Dynamics of Hydrogen Molecules Produced on a Graphite Surface

Dynamics of Hydrogen Molecules Produced on a Graphite Surface

YoonheeKo, Jongbaik Ree,* YooHangKim： andHyung KyuShin*

*Author to whom correspondence should be addressed. E-mail:

jbree@chonnam. ac .kr

Department of Chemistry Education, Chonnam National University, Gwangju 500-757, Korea

‘Departmentof Chemistry and Center for ChemicalDynamics, Inha University, Inchon402-751, Korea

^Departmentof Chemistry, University ofNevada,Reno, Nevada 89557, USA Received May29, 2002

Wehavestudied the dynamics of energy-rich hydrogenmoleculesproduced on a graphite surface throughH(g) +H(ad)/C(gr) tH2(g) + C(gr) at thermal conditions mimicking the interstellar medium using a classical trajectoryprocedure. The recombinationreaction of gaseous H atom at 100 Kand theadsorbed H atom onthe interstellargraphite grains at 10 K efficiently takesplace on a subpicosecondtime scale with most of the reaction exothermicity depositingin the productvibration, which leads to a strongvibrational population inversion. The moleculesproducedin nearly end-on geometry where H(g) is positionedbelow H(ad) rotate clockwise and are morehighly rotationally excited, but inlow-lyingvibrationallevels.The rotationalaxisof most of the molecule rotating clockwise istilted from the surface normalby more than 30o, the intensity peakingat35o. The moleculesproduced when H(ad) isclose to thesurface rotate counter-clockwise and are weakly rotationally excited, but highly vibrationally excited. These molecules tendtoalign their rotational axes parallelto the surface. The number of molecules rotating clockwise is eight times largerthan thatrotating counter-clockwise.

Key Words : Graphite,Hydrogen, Classical trajectory, Interstellar, Vibration

Introduction

Therecombination reaction ofgas-phaseatomichydrogen with adsorbedhydrogenatoms on a solid surface has been known to occur in a direct gas-adatom collision.1-7 An amorphous graphite surface is one such system on which hydrogen recombination has been studied extensively in recent years as a result ofastrophysical interests. Atomic hydrogenis by farthe most abundantgaseousconstituentin the interstellar medium. When graphite grains are highly porous, hydrogen atoms which interact weakly with the surface sites can be trapped interstitially. In such an environment,theweakly adsorbedatomcanbe formed on a graphite site8 where it interacts with the incidentgas atom, and their recombination on interstellar dust grains is believed to be the leading hypothesis for the formationof H2 incold interstellarclouds.9-15

In ref. 16, we have studied the reaction of gas-phase atomic hydrogen reacting with adatoms in the limits of chemisorption and physisorption. Inthe chemisorptionlimit theadatom-surfaceinteractionisconsidered to bethetypical C-H bond energy (3.30 eV), whereas in the physisorption limit it is a weak van der Waals (vdW) interaction (39.3 meV). On the otherhand, density functionaltheory (DFT) shows17 that hydrogenatoms exclusively chemisorb on top of a carbonat shortrange (around 1.5 A), the regionwhich has been considered in recent studies.18-21 The DFT study also shows the existence of a physisorption region around 3 A and thepresenceof both adsorption regionsseparated by a barrier.17 The latter study indicatesthat the physisorption

description is consistent with the vdW model. We have already explored the role of this region in the formation of hydrogen molecules.16

In this paper, as anextension of the work in ref. 16, we study the recombination dynamics of hydrogenatoms ona graphitesurfaceatthe thermal conditionsappropriate to the interstellar medium,wheretheinterstellar grains arenear 10 K and the gas is at 10-100 K,18 using the physisorption region consistent with the vdW model.16 In thephysisorption limit, vibrational and rotationalstatesare found to behighly excited. The major focus ofour study is to elucidate the vibrational and rotational distributions and extent to which these distributions are related to rotational orientation and alignment inthe interstellarmedium. From the solution of equations of motion ofprimary system atoms, we firstesta­ blish the occurrence ofreaction and extents ofvibrational and rotational excitation. We then study the dependence of reaction probability onthe impact parameter, rotational and vibrational population distributions in relation to the orientationof product molecules.

InteractionMod이

The incidentgas atom H(g) approaches a graphitesurface on which hydrogen atoms are adsorbed. We consider the reaction between H(g) and H(ad) preadsorbed onthecenter atom C(0), whichis surrounded by12nearby carbonatoms of threebenzene rings. H(g) is in interactionwith all 12 surface sites C(i), i = 1-12. Figure 1 shows the numberingof these atoms on the surface layer anddefinitions ofthe pertinent coordinates. The reaction zone atoms are the incident gas atom H(g), the preadsorbed atom H(ad) and the center

Figure 1. Interaction model showing the gas-phase atom H(g) denoted by H(p, Z,也)，interacting with the adsorbed atom H(『ch, Q 0), H(ad), adsorbed on C(o), which is coupled to the N- atom chain and is surrounded by 12 sites. The Nth atom of the chain is coupled to the heat bath. The H(g)-to-C(i) distance is denoted by zhs,l For clarity, the 2nd and 3rd surface atoms are not shown.

graphite atom C(0). The model considers C⁽⁰⁾ as the Oth member ofthe (N+1)-atom chain which links the reaction zone to the heatbath, providing a quasiphysical picture of energy flow betweenthe reaction zone and thechain atoms and,inturn, between thechain and theheat bath.22,23

A totalof six degrees offreedom isnecessary to describe themotionsof H(g)and H(ad)abovethesurface.Although it is straightforward to transform these coordinates to the center-of-mass and relativecoordinate systems, we find that itis convenientto describe the collision system in terms of theatomiccoordinates for the gasatom H(xh,⁾h,zh) andfor the adatom H(xh’jh’,zh’).16,23 The H(ad) coordinates arexh’

=rcisinHcosQ)h’ = rcHsinOsin。^，andzh’ = rcicosQ i.e., H(xh’, yr, zh’)= H(rcH,0,0), where rcH is the adatom-to- C(o) distance and 0, 0 determine the orientation of the adatom-C(o) bond with respectto the surface normal and the x-axis, respectively; see Figure 1. The H(g)-to-H(ad) distance rHH is (p2 + z2)1/2, wherep is the distancebetween H(g) and H(ad)-surface normal axis, and z is the vertical distance from H(g) to the horizontal line determining the position of H(ad).Notethat theinitial (t — -00) valueof p is the impact parameter b. TheprojectionofrHH onthe surface plane is oriented by the angle 鱼fromthe x axis. Thus, the coordinate (xh, yH, zh) can be transformed into the cylindrical system (p, Z,⑵，where Z is the normalH(g)-to- surface distance. The vertical distance z is then z = Z- rcHcosO. The initialstateof the reaction zone is the gasatom approaching the surface atthe initialcondition of(p, Z,⑵

with thecollisionenergy E when theadatomtakestheinitial valuesof (rcH,0, 0).Thus, the occurrence of each eventcan be determined by studyingthe time evolution of the H(g)- surfacedistance Z, theH(ad)-surface bond distance rCH and the H(g)-to-H(ad) distance rHH for the ensemble of gas atoms approaching the surfacefromalldirections.

Each reactive events can be described in terms of the interactions of H(g) with H(ad), C(o), 12 adjacent carbon atoms and N chain atoms. We construct ananalytical formof thepotentialenergysurface(PES)by combining a modified London-Eyring-Polanyi-Sato (LEPS) potential energy function with the 0, 0-hindered rotational motions and the harmonic motions ofthe (N+1)-chain atoms including the vibrationofC(o).23 ThecompletePESis

U ={Qhh+ Qhc+ Qhs - [Ahh2 +，hc2 + Ahs2 - Ahh&c

-(A^hh4hc)/4^hs]1/2} + 1/2k^o(O - 0^e)2+ 1/2k⁰0- 0^e)2 + £ (1/2Mc 她2&2)

i

+ £ (terms of type 1/2M^c处f&-1&,

i

1/2M^cffl^b,」+¹2掂+1,etc.), (1) where k^o and k^© are force constants, 0^e and 0^e are the equilibrium angles, M^c is the mass ofthe carbon atom, g's arethevibrationalcoordinates of the (N+1) atoms,㈣ is the Einstein frequency, and 气 is the coupling frequency characterizingthechain. The explicitforms of thecoulomb terms (Q，s) and exchangeterms (4s) written in the Morse­ typefunctions are well known. These energy terms contain theadjustableSato parameters0's). In the reactionzone, we have three interactions, namely H(g)-H(ad), H(ad)-c(0) and H(g)-c(0). For these interactions, the coulomb and exchange energies are

Qk =1/4[Dk/(1+Ak)][(3+Ak)e(zke-砂k - (2+6Ak)e(%-zk⁾/2ak], (2a) Ak= 1/4[Dk/(1+Ak)][(1+3Ak)'福_zk)/ak - (6+2Ak)e(zke-zk⁾/2ak],

(2b) where k= HH, H(ad)C(o) and H(g)C(o) for H(g)-H(ad), H(ad)-C(o) and H(g)-C(o),respectively.Here, Zke is the equili­ brium value of the kth atom-atom distanceZk and ak is the Morse-type range parameter. The H(g)-H(ad), H(ad)-C(o)

and H(g)-c(0) distances are

zhh={p2+ [Z - (dcH + xch)cos

0

]2}1/2, (3a)

zhc=0ch + xch) +go, (3b)

zhs(0)={Z2+ [psin⑦_{+ (}dcH +xcH)sin0]2

+[(dcH + xcH)sinO+ cos/]2}1/2, (3c) respectively, wherexch is the displacementofthe H(ad)-C(o)

distance from its equilibrium value dcH i.e.,rcH =dcH+xch. We now add the 12 terms ofthe interaction between H(g) and adjacentsurface sitesto Qhs(0) and Ahs(0) andreferto the sumastheH(g)-surfaceinteraction:

Q^hs= Q^hs(0)+ 1/4[Dhs/(1+ Ahs)] Z[(3 + 晶部网防辑»따프； -(2 +6A^Hs)e(zHSe-H,i)/2aHs], (4a) /hs= /hs(o)+ 1/4[Dhs/(1 + Ahs)] £[(1 +3A^Hs)e('ZHSe'ZHS-i)lc^，HS

-(6+2AHS)e(ZHSe-W/aHS], (4b) wherezHs,i is the distance between H(g) and the ithcarbon atom. Since each H(g)-to-surface atom distance zhs,i is ZHs,i(rCH0O,p,Z,⑵，the potential energy surface has the functional dependence U(rCH0©,p,Z,@{g}), where {g}=

(g^o, &,…,

&

ⁿ) for the vibrational coordinates ofthe (N+1)- chain atoms.

Forthe H-Hinteraction,thebinding energy is D0 =4.434 eV at Z^HHe=0.7414 A.24Withthefrequency 6«hh/2

^

c=4401 cm-1,24 we find the exponential range parameter a^HH = (Dhh/2j

U

hh)1/2/

"

Hh = 0.257 A, where Dhh = D0+1/2h

"

^Hh

and 段田 isthereduced mass.

The vibrational frequency of the van der Waals bond between H(ad) and the graphite surface can be determined using the inverse-power-law potential V(rcH)= Dvdw

x [(o/rcH)10-(o/rcH)6] in the WKB eigenvalueexpression25 幣*H [Ev -Dhs - V(rCH)]1/2drCH= ^v+ ；), (5)

where r*CH and r*C*H are theouter and innerturning points, respectively. Using b=3.38A and the well depth D^vdw = 39.3 meV,8 we find the vibrationalfrequency 188 cm-1 for the weak H(ad)-C^(o)bond.Therange parameter for the vdW bond is found to be 0.387 A. We use the same sato parameters as in Ref. 16. The set is ^Ahh= 0.30for H(g)- H(ad), AH(ad)c(o)= 0.40 for H(ad)-C(o), and ^Ahs=0.40 for H(g)toeachof the 13 surface-layergraphite atoms.

To study thereactive event, we follow thetime evolution of the reaction system by integrating the equations of motion, which describe the motions ofthe reaction-zone atoms and N-chain atoms. An intuitive way to treat the dynamics ofthereactioninvolvingmanysurface atoms is to solve themotionsof thereaction-zone and N-chainatoms in the presence of 12 H(g)-C interactions governed by the molecular time scale generalized Langevin set of the equations of motion.22 The details of the formulation of these equationshavebeendescribedelsewhere,26 butwill be reviewedbriefly here withseveral relevantexpressions. The equations ofmotion for the gas atomand adatom areinthe form

mjYj (t) =-dU( rcH，e0P^，Z,^,{g}) Xj, (6) where Y's are Zp,^rCH,^。,。forj =1, 2, ..., 6, respectively, with mi = mH, m2 =

^

hh, m3 =/hh, m4 =/hh, and m5 = mm

= /hh. Here 卩 is the reduced mass and Iis the momentof inertia. For the (N+1)-atomchaindynamics,wehave23

g^o (t)=-就^og^o( t)+戒写(t)

-M-i du(Z^hs,,O0P,Z,0,(g})/dg^o (7a)

g^j(t) =-"^jj(t)_+就jg^j-i( t) + 就_,j +i g^{j +i}(t )^，

j=1,2,.., N-1 (7b)

gN(t) = -^NgN(t)+ "c NgN - i (t) -

P

^{n + i} gN(t) 뉘N + i (t) (7c) Here, Qnis the adiabatic frequency andfN⁺ⁱ(t) determines the random force on the primary system arising from thermal fluctuation inthe heat bath. The friction coefficient

P

ⁿ+i is very close to n"D/6, where

"

^d is the Debye frequency. The Debye temperature of graphite is 420 K.27 All values of the frequencies andfriction coefficients have beenpresented elsewhere.28 The initial conditions required to solve these equationshavealreadybeen given inanearlier paper.26

Thenumerical procedures include extensiveuse of Monte Carlo routines to generate random numbers for initial conditions. The first step is to sample collision energies E fromaMaxwelldistributionat the gastemperature T^g andto weight theinitialenergyofH(ad)-surface and all chainatom vibrations by a Boltzmann distribution at the surface temperature T. Insampling impact parameters,we takethe flat rangeof0< b < bmax,where bmax = 2dCC =2.842 A. Also sampled are the initial values &⁾, @⁾and 血.Thus, each trajectory is generated with the set (E,b,e" ,&⁾,@^o,血,

{g}o), where E^ch is theinitialenergyofthe adatom-surface vibration and{g}o representstheinitialvalues of {g^o,gⁱ,....,

&

ⁿ}. Thetotal numberof trajectories sampledis 30000. We

follow each trajectory for 50ps, which isa sufficiently long time for H²(g) to recede from the influence of surface interaction, to confirm the occurrence of a reactive event forming H²(g). Furthermore, we confirmthateachtrajectory can be successfully back-integrated in the computational procedure. Wetakethechainlength of N= 10.28

Results andDiscussion

A.Reaction Probability. Theprobability ofH² formation in the reaction H(g)+H(ad)/C(gr)t H²(g)+C(gr) is 0.248 at Tg= 100 K and Ts= 10 K,and the H2 formationoccursin a direct collision between H(g) and H(ad) on a subpico­ second scale. It can be compared with the probability of 0.534at different thermal conditions for thesamesystem T

=1500 K, Ts = 300 K).i6 The ensemble-averaged reaction time is 0.198 ps. Thus the recombination takes place efficiently at such an extreme thermal condition which mimickstheinterstellar medium. But, it is interesting to note that this probabilityis significantly smallerthan that forthe hydrogenchemisorbed surface. That is, Farebrotheret al.i8 showed that atthegastemperature 100 K forwhich the most probable energy is 0.013 eV, the recombination is more efficient for the hydrogen chemisorbed surface. somewhat largerprobabilities 0.4-0.6 are found atthe collision energy 0.1 eV inthecalculation by Parneix and Brechignac,15 who haveused Dch= 0.665eV, whileFarebrother et al. used Dch

=1.58 eV18On theother hand,theprobability based on Dch

=0.57 eV the calculations of Jeloaica and Sidis17 represent-

(q)d-

= - -

a o -

£

a*응

0.0 -

o 2 3

Impact Parametner b (A)

Figure 2. Dependence of the reaction probability P(b) on the impact parameter b. The thick solid line is for the cw orientation and the thin solid line for ccw.

ingrelatively weak chemisorption sites, is 0.503 at Tg= 100 Kand Ts = 10K.20

In Figure 2,we showthe dependence of H2 formation on theimpact parameter in the range from b= 0 to bmax = 2.84 A. (We will discuss the two curves denoted by "cw” and

“ccw” in the next section.) Except near 0.2 <b< 1.2 A collisions, the opacity function takes a significant value, in particular in the collisions where b>2.4 A. Nine carbon sites are configured in the range between this distance and 2dcc =2.842 A. This result indicates that H(g) approaching close proximity to the surface with an impact parameter fallinginthis range tends tomove toward H(ad) onC(0). At shortrange,the surface atoms produce a repulsivewall and steer H(g) in the direction of H(ad) forH² formation. We note that the total reaction cross section defined as G= 2n

j

P(b)bdb is as large as 9.22 A2. Sha and Jackson, using quantumscatteringmethods and theenergy of the physisorb- ed H of0.036 eV, reported cross section to be about 8 A2 around Ei = 0.1 eVfor thephysisorbed H case.21

B. Reactive Trajectories. In Figures3a and 3b we show two trajectories, each representing the representative trajectory producingthe samedirectionof orientationof H² when it begins the upward journey from the surface. To study this orientation problem, we first note that in both figures, the trajectories at the instant of the initial impact (i.e., the first minimum ofthe H(g)-surface distance) are below the H(ad)-surface distance. When H(g) approaches closerange to thesurface, its interaction with H(ad)weakens theH(ad)-surface bond. The upward motion ofH(ad) when H(g) approaches the first H(g)-surface minimumrepresents this situation and the motion results in the H(ad)-surface distancebeingincreased by nearly 1A.As shown in Figure 3a, after reachingthe first minimum H(g) begins to attract

(V)Q°

u --뜨

a

-0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5

Time (ps)

Figure 3. Time evolution of the H(g)-surface, H(ad)-surface, and H(g)-H(ad) distances for (a) the cw orientation and (b) the ccw orientation.

the outgoing H(ad) to form H(g)-H(ad), i.e., H2. The well- organized oscillation ofthe H-H distance beyond the first maximumconfirmstheformation of a stableH2 molecule. It is important to notice that the first minimum ofthe H(g)- surfacedistance and thefirstmaximumoftheH(ad)-surface distance occur at nearly the same instance, thus indicating that H² forms with nearlyend-on(or vertical) geometrywith H(g)atthebottom. In Figure 3b, H(g) rebounding from the surface after theinitial impact affectstheadatomtoformH2. In this case, unlike the previous case shown in Figure 3a, H(ad) is now closer to the surface at the instant ofthe H2

formation. For some trajectories, the H(g)-surface and H(ad)-surface distances are not significantly different from each other,but theH(ad) end isstill closer tothe surface.We now discuss this difference between the two representative trajectories.

Fortherepresentativetrajectory shown in Figure 3a, H(g) at thesecond minimum is asclose to thesurface as that atthe minimum (the first impact) at which H² is formed. But

thereafter the minima ofthe H(g)-surface distance diverge.

Inanonzero-^collision,H(g)of the rotatingH2 immediately after the H2 formation is attracted toward the surface site which has just released H(ad). As the nascent molecule begins its journey away from the surface, this attraction causes the H(g) endto movetoward the axisnormal to the C(o)site so that the molecule commences a clockwise (cw) rotation. In particular, since the forces of the subsequent impacts (second in the representative case) exert a large torque,thereceding molecule is hurledintoa high rotational state with the cartwheeling-type rotation. A similar result has been observed in the scattering ofN2 on Ag(111).29 Nearly 89% of the reactive trajectoriesundergo this type of rotation. In this case, the reaction takes place on a sub­ picosecond scale when H(g)reachesthefirst turning point, so the incident angle determines the angle at which H² forms.

In Figure 3b, on the other hand, the second minimum of theH(g)surfacedistance is now much farther away from the surfacethanthe firstminimum. Itis morethan 2 A farther.

As shown in Figure 3b, the dynamics of this representative case is verydifferentfrom that of Figure3a. In particular,the incidentatomapproachesthesurface much closerthan in the case shown in Figure 3a and then rebounds to a larger distancebefore it is attractedback by H(ad) toform H². In thiscase,whentheH(ad)-surfacebond breaks and H² forms, the H(ad) end of H² tends to move away from the surface site, thus causingthe nascent molecule to begin a counter­

clockwise (ccw) motion. The product molecule for therest ofreactivetrajectories(11%)undergoesthistype oforienta­ tion. We now notethat,asH(g) turns aroundthecorner atthe closest approach and bounces back tothefirstmaximum, a significant amountof acceleration ofthe trajectory occurs.

This acceleration produces strong vibrational excitation as seen by a large amplitude motion with a large vibrational periodoftheH-Hdistancebeyondthefirstmaximumofthe trajectory (compare theH-Hdistance in Figure3b with that in3a).

Now we return to Figure 2 to discuss the cw and ccw curves. The hydrogen molecule produced in a large-b collisionhas a strongtendencytorotate clockwise. Whereb

> 2.4 A, theprobability of forming such molecules is signifi­ cantly large. Thisrange is J3 dec <b< 2dcc, corresponding tothe region near H-C(i), i =2, 3, 4, 6, 7, 8, 10, 11 and 12.

However, in H(g)-H(ad) interactions where the impact parameter is smallerthan 1.0 A, theprobability offorming cw molecules diminishes. On the other hand, the ccw probabilitytakesmaximumvaluesnear b = 0,and decreases to zero in the region where the impact parameteris larger than 0.4 A. In Figure 2, the ccw andcw curves show their maximumnearb=0 and 2.8 A,respectively, corresponding approximatelytotheregionsnearH(ad)-C(0) and near H-C(i), i = 2, 3, 4, 6, 7, 8, 10,11 and12, respectively. Thiscalculated rotational orientation arises from corrugation in the gas­ surface interactionpotential.

The dynamics ofH(g)approaching thesurface closer than theH(ad)-surfaceseparationimplies that the incident angle,

Figure 4. Relative intensity distribution of the alignment angle r for the molecules undergoing cw and ccw orientations. The dotted lines is the sum of cw and ccw components.

어nc defined in Figure 1, is larger than 90o. In a direct collision, which takes place onthe subpicosecond scale,the value of this angle at the instant of the H² formation is strongly correlated with the alignment of the H² rotational axis. Theangle r between theaxisof rotation of H2 and the surface normal at the instant of H² formation can be determinedfromthis angle, and its distributionprovidesthe information on the rotational alignment ofH². InFigure 4, weplotthedistribution ofr for all reactivetrajectories. The cw case has the maximum distribution near 35o. That is, whenH(g) is closer to thesurface and binds with H(ad), the product molecule tends to leave the surface in an inter­ mediatestate betweenthe cartwheel-like and helicopter-like rotations. It is interesting to compare this result with the cartwheeling-type rotation of N², when it scatters from Ag(111) in nearlyend-ongeometry.29Ontheother hand,for themajority of H² leavingthesurface with ccw rotation, the rotational axis is over 80o, in particular the maximum distribution occurs near 90o, indicating cartwheel-like rotations when H(ad) iscloser tothe surface and binds with H(g) in nearlyhead-on geometry. Themolecule, which starts out with suchhead-on geometry, is notparticularlyefficient in carrying a large amountofrotational energy. As shownin Figure 4, we find no productmolecules with the rotational axisperpendicular to thesurface.

C. Vibrational and Rotation지 Energies. The difference between the H-H andH-surface interaction energy is 4.751 eV,sotheenergyavailable to theproductstate is 4.751 + E + E^ch . The vibrational motion is found to share most of the reaction exothermicity, thus producingvibrationally highly excited H² molecules. The ensemble-averaged vibrational energyof H² is aslarge as 3.43 eV.

Vibrational Quantum Number v

Figure 5. Relative intensity distribution of the vibrational popula­

tion for the cw and ccw molecules. The solid line is the sum of cw and ccw components.

>

'-su£

UI O A - U- H

Rotational Quantum Number J

Figure 6. Relative intensity distribution of the rotational population for the cw and ccw molecules. The solid line is the sum of cw and ccw components.

Thevibrationalenergyof H2 for the representative trajec­

tory considered in Figure 3a is 0.750 eV, whereas that in Figure 3b is 3.45eV. Such a largedifferencecan beexpected from aqualitative comparisonofthe H-Hdistance shown in the two figures. Here we have determined the energy deposited inthevibrational motion of H²(g) from theusual expressionEvb =p비‘2mH2 + D^hh[1 -e(2HHe-2HH)/2aHH]2, sum of kinetic and potential energies. To mimic the quantum vibrational distribution, we use a binning procedure of assigning quantum number v correspondingto E^vbthrough the relation v= int[E^vib/E(v)], correspondingtothevalues of Kolos et al.30 As shown in Figure 5, the intensity of vibrational population distribution for hydrogen molecules produced in the reaction is trimodal (see the curvefor the sum), which is anoverlap of thedistributionsof cw andccw rotatingmolecules.Thepopulationdistributionisthe largest for v=9, but the intensity is still significant event near the dissociationthreshold. On the otherhand, it is interesting to note that the vibrational excitation for the chemisorbed case16showsthepopulation maximumappearingatv= 3. In general, for both cw and ccwcases vibrationalenergies are highlyexcited, and theresulting populationdeviatesserious­ ly from the Boltzmann distribution. In particular, highly vibrationally excited states are dominated by H² rotating ccw. As noted above in Figure 3b, a significant amount of accelerationofthetrajectory occurs afterturningthe closest approach,resultingin suchhigh vibrationalexcitation.

The distributions ofrotational population are shown in Figure 6, where the rotational quantum number J corre­

sponding to the calculated energy Erot is determined using the same binningprocedure introduced above: J=int[Erot/ E(J)] with Erot = Z2/2UHHrHH2 and EJ)= J(J+1) h 2/2Ihh,

where L is the angular momentum

^

hh(z/7 -pZ). The cw trajectory receives a torquefrom the steep sideofthe H(g)- surface interaction as the H(g) end rapidly goes around the turning point(see Figure3a). Asa result, a closer approach of H(g) to thesurface atthe second impact after thefirst full rotation results in strong rotational excitation. These cw molecules begin their orientation and alignment when the two atoms combine in nearly end-on geometry and the highest cwpopulation occurs at J = 4. However, the distri­ bution of ccwrotationalpopulation is concentrated atlower rotational states. Since lowrotationalexcitationleavesmore energy for vibration, a ccw rotatingmolecule usually has a larger amount of vibrational energy compared with a cw molecule. The ensemble-averagedvibrationalenergyis4.69 eV for the ccwmolecules, but the corresponding energy is only 3.27 eV for the cw case.

ConcludingComments

We have studied the recombination ofgaseous hydrogen atoms with weakly adsorbed hydrogen atoms on a graphite surface atthe thermalconditionsmimicking the interstellar medium. Therecombination reaction is veryefficient and H² formation occurs on a subpicosecond time scale. Product molecules are strongly vibrationallyexcited and their popu­

lationdeviatesseriouslyfromtheBoltzmanndistribution.

Therotational motion of H2 can be oriented either clock­ wise or counter-clockwise. We have determinedtheorienta­ tion by followingthe trajectories atthe very early stage of recombination. Clockwise orientation results for the mole­ culeforming fromnear end-ongeometryonthe surface. The molecules rotating clockwise are in low-lying vibrational

levels. However, the molecules rotating counter-clockwise havethe rotational alignment closelyparallel tothe surface with weak rotationalexcitation. The molecules withrotational motion oriented counter-clockwise are highly vibrationally excited. The number of molecules oriented clockwise is significantly largerthan that of molecules oriented counter­ clockwise.

Acknow ledgment. Computationaltime wassupported by a NSF Advanced Computing Resources grant at the San Diego SupercomputingCenter and bythe 3rdSupercomput­ ing Application Support Program of the KISTI (Korea Institute of Science and Technology Information). J. R.

gratefully acknowledges the financial support from the Chonnam National Universityin hissabbatical year of 2001.

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