8371
J. Phys. Chem. 1991, 95, 8371-8376
An Image Charge Model for the Classical TraJectorySimulations of Molecule-Surface Scattering: Steric Effects In the Scattering of CHF, on Graphlte(0001) Irina V. Ionova, Stanislav I. Ionov,* and Richard B. Bernsteint Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90024 (Received: February 6, 1991)
An image charge model is presented for the molecultsurface interaction potential. This model may be a convenient analytical
appmximation of quantum chemistry calculations because it give9 correct asymptotical behavior of the interaction potential at large molecultsurface separations. The image charge potential is used for classical trajectory simulations of the scattering of oriented CHF, molecules on a graphite (0001) surface. The thermal motion of the surface is described by a simplified generalized Langevin equations (GLE)method. The model predicts a higher sticking probability and a larger translational energy loss at the impact for the "hydrogen down" orientation of the incoming molecules, which agrees with recent experimental observations. The calculations recover the experimentally observed functional dependencies of the probability of direct scattering and the steric effect in the scattering probability vs surface temperature. However, the calculations give smaller sticking probabilities than those experimentally observed. The quantitative discrepancy is attributed to the oversimplified treatment of the surface motion.
Introduction In the past few years there have been several successful experimental investigations of the stereospecificity of moleculesurface interaction via scattering of oriented molecule^.^-'^ In a series of papers, Stolte and Kleyn with ~eworkers'-~J-~ and then Heinzmann with co-~orkers'.~~ reported orientation effects in the scattering of NO on several metal surfaces. It has been found that the orientation of the molecules in the incident beam affects the angular distribution of the directly scattered beam,' the trapping/scattering pr0bability,2~*''and the postcollisional rotational state distribution.' Most of these experimental results have been interpreted by a theor&ical analysis which included classical trajectory simulation^'^^'^ and quantum calculations of wave packet pr~pagation.'~J*In the calculations, the orientation dependence of molecule-surface interaction was introduced phenomenologically by including into empirical moleculesurface interaction potentials the terms proportional to Pl(cos e) and P2(cos e), where PI and P2 conventionally stand for the first and the second spherical harmonics and 0 is the angle between the surface normal and the molecular axis. Recently, the Bernstein group at UCLA has reported the orientation dependencies of the scattering probability for 13 plyatomic molecules on graphite(OOO1).&l' The authors observed that the molecules prefer to stick if they have been preliminarily oriented with respect to the surface in such a way that the side of the molecule having the highest charge density attacks the surface. This observation implies an electrostatic nature of molecule-surface attractive interaction. In the following experiments the group examined in detail the surface temperature effects in the scattering of oriented CHF3 and t-BuCI molecules on the same ~ u r f a c e . Q The ~ ~ experimental results of the Bernstein group can be summarized as follows: (i) The sign of the steric effect, which has been defined as the relative difference in the scattering probabilities for the opposite initial orientations R = AP/P,correlates with the charge distribution within the molecule.'O*ll(ii) The magnitude of the steric effect is proportional to the average degree of molecule orientation in the incident beam,&12R a (cose). (iii) The net probability of direct scattering obeys an Arrhenius dependence P a: exp(-B/ T ) , where Tis surface temperature.I2 (iv) The steric effect declines with the surface temperature asI2 R a a / T b. (v) The steric effect in the scattering probability is accompanied by the orientation dependence of the postcollisional translational energy of the directly scattered beam.I3 These experimental observations can be understood qualitatively from simple classical 'hard-cube"
+
To whom correspondence should be addressed.
'Deceased July 8, 1990.
0022-3654191 /2095-8371S02.50/0 .~ , I
I
-
TABLE I: Bod Length8 (A), Bond Angles (de& Atomic Chrgea of a Neutral CHF, Molecule, rad tbe van der W u l s RIdjlg (A) of tk Atom Constitutin~tbe Molecule
C-H
C-F LFCF
1.098 1.332 108°48'2"
atom
chargea
H
0.665 0.184 -0.283
C F
van der Waals radiusz6 1.2
1.35
consideration^'^ as well as from a more involved quantum approach based upon the concept of optical potentiaLm Both approaches rely upon the existence of some orientation dependence in the molecule-surface interaction without analysis of its origin. In the current study, we introduce an image charge model of molecule-surface interaction in order to carry out classical trajectory simulations of the scattering of oriented CHF3 molecules (1) Kuipers, E. W.; Tenner, M. G.; Kleyn, A. W.; Stolte, S.Nature 1988, 334, 420.
(2) Tenner,M. G.; Kuipers, E. W.; Kleyn, A. W.; Stolte. S.J. Chem.Phys.
1988,89, 6552.
(3) Kleyn, A. W.; Kuipcrs, E. W.; Tenner,M. G.; Stolte, S.J. Chem.Soc., Faraday Trans. 2 1989,85, 1337. (4) Fecher, G.; Volkmer, M.; %wering, N.; Pawlitzky, B.; Hcinzmann, U. J . Chem. SOC.,Faraday Trans. 2 1989,85, 1364. (5) Kuipers, E. W.; Tenner, M. G.; Kleyn, A. W.; Stoltc, S. Chem. Phys. 1989, 138, 451. (6) Kuipers, E. W.; Tenner, M. G.; Kleyn, A. W.; Stoltc, S.Phys. Reu. Lett. 1989, 62, 2152. (7) Tenner, M. G.; Genzebrock, F. H.; Kuipers, E. W.; Wiskerkc, A. E.; Kleyn, A. W.; Stolte, S.;Namuki, A. Chem. Phys. Lett. 1990, 168, 45. ( 8 ) Curtiss, T. J.; Bernstcin, R. B. Chem. Phys. Lett. 1989, 161, 212. (9) Mackay, R. S.;Curtis, T. J.; Bernstein, R. B. J. Chem. Phys. 1990, 92, 801. (IO) Mackay, R. S.;Curtis, T. J.; Bernstein, R. B. Chem. Phys. Lett. 1989, 164, 341. ( I 1 ) Curtiss, T. J.; Mackay, R. S.; Bernstein. R. B. J. Chem. Phys. 1990, 93, 7387. (12) Ionov, S.I.; LaVilla, M. E.; Mackay, R. S.;Bernstein, R. B. J. Chem. Phys. 1990, 93, 7406. (13) Ionov, S.I.; Lavilla, M. E.; Bernstein, R. B. J. Chem. Phys. 1990, 93, 7416. (14) Fecher, G. H.;Ewering, N.; Volkmcr, M.; Pawlitzky, B.; Heinzmann, U. Surf Sci. Lett. 1990, 230, L169. Fecher, G. H.; Volkmer, M.; Powlitzky, B.; Heinzmann, U. Vacuum 1990.41, 265. (15) Muhlhausen, C. W.; Williams, L. R.; Tully, J. C. J . Chem. Phys. 1985, 83, 2594. (16) Kuipers, E. W.; Tenner, M. G.; Kleyn, A. W.; Stolte, S.SurJ Sci. 1989,211/212, 819. (17) Hollowav. S.: Halsted. D. Chem. Phvs. Lett. 1989. 154. 181. (18) Corey, 6,C.i Lemoine, D. Chem.Phys. Lett. 1989, 166, 324. (19) Ionov, S. I.; Bemstein, R. B. J . Chem. Phys. 1991, 94, 1564. (20) Levine, R. D. Chem. Phys. Lett. 1990,174, 1.
0 1991 American Chemical Society
Ionova et al.
8372 The Journal of Physical Chemistry, Vol. 95, No. 21, 1991
on a graphite (0001) surface. The model incorporates the ideas of distributed multiples2' that have been successfully implemented by Buckingham and Fowler22for the calculations of the structure of simple van der Waals clusters. The distributed multipole model, which describes the electrostatic field generated by a polyatomic molecule, has been also used recently for the analysis of the preferential orientation of a molecule physisorbed on a surface.23 The presented classical trajectory simulations of the scattering of oriented CHF3 molecules on a graphite (0001) surface recover the experimentally observed direction of the steric effect. The computational results agree qualitatively with the experimental data of Ionov et al.'Zl3 However, the quantitative agreement has not been achieved for the absolute value of the probability of direct scattering which is attributed to the oversimplified treatment of the surface thermal motion. Image Charge Model of MoleculeSurface Interaction The proposed model is based upon the following picture of molecule-surface interaction. The charge distribution within a neutral polyatomic molecule creates an electrostatic field. This electrostatic field polarizes the crystal which, in turn, creates an additional electrostatic field imposing a force and a torque on the incoming molecule. In the current study we assume that the electrostatic field around an isolated polyatomic molecule can be approximately given by the field of point charges located on every atom of the molecule. The sum of those charges is equal to zero because we are considering neutral molecules only. In fact, the above approximation is the first term in the expansion given by the distributed multipole model.21 The magnitudes of those charges can be calculated by quantum chemistry. In the following trajectory calculations of the scattering of CHF3 on graphite(0001) we use the charges and bond lengths reported in refs 24 and 25, respectively (see Table I). It is well-known from the textbooks on electricity that a point charge q above a dielectric (or metal) surface induces a polarization in the solid such that the field from the polarized media outside the solid is equivalent to the field from an image charge q'which is located under the surface in the position of the mirror image of the real charge.27 The magnitude of this image charge is given by
Figure 1. The image charge model describing the attractive forces between a molecule and a surface as the electrostatic forces between molecular charges and their images under the surface. It has been assumed that the electrostatic field from the molecule can be represented by the field of point charges located on every atom of the molecule.
where qj is the charge of thejth atom and Fii is the vector from the image of thejth atom to the ith atom of the molecule. The repulsive interaction which dominates at short distances is considered to be directed along the surface normal. We use the following expression for the repulsive force imposed on the ith atom Frcpi= -ci exp(-&(zi - R,))
(3)
where zi is the distance between the ith atom and the surface and
Ri is the van der Waals radius of the atom. The parameters pi
Levine, R. D. Submitted to J. Phys Chem. (24) Brundle, C. R.; Robin, M. B.; Basch, M. J. Chem. Phys. 1970, 53,
characterize the steepness of the repulsive wall. In the following calculations we use p = 8.8 au (4.65A-*) for all atoms, which is consistent with Lennard-Jones potential.28 It should be mentioned, however, that reljable values of pi can hardly be determined from "hand-waving" arguments. In general, they should be obtained from quantum chemistry calculations; otherwise, they may be treated as adjustable parameters. The coefficients ci can be found numerically assuming that at the minimum of the interaction potential for a given orientation the closest to the surface atom is separated by the correspondent van der Waals radius from the surface. For CHF3, we have obtained cH = 1.64 X au and cF = 5.0 X 10" au from the analysis of the "hydrogen up" and "hydrogen down" orientations. It is assumed that no repulsive force is acting directly on the central carbon atom of the molecule. The only problem that has been swept under the carpet so far is the value of ell in eqs 1-4. It has been assumed in the above discussion that the surface is polarized by an electrostatic field from a molecule. However, in the course of scattering the field from incoming and outgoing molecules on the surface is ac. The frequency of this field can be estimated asf = (dE/dt)/E = 3u/& where E 0: 1 / 3 is the electric field, u is the velocity of the molecules, and Ro is the equilibrium distance between a molecule and the surface. Assuming & = 5 and u = 5 X lo4 cm/s, we getf= 3 X 10l2Hz, which corresponds to the far-infrared region of the spectrum (A = 100 pm). Consequently, one should use the dielectric constant corresponding to this frequency. Unfortunately, we have not been able to find the value of ell for graphite a t f x 3 X 10l2Hz. It has been reported in refs 29 and 30 respectively that ell = 2.8 in the optical region and ell 1 10 at lo6 Hz. The corresponding coefficients (ell - l)/(ell + 1) at these frequencies are equal to 0.5and 2 0.9, respectively. In the far-infrared region one may expect the coefficient (eII - l)/(cll + 1) to be between those numbers, probably closer to 0.9. In the following trajectory simulations we use (ell - l)/(el, + 1) = 0.8.
2196. (25) Ghosh, S. N.; Trumbarulo, R.; Gordy, W. J. Chem. Phys. 1952,20, 605. (26) Pauling, L. The Nature of the Chemical Bond; Cornell University Press: New York, 1960. (27) See, for example: Landau, L. D.; Lifshitz, E. M. Electrodynamics of Continuous Media, 2nd ed.; Pergamon Press: Oxford, 1984; rev. enl. by
(28) Allen, M.P.;Tildesley, D. J. Computer Simulation of Liquids; Oxford University Press: New York, 1987. (29) Kelly, B. T. Physics of Graphite; Applied Science Publishers: London, 1981. (30) Groenewege, M. P.; Schuyer, J.; van Krevelen, D. W. Fuel 1%5,34,
ell
-1
-
where ell is the dielectric constant of the solid in the direction of the surface plane. (In the case of a metal ell and q' = -4.) As seen from the negative sign in the formula, this image charge imposes an attractive force on the charge above the surface because ell is usually greater than 1. Similarly, a system of charges creates the mirror image system as depicted in Figure 1 for CHF3. Therefore, the attractive part of the force acting on the ith atom of the incident molecule is given by
(21) Stone, A. J. Chem. Phys. Lett. 1981,83, 233. (22) Buckingham, A. D.; Fowler, P. W. J. Chem. Phys. 1983, 79,6426. Buckingham, A. D.; Fowler, P. W. Can. J. Chem. 1985, 63, 2018. Buckingham, A. D.; Fowler, P. W.; Stone, A. J. Int. Rev. Phys. Chem. 1986, 5, 107. Buckingham, A. D.; Fowler, P. W.; Hutson, J. M. Chem. Rev. 1988, 88, 963. (23) Whitehouse, D. B.; Buckingham, D. A.; Bernstein, R. B.; Cho, V. A.;
E. M. Pitaevskii.
339.
The Journal of Physical Chemistry, Vol. 95, No. 21, 1991 8373
Scattering of CHF3 on Graphite(0001)
1-1 I
I
@a Particle 2. y ,
Center of mass - surface distance / A The CHF3-graphite(0001) interaction calculated for ‘hydrogen up”, “hydrogen down” (solid curves), and “broadside”(dotted curves) orientations. The “broadside”orientation gives a twdimensional potential energy surface with the first argument being the moleculesurface separation and the second, the angle describing rotation of the molecule around its C, axis. Figure 2.
The virtue of the molecule-surface force field given by eqs 2 and 3 is that it can be integrated analytically, which gives the moleculesurface interaction potential
u = vat+ (Inp (4)
As follows from Cq, = 0, Vat a r-’ at large moleculesurface separations. Expressions 4 may be useful for analytical fit of interaction potentials obtained from quantum chemistry calculations. Figure 2 shows the slices of the potential energy surface for CHF3 at the orientations “hydrogen up”, “hydrogen down”, and “broadside”. As one can see, the model gives a reasonable depth of the attractive well in view of the enthalpy of vaporization for fluoroform, AH 0.2 eV. Moreover, the model predicts a deeper well for the “hydrogen down” orientation which is in a qualitative agreement with the experimental results of refs 9-1 2. The described model of moleculesurface interaction possesses several advantages and disadvantages that originate from the same root, Le., the treatment of the solid as a continuous media. The major advantages of the model are that (i) it takes into account chemical shape of the molecule under study, (ii) gives analytical potential energy surface with correct asymptote at large moleculesurface separations, and (iii) does not require many adjustable parameters. The major deficiency of the model is that it is, probably, not precise in the vicinity of the potential energy minimum where the atomic structure of the solid may be important. Another drawback of the model in its current formulation is that it uses only the first approximation of the distributed multipole model2I (Le., charges) and does not take into account additional polarization of the molecule in the vicinity of the surface. In principle, these effects can be incorporated into the model in the same way as it has been done for van der Waals molecules by Buckingham and
-
Surface Motion
In order to describe surface temperature effects in gassurface scattering, the model should take into account thermal motion of atoms in the solid. A general way to account for thermal motion in gas-urface scattering is provided by the generalized Langevin equations (GLE)m e t h ~ d . ~ IThe J ~ method is based upon separate consideration of those atoms in the solid that participate in the collision directly. These atoms are usually called primary zone. The interaction between the primary zone and the rest of the (31) Adelman. S. A.; Doll, J. D.J . Chcm. Phys. 1976, 69, 2375. (32) Tully, J. C. J. Chcm. Phys. 1980, 73, 1975.
Figure 3. A schematic representation of surface motion. The two particles represent two top layers of graphite; the “ghost”particles dcscribe the interaction of the two top particles with the rest of the crystal.
crystal is described by (i) a “ghost” atom connected to each atom in the primary zone, (ii) damping in the oscillation of the “ghost” atoms, and (iii) a random force acting on every “ghost” atom. The damping and the random force are related to each other through the fluctuation-dissipation theorem. This scheme has been successfully realized by Tully in excellent papers on the scattering of atoms32and diatomicsl5 on metal surfaces and then in a simplified version by Polanyi and W01P3 and Wolf and Davis.)‘ However, an implementation of this procedure for our study would require a fairly large computer time because one would have to consider a large number of carbon atoms in the primary zone. Indeed, the geometrical size of a CHF3 molecule is much larger than the size of an atom in a typical problem of atomsurface scattering. Therefore, a wide surface area is expected to be involved in the collision. Moreover, the mass of the molecule is ca. 6 times that of carbon. As a result, many surface atoms must hit incoming molecules in order to reverse its momentum. Another strong reason not to consider every single atom in the solid independently is that we have already neglected surface atomic structure in the above calculations of the moleculesurface interaction. In the current study we employ a simplified treatment of the surface motion which allows a qualitative description of the surface temperature effects in moleculesurface scattering. Instead of considering each atom in the primary zone independently,we take a group of atoms and assume that they interact with gas molecules and the rest of the solid as a single particle. The mechanical equivalent of the model is shown in Figure 3. The motion of this system is described by the following equations:
Here yo is the coordinate of the top particle and FW8 is the force acting on it from the gas molecule. This force was calculated as described in the previous section. This top layer oscillator interacts with its “ghost” particle and with the second layer oscillator, which in turn interacts with its own, second “ghost” particle. In the following trajectory simulations we take the mass of each particle M be equal to the mass of 12 carbon atoms. The variables y I , so, and s1 are respectively the coordinates of the second layer oscillator and the “ghosts”; Fo and Fl are the random forces acting on the “ghost” particles. These forces are calculated according (33) Polanyi, J. C.; Wolf, R. J. J. Chcm. Phys. 1985, 82, 1555. (34) Wolf, R. J.; Davis, R. C . J. Phys. Chcm. 1985, 89, 2751.
Ionova et ai.
8374 The Journal of Physical Chemistry, Vol. 95, No. 21, 199'I to the fluctuationdissipation theorem
F = g(2yk~TM/At)'/~
(6)
where y is the damping coefficient of the corresponding ghost particle, T the surface temperature, At the integration step in numerical calculations, and g a Gaussian random number with the dispersion equal to 1. The parameters A,, AI, a,-,, q ,w ,and y have been chosen from the assumption that the first a n t second particles describe respectively the top and the second layers of carbon atoms in graphite. The coefficients A. and AI characterize the interaction of the first two layers with the rest of the crystal. The interaction constant AI = 1.74 X lo-' au may be easily calculated from the atom-to-layer interaction potential for graphite which has been reported in ref 35. However, this approach is not valid for A, because the interaction of the top layer with the rest of the crystal is attenuated by the intermediate second layer. We have arbitrarily taken
A,, = ( w ~ / w ~ ) A=l 1.1
X lo-'
au
where w! and w i are the Debye frequencies of the surface and bulk carbon atoms in graphite, respectively. The parameters wo2, w12, and w t have been found from the assumption that the oscillation frequency of each particle shown in the figure is proportional to the corresponding Debye frequency when all the other particles are kept fixed at their equilibrium positions 002
+ A,, = az,
wgz = a(f&)2,
w12
I
+
002
= cY(w;)2
The parameter a = 0.57 has been then adjusted in order to achieve the correct value of the mean-square displacement of the top particle (yo+) = (a2/12)(T/300K), where II = 0.1 A is the mean-square vibration amplitude of a single carbon atomB in the direction of the surface normal at T = 300 K.
0
1
e
9
4
Time / ps Figure 4. Sample trajectories for two opposite initial orientations cos 0, = +0.8 (top panel) and -0.8 (bottom panel) of incoming CHF3molecules
with respect to a graphite (OOO1) surface; all the other initial conditions
were the same. Top traces on each panel: the molecule's center-of-mass separation from the surface vs 1; two lower traces: the coordinates of the top and the next layer particles (not in scale).
was 14 au (26.5 A) above the surface; the initial normal translational energy 0.86 eV was chosen in accord with the experimental conditions of refs 12 and 13. The generalized Langevin equations were sampled by using YO(0) = d(Yo:))1/2
Trajectory Metbod and Initial Conditions The equations of motion for the surface ( 5 ) plus that for the molecule were numerically integrated by the fourth-order RungtKutta method. In order to obtain well-behaved equations, quaternions and angular velocities were used as the variables that describe rotation of the molecule (for details see, for example, ref 28). The integration step was adjusted to provide sufficient accuracy of numerical integration. The integration procedure was checked at y = 0 (and, hence, the random forces Fo,Fl = 0), Le., when the system is conservative. It has been found that with the integration step At = 100 au 2.4 fs the total energy is conserved (0.001) along a whole trajectory, and the integration back brings the system to the initial position within the accuracy of 0.02. The initial conditions for the molecule and the surface were chosen by the Monte Carlo method for a given rotational state of the molecule and thermal surface motion. Most of the calculations except the dependence of the steric effect upon the initial degree of orientation were carried out for the 11 11) rotational state, which approximately corresponds to the experimental conditions of refs 12 and 13. In the calculations of the steric effect vs the degree of the initial molecular orientation, the states were 11 11), 1222), 1333), 1211), 1221), and 1212). The cos 8, where 8 is the angle between the surface normal and the axis of the molecule, was a random number with distribution P(c0s 8) d cos 8 = JSJXM(cos8)12 d cos 8 corresponding to the rotational quantum state under study. The two other Eulerian angles specifying molecular orientation with respect to the surface were random numbers with a uniform distribution. The initial rotations of the molecule were then calculated by the procedure described in refs 36 and 37. The initial position of a molecule
-
Santcs, E.; Villagra, A. Phys. Reo. 1972, 86, 3134. Townes, C. H.; Schawlow, A. L. Mlcrowaue Specrroscopy; McGraw-Hill: New York, 1955. ( 3 7 ) Choi, S.E.; Bernstein, R. B. J . Chem. Phys. 1986, 85, 150. (35) (36)
where g is a Gaussian random number with a unit dispersion and (yo;) is the mean-square displacement of the top particle, as defined above. Each trajectory was integrated from t = 0 to t = 4.5 ps, which is approximately 3 times longer than the time required for a molecule to reach the surface from its initial position. A molecule was considered "stuck" if it began to move toward the surface at some moment after the first encounter. Figure 4 presents two sample trajectories for the opposite initial orientations of CHF, with all the other initial conditions being the same. These sample trajectories demonstrate the origin of the steric effect in the surface scattering of oriented molecules. In general, the molecules with the initial orientation "hydrogen down", which is attracted stronger (see Figure 2). experience larger acceleration in the attractive well and acquire lager translational energy prior to the impact. This feature is manifested in Figure 4 by an earlier collision of such a molecule with the surface. As a result, these "hydrogen down" molecules hit the surface harder and transfer a larger amount of their translational energy to the surface which prohibits their escape from the attractive well after the impact. The average probabilities of direct scattering 0.5(Pu + Ph,,) for several surface temperatures are shown in Fire 5. h e initial orientation of the molecular axis with respect to the surface normal was distributed as P(cos 8) d cos 8 = (3/8)(1 f cos d cos 8 for the "hydrogen up" and "hydrogen down" orientations, respectively. This distributions correspond to the 1111) and 111-1) rotational quantum states of the incoming molecules.
The Journal of Physical Chemistry, Vol. 95, No. 21, 1991 8375
Scattering of CHF3 on Graphite(0001) 1.001
h
g
aa
0.75
i
I
T
h
1
t
-1311,
I
.
-0.2
+
k 2 Y
2 -0.81 &
400
800
000
Surface temperature / K Figure 5. The probability of direct scattering as a function of surface temperature: &lid squares, current compute; simulations; bars, experimental results of ref 12. Initial conditions for trajectories correspond to the II I f l ) quantum states of CHF,. Solid line, the best fit of the points by A exp(-B/7'); dotted line, the best tit of the experimental results by the same function.
-
g a8
1222)
f
r A
&
0.4
0.2
-O*fl.O
0.8
1333)
0.0
1.0
c COS e > Flgure 7. The steric effect vs the average degree of the initial molecular orientation. The squares are computer simulations of the scattering of CHF,being initially in the indicated quantum states (see text for details).
T=300K.
-0.10
75
I
Y
t - 4 .
II
&
200
-0.70,
200
400
800
000
Surface temperatun / K
Figure 6. The steric effect of the probability of direct scattering vs surface temperature. Solid squares represent computer simulations. Initial conditions for trajectories correspond to the 11 1f1) rotational states of CHF,. Solid line, the best fit of the squares by u + b/T; bars, experimental results of ref 12; dotted line, the best fit of the experimental results by the same functional dependence.
As Seen from the figure, the probability of direct scattering decreases with surface temperature as exp(-B/7') in accordance with the experimental data of ref 12 and with the predictions of a simplistic "hard-cube" analy~is.'~ However, the model calculations predict higher probabilities of direct scattering than those experimentally observed. We have not been able to achieve a better agreement by varying the adjustable parameters of the model within reasonable limits. Two possible explanations of the observed discrepancy can be offered. We believe that the most important drawback of the model is the rough description of surface motion. It is quite possible that neglecting independent motion of every surface atom we underestimate considerably the energy transferred to the surface in the course of an impact, and consequently, the sticking probability is also underestimated. Another possible source of discrepancy is that the image charge model in its current formulation does not take into account higher terms of the distributed multipole expansion of the electrostatic field from an isolated molecule and also neglects the polarization of the molecule near the surface. As a result, the strength of the moleculesurface attractive interaction may be underestimated in the current study. These effects can be in principle incorporated into the model as has been already mentioned. The calculated steric effect (i.e., the relative difference in the direct scattering probability R = 2(Pup- Pdov!)/(Qup+ P h ) ) is plotted as a function of surface temperature in Figure 6 along with the best fit of the experimental results of ref 12 by a + b/T. As seen from the figure, the trajectory simulations give the same functional dependence of the steric effect R = a b / T as was
+
400
800
I
800
Surface temperature / K
Figure 8. The postcollisional translational energy of CHF, as a function of surface temperature for the 1111) ("hydrogen up") and 111-1) ("hydrogen down") rotational states. Dotted lines are the best fit of the experimental results of ref 13 by straight lines. observed experimentally and then explained in ref 19 by the "hard-cube" analysis. Moreover, the quantitative agreement between the trajectory simulations and the experimental data is reasonably good. In order to calculate the dependence of the steric effect upon the degree of molecular orientation, we carried out trajectory simulations for several rotational quantum states of the incoming molecules IJKM) = ( l l l ) , 1211), (212), 1221), 1222), and 1333). The steric effect is plotted in Figure 7 as a function of the average orientation (cos 8 ) which is given for a IJKM) quantum state by (COS e) = K M / J ( J + 1) As expected, the magnitude of the steric effect is increasing with the increase of the average orientation. Moreover, the trajectory simulations give a near-linear orientation dependence of the steric effect upon the degree of Orientation, as was observed in refs 8-12. Figure 8 presents the postcollisional translational energy of CHF, as a function of surface temperature for two opposite orientations. The initial conditions for the "hydrogen up" and "hydrogen down" orientations were chosen to describe 11 11) and 111-1) rotational states, respectively. As seen from the figure, the orientation "hydrogen down" (I1 1-1 )), which gives higher trapping probability, results in a larger translational energy transfer as compared to the opposite orientation. This intuitively clear result agrees qualitatively with the experimental results of Ionov et aLi3
Conclusions The main results of the work may be summarized as follows: 1. The image charge model for the interaction between a polyatomic molecule and a surface which gives correct asymptotic behavior of the interaction at large moleculesurface separations is presented.
8376
J. Phys. Chem. 1991, 95, 8316-8319
2. The image charge force field has been used to simulate the scattering of oriented CHF, molecules on a graphite (Oool) surface which has been recently studied e~perimentally.'~J~ In the calculations, the surface motion was treated by the simplified GLE method. 3. The trajectory simulations recover the experimentally observed direction and the magnitude of the steric effects in the scattering of CHF3 on graphite but fail to achieve quantitative
agreement with the experimental probability of direct scattering. This discrepancy is believed to be due to the oversimplified treatment of the surface motion.
Acknowledgment. The work has beem supported by NSF Grant CH86- 15286, hereby acknowledged with thanks. Registry No. CHF3, 75-46-7; graphite, 7782-42-5.
Rotational Product State Dlstrlbution and Allgnment of Associatively Desorbing CuF Molecules U. Niiber, A. Bracker? X. R. Chen,* P. Jakob,i and J. Wanner* Max-Planck-Institut fiir Quantenoptik, 0-8046 Garching, Federal Republic of Germany (Received: January 28, 1991)
We report a rotational product state analysis of CuF molecules associatively desorbing from copper surfaces in reaction with an F2 molecular beam. Laser-induced fluorescence spectra of the X'Z+(o"=O) manifold were recorded under conditions of coherent saturation. The rotational distribution was non-Boltzmann and showed a 'rotational cooling effect" with an accommodation factor of 0.8 for surface temperatures between 890 and 985 K. Preliminary polarization measurements showed that the J axes of the desorbing molecules are preferentially aligned parallel to the surface normal. The prwalence of helicopter motion for the associative desorption of CuF agrees with theoretical predictions of others.
Introduction The reaction between fluorine and solid copper surfaces is a system for which a complete product characterization of desorbing CuF molecules may be obtained from a laser molecular beam experiment. In an earlier paper, we reported a preliminary product-state analysis showing that the vibrational distribution of the gaseous products is largely determined by the surface temperature.'* The distributions were not affected when the fluorine reactant beam energy was increased or when fluorine molecules were replaced by atoms, both of which increase the exoergicity of the initial reaction. We thus concluded that the analysis only yields insight into the final step of the surface reaction, namely, the desorption of the products. In a subsequent publication we reported on a first rotational product analysis.'b In other studies of associative or recombinative desorption reactions, OH(OD)/Pt( 111): NO/Pt( 11l)? and H2,D2/Pd(loo)! rotational product analysis showed a "rotational cooling" effect, in which the desorbing diatomics take up on average less rotational energy per molecule than accommodation to the surface temperature would allow. Microscopic reversibility arguments by Brenig et aL5 and Tully et a1.6 provide a plausible explanation of this effect: strongly rotating molecules have a lower sticking coefficient, which implies a lower desorption yield at high J. In a recent detailed theoretical treatment of associative desorption, Yang and Rahman' predicted that rotational cooling should be associated with an alignment effect, where the rotational angular momentum is preferentially aligned parallel to the surface normal. Experimentally, no alignment effect was observed for the associative desorption of OH and OD from Pt( 11l ) , k but preliminary measurements do show such behavior for the recombinative desorption of H2 from Pd(100).438 The following study presents detailed results on rotational product distribution and shows first evidence for the alignment of desorbing CuF giving insight into the dynamics of associative desorption. Our experiment was stimulated by recent observations 'Present address: Department of Chemistry, University of California,
Berkeley, CA 94720. rPermanent address: Chinese Academy of Sciences, Dalian Institute of Chemical Physics, Dalian, People's Republic of China.
IPresent address: A T L T Bell Laboratories, Murray Hill, NJ 07974.
0022-3654/91/2095-8376$02.50/0
of Jacobs et al., showing that in the trapping desorption of NO from a Pt( 11 1) surface the helicopter mode was preferred, while inelastic scattering was dominated by the cartwheel m ~ t i o n . ~ Experimental Section
Figure 1 is a diagram of the experimental setup. A molecular beam of fluorine impinged on a copper surface in a cryobaffled vacuum chamber at 1 X lo-' mbar. The surface temperature could be controlled up to 1050 K. The polished Cu(ll1) single crystal is 99.999% pure. Since the outcome of the reaction was found to be independent of the copper crystal face, a polycrystalline sample of purified W u was also prepared. This sample was used to simplify data analysis and for additional experiments with increased spectral resolution. The molecular fluorine beam expanded at a typical flow of 0.5 sccm from a sapphire nozzle with an i.d. of 0.2 mm which was mounted in a differentially pumped chamber. The fluorine beam entered the main chamber through a skimmer. Rotationally resolved excitation spectra of the C'II-X'2+ band system of the desorbing CuF molecules were recorded with a ring dye laser (with coumarin 102 dye) pumped by a Kr+ laser. In single-mode operation at 50-MHz bandwidth, the tunable laser yielded a typical output power of 60 mW. The laser wavelength was measured by a wavemeter with an accuracy of f0.02 cm-'. The laser beam was directed parallel to the copper surface at a distance of 13 mm. CaF2 laser windows with an antireflection coating were mounted on the chamber perpendicular to the laser (1) (a) Chen, X.R.; Wagemann, K.; Wanner, J.; Brcnig, W.; Ktichenhoff, S.Surf. Sci. 1989, 224, 570. (b) Wagemann, K.; Chen, X. R.; Ngher, U.; Wanner, J. Yacuum 1990, 41, 733. (2) (a) Hsu, D. S. Y.; Hofibeuer, M. A.; Lin, M. C. Surf. Sei. 1987,184, 25. (b) Hsu,D. S.Y.; Lin, M. C. J. Chem. Phys. 1988,88,423. (3) (a) -her, M.; Guthrie, W. L.; Lin, T.-H.; Somorjai, G. A. J. Phys. Chem. 1!W, 88,3233. (b) Hsu, D. S. Y.;Squire, D. W.; Lin, M. C. J. Chem.
Phys. 1988,89, 2861. (4) SchrBtcr, L.; Ahlers, G.;Zacharias, H.; David, R.J . Electron Spectrosc. Relar. Phenom. 1987, 45, 403. (5) Brenig, W.; Kasai, H.; Mtiller, H.Sur/. Sci. 1985, 161, 608. (6) Muhlhausen, C. W.; Williams, L. R.; Tully, J. C. J . Chem. Phys. lM, 83, 2594. (7) Yang, K.; Rahman, T. S. J . Chem. Phys. 1990, 93,6834. (8) Zacharias, H. Appl. Phys. A 1988,47, 37. (9) Jacobs, D. C.; Kolasinski, K. W.; Shane, S.F.;Zare, R. N. J . Chem. Phys. 1989, 91, 3182.
0 1991 American Chemical Society
