We report six-dimensional quantum dynamical calculations of dissociative
adsorption and associative desorption of the system H_2/Pd(100) using an
ab-initio potential energy surface. We focus on rotational effects in the
steering mechanism, which is responsible for the initial decrease of the
sticking probability with kinetic energy. In addition, steric effects are
briefly discussed.Comment: RevTeX, 11 pages, 4 figure

Alnot

Axel Gross

Berger

Beutl

Blaha

Brenig

Brunner

Butler

Chiba

Darling

Dixon-Warren

Engdahl

Gross

Halstead

Hammer

Holloway

Jackson

Kohler

Kumar

Küchenhoff

Matthias Scheffler

Michelsen

Mowrey

Perdew

Rendulic

Resch

Rettner

Schröter

Steffen Wilke

White

Wilke

Zangwill

English

arXiv

Groß, Axel

Wilke, Steffen

Scheffler, Matthias

Max Planck Society eDoc Server

Six-dimensional quantum dynamics of adsorption and desorption of H_2 at Pd(100): no need for a molecular precursor adsorption state

Groß, A.

Wilke, S.

Scheffler, M.

MPG.PuRe

arXiv:mtrl-th/9603003v1  5 Mar 1996Six-Dimensional Quantum Dynamics of Adsorption andDesorption of H2 at Pd(100):No Need for a Molecular Precursor Adsorption StateAxel Gross, Steffen Wilke, and Matthias SchefflerFritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D-14195 Berlin-Dahlem,GermanyAbstractWe report six-dimensional quantum dynamical calculations of dissociativeadsorption and associative desorption of the system H2/Pd(100) using an abinitio potential energy surface. We focus on rotational effects in the steeringmechanism, which is responsible for the initial decrease of the sticking prob-ability with kinetic energy. In addition, steric effects are briefly discussed.Typeset using REVTEX1I. INTRODUCTIONIn recent years the dynamics of dissociative adsorption has been the subject of a largenumber of experimental and theoretical investigations (see, e.g., Refs. [1,2,3,4]). As faras quantum dynamical simulations were concerned, these studies were restricted to low-dimensional calculations on model potentials due to computational constraints and the non-availability of ab initio potential energy surfaces (PES). By varying potential parametersexperimental results were tried to be reproduced qualitatively. These studies laid the foun-dations of the current understanding of simple surface reactions and of the topological fea-tures realistic potentials should have. The main effects of molecular vibration [5,6,7,8,9,10],rotation [11,12,13,14,15,16] and lateral corrugation [17,18] on the dissociative adsorptionprobability seemed to be understood to a large extent, but it remained unclear whetherthe qualitative explanations would still be valid in high-dimensional dynamical calculationsincluding all crucial degrees of freedom.Just recently it has become possible to evaluate the six-dimensional potential energy sur-face of hydrogen dissociation on metal surfaces [19,20,21,22] by density-functional theory.This development also enforced new efforts for improving the quantum dynamical algo-rithms. Indeed it is now feasible to perform studies of hydrogen dissociation where all sixdegrees of freedom of the hydrogen molecule are treated quantum mechanically [23]. Thesecalculations showed that the initial decrease of the sticking probability with kinetic energyfound experimentally for H2 on Pd(100) [24] and on many other transition metal surfaces[25,26,27,28,29,30] is not due to a precursor mechanism, as was commonly believed, but canbe explained by dynamical steering.In this contribution we will – after briefly recalling the theoretical background and themain result of our previous study [23] – focus on the influence of rotations on the adsorptiondynamics in the system H2/Pd(100). We will describe the dependence of the sticking proba-bility on the initial rotational quantum number ji of the impinging hydrogen molecules andshow how this dependence could be verified experimentally. We end with a brief discussion2of steric effects and concluding remarks.II. THEORETICAL BACKGROUNDThe potential energy surface of H2/Pd(100) has been determined using the density-functional theory together with the generalized gradient approximation (GGA) [31] and thefull-potential linear augmented plane wave method [32,33]. Ab initio total energies havebeen evaluated for more than 250 configurations and have been parametrized in a suitableform for the dynamical calculations [23]. The substrate atoms are assumed to be fixed sincedue to the large mass mismatch between adsorbate and substrate for H2/Pd there is onlylittle energy transfer to the substrate phonons. The quantum dynamics is determined ina coupled-channel scheme within the concept of the local reflection matrix (LORE) [34,35]and the inverse local transmission matrix (INTRA) [36]. This very stable method, whichhas been employed before in a high-dimensional study of the adsorption of H2/Cu(111)[37], is closely related to the logarithmic derivative of the solution matrix and thus avoidsexponentially increasing evanescent waves which cause numerical instabilities. By utilizingall symmetries of the hydrogen wave function it has been possible to effectively include upto 21,000 channels per total energy in the dynamical calculations.III. RESULTSFigure 1 presents the results for the sticking probability as a function of the kinetic energyof the H2 beam incident on a Pd(100) surface [23]. The dashed curve, which correspondsto H2 molecules initially in the rotational ground state ji = 0, exhibits a strong oscillatorystructure for low energies. These oscillations are a consequence of the quantum nature ofthe hydrogen beam [18,38]. They are smoothed out if the initial rotational population andthe energy spread typical for molecular beam experiments [24] are taken into account (solidline in fig. 1). This curve should be compared with the experimental results of Rendulic etal. [24]. The theoretical curve agrees quite well with the experimental data. Although no30.0 0.1 0.2 0.3 0.4Kinetic energy Ei (eV) 0.00.20.40.60.81.0Sticking probability Experiment6D quantum dynamics, ji = 06D quantum dynamics, beam simulationFIG. 1. Sticking probability versus kinetic energy for a H2 beam under normal incidence on aPd(100) surface. Experiment: circles (from ref. [24]); theory: H2 molecules initially in the rotationalground state (dashed line) and with an initial rotational and energy distribution adequate formolecular beam experiments (solid line) (from ref. [23]).precursor state exists in the PES and the energy transfer to substrate phonons is not takeninto account, the initial decrease of the sticking probability with increasing kinetic energyis well reproduced.The initial decrease results from a dynamical steering effect which had been proposedearlier (see, e.g., [25,28]), but not confirmed theoretically. Molecules approaching the surfacefrom the gas phase will be attracted to non-activated paths towards dissociative adsorptionby the potential gradient. The slower the molecules are, the more likely it is that theyactually follow these attractive paths. By increasing the kinetic energy the time that thegradient acts upon the molecules is shortened. More molecules will then hit the repulsivepart of the potential without being steered to non-activated paths and will be scatteredback into the gas phase [23]. This causes the decrease in the sticking probability. By furtherincreasing the kinetic energy the molecules will eventually have enough energy to directlycross the barrier which leads to the increase of the sticking probability at higher energies(see fig. 1). In the quantum dynamical coupled-channel description the steering effect isreflected by the fact that at low energies more channels are needed in order to get convergedresults than at high energies. This indicates that there is a strong rearrangement between40.0 0.1 0.2 0.3 0.4Kinetic energy Ei (eV) 0.00.20.40.60.81.0Sticking probability ji = 0ji = 1ji = 2ji = 3ji = 4FIG. 2. Orientationally averaged sticking probability versus kinetic energy for different initialrotational quantum numbers ji of the incoming molecular beam. The molecular beams are assumedto have an energy spread of ∆E/Ei = 2∆v/vi = 0.2 [24] (Ei and vi are the initial kinetic energyand velocity, respectively).the different channels at low energies due to the steering.The steering occurs in all dynamical degrees of freedom. Therefore by increasing theenergy of, e.g., the rotational degree of freedom of the hydrogen molecule the steering andthus the sticking probability should be diminished. This can already be seen in fig. 1, wherethe sticking probability of the rotationally populated beam is on the average slightly loweras compared to molecules in the rotational ground state. This effect is shown in more detailin fig. 2, which displays the orientationally averaged sticking probabilityS¯ji(E) =12ji + 1ji∑mi=−jiSji,mi(E), (1)versus initial kinetic energy for ji = 0, . . . , 4. Figure 2 clearly demonstrates that rotationalmotion hinders sticking, especially at low kinetic energies, i.e., the regime where the steeringeffect is operative. The faster the molecules rotate, the more the dissociative adsorption issuppressed, because molecules with a high angular momentum will rotate out of a favor-able orientation towards adsorption during the dissociation event. This hindering effect ofrotations becomes smaller, however, at kinetic energies larger than ∼0.2 eV, where directactivated adsorption is dominant.5The suppression of the sticking probability by additional rotational motion can actuallybe used to discriminate between the precursor and the steering mechanism. The precursorstate is usually assumed to be a physisorption state. There are only little directional forcesfor molecules adsorbed in a physisorption state, they can almost freely rotate [39]. Thetrapping probability into the physisorption state and thus the sticking probability in theprecursor model should be almost independent of the initial rotational state, in contrastto the steering mechanism. Unfortunately it is not easy to prepare a molecular beam ina single quantum state. However, by seeding techniques the translational energy of a H2beam can be lowered in a nozzle experiment without changing the rotational population ofthe beam (the translational energy can not be increased since there is no lighter seeding gasthan H2). In fig. 3 we have plotted the orientationally averaged sticking probability versusthe rotational temperature for different kinetic energies. Experimentally the rotational tem-perature of a H2 beam can not be lower than the corresponding translational temperature(a kinetic energy of 200 meV, e.g., corresponds to a nozzle temperature of 1200 K), however,theoretically all combinations of kinetic energy and rotational temperature are feasible. Forkinetic energies below ∼40 meV there is a strong dependence of the sticking probability onthe rotational temperature. By increasing the rotational temperature the sticking probabil-ity can be decreased by more than a factor of two at these kinetic energies which should beobservable in experiment. At large kinetic energies the suppression is less pronounced whichcould already be inferred from fig. 2.Interestingly enough, rotational motion seems to suppress sticking in general in the sys-tem H2/Pd(100). We have checked this for kinetic energies Ei ≤ 0.45 eV and rotationalquantum numbers ji ≤ 8. Also the observed rotational cooling in desorption of H2/Pd(100)[23,40] supports these findings. This situation is different in the system H2/Cu(111) wherea non-monotonous dependence of the sticking probability on rotational quantum number jihas been observed [2,41]: Rotational motion is found to hinder adsorption for low rotationalstates (ji < 4) and enhance adsorption for high rotational states (ji > 4) [2]. The enhance-ment for high j states is related to the elongation of the molecular bond at the barrier60 500 1000 1500 2000 2500 3000Rotational temperature (K)0.00.10.20.30.40.5Sticking probability Ei = 10 meVEi = 35 meVEi = 60 meVEi = 100 meVEi = 200 meVFIG. 3. Orientationally averaged sticking probability versus rotational temperature of the in-coming beam for different kinetic energies.position in the late barrier system H2/Cu(111) which leads to a decrease of the rotationalconstant and thus to an effectively lowered barrier for high j states [12,13,14,15,16,42]. Inthe system H2/Pd(100) these late barriers, however, are absent [21].There is still an effect that can over-compensate for the suppression of the sticking proba-bility by rotational motion, namely the orientational or steric effect [23]. The most favorableorientation to adsorption is with the molecular axis parallel to the surface. Molecules withazimuthal quantum number m = j have their axis preferentially oriented parallel to thesurface. These molecules rotating in the so-called helicopter fashion dissociate more easilythan molecules rotating in the cartwheel fashion (m = 0) with their rotational axis preferen-tially parallel to the surface since the latter have a high probability hitting the surface in anupright orientation in which they cannot dissociate. This steric effect, which has also beeninvestigated in a number of model studies for purely activated adsorption [11,12,13,14,15,16],can clearly be seen in fig. 4 where the sticking probability for one fixed kinetic energy ofEi = 0.175 meV is plotted. Indeed the mi = ji data even rise with increasing quantumnumber ji at this relatively high kinetic energy, while the mi = 0 and the orientationallyaveraged results are decreasing. At lower kinetic energies (which is not explicitly shownhere), where the steering is more pronounced, also the mi = ji data decrease.70 1 2 3 4 5 6Initial rotational quantum number ji0.00.10.20.30.40.50.6Sticking probabilityorientationally averagedmi = 0, cartwheel rotationmi = ji, helicopter rotationEi = 0.175 eVFIG. 4. Sticking probability versus initial rotational quantum state ji. Diamonds: orientation-ally averaged sticking probability (eq. 1), triangles: mi = 0 (cartwheel rotation), circles: mi = ji(helicopter rotation). The initial kinetic energy is Ei = 0.175 eV.IV. CONCLUSIONSIn conclusion, we have reported a six-dimensional quantum dynamical study of adsorp-tion and desorption in the system H2/Pd(100) using an ab initio potential energy surface.We have shown that the initial decrease of the sticking probability with increasing kineticenergy is due to dynamical steering. We have focused on the steering effect in the rotationaldegree of freedom of the hydrogen molecule and shown how the steering effect can be furtherconfirmed experimentally. Our study demonstrates that the combination of ab initio poten-tial energy surfaces with high-dimensional quantum dynamical calculations can lead, due tothe microscopic information, to a quantitative as well as new qualitative understanding ofprocesses at surfaces.ACKNOWLEDGEMENTSWe like to thank Prof. K. D. Rendulic for suggesting the detailed investigation of rota-tional effects in the steering mechanism.8REFERENCES[1] K.D. Rendulic and A. Winkler, Surf. Sci. 299/300 (1994) 261.[2] C.T. Rettner, H.A. Michelsen, and D.J. Auerbach, J. Chem. Phys. 102 (1995) 4625.[3] S. Holloway, Surf. Sci. 299/300 (1994) 656.[4] G.R. Darling and S. Holloway, subm. to Rep. Prog. Phys.[5] B. Jackson and H. Metiu, J. Chem. Phys. 86 (1987) 1026.[6] D. Halstead and S. Holloway, J. Chem. Phys. 93, (1990) 2859.[7] G.R. Darling and S. 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Six-dimensional quantum dynamics of adsorption and desorption of H<sub>2</sub> at Pd(100): no need for a molecular precursor adsorption state

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Six-dimensional quantum dynamics of adsorption and desorption of H2 at Pd(100): no need for a molecular precursor adsorption state

Six-Dimensional Quantum Dynamics of Adsorption and Desorption of H_2 at
  Pd(100): No Need for a Molecular Precursor Adsorption State

Six-Dimensional Quantum Dynamics of Adsorption and Desorption of H_2 at Pd(100): No Need for a Molecular Precursor Adsorption State

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