molecular dynamics simulations of collision-induced...

JOURNAL OF CHEMICAL PHYSICS VOLUME 110, NUMBER 6 8 FEBRUARY 1999

Molecular dynamics simulations of collision-induced desorption. I. Lowcoverage N 2 on Ru „001…

Leonid Romm and Micha AsscherDepartment of Physical Chemistry and Farkas Center for Light Induced Processes, The Hebrew University,Jerusalem, 991904, Israel

Yehuda ZeiriDepartment of Chemistry, Nuclear Research Center, Negev, P.O. Box 9001, Beer-Sheva, Israel

~Received 21 July 1998; accepted 5 November 1998!

Classical molecular dynamics simulations have been performed to study the details ofcollision-induced desorption~CID! of nitrogen molecules adsorbed at low coverages on Ru~001!.Semiempirical potential energy surfaces~PES! were used to describe the movable two layers of 56ruthenium metal atoms each, the nitrogen adsorbate, the Ar and Kr colliders, and the interactionsbetween them. An experimentally measured threshold energy for the CID process of 0.5 eV and thedependence of the cross sectionsdeson incidence energy and angle of incidence have been preciselyreproduced in the energy range of 0.5–2.5 eV. Strong enhancement of thesdes is predicted as theangle of incidence increases. Kinetic energy and angular distributions of the scattered rare gas andthe desorbing nitrogen were determined as a function of the dynamical variables of the collider. Itis predicted that half of the collision energy is transferred to the solid and the other half is sharedamong the two scattered species. While no vibrational excitation is observed, efficient rotationalenergy excitation is predicted which depends on both incident energy and angle of incidence. Polarand azimuthal angular distributions were found to be strongly dependent on the incidence angle andenergy of the colliders. These results suggest a new CID mechanism for the weakly chemisorbednitrogen molecules on Ru~001!, based on extensive analysis of individual trajectories. According tothis mechanism, the CID event is driven by an impact excitation of frustrated rotation or tilt motionof the adsorbed molecule as a result of collision with the energetic rare gas atom. In addition, lateralmotion along the surface is also excited. Strong coupling of these two modes with the motion in thedirection normal and away from the surface eventually leads to desorption and completes the CIDprocess. The efficiency of this coupling is dictated by the details of the corrugation of the Ru–N2

PES. It is concluded that the simple hard cube–hard sphere model, frequently used to analyze CIDprocesses, is insufficient for the description of this system. While reasonably well predictingthreshold energy, it cannot explain the full dynamical picture of the CID event. ©1999 AmericanInstitute of Physics.@S0021-9606~99!71206-7#

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I. INTRODUCTION

Industrial high pressure and temperature conditionspose adsorbates on solid surfaces to collisions with gasoms and molecules which have sufficient kinetic energyinduce dissociation or desorption.1–8 At the low kinetic en-ergy regime, these collision-induced reactions are possvia a strong chemisorption of gas phase molecule whichduces the desorption or dissociation of preadsorbed spein a process identified as adsorption assisted desorption8–11

In order to eliminate the effect of the new surface bondformation on the desorption or dissociation of the adsorba rare gas collider replaces the reactive gas in model expmental and theoretical simulations of the collision-inducevents. This enables one to define and characterize thegas-adsorbate collision dynamics and its role in the collisiinduced reactivity of adsorbates.

Here we have limited ourselves to the simplest collisioinduced process which leads to desorption—CID. The fiquantitative description has been a theoretical one by Zet al.,2 who investigated the CID of Xe on Si by energetic X

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from the gas phase. It was then followed by similar studof the CID of N2 and Ar from W~100!.3,12 Experimentally,the CID process has been demonstrated and characterizethe first time by Ceyer and co-workers, who studied the Cof weakly bound CH4 on Ni~111!.4 Classical trajectoryanalysis based on a hard cube model13 has emphasized thdominance of direct impact collisions on the outcome ofactive CID events with highest probability for small impaparameter collisions. A more recent work by Levis and cworkers has focused on the ability to extract binding eneof an adsorbate from the threshold energy for CID. This hbeen demonstrated for the CID of NH3 and C2H4 fromPt~111!.6,14 The CID cross sections of these molecules bemore strongly bound~chemisorbed! are orders of magnitudelower than those measured for CH4 on Ni~111! at compa-rable incident kinetic energies of colliders. These studwere based on the hard cube model analysis,15 estimating aneffective surface mass as a fitting parameter.16 The CID ofadsorbed Xe on Pt~111! has recently been investigated folowing collisions with energetic Ar.8 In this study molecular

3 © 1999 American Institute of Physics

license or copyright, see http://jcp.aip.org/jcp/copyright.jsp

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3154 J. Chem. Phys., Vol. 110, No. 6, 8 February 1999 Romm, Asscher, and Zeiri

dynamics simulations were used to examine and analyzeexperimental data, concluding that for this system, at zcoverage limit, the dynamics can be well understood bysimple hard sphere–hard cube model. A unique enhancemof CID at grazing angles of incidence has been reportedthe O2/Ag(001) system. For off-normal incidence the crosection for CID was found to be 40 times larger than thatthe normal incidence collision geometry. The strong copling of the adsorbatex–y motion on the surface with itsmotion along thez direction mediated by the surface corrgation, was suggested as an explanation forobservation.17~a! Finally, desorption and dissociation of O2

from Pt~111! following energetic Xe collisions were verrecently reported as well.17~b!

The present work provides details on molecular dynaics ~MD! simulations of the CID process of N2 fromRu~001!. This system was recently investigated experimtally and the results have been presented in a prevpublication.18 The N2/Ru~001! system has been very wedefined by various surface characterization tools, e.g., lenergy electron diffraction,19 high-resolution electron-energy-loss spectroscopy~HREELS!,19–22 as well as workfunction and temperature programmed desorption~TPD!.23

Nitrogen interaction with ruthenium is a particularly intereing model system because of its high efficiency as a non-ammonia synthesis catalyst.24 The nitrogen molecule is adsorbed perpendicular to the surface at an on-top site.19 AnorderedA33A3R30° overlayer is formed atQ~nitrogen!5N2/Ru50.33, but the coverage can almost be doubledadsorption temperature below 85 K.19 Two TPD peaks aredetected following adsorption temperature below 85These seem to arise from two different adsorbed speciesto their quite different effect on the system wofunction.19,23 The low temperature species has been sgested to originate from laying down molecules formedhigher coverages,19 but there is no agreement on thassumption.20

II. MD CALCULATIONS

The simulations were performed using the stochaclassical trajectory approach.2,25 The surface was representeby a slab having two layers of movable Ru atoms whwere attached to two additional layers clamped to theirtice positions. Two movable layers have been verified tosufficient for a reliable description of energy exchangetween the collider and the substrate.2 Each one of the mov-able and the fixed layers were composed of 738556 metalatoms arranged to represent the Ru~001! surface. Periodicboundary conditions were imposed in the directions parato the surface~X and Y!. The interaction of the slab withdeeper layers of the crystal was represented by 56 fictitparticles2,3 coupled to the second layer atoms along theZdirection ~normal to the surface!.

The adsorbed N2 molecule was positioned at the centof the slab. Once the adsorbate was positioned on theeach atom was assigned an initial velocity. The initial veloties were sampled from a Boltzmann distribution at the sface temperature, fixed in all simulations at 90 K. After t


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initial positions and velocities of the slab atoms and thesorbate were defined, a standard thermalization procewas employed to obtain the initial conditions for eatrajectory.2,8

Following the thermalization, a collider~Ar or Kr! wasintroduced. Its initial position was fixed at a normal distanfrom the surface of'10 Å. The lateral position of the collider was fixed according to its predefined incidence poand azimuthal angles with respect to a random point onsurface near the location of the adsorbate. The collider’stial velocity was assigned according to the magnitude ofkinetic energy examined.

The parameters varied in the different calculationsclude the initial collider kinetic energy and its incidencangles~polar and azimuthal!. For each set of parameter1000–10 000 trajectories were calculated. A trajectory wterminated if one of the following conditions was fulfilled:

~1! A predefined maximum number of integration stepNmax, was reached. In the first set of simulations wassignedNmax52000, however, due to relatively smanormal velocity of some desorbates not all CID evewere accounted for. Hence, the results described becorrespond toNmax510 000. Since the time step usewas 1 fs, the above values ofNmax correspond to 2 and10 ps, respectively.

~2! Desorption of the adsorbate was recorded.

The quality of the simulations of systems such as thedescribed in the present work depends on the accuracy opotential energy surfaces~PES! used. In order to achievequantitative agreement between the calculation and theperiment, a reliable PES should be employed. In the folloing sections we shall describe the semiempirical potenfunctions used to represent the various interactions insystem.

A. Interaction among metal atoms

The interaction among the slab~movable! atoms hasbeen described by a model due to Head-Gordonco-workers,26 and assumed to be harmonic. It was demostrated there that harmonic interaction between nearneighbor ~n.n.! and next-nearest-neighbor~nnn! Ru atomsprovides an accurate representation of the Ru~001! surface.

B. Collider–substrate interaction

The interaction between the collider rare gas atom athe Ru~001! surface was described by a pairwise sumtwo-body potentials. Also in this case we have followHead-Gordon and co-workers26 and represent the Ar–Rupair interaction as a truncated Morse potential. This PESproven to reproduce accurately the results of adsorptionperiments by Menzel and co-workers.26 For the case whereKr was the collider, the equilibrium distance from the surfawas increased from 3.8 Å~Ar–Ru! to 4.3 Å ~Kr–Ru!.


3155J. Chem. Phys., Vol. 110, No. 6, 8 February 1999 Romm, Asscher, and Zeiri

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TABLE I. Parameters used to evaluate the PES for the Ar, Kr/N2 /Ru~001! system.

Interacting pair

Ar–N «Ar-N56.82731023 eV sAr-N53.252 ÅKr–N «Kr-N58.53431023 eV sKr-N53.685 ÅN–N DN-N59.773 eV bN-N52.670 Å21 Re,N-N51.10 ÅRu(i ) – N2~c.m.! Di -c.m.57.239531022 eV b i -c.m.52.500 Å21 Re,i -c.m.53.20 Å

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C. Collider–adsorbate interaction

The Ar–N2 interaction was represented by a sum of pawise potentials between the rare gas atom and each onitrogen atoms. The pair interaction was representedLennard-Jones~LJ! potentials,

V~RAr-N!54«Ar-NF S sAr-N

RAr-ND 12

2S sAr-N

RAr-ND 6G . ~1!

The parameters in Eq.~1!, « and s, were chosen such thaAr–N2 scattering data in the gas phase couldreproduced.3,27 The values of« ands used in the simulationsare shown in Table I for both Ar and Kr, the Kr values weestimated from comparison of gas phase interactions to gsurface data.27~c!

D. Adsorbate–substrate interaction

Billing et al.28 developed a semiempirical PES for thinteraction of nitrogen with Re~001!. This PES reproducethe available experimental data for this system. The expmental data for the N2/Ru~001! system, related to vibrationafrequencies and binding energies of molecular adsorptare quite similar to those of N2/Re~001!. The main differencebetween the two systems is that the dissociation probabof nitrogen on the Re~001! surface29 is an order of magnitudelarger than the corresponding value on Ru~001!.22,30,31Thus,the PES for N2/Re~001! included a dissociative channel anassumed that the lowest energy molecular adsorption geetry is with the molecular axis parallel to the surface.28 Thismolecular adsorption geometry was chosen since it issumed to be the transition state for dissociative adsorptIn the present study dissociative adsorption was not includue to its negligible probability for nitrogen oRu~001!.22,30,31However, it is well established that the molecular adsorption of nitrogen on Ru~001! is with the mo-lecular axis normal to the surface.19–21 Thus, the followingform modeled the adsorbate–substrate PES in the prestudy:

V~N22surf!5VMorse~N2!1 f ~u!(i 51

N

VMorse~Ri -c.m.!, ~2!

where Ri -c.m. represents the distance from theith surfaceatom to the position of the molecular center of mass andN isthe number of surface atoms in the simulation (N556). TheN–N and the Ru–N2~c.m.! interactions were represented bMorse functions:

VMorse~N2!5DNN~12e2bNN~RNN2Re,NN!!2, ~3a!

VMorse~Ri -c.m.!5Di -c.m.~12e2b i -c.m.~Ri -c.m.2Re,i -c.m.!!2.~3b!

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The Morse parameters for the nitrogen–Ru~001! poten-tial, Eq. ~3b!, were designed to reproduce the experimenbinding energy, N2 center of mass to metal distance aN2-surface vibrational frequency of the system.19–21The val-ues of the parameters of Eqs.~3a! and ~3b! used in thepresent study are shown in Table I. The termf (u) in Eq. ~2!ensured that the largest N2–Ru~001! binding energy is ob-tained at normal molecular adsorption geometry~choosingAtheta51.1, so that a ratio of 1:10 is obtained betweenadsorption energy in the normal adsorption configuratcompared to the energy of the laying down configuratioThe value ofAtheta does not affect the results of the CIdynamics!. The functional form used

f ~u!5~Atheta21!1cos2 u

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whereu represents the angle between the molecular axisthe surface normal. It should be noted that if parallel adsotion geometry is required the cos2 u term in Eq.~4! should bereplaced by sin2 u. For most of the simulations describebelow normal adsorption geometry was used to mimicN2/Ru~001! system. In a small number of calculations thparallel adsorption geometry was assumed in order to exine the influence of the adsorption geometry on the Cprocess. These situations may represent systems such2adsorbed on transition metals.

The N2/Ru~001! interaction potential for normal adsorption geometry, which had been verified by HREELS andmeasurements,19 is shown in Fig. 1 as a contour plot oftwo-dimensional cut parallel to the surface. The distancetween the N2 center of mass and the surface was fixed herZc.m.52.8 Å, which is the equilibrium separation. The threfold symmetry of the adsorption site is clearly seen. Tfunctional form chosen to represent the adsorbate–surinteraction results in adsorption sites located at the threehollow sites on the surface~Fig. 1, site A through all calcu-lations!, while high energy barriers are obtained at the on-site. This is in contrast to the experimental evidence whsuggests that the N2 adsorbs to the on-top sites on thRu~001! surface.19–21 To correct this discrepancy one hasformulate the adsorbate–surface interaction with a mmore complicated potential function~as compared to the onused here!. Since the proper symmetry of the PES is obtainusing the functional form described above, it was used incalculations discussed below. It is realized that this appromation may introduce some minor inaccuracies in thescription of energy transfer between the adsorbate andsolid atoms.

The energy barriers associated with the adsorbate moalong various pathways parallel to the solid surface are p


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sented in Fig. 2. The reaction path for surface diffusionbetween two neighboring threefold sites where the transistate is located at the bridge site. The energy barrier assated with such surface diffusion is about 20 meV. Such abarrier corresponds to a nearly free motion of the adsorbbetween neighboring threefold sites even at low tempetures. The magnitude of the energy barriers along two ational pathways is much larger~in the range 100–250 meV!.Thus, the Ru~001! surface is quite flat for motion amonneighboring threefold sites but it exhibits a much larger crugation along other directions.

The PES described above was designed to reprodmost of the available experimental data for the N2/Ru~001!system. However, it should be emphasized that it is a seempirical model to describe the various interactions insystem.

FIG. 1. Contour plot of the adsorbate–substrate PES in a cut parallel tosolid surface. The threefold adsorption sites are marked as A,B,C, anSee Fig. 2. The contour line spacing is 0.017 eV.

FIG. 2. Diffusion barriers along different directions parallel to the substrThe potential energy refers to the molecular nitrogen at the gas phase


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III. RESULTS AND DISCUSSION

The results of the simulations reported below correspoto the low coverage limit studied in the experiment wheninteraction among adsorbates can be neglected. Hence,the calculations a single adsorbate was used. In the followsections we present results of the calculation and a dission of the dynamics and mechanism governing the CID pcess in the following sequence: the cross section for CID,threshold energy for desorption, the distribution of final knetic energies of both desorbate and collider, final interenergy distribution, angular distribution of the desorbate acollider. After a summary of the basic results we draw tdominant mechanism of the CID event. The mechanism psented below is supported by thorough inspection of mspecific trajectories obtained under various initial conditio

A. Cross section for CID

The basic quantity calculated is the cross section,sdes,for the CID process. It is computed for a given set of indence energy, angle of incidence, and adsorption geomThe cross section for CID is defined as was previously sgested by Beckerle and co-workers13 as an area on the surface in which an impact of rare gas atom yields a CID evper one adsorbed nitrogen molecule. These cross secwere calculated by numerical integration of the opacfunction,32

sdes5E0

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wheref is the polar angle of the vector connecting the leral position of the adsorbate c.m. with the position of tpredefined impact point on the substrate,b is the impactparameter~the length of this vector,Z coordinates of the c.mand impact point are equal!, P(b,f) is the opacity function,andbmax is the largest impact parameter value beyond whno CID is observed. The opacity function was obtained frothe trajectory results.

The results of the simulations describing the variationsdes as a function of the incidence energy of the collideEin , at normal incidence (u in50°) and normal adsorptiongeometry are presented in Fig. 3. For comparison the expmental results18 are also shown in Fig. 3. Due to experimetal limitations, Ar was used as the collider forEin up to 2.25eV ~open triangles! while for largerEin values Kr was used~open circles!. This data should be compared to the corsponding calculated results with Ar and Kr as collid~closed triangles and circles, respectively!. Both experimentand simulation indicate that the CID process has a threshenergy,Ein5Ethr , below which no desorption is observeFor the N2/Ru~001! system both experiment and simulatioyield Ethr50.5 eV. This value ofEthr is about twice the mag-nitude of the adsorbate–surface binding energy. Moreoboth experiment and simulation results indicate that the mnitude ofEthr is independent of the incidence angle18 ~see thefurther discussion below in Sec. III B!.

Comparison between the experimental and calculatedsults forsdes(Ein ,u in50°) shows an excellent agreement fincidence energies up to;3.0 eV. Above thisEin value the

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FIG. 3. sdes as a function of incidence collider energyexperimental~open symbols!, calculated for normal ad-sorption geometry~closed symbols!, calculated for par-allel adsorption geometry~closed symbols!. The dottedline through the experimental data points is based onexpression described in Ref. 18.

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increase of the experimentalsdesis faster than the calculateone. This discrepancy is unclear at the moment.

To examine the dependence ofsdes on the adsorptiongeometry simulations were performed at threeEin values us-ing parallel adsorption. The calculatedsdes’s for this adsorp-tion geometry are also shown in Fig. 3 as closed invertriangles. It is clear that in theEin range examined here thcross section for CID is independent of the adsorption geetry atu in50°.


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Another comparison between experimental and callated results is shown in Fig. 4. Here, the relationshiptweensdes and the collider incidence polar angle~measuredfrom the surface normal!, u in , is presented for fourEin val-ues. Again, very good agreement between the experime~open squares! and calculated~closed triangles! data is ob-served for the case of normal adsorption geometry. Forenergy valuessdes exhibits a small increase as a functionu in up to u in540°. For larger incidence angles a rapid i

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FIG. 4. Experimentally measured~open squares! andcalculated~up triangles for normal adsorption geometrand inverted triangles for parallel adsorption! sdes as afunction of incidence angle for four incidence energvalues.


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crease in the magnitude of the CID cross section is obserCalculated cross-section values forEin52.25 eV using par-allel adsorption geometry are also shown for threeu in values.It is clear that for off-normal incidence angles thesdesvaluescorresponding to normal adsorption are much larger tthose for parallel adsorption. This variation ofsdesas a func-tion of the u in is manifested by the changes in the opacfunction obtained for different incidence angles. Figureexhibits the variation ofPdes(b) as a function ofb ~inte-grated overf! for two u in values at normal and paralleadsorption geometry. It should be noted that the opafunctions for both normal and parallel adsorption correspoto Ein52.25 eV. Foru in50° at both normal and paralleadsorptionPdes(b) exhibits a peak nearb51.0 Å followedby a rapid decay to zero atbmax>3.0 Å. The difference be-tween the two adsorption geometries is at near zerob values.For normal adsorptionPdes(b) is close to unity atb50,while in the case of parallel adsorptionPdes(b) starts at amuch lower value. These results suggest that the magniof bmax for u in50° is independent of the adsorption geometry. An increase ofu in to 60° results inPdes(b) which maxi-mizes atb50 Å and decreases monotonically as the impparameter increases. Here, for both normal and parallel

FIG. 5. Opacity function for normal and parallel adsorption atEin52.25 eV,u in50° and 60°.


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sorption the opacity function has a low probability tail whicextends to largeb values. Comparison ofPdes(b) for bothadsorption geometries shows that the low intensity tailPdes(b) for parallel adsorption extends to a smallerbmax

value than that for normal adsorption. This difference istributed to the smaller geometrical cross section ‘‘seen’’the collider in the case of parallel adsorption geometry. Tgeometrical cross section is defined8 as an area on the surfacep(r ads1r gas)

2/cosuin in which the gas atom~presentedas a hard sphere! impacts the adsorbate~presented as a harsphere as well!. Here, r ads and r gas are the van der Waalsradii of the adsorbate and gas atom, respectively. Theduced geometrical cross section for parallel adsorptionto its lower profile at the adsorbed state results is musmallersdes value atu in560°.

To summarize, the good agreement between the expmental and calculated results indicates that the semiempiPES used in the simulation allows a reliable descriptionthe Ar/N2/Ru~001! system.

B. Threshold energy for CID

The threshold energy (Ethr) for desorption is defined athe minimum energy of the collider required to induce dsorption. As it follows from this definition,Ethr is closelyrelated to the binding energy of the adsorbate. Levis aco-workers6,14,16,33,34proposed a new method to establish tbinding energy of an adsorbate based on the experimenmeasured threshold energy for desorption. Employinghard sphere–hard cube~HSHC! model for CID, the bindingenergy was calculated by the following equation, as sgested by Kulginov and co-workers:8

Ebinding5Ethreshold

4mcolmads

~mcol1mads!2 F12

4madsmM

~mads1mM !2G3cos4S u in

2 D , ~6!

wheremcol and mads are the collider and adsorbate massrespectively,mM is an effective substrate mass, whichequal to a few times of the mass of a surface atom, andu in isthe angle of incidence. Expression~6! yields Ebin(N2–Ru)50.23 eV with Ar as the collider and the substrate effectmass is 1.5 times that of Ru atom. This value is in goagreement with our independent measurement of the action energy for desorption of N2 from Ru~001! based on TPDline shape analysis. However, it contradicts the valueabout 0.4 eV obtained by Menzel and Feulner.19 To obtainEbin50.4 eV by Eq.~6! one should substitutemM56mRu

which is thought to be physically meaningless. To furthclarify the relationship between the binding energy andthreshold energy for the CID process we increasedDi -c.m.

~see Table I! to obtainEbin50.4 eV and used this modifiedPES in the MD simulation. The trajectory calculation prducedEthr'0.85 eV, which agrees very well with the valucalculated from Eq.~6! given mM51.5mRu, but is 70%higher than the experimental value shown in Fig. 3.

Although the simplified HSHC model provides gooagreement with the experimentally measured quantit



FIG. 6. Final kinetic energy distributions for N2 ~a! and Ar ~b! at normal incidence, together with those of N2 ~c! and Ar ~d! for u in560° atEin52.25 eV.

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Ethr (u in50°) andEbin , for N2/Ru~001! system, assumingthe abovemM value, it cannot explain the experimental oservation thatEthr is independent of the angle of incidence18

As follows from Eq. ~6!, Ethr is expected to increase witu in .

The total cross section for CID,sdes, was shown byBeckerle and co-workers13 to increase withu in . This is dueto the faster increase of the geometrical cross section~corre-lates with cosuin!, versus the decrease of the normal enecomponent~correlates with cos2u in ), considered to be relevant for CID within the HSHC model. The magnitude of tincrease, however, is far too small to explain the resultsserved in the N2/Ru~001! system. Moreover, the HSHCmodel predicts the same results for any adsorbed moleregardless of the specific details of the molecule–metalteraction potential. This is shown to be incorrect in our cawhere we compare the two model adsorption configuratiof N2 — the normal and the parallel ones. The strong depdence onu in is observed only in the case of the normadsorption while the parallel geometry reveals practicallydependence on the angle of incidence, as seen in Fig. 4.limited ability of the HSHC model to treat polar angle dpendence of the CID cross section is further demonstratethe O2/Ag~100! system.17 Here,sdes increases by a factor o40 asu in increases from normal incidence to 60°. This canbe explained by any version of the HSHC model.

Since the total threshold energy scaling, as well assdes

enhancement withu in for N2/Ru~001! CID ~see Sec. III A,


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C. Kinetic energy distributions

Following the impact of the rare gas collider with thadsorbate, it scatters back into the gas phase. The detathe scattering event are dominated by the PES, whichscribes the interaction among the collider, adsorbate, andsubstrate atoms. The amount of energy transferred fromcollider to the adsorbate–substrate system depends onmass ratios, the magnitude of the impact parameter ofrare gas atom with respect to the adsorbate, and the natuthe interaction potentials. The presence of the adsorbatthe surface may be viewed as a source of surface corrugaas seen by the collider. Following the inelastic scatterevent, in addition to a change in the collider’s translationenergy, one also expects changes in its momentum vewhich in turn determines its angular distribution.

1. Total energy distributions

Typical kinetic energy distributions,F(Ekin), of Ar ~atEin52.25 eV! and the desorbed N2 molecules following aCID event are shown in Fig. 6 for two incidence angleu in50° and 60°. In the case of normal incidence, both dorbed N2 and Ar exhibit a relatively narrow distributionpeaked at 0.4 and 0.6 eV, respectively@Figs. 6~a! and 6~b!#.


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At low b values, near head-on collision between the Ar athe adsorbed N2, the collider might scatter back to the gaphase with negligible interaction with the substrate. Hoever, in most cases it is deflected by the adsorbate towardsubstrate and scatters back to the gas phase following alision with the surface@see Fig. 14~a!, for example#. Forlarge b values, the collision between the Ar atom and tadsorbate results, in all cases, in a deflection of the rareatom from its initial trajectory followed by its collision withthe solid surface@Fig. 14~b!#. Mirror collisions were rarelyobserved for highEin and u in560°. According to the massratio of Ar/N2 the expected energy transfer from the rare gto the adsorbate is 97%~based on kinematics!. On the otherhand, in a collision between Ar and the substrate about 6of the collider normal energy is expected to be transferrethe solid~based on the hard cube model with substrate eftive mass of 1.5 the Ru atomic mass!. The kinetic energydistribution of the scattered Ar@Fig. 6~b!# indicates that onlya negligible fraction of the scattering events correspondcollision between the Ar and the adsorbate followed bydirect deflection of the collider back to the gas phase~with-out collider–surface interaction!. In most cases the Ar atominteracts with both adsorbate and substrate prior to its reto the gas phase. This is also supported by the kinetic endistribution of the desorbed N2 molecules which is peaked amuch lower energy than that expected based on kinemconsiderations with no surface presented. Detailed anaof energy transfer processes between the collider andadsorbate–substrate system is complicated since the Ar2

interaction also induces redistribution of the collider enebetween normal and parallel motion of the adsorbate.both species the kinetic energy distributions extend toproximately half of the magnitude ofEin at all incidenceenergies examined with somewhat less kinetic energy in2.

The desorbate and collider kinetic energy distributiocorresponding to off-normal incidence angle exhibit differeshapes@Figs. 6~c! and 6~d!#. In this case,F(Ekin) for Ar@Fig. 6~d!# is broad and bimodal extending to high energwith peaks at approximately 0.2 and 1.8 eV. A similar bimdal distribution is observed for the desorbates with peak0.2 and near 1.4 eV@Fig. 6~c!#. The analysis of the trajectorresults shows that the desorbate high energy peak, andspectively, low energy peak of Ar stem from the direct clision with small impact parameter (0,b,2.5 Å!. In con-trast to the normal incidence case, here the collider odoes not interact directly with the substrate and scatters bto the gas phase after collision with the adsorbate. Asimpact parameter increases, the interaction between thesorbate and the collider becomes weaker, and less enflows to the desorbate and the CID yield decreases. Scollisions withb.3.5 Å do not produce desorption. In addtion, mirror collisions were rarely observed for high incdence energy.

These variations in the shape of the kinetic energy dtributions at off-normal incidence may be rationalized by tfollowing argumentation. The sequence of collisions, i.collider–adsorbate and collider–substrate, is expected topend not only on the magnitude ofb but also on the positionof the impact point on the surface,Rim , with respect to the


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adsorbate. WhenRim is positioned between the adsorbate athe initial position of the collider the rare-gas atom is epected to collide first with the substrate and then, on its wout to the gas phase, with the adsorbate presenting so-c‘‘mirrorlike’’ collision. A reversed sequence of collisions iexpected to occur whenRim is located behind the adsorbatMoreover, in this case one expects that in many eventscollider will be deflected to the gas phase directly aftercollision with the adsorbate in a ‘‘gliding collision.’’ Thesequence of collisions together with the magnitude ofimpact parameter will determine the energy distributionsthe system after the scattering event.

2. Energy distributions by impact parameter

To illustrate the variation of the kinetic energy distribtions as a function ofb, at the twou in values examined, thechanges in average kinetic energies,^Ekin(b)& for the givenimpact parameter range are shown in Fig. 7. For normalcidence the Ekin(b),Ar& @Fig. 7~b!# first decreases whenbincreases from 0 to;1.5 Å, passes through a minimum, therises back and levels off, while for the desorbate N2 the^Ekin(b),N2& @Fig. 7~a!# exhibits an initial monotonic shift tohigher energies asb increases from 0 to;1.5 Å followed by

FIG. 7. Distributions of average final kinetic energies of N2 ~a! and Ar~b! asa function of impact parameter.



FIG. 8. Variation of Êkin& as a function ofEin fornormal angle of incidence~desorbates and collider!.

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a shift to low energies for larger impact parameters. Sbehavior is expected since lowb values correspond to stronAr–N2 interaction that decreases as the impact paramincreases, however the minimum inÊkin(b),Ar& and maxi-mum in Êkin(b),N2& for the same value of the impact parameter indicates that the most effective collision geomeis not the line of centers at normal incidence. It is interestto note that CID events at incident energy of the collider nEthr andu in50° were obtained at average impact parameequal to 0.9 Å. This is very similar to the value of 0.7reported at the threshold for CID of Xe from Pt~111! studiedby Rettner and co-workers.8

The variation ofÊkin(b)& as a function of the impacparameter for off-normal incidence shows a completely dferent behavior~Fig. 7!. Here, smallb values result in amarked excitation of the desorbates leaving the collider wvery small energy. Increasing the impact parameter leadsdecrease in the amount of energy transferred from thelider to the desorbate@Fig. 7~a!#. Hence, an increase ofbresults in a monotonic decrease of the desorbate enewhile collider energy is shifted to higher energies. Thecharacteristics of Ekin(b)& for the collider and desorbateare consistent with the discussion above. It should be nothat theÊkin(b)& for the collider includes both reactive annonreactive events. Analysis of the data clearly showsmost of the high energy tail in theEkin(b)& of Ar corre-sponds to nonreactive scattering.

The shape ofF(Ekin) andF(Êkin(b)&) was found to beindependent of the incidence energy in the range 0.8,Ein

,6 eV. However, these distributions were shifted to highenergies as the magnitude ofEin increases. In addition, thtranslational energy distributions obtained in the case of pallel adsorption geometry were very similar to those for nmal adsorption~described above!. The shift ofF(Ekin) as afunction of Ein for the two adsorption geometries examincan be deduced from the variation of the average colliderdesorbate kinetic energy,Êkin&.

3. Average final kinetic energy

The dependence ofÊkin& on Ein for u in50° ~integratedover impact parameters! is shown in Fig. 8. In addition to


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Êkin(N2)& ~open circles! and Êkin(Ar) & ~closed triangles!the average energy of collider following only CID eventsalso shown~closed squares! as well as the results obtainefor parallel adsorption geometry. In the entireEin range theaverage kinetic energy of the desorbates is less than theresponding values for the collider. It is also clear that evewhich do not lead to desorption, result in largerÊkin(Ar) &.Comparison of the results obtained for normal and paraadsorption geometry shows thatÊkin(N2)& does not exhibitany marked dependence on the initial adsorbate configtion with respect to the substrate. The variation ofÊkin(Ar) &with its incidence energy, looks nearly linear within the icidence energy range examined, with a slope of appromately 0.3. In the case ofEkin(N2)& the initial rate ofchange is approximately 0.25 in the range 0.5–1.5 eV.larger Ein values the rate at whichEkin(N2)& changes de-creases to approximately 0.18. This change in the ratewhich Êkin(N2)& varies is related to an increased enertransfer into the rotational mode of the desorbate~see thediscussion below!. We note that the sum of the average knetic and rotational energy of desorbates and collider eqapproximately half of the magnitude ofEin . Hence, in theincidence energy range studied, approximately half ofinitial collider energy is channeled into the substrate degrof freedom. Similar examination of the variation ofÊkin& asa function ofu in shows a nonlinear increase as the incidenangle increases for both desorbates and collider. It is fothat up tou in530°, Êkin& is practically constant, while forlarger incidence anglesEkin& exhibits a near linear increaseMoreover, the rate at whichEkin& changes for largeu in in-creases as a function ofEin . Again, practically identical be-havior was observed for the two adsorption geometries sied.

D. Internal energy distributions of N 2

The analysis of the internal energy distributions in all tsimulations performed did not yield any vibrationally excitedesorbates. The energy transferred from the collider toadsorbate was found to be distributed among the trantional and rotational modes only. Typical rotational distrib


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tions, F(Erot), of the desorbates foru in50° and 60° atEin

52.25 eV are shown in Fig. 9~a!. These results clearly suggest that at normal incidence the energy transferred toadsorbate is channeled more efficiently into rotational mtion than in the case of off-normal incidence. Both distribtions exhibit a low energy peak which is followed bymonotonic decrease with long high energy tail. For normincidence, the high intensity part ofF(Erot) is broad andnearly uniform up to;4.0 kcal/mole and the high energy taextends up to approximately 17 kcal/mole. Foru in560° thedistribution is dominated by the peak atErot50.25 kcal/molewhile the high-energy tail extends only to approximately

FIG. 9. ~a! Rotational energy distribution of desorbates forEin52.25 eV atnormal angle of incidence andu in560°. ~b! Distributions of average finalrotational energy of N2 as a function of impact parameter for bothu in50°and 60° atEin52.25 eV.


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kcal/mole. Analysis ofÊrot(b)& @Fig. 9~b!# for u in50°shows that forb in the range 0–1 Å the average rotationenergy grows and then rapidly falls down for larger impaparameters,b.1 Å. Similar examination of Erot(b)& foru in560° reveals practically constantÊrot(b)&. In all the im-pact parameter range the tails of the rotational energy dibutions extend to much lower maximumErot values as com-pared to the corresponding values in the case of norincidence.

Similar analysis ofF(Erot) for parallel adsorption geometry at the sameEin value shows that the distributions anearly independent of the incidence angle. Here for both nmal and off-normal angles of incidence the rotational disbutions are strongly peaked atErot50.25 kcal/mole followedby a fast decrease, having a high energy tail up to apprmately 12 kcal/mole. These shapes are very similar to thobtained for off-normal incidence angle in the case of normadsorption geometry.

In order to examine the relation between the desorbrotational energy and the collider incidence energypresent the dependence ofÊrot& on Ein for u in50° in Fig.10. A nonlinear relationship betweenÊrot& and Ein is ob-tained. At low collider incidence energy~up to approxi-mately 1.0 eV! Êrot& is small and nearly constant, above thvalue,Êrot& increases more rapidly and reaches a near lindependence onEin above 1.5 eV. This nonlinear variation oÊrot& may account for the change in slope ofÊkin(N2)& vsEin nearEin51.5 eV discussed above. Comparison betwethe Êrot& values obtained for the two adsorption geometrshows that in the case of parallel adsorption a smaamount of energy is channeled into the desorbate rotatiomode. This difference is related to the CID mechanism oftwo adspecies and will be discussed below.

The variation ofÊrot& as a function of the incidenceangle for fiveEin values corresponding to normal adsorptiand one to parallel adsorption is shown in Fig. 11. In the cof normal adsorption geometryErot& exhibits a linear de-crease for increasing values ofu in . Again, the rate of Erot&decrease varies as a function ofEin , namely, larger incidenceenergy corresponds to a faster decrease ofÊrot& as a func-tion of incidence angle. A quite different behavior is o

FIG. 10. Êrot& as function ofEin for normal and paral-lel adsorption at normal incidence.


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served for parallel adsorption geometry. In this caseÊrot&exhibits a slow increase when the incidence angle increaThus, Êrot& at u in560° is larger by about 25% than thcorresponding value atu in50°. These characteristics of thdependence ofErot& on u in are closely related to the CIDmechanism and will be discussed in Sec. IV.

FIG. 11. Êrot& as a function ofu in for different Ein values. The paralleladsorption case is shown for comparison~crosses!.


es.

E. Angular distributions

1. Polar angles

The polar angle distributions,F(uout), for both colliderand desorbates atu in50° and 60° for Ein52.25 eV areshown in Fig. 12. In all cases the initial azimuth incidenangle of the collider was chosen to bef in50°, namely, theprojection of the velocity vector of the incident particle othe ~001! XY plane is directed along the110& crystallo-graphic axis~negative direction of theX axis in Fig. 1!. In allsimulations a broad distribution was obtained, which covthe entire angular range. For normal incidence the collidistribution @Fig. 12~b!# exhibits broad and nearly constaprobability for scattering into the angular range of 1,uout,35°. The correspondingF(uout) for the desorbates@Fig. 12~a!# shows a much narrower distribution with a pecentered arounduout560°. The distributions for both col-lider and adsorbate for off-normal incidence [email protected]~d! and 12~c!# are similar. Here, the distribution is shifteto large scattering angles and the peaks for both colliderdesorbate are located nearuout565° – 70°. Inspection of thecorrespondingF(uout(b)) shows that at normal incidencebroad and almost uniform distributions are obtained for

FIG. 12. Polar angular distributions (uout) of both Arand N2 at Ein52.25 eV at u in50° ~a!, ~b! and u in

560° ~c!, ~d!.


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,b,0.5 Å for both collider and desorbate. At larger impaparameters, in the range 0.5–1 Å, a peak centered aro65° is observed for both species. Further increase ofb resultsin a shift of the collider distributions toward low scatterinangles with peak centered around consecutively decreauout values. Similarly, the desorbate distributions correspoing to b.1 Å exhibit a single peak whose center is shiftgradually to larger scattering angles. Since the probabilityCID decreases for increasing values ofb, the broad peakobserved for the collider in the range 10°,uout,35° ismainly a result of nonreactive events. In the case ofu in

560° narrow distributions are obtained for both Ar and2for the entire impact parameter range. In this case the peof all distributions are near 65° independent ofb value.These results indicate that a large fraction of the enetransferred to the adsorbate is converted into desorbatenetic energy in the directions parallel to the surface. Texcitation of the adsorbate translational motion alongsurface is related to the mechanism by which the CID pcess occurs and will be discussed below.

Examination of the polar angle distributions obtainedparallel adsorption geometry shows features similar to thdescribed above. The main difference is that for normalcidence angle the peak of the desorbate distributionF(uout)is located closer to the surface normal, nearuout545°. Themain contribution to this lower scattering angle is due to Cevents with impact parameters in the range 0.5–2 Å. TCID events which correspond to theb values outside thisrange lead to broad uniform distributions covering the enuout range.

2. Azimuthal angles

Here we define the azimuthal angle of the desorbatescolliders after the scattering event as an angle between^110&direction ~positive direction of theX axis! and projection ofthe velocity vector of the projectile on theXY plane. Thisdiffers from the definition of the azimuthal angle of incdence~see Sec. III E 1!.

The distributions of the azimuthal angles,F(fout), ofthe various species are expected to depend strongly onincidence polar angle of the collider. Foru in50° one wouldexpect a uniformF(fout) while for off-normal incidenceangleF(fout) is expected to be much narrower with a pein the forward direction. The azimuthal angle distributionthe desorbates at normal adsorption geometry forEin55.5eV at twou in values are shown in Fig. 13. Indeed, at normincidence a broad distribution~which spans the whole 2prange! is observed, Fig. 13~a!. The broad distribution ob-tained for normal incidence is nonuniform and it exhibthree peaks located nearfout530°, 150°, and 270°. Thesvalues correspond to the directions at which the three brisites are located around the threefold hollow adsorption~Fig. 1, site A!. Thus, the structure ofF(fout) at u in50°reflects the symmetry of the substrate dictated by the cogation seen by the adsorbate. Similar results were obtawhen parallel adsorption geometry was used. Examinatiothe distribution of the average desorbate kinetic energyfunction of fout results in a broad distribution with threpeaks located at the angles whereF(fout) exhibits high in-


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tensity. This correspondence between the two distributiindicates that the corrugation seen by the adsorbate alongsurface has a major role in the successful completion ofCID process.

The F(fout) corresponding to off-normal incidencangle atu in560°, Fig. 13~b!, is much narrower with a peakat fout5180°. This distribution is expected based on kinmatic considerations and due to the symmetry of the sstrate. Nearly opposite to this incidence azimuthal anglefinds a bridge site through which the desorbate can peneto collide with the substrate atom located behind the bridsite. In most of the events studied this interaction leads toescape of the adsorbate to the gas phase, see Fig. 1incidence azimuthal anglesf in other than along the110&direction the variation ofF(fout) should correspond to dif-ferent corrugation seen by the desorbate on its way to thephase. Comparison betweenF(fout) observed forf in50°,30°, 90°, and 270°~here f in is defined as in Sec. III E 1!shows that the narrowest distribution corresponds tof in

50° and broadest one tof in530°. In all cases the distribution is centered aroundfout5180°1f in as expected fromkinematic considerations.

FIG. 13. Azimuth angular distributions (fout) of N2 for Ein55.5 eV, f in

50°, atu in50° ~a! and 60°~b!.



FIG. 14. Four typical trajectories (Ein54 eV! at u in50° and 60°. Foru in50°, b51 and 2.6 Å~a!, ~b!, for u in560°, b51 and 4.9 Å~c!, ~d!.

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IV. CID MECHANISM

To gain insight into the details of the CID mechanismlarge number of individual trajectories with different impaparameter values were carefully examined for the enerange Ein50.8– 5.5 eV and both normal and off-normangle of incidence. Four typical examples forEin54 eV areshown in Fig. 14. For each incidence angle a pair of trajtories are shown to illustrate the sequence of events at vous b values that lead to desorption. Note that theX,Y,Zscales are not identical. Foru in50° the two trajectories correspond tob51 and 2.6 Å@Figs. 14~a! and 14~b!#, respec-tively. As the projectile approaches the adsorbed nitromolecule, the repulsion between the collider and uppeatom rises and causes the molecule to tilt and bend tow


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the surface plane approaching a parallel geometry. Thesorbate acquires the largest torque when the collision geetry is not line of centers, but with the impact parameterthe range 1–1.5 Å@see Fig. 7~a!#. In this case, the collisionbetween the Ar atom and the adsorbate results in a laamount of energy transferred into the frustrated rotatiomode of the adsorbed molecule as well as into translaparallel to the surface@note the large polar angle at which thdesorbate leaves the surface,uout Fig. 12~a!#. Part of theenergy in these two modes is transferred into kinetic enein the direction normal to the substrate, which in turn leato desorption. The energy transfer into motion along the sface normal is possible due to the coupling of this mode wthe frustrated rotation and parallel motion modes by the crugation of N2–Ru PES. A detailed dynamic picture of th


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kind discussed above is of course impossible withinHSHC model, where parallel momentum is assumed cstant.

For off-normal incidence the motion of the molecuparallel to the surface prior to its desorption becomes mprobable. Figures 14~c! and 14~d! demonstrate the CIDevents forEin54 eV andu in560° at two impact parametevalues. The parallel momentum transfer from the incomAr atom into translational and rotational modes of the asorbed N2 molecule leads to the tumbling of the adsorbaalong the surface. This motion is again coupled withmotion normal to the surface by virtue of the PES corrution.

Thus, the dominant mechanism of the CID is direct ipulsive bimolecular collision, in which collider energytransferred into the frustrated rotation of the adsorbatekinetic energy along the surface plane, and into the surfAlthough the amount of energy transferred into each of thchannels is dictated by the collision geometry, the eneacquired by the adsorbate upon collision is effectively chneled by the corrugated molecule-surface PES into thetion normal to the surface. At normal incidence as a resulsignificant excitation of the frustrated rotation this degreefreedom is kept by the molecule all the way to the gas phfollowing desorption. At off-normal incidence the frustraterotation is less important in the CID sequence, and desorleaves the surface rotationally colder. Meanwhile, at onormal incidence the kinetic energy of the collider morefectively channels into the kinetic energy of the desorbaand the latter leaves the surface translationally more excrelative to the normal incidence case.

V. CONCLUSIONS

Classical molecular dynamics simulations have beperformed to understand the details of the collision-indudesorption~CID! of very low coverage N2 from Ru~001!,following collisions of Ar and Kr in the energy range o0.5–5.5 eV. Semiempirical potential energy surfaces~PES!have been employed to describe the slab of two layers omovable surface atoms and the interactions of the nitromolecules with the metal and between the colliders andadsorbed nitrogen and the metal. These potentials are bon dynamical observables which have been determinedperimentally. The computed CID cross sections (sdes) basedon these PES were found to describe very well the expmentally determinedsdes as a function of incident energand angle of incidence.

The threshold for CID has been determined at 0.5which is half of the binding energy of N2 to Ru~001!, in fullagreement with the experimental data. This is used asindependent determination of the adsorption energy of mlecular nitrogen of 0.25 eV, erroneously used in the literatas 0.4 eV. Enhancement of the CID cross section at laangles of incidence has been reproduced accurately, reing a unique CID mechanism. At the same time it rulesthe ability to analyze the results on the basis of the simhard cube–hard sphere~HCHS! model, often used to explainCID processes.


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Kinetic energy distributions of the scattered rare-gasoms following direct collision with the adsorbate and of tdesorbing nitrogen molecules were obtained and resolvea function of the collision impact parameters. These distritions suggest that direct hit of the collider on the adsorbatthe predominant way to lead for CID. Close to half of thinitial colliders’ kinetic energy is transferred to the solialmost independent of the incident energy.

Polar and azimuthal angular distributions of the desoing nitrogen have been calculated. Both are strongly depdent on the colliders’ angle of incidence but hardly chanwith incidence energy. At normal incidence collisions, tazimuthal distribution of the desorbing molecules is pdicted to reproduce the substrate hexagonal symmetry.

There is absolutely no vibrational energy excitationthe desorbing N2 as a result of the CID process. Rotationexcitation, on the other hand, is significant and providesimportant insight into the CID mechanism. It increases learly with incidence kinetic energy, but it decreases asangle of incidence increases for the same colliders’ kineenergy.

Finally, these observations have led to the followiCID mechanism for the weakly chemisorbed N2 on Ru~001!,with its molecular axis perpendicular to the surface: Asresult of the impact between a rare-gas atom and the nitroadsorbate, energy is transferred into frustrated rotation ormotion of the nitrogen molecule. In addition, translationmotion and migration along the surface is also caused byimpact. The coupling between these modes and the monormal to the surface results in desorption. This couplingdominated by the PES corrugation.

ACKNOWLEDGMENTS

This work has been partially supported by a grant frothe Israel Science Foundation and by the German IsFoundation. The Farkas Center for Light Induced Procesis supported by the Bundesministerium fu¨r Forschung undTechnologie and the Minerva Gesellschaft fu¨r die ForschungmbH.

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molecular dynamics simulations of collision-induced...

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