role of intramolecular vibrations on the sticking of CO_{2} on Pt(111). Vibrations could, in principle, be excited at the incident energies of interest. The bending or “scissor” vibrational mode of the CO_{2} molecule has the lowest frequency of 83 meV, but is probably coupled to the translational motion weaker than the symmetric stretching mode that has twice as large frequency.^{9} The anti-symmetrical mode can hardly be excited at E_{i} < ∼ 1 eV because of its high frequency and weak coupling. The quantum excitation probabilities of these modes can be estimated in a forced oscillator model description from the time Fourier transforms of the forces acting on these two modes. At least up to E_{i} ∼ 1 eV, we find that these probabilities never exceed few per cent. The quantum-mechanical calculations by Clary and DePristo result in even smaller numbers.^{10}. The intramolecular vibration may thus be safely neglected in the sticking calculations.

V. COMPARISON WITH EXPERIMENT

Our crude model of the molecule surface interaction, as dictated by the lack of detailed knowledge about this interaction, suggests that a comparison of the calculated S_{0} of CO_{2} on Pt(111) with the experimental values should at most be viewed as semi-quantitative. Our primary goal has been to understand the role of the intramolecular vibrations and molecular rotations in the sticking process.

The calculated S_{0} for α = 0.6 is able to reproduce the observed magnitude of S_{0} at incident energies E_{i} > ∼ 0.5 eV as shown from a comparison of the results in Fig. 2a) and Fig. 1. We believe that this agreement gives strong evidences that the observed high energy tail of S_{0} is due to energy transfer to rotations. At lower E_{i}, our calculations result in values that are much closer to unity than the experiment. This discrepancy is most probably due to the surface temperature effects. Another possible origin of this discrepancy is a too simplistic description of the anisotropy of the attractive part of the molecule–surface interaction. This part becomes important at low incident energies. These effects are going to be checked by extending the calculations of S_{0} to non-zero surface temperatures and off-normal incidence.

VI. SUMMARY

The role of the internal energy and kinetic energy on the sticking of CO_{2} on Pt(111) has been studied both by molecular beam scattering and classical trajectory calculations.

Characteristic features of this system include a freely rotating molecule in a shallow physisorption well with intramolecular vibrational energies slightly shifted from the gas-phase. Thus, how the translational-rotational (T–R) and -vibrational coupling affects the sticking is an interesting issue, in particular, in the view of the presence of a rather low energy, ∼ 80 meV, intramolecular vibration and a low rotational constant of the relatively long and linear CO_{2} molecule.

The non-dissociative sticking coefficient, S_{0}, of CO_{2} on a 85K Pt(111) surface have been measured in the zero coverage limit both as a function of incident energy, E_{i}, and for two different angles of incidence, θ_{i}. The conditions of the molecular beam are such that the incident molecules have negligible rotational energy and population of the vibrational states. The observed E_{i} dependence of S_{0} for θ_{i} = 90^{∘} and 45^{∘}, respectively, suggests that S_{0} scales with the total incident kinetic energy of the molecule. A most interesting feature of the measured S_{0} is the slow decline from a high initial sticking coefficient of ∼ 0.6 at 60 meV towards a value of S_{0} ∼ 0.1 at the highest measured energy (1.2 eV). This high energy tail of S_{0} is somewhat surprising for sticking into a physisorption well.

The classical trajectory calculations is based on a cluster model of the Pt(111) surface with harmonic interatomic forces and a sum of pairwise interaction potentials between the molecule and the surface atoms. The present knowledge about the molecule-surface interaction potential is quite limited and has dictated our primitive model for this interaction. However, this model reproduces the observed potential well-depth and has a reasonable description of the steepness of the repulsive wall that makes us believe that it captures the gross features of the interaction potential that are important for the sticking. The trajectory calculations suggest that the observed high energy tail of S_{0} is primarily due to translationalrotational energy transfer in the initial collision of the molecule with the surface. The role of the intramolecular vibrations on the sticking process is found to be negligible from an estimate of the energy transfer to these vibrations. The effect of the T–R coupling on the S_{0} has been studied by varying the anisotropy of the molecule-surface interaction and is found to be rather intriguing; S_{0} depends non-monotonically on the anisotropy. This can be understood from the dramatic influence of the number of bounces made by the two ends of the molecule against the surface in the initial collision on the T–R energy transfer. This bounce-like behaviour of the molecular trajectories is an effect of the fact that the dominant part of the anisotropy is assumed to be in the repulsive part of the interaction.

ACKNOWLEDGMENTS

This work was financed by the Swedish Natural Sciences Research Council (Grant No. E-EG 03106-336) and the Swedish Research Council for Engineering Sciences (Grant No. 92-951). We are also grateful to Göran Wahnström for sharing his experiences with us.

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FIGURES

FIG. 1. Measured initial sticking probability, S_{0}, of CO_{2} on Pt(111) at normal incidence, as a function of incident energy, E_{i}. Surface temperature is 85 K. The solid curve through the measured values (diamonds) is provided as a guide to the eye.

FIG. 2. Calculated initial sticking a) and trapping b) probability of CO_{2} on Pt(111) at normal incidence, as a function of incident energy, E_{i}, for different values of anisotropy parameter. α = 0 (solid lines), 0.6 (long-dashed lines), and 1 (dashed lines). Surface temperature is 0 K.

FIG. 3. Two different representative trajectories of CO_{2} at incident energy E_{i} = 900 meV and for the anisotropy parameter α = 1. a) single-bounce collision leading to high rotational excitation and trapping, θ_{i} = 25^{∘}; b) double-bounce collision leading to low rotational excitation, θ_{i} = 50^{∘}. The molecule is depicted as a stick with the same length as the separation between the oxygen atoms. The bounces are indicated by arrows. The time step is 48 fs.

FIG. 4. The average energy of rotation, ΔE_{rot} (solid line), lattice vibration, ΔE_{latt} (long-dashed line), and normal motion of the molecule, E_{z} (dashed line), after the initial collision with the surface, as functions of the initial orientation, θ_{i}. a) α = 0.6 and b) α = 1.