Dynamics of NO reduction by H2 on Rh(111): Velocity and angular distributions of the N2 product

Article abstract of DOI:10.1063/1.471349

The velocity and angular distributions of N₂ produced from the reduction of NO by H₂ on Rh(111) have been measured in the low nitrogen coverage limit as a function of surface temperature. Both the angular and velocity distributions are well fit by bimodal forms. The high energy channel has average translational energies about six times that expected for molecules accommodated at the surface temperature, an unusually sharp angular distribution, and angle dependent velocity distributions. The low energy channel is also hyperthermal, with average translational energies about twice thermal, a cosine angular distribution, and velocity distributions which are independent of angle. Application of surprisal analysis to the data shows that the high energy channel may be characterized by constraints on the normal velocity and the total energy; the low energy channel may be characterized by a single constraint on the velocity.

Full text of DOI:10.1063/1.471349

Dynamics of NO reduction by H2 on Rh(111): Velocity and angular distributions of the
N2 product
J. I. Colonell, K. D. Gibson, and S. J. Sibener
Citation: The Journal of Chemical Physics 104, 6822 (1996); doi: 10.1063/1.471349
View online: http://dx.doi.org/10.1063/1.471349
View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/104/17?ver=pdfcov
Published by the AIP Publishing
Articles you may be interested in
Two-dimensional ion-imaging of fragment angular distributions after photolysis of state-selected and oriented
triatomic molecules
AIP Conf. Proc. 388, 175 (1997); 10.1063/1.52162
TDMP2 calculation of dynamic multipole polarizabilities and dispersion coefficients of the triplebonded molecules
CO, N2, CN−, and NO+
J. Chem. Phys. 105, 9948 (1996); 10.1063/1.472827
Kinetics and dynamics of the initial adsorption of nitric oxide on Ir(111)
J. Chem. Phys. 105, 8362 (1996); 10.1063/1.472691
Normal to tangential velocity conversion in clustersurface collisions: Ar N on graphite
J. Chem. Phys. 105, 7828 (1996); 10.1063/1.472563
Kinetic oscillations and hysteresis phenomena in the NO+H2 reaction on Rh(111) and Rh(533): Experiments and
mathematical modeling
J. Chem. Phys. 105, 7210 (1996); 10.1063/1.472524
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
128.252.67.66 On: Tue, 23 Dec 2014 18:50:48

Dynamics of NO reduction by H2 on Rh(111): Velocity and angular
distributions of the N2 product
J. I. Colonell, K. D. Gibson, and S. J. Sibener
The James Franck Institute and the Department of Chemistry, The University of Chicago,
5640 S. Ellis Avenue, Chicago, Illinois 60637
͑Received 17 August 1995; accepted 17 January 1996͒
The velocity and angular distributions of N2 produced from the reduction of NO by H2 on Rh͑111͒
have been measured in the low nitrogen coverage limit as a function of surface temperature. Both
the angular and velocity distributions are well fit by bimodal forms. The high energy channel has
average translational energies about six times that expected for molecules accommodated at the
surface temperature, an unusually sharp angular distribution, and angle dependent velocity
distributions. The low energy channel is also hyperthermal, with average translational energies
about twice thermal, a cosine angular distribution, and velocity distributions which are independent
of angle. Application of surprisal analysis to the data shows that the high energy channel may be
characterized by constraints on the normal velocity and the total energy; the low energy channel
may be characterized by a single constraint on the velocity. © 1996 American Institute of Physics.
͓S0021-9606͑96͒00116-X͔
INTRODUCTION
desorption angle and surface temperature. Although the con-
ditions are far from those of practical catalysts—ultrahigh
vacuum and reducing conditions—these velocity distribu-
tions provide information about the potential energy surface
͑PES͒ governing the final step in the formation of N2, a
crucial element in a description of the catalytic activity of
rhodium in this reaction.
Product velocity distributions have been measured for a
number of surface reactions, and show a wide variety of
angular and temperature dependencies.16–29 In general, if
there is no barrier in the final step of the reaction ͑e.g., de-
sorption of a physisorbed molecule͒ angular distributions are
expected to be roughly cosine and velocity distributions are
expected to be similar to Maxwell–Boltzmann distributions
at the surface temperature, Ts, with an average energy of
2kbTs . Peaked angular distributions and average energies
greater than 2kbTs are associated with energy barriers in the
final step of the reaction.30
Rhodium is included in three-way catalysts primarily for
its ability to reduce nitric oxide and nitrogen oxide to
nitrogen.1,2 Platinum and palladium also catalyze the reduc-
tion of nitric oxide, but the primary products are ammonia
and nitrous oxide rather than the desired N2. The origin of
the selectivity of rhodium catalysts for the formation of N2
has been the subject of a great deal of study.3 N2 formation is
also interesting as an example of a bimolecular surface
reaction with a large barrier, an extremely important class
of reactions which, though basic, are not yet fully under-
stood.
Little is known about the dynamics of NO reduction on
Rh͑111͒. At low ͑room temperature thermal͒ energies N2
does not dissociatively adsorb on rhodium,4 so the dynamics
of N2 sticking and recombinative desorption are also un-
known. In contrast, the dynamics of N2 interactions with iron
have been widely studied, due to their importance in ammo-
nia synthesis.5 N2 sticking on Fe͑111͒ is translationally acti-
vated with a barrier of ϳ1–2 eV,6 while vibrational energy
does not promote the reaction.7,8 The sticking coefficient is
also temperature dependent, increasing with surface tempera-
ture, which suggests that the reaction occurs through a mo-
lecularly chemisorbed precursor.6 N2 dissociative adsorption
on Re surfaces is also temperature dependent, and TPDs of
N2 recombinatively desorbing from Re͑001͒ have a marked
isotope effect.9,10 Tunneling has been suggested to be impor-
tant in the dynamics of N2 interactions with both iron and
rhenium surfaces.11,12 The dynamics of N2 sticking on tung-
sten surfaces have also been explored:5 Direct activated ad-
EXPERIMENT
These experiments were performed in a molecular beam
scattering machine which has been described pre-
viously:27,31,32 only the features essential to these experi-
ments will be described in detail here. The UHV scattering
chamber is pumped by a 400 l /s ion pump and a TSP, con-
tains a three-axis crystal manipulator, and an independently
rotatable differentially pumped quadrupole mass spectrom-
eter detector. Continuous beams of N2 and hydrogen are pro-
duced by supersonic expansion in the source chamber. The
beams are in a plane perpendicular to the scattering plane,
one ͑the center beam͒ in the scattering plane defined by the
plane of rotation of the detector, which can be chopped be-
fore the crystal, and the other ͑the side beam͒ inclined by
15°. The beam spots overlap at the crystal and are about 5
mm in diameter. The intensity of the side beam may be es-
timated from measurements of Ar beams in ion gauge
13
sorption with a barrier is seen on W͑110͒ and both acti-
vated and precursor-mediated channels are found on
W͑100͒.14,15
In this work, we examine the dynamics of the NOϩH2
reaction on the Rh͑111͒ surface by measuring the velocity
distribution of the product N2 molecules as a function of
6822
J. Chem. Phys. 104 (17), 1 May 1996
0021-9606/96/104(17)/6822/12/$10.00
© 1996 American Institute of Physics
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
128.252.67.66 On: Tue, 23 Dec 2014 18:50:48

Colonell, Gibson, and Sibener: NO reduction by H2 on Rh(111)
6823
fluxmeters, and may be varied from about 1013 to 1014 sϪ1
RESULTS
͑0.1 to 1 ML/s͒. The crystal may be moved out of the path of
the center beam and the detector rotated to measure the ve-
locity distribution of the incident beam directly.
With NO and H2 beams of ϳ1014 sϪ1 we measured N
coverages less than 0.05 ML at all temperatures from 700 to
1000 K; the saturation coverage of nitrogen on Rh͑111͒
when dosing with atomic nitrogen is ϳ0.6 ML.4 The oxygen
coverages were also small, less than 0.1 ML. The TOF spec-
tra, within our error, were not dependent on the NO beam
intensity, suggesting that the coverage dependence of the dy-
namics is weak in this low N coverage regime.
The only products observed were N2 and H2O. We did
not detect any NH3 or N2O. TOF spectra of the H2O product
produced in this reaction were found to be identical to those
measured from the H2ϩO2 reaction, which suggests that the
final step of water formation involved only the adsorbed oxy-
gen atom, rather than the NO molecule. When the hydrogen
beam is turned off, N2 production rapidly decreases and be-
comes undetectable, perhaps because O atoms fill up the
A doubly differentially pumped post-crystal chopper is
used to obtain the product velocity distributions. An ion
pumped housing containing the motor ͑an ac hysteresis mo-
tor with high temperature windings͒, a small light bulb, and
photodiode is bolted to the detector and rotates with it. A
small slotted disk on one end of the motor shaft interrupts the
light from the bulb which is detected by the photodiode to
create the trigger signal. The other end of the motor shaft
extends through a second ion pumped region into the scat-
tering chamber, where the cross-correlation chopper is keyed
to it. The chopper interrupts the product flux from the crystal
10.5 cm from the ionizer of the mass spectrometer.
The chopper pattern is a pseudorandom sequence of 511
slots and holes, and the wheel speed was 195.69 Hz, or a
channel time of 10 ␮s. The N2 TOF spectra were generally
collected in 3ϫ105–106 shots, or 15 min to 1 h of data col-
lection. The surface was annealed at 1300 K after every 15
min of data collection to remove any oxygen absorbed in the
bulk of the Rh crystal. The TOF spectra were fit by decon-
volving them from the chopper pattern, and fitting the peak
to a model function corrected for the velocity dependence of
the ionization probability and convolved with the instrumen-
tal broadening due to the finite length of the ionizer.
available sites for
N
adsorption and prevent NO
dissociation.36
Typical N2 TOF spectra are shown in Fig. 1. The surface
temperature is 700 K and the fits are simply shifted Boltz-
manns:
2
Ϫ
v
v0
3
f
͒ϭN exp Ϫ
.
͑1͒
͑v
v
ͫ
ͩ
ͪ
ͬ
␣
This form was chosen primarily for its flexibility: it varies
The Rh͑111͒ sample ͑Cornell Materials Preparation Lab͒
was cut and polished to within 1° of the ͑111͒ face and
checked by x-ray Laue back reflection. The primary contami-
nants were S, B, and C. S and B were removed by cycles of
Arϩ sputtering ͑10 ␮A, 900 K͒ followed by annealing at
1300 K. C was removed daily by exposing the crystal to
oxygen at 900 K and annealing at 1300 K. Oxygen absorbed
into the bulk of the sample was removed by annealing the
crystal at 1300 K for 3 min between measurements. Cleanli-
ness was checked by Auger spectroscopy, and surface flat-
ness by He reflectivity.
smoothly from a Maxwell–Boltzmann distribution ͑with
v0
ͱ
equal to zero and ␣ equal to (2kbTs)/(m)͒ to a narrow
Gaussian typical of a supersonic beam. The TOF spectra
become slower and broader at more glancing desorption
angles, but never approach a Maxwell–Boltzmann at the sur-
face temperature ͑shown by the dashed lines in Fig. 1͒.
There is no physical interpretation of the parameters of
the shifted Boltzmann, but fitting the spectra allows them to
be conveniently integrated to obtain the average energy and
total intensity of the velocity distributions. The average en-
ergy near normal ͑
␪ ϭ2°͒ is shown as a function of tempera-
f
ture in Fig. 2. The dashed line shows the expected energy for
molecules equilibrated at the surface temperature, that is,
In all of these measurements, we used continuous beams
of NO and H2, with fluxes of ϳ1014/s ͑ϳ1 ML/s͒ as esti-
mated from fluxmeter measurements of Ar beams. The N
atom coverage was measured by monitoring the N2 intensity
after the NO beam was turned off. The integral of this inten-
sity was compared to the integrated H2O signal from titrating
a saturated ͑0.5 ML͒ oxygen overlayer with H2. The ioniza-
tion probabilities of N2 and water are roughly equal;33 the
efficiency of the mass filter for the two species is assumed be
similar. The surface coverage of oxygen was measured by
titrating with H2 after the NO beam was turned off. The
coverages of NO and hydrogen could not be measured using
these methods because they desorb too quickly. Estimating
coverages from sticking coefficients and kinetic parameters
determined from temperature programmed desorption
measurements34,35 yields ϳ10Ϫ5 ML for molecular NO and
ϳ10Ϫ4 ML for hydrogen in the temperature range of these
measurements ͑700–1000 K͒.
E ϭ2k T ,
͗ ͘
͑2͒
b
s
the average energy of a Maxwell–Boltzmann distribution at
the surface temperature. The energy of the product N2 is
nearly four times this value, and increases with a slope of
5.5kbϮ1kb . The precision of the measurement of the aver-
age energy may be gauged from the scatter in the data which
is about Ϯ30 meV; similar error bars should be assumed for
all of the energy measurements. The accuracy of the energy
measurement, that is, the calibration of the time of flight, was
checked using effusive beams of He and O2: These measure-
ments suggested errors of less than 5 meV, much smaller
than the scatter inherent in the current measurements, which
is due to the low energy resolution at high energies. The
angular dependence of the average energy is shown in Fig. 3.
J. Chem. Phys., Vol. 104, No. 17, 1 May 1996
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
128.252.67.66 On: Tue, 23 Dec 2014 18:50:48

6824
Colonell, Gibson, and Sibener: NO reduction by H2 on Rh(111)
FIG. 1. TOF spectra at Tsϭ700 K, deconvolved from the chopper function. The solid lines are fits to shifted Boltzmanns ͓Eq. ͑1͔͒; the dashed lines are
Maxwell–Boltzmann distributions at the surface temperature.
I ␪ ͒ϭa cosn ␪ ͒ϩ 1Ϫa͒cos ␪ ͒,
͑3͒
The energy decreases rapidly at small desorption angles and
͑
͑
͑
͑
f
f
f
approaches a constant value at glancing angles. However,
even at 60°, the average energy is nearly twice that expected
for molecules equilibrated at the surface temperature. The
intensity decreases sharply with increasing desorption angle:
Angular distributions measured at surface temperatures of
700 and 900 K are shown in Fig. 4. The angular distributions
are best fit by the bimodal form
where n is ϳ25Ϯ5, and is roughly constant with tempera-
ture. This is unusually sharp for an angular distribution, even
for a reaction with a large barrier: For H2 desorbing from
Cu͑111͒37,38 nϳ14, while for CO2 formed by oxidation of O
on Rh and Pt,21,39 nϳ9. Only extremely energetic systems
show such sharp angular distributions, e.g., N2 formed by the
J. Chem. Phys., Vol. 104, No. 17, 1 May 1996
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
128.252.67.66 On: Tue, 23 Dec 2014 18:50:48

Colonell, Gibson, and Sibener: NO reduction by H2 on Rh(111)
6825
FIG. 2. Average energy of the N2 desorbing at ␪fϭ2° as a function of
surface temperature. The solid line is linear fit to the data:
E ͑meV͒ϭ5.5͑Ϯ1͒k T ϩ97͑Ϯ50͒. The dashed line is Eq. ͑2͒, the expected
a
͗
͘
b
s
FIG. 4. Angular distribution of the intensity of desorbing N2 . Open circles:
Tsϭ700 K; filled circles: Tsϭ1000 K. The solid lines are fits to Eq. ͑3͒ and
energy for molecules equilibrated at the surface temperature.
the dashed line is cos͑␪ ͒.
f
decomposition of hydrazine,40 for which nϳ100 and CH4
formed by the photoinduced hydrogenation of CH3 on
Pt͑111͒,41 for which nϳ30. The second parameter, a, in-
creases from ϳ0.4 to ϳ0.55 as Ts increases from 700 to
1000 K, that is, the fraction of the cosn portion increases with
increasing surface temperature.
The fact that the average energy becomes roughly inde-
pendent of angle at large desorption angles coupled with the
bimodal angular distributions suggests that the TOF distribu-
tions might also be bimodal. The observed angular depen-
dence of the average energy suggests that the component
is assumed to be independent of desorption angle, are shown
as a function of temperature in Fig. 6. For both, the energy
increases with a slope of ϳ2kbTs . The average energy of the
high energy peak is shown as a function of angle in Fig. 7: It
decreases with increasing desorption angle. The two peaks
may be integrated over all angles to yield the relative inten-
sities of the two channels: The ratio of the high energy to the
low energy N2 is shown as a function of temperature in Fig.
8.
which has a cos͑␪ ͒ angular distribution, and dominates at
f
DISCUSSION
large desorption angles, has velocity distributions which are
independent of desorption angle. The second component has
a sharper angular distribution and higher energies, and its
velocity distributions are angle dependent. The resulting
form of the TOF spectrum is
The adsorption and decomposition of NO has been stud-
ied on a variety of Rh surfaces.34,36–48 The kinetics of the
reduction of NO by H2 and CO have also been studied on
Rh3,49–57 and PtRh3,58–60 alloy surfaces, and show a rich va-
riety of behaviors, from oscillations in reaction rates and
selectivities to square chemical waves. The reaction mecha-
nism for the reduction of NO by H2 in the absence of am-
monia formation is believed to be58
2
Ϫ
␪ ͒
f
v
v0͑
3
f
͒ϭN ␪ ͒ exp Ϫ
͑v
͑
v
ͫ
ͩ
ͪ
ͬ
f
␣ ␪ ͒
͑
f
cos ␪ ͒
͑
f
ϩ
f
͒,
͑4͒
͑v
60
ͫ
ͬ
cos 60͒
͑
NO ↔NO
,
͑5͒
͑6͒
͑g͒
͑ad͒
where f ( ) is simply a shifted Boltzmann fit to the data at
60°. Fits to this form of TOF spectra taken at a surface tem-
v
60
H2͑g͒↔2H
,
͑ad͒
NO →N ϩO
,
͑7͒
͑ad͒
͑ad͒
͑ad͒
perature of 900 K are shown in Fig. 5. The average energies
of the high energy peak at 2° and the low energy peak, which
2H ϩO →H2O
,
͑8͒
͑ad͒
͑ad͒
͑g͒
N
͑ad͒
ϩN →N2͑g͒
,
͑9͒
͑ad͒
N
͑ad͒
ϩNO →N2͑g͒ϩO
.
͑10͒
͑ad͒
͑ad͒
One of the unsettled questions concerning this mecha-
nism is the relative importance of reactions ͑9͒ and ͑10͒. The
two channels were originally proposed in the mechanism of
N2 formation in temperature programmed desorption spectra
of NO on polycrystalline rhodium by Campbell and White.43
They observed two peaks in the N2 TPD spectra which they
suggested could be due to the operation of these two mecha-
nisms for nitrogen formation. Root and Schmidt36 also ob-
served two peaks in the TPD of NO on Rh͑111͒ and inter-
preted them in the same way, assigning the low temperature
͑ϳ450 K͒ peak to reaction ͑10͒ and the high tem-
FIG. 3. Desorption angle dependence of the average energy. Open circles:
Tsϭ700 K; filled circles: Tsϭ900 K.
J. Chem. Phys., Vol. 104, No. 17, 1 May 1996
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
128.252.67.66 On: Tue, 23 Dec 2014 18:50:48

6826
Colonell, Gibson, and Sibener: NO reduction by H2 on Rh(111)
FIG. 5. Fits of TOF spectra at 900 K to the bimodal form in Eq. ͑4͒. The dashed lines show the decomposition into a high energy cosn(␪f) distributed
component and the cos͑␪ ͒ distributed component which is independent of angle. The solid line shows the sum.
f
perature ͑ϳ700 K at low coverages͒ to reaction ͑9͒. How-
ever, Bugyi and Solymosi4 have since measured TPD spectra
of N2 desorbing from Rh͑111͒ dosed with atomic nitrogen
and found they are identical to those from NO dosed
Rh͑111͒.34 Therefore, the reaction of adsorbed NO with N to
form N2 is not seen in TPDs of NO on this surface.
temperatures. Obuchi et al.52 measured the kinetics of NO
reduction by hydrogen on Rh foil and also measured TPD
spectra of recombining N atoms accumulated on the surface
during the reaction. They found that the kinetics of N2 for-
mation during the steady state reaction and during the N2
TPDs were the same, and concluded that N2 formation pro-
ceeds by the same mechanism in the two cases, though re-
combination of nitrogen atoms. They also studied the kinet-
The more relevant situation, however, is the reaction of
NO and H2 under steady state conditions at high surface
J. Chem. Phys., Vol. 104, No. 17, 1 May 1996
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
128.252.67.66 On: Tue, 23 Dec 2014 18:50:48

Colonell, Gibson, and Sibener: NO reduction by H2 on Rh(111)
6827
FIG. 6. Temperature dependence of the average energy of the two peaks.
The filled circles are the average energy of the high energy peak at ␪fϭ2°.
FIG. 8. Ratio of intensities of the high energy and low energy components
of the TOF distribution, integrated over desorption angle, as a function of
surface temperature.
The solid line is
ϭ3.3͑Ϯ1͒kbTsϩ350͑Ϯ90͒. The open circles show the average energy of the
low energy peak. The solid line is fit to these data:
E ͑meV͒ϭ1.9͑Ϯ1͒k T ϩ130͑Ϯ60͒. The dashed lines are fits to the van
a
linear fit to these points:
E ͑meV͒
͗ ͘
a
͗
͘
b
s
Willigen model.
positive if the process is endothermic. Unfortunately, the en-
ergy of dissociative adsorption of N2 on Rh͑111͒ is
unknown—when there is a barrier to adsorption, TPD mea-
surements yield an estimate of the activation energy, not of
Eadsorption . Bugyi et al.4 found an activation energy of 205
kJ/mol ͑2100 meV͒ from their low coverage N2 TPDs. As-
suming that the adsorption of N2 on Rh͑111͒ is exothermic,
this provides an upper limit on the total energy available for
partitioning among the modes of the product N2 molecule
and the surface.
Essentially nothing is known about the energetics of the
reaction of adsorbed NO and nitrogen atoms. Again, the
binding energy of the nitrogen atom is unknown. The acti-
vation energy for the reaction has not been measured even on
PtRh surfaces where it is known to occur, since it is difficult
to study it independently from nitrogen atom recombination.
ics of N2 formation during the decomposition of NH3, and
found that it, too, had the same kinetics, supporting their
conclusion. Reaction ͑10͒ has been shown to be significant
on PtRh surfaces at high NO pressures and low temperatures
͑Ͻ500 K͒;58 N2O is a major product in the reaction of CO
and NO on Rh͑111͒ at high pressures,49 so the reaction of
NO and N may also occur on Rh͑111͒. In short, both chan-
nels may be active under our reaction conditions, but since
the surface temperature is relatively high, and the NO pres-
sure low, nitrogen atom recombination is expected to domi-
nate.
The overall reduction of NO to N2 and water is exother-
mic by 79 kJ/mol ͑820 meV͒. However, the energetics which
affect the dynamics of N2 formation are those of reactions
͑9͒ and ͑10͒ in the mechanism outlined above, particularly
reaction ͑9͒, the recombinative desorption of two adsorbed
nitrogen atoms. The excess energy of a newly formed N2
molecule ͑Etotal͒ is
Origin of the bimodality
One possibility for the two channels observed in the an-
gular and velocity distribution is that they represent reactions
͑9͒ and ͑10͒ in the reaction mechanism suggested. This ques-
tion can only be decided by measuring the corresponding
velocity distributions for N2 recombination in the absence of
NO. Unfortunately, neither N2 nor NH3 decomposes on
Rh͑111͒,4,61 so a source of atomic N or, perhaps, excited N2
is necessary for this definitive experiment. It is important to
note, however, that it is also possible that the two peaks
represent two channels of N2 recombination. As mentioned
earlier, there are two peaks in the N2 TPDs: If the second
peak is due to a second adsorption site ͑instead of nitrogen
atom islands, or some other state which is only accessible at
high coverages͒ the two peaks could correspond to the two
peaks seen in the velocity distributions. Another possibility
is that the two channels correspond to different vibrational
states of the product N2. Since the transition state for the
reaction is likely an elongated N2 molecule parallel to the
surface, the PES for desorption into a vibrationally excited
N2 molecule might be expected to be considerably different
than for desorption into the vibrational ground state.
E
totalϭEactivationϪ⌬HreactionϭEactivationϪEadsorption N ͒.
͑
2
͑11͒
Eadsorption͑N2͒ is the heat of dissociative adsorption, and, fol-
lowing convention, is positive if the adsorption is exother-
mic. ⌬Hreaction is the enthalpy change for desorption, and is
FIG. 7. Average energy of the high energy peak as a function of desorption
angle. Tsϭ700 K: filled circles: Tsϭ900 K.
J. Chem. Phys., Vol. 104, No. 17, 1 May 1996
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
128.252.67.66 On: Tue, 23 Dec 2014 18:50:48

6828
Colonell, Gibson, and Sibener: NO reduction by H2 on Rh(111)
Temperature and angular dependence of the average
energy
pendicular to the surface normal: Only molecules with
enough ‘‘normal energy’’ overcome the barrier and desorb.
The temperature dependence of the average energy of both
channels may be fit fairly well with this model, with barrier
heights of 350 meV for the high energy channel and 130
meV for the low energy channel ͑dashed lines in Fig. 6͒.
However, the model also predicts a sharp cutoff in the TOF
spectra at the barrier height which we do not see for either
Apart from detailed molecular dynamics simulations,
which require a calculation of the entire PES for the reaction,
most dynamical models of surface reactions are based on the
idea of one dimensional barriers, or a distribution of one
dimensional barriers. The earliest and simplest of these is the
van Willigen model,62 which assumes a single barrier per-
FIG. 9. TOF spectra at Tsϭ1000 K fit to the surprisal form in Eq. ͑15͒.
J. Chem. Phys., Vol. 104, No. 17, 1 May 1996
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
128.252.67.66 On: Tue, 23 Dec 2014 18:50:48

Colonell, Gibson, and Sibener: NO reduction by H2 on Rh(111)
6829
channel. Also, the predictions for the angular dependence of
both the energy and the intensity are incorrect. According to
this model, the sharply peaked angular distribution of the
high energy peak should correspond to a barrier height of
600 meV, and the energy should increase sharply with in-
If a particular measured distribution can be defined by a
single parameter, a plot of its surprisal vs i will be linear.
To apply surprisal analysis, one must choose a prior dis-
tribution and make an educated guess about the constraints.
For the case of molecules desorbing from a surface, a logical
choice for the prior distribution is that which arises from
‘‘equilibrium’’ desorption, where the desorbing molecules
have accommodated at the surface temperature,
creasing desorption angle. Similarly, the cos͑␪ ͒ angular dis-
f
tribution of the low energy peak would correspond to a bar-
rier height of zero.
Another version of the single one-dimensional barrier
model was suggested by Doyen,63 with important refine-
ments by Verheij et al.19 and Anger et al.64 It relates the
energy of the desorbing molecules to the angular distribution
using a simple model for the interaction of the desorbing
molecules with the surface phonons. This model predicts that
the average energy scales with the sharpness of the angular
2
Ϫm
v
3
f0 ͒ϭN cos ␪ ͒exp
͑v
.
͑14͒
v
͑
ͩ
ͪ
f
2kbTs
Surprisal analysis of the high energy peak
In the case of the high energy peak, the high energies
indicate a constraint on the velocity or energy. However,
surprisal plots of the velocity distributions using either of
these constraints are nonlinear, suggesting that more than
one parameter is required to describe the velocity distribu-
tions. The sharply peaked angular distribution indicates a
constraint on the desorption angle, probably either on the
normal velocity or the normal energy. Surprisal plots of the
angular distributions were found to be linear for both con-
straints: The angular range is not large enough to distinguish
between cos͑␪ ͒ and cos2͑␪ ͒, but one or the other is the key
constraint on the angular distribution. Thus we tried combi-
nations of constraints on the normal velocity, normal energy,
total velocity, and total energy. The form which we found fit
the velocity distributions at all desorption angles is ͓to make
the sign of ␭ positive, the sign of the surprisal parameters
has been changed from Eqs. ͑12͒ and ͑13͔͒
distribution. For the cos25͑␪ ͒ distribution of the high energy
f
peak, it predicts an average energy of 14kbTs , while for the
cos͑␪ ͒ distribution of the low energy peak, it predicts an
f
average energy of 2kbTs .
Surprisal analysis
Given that the actual potential energy surface has at least
6 degrees of freedom, it is not surprising that a one dimen-
sional model might not be able to account for all aspects of
the dynamics. However, when only two of those degrees of
freedom are being measured it is actually unlikely that all of
the degrees of freedom need to be included in a model which
accounts for the data. A standard method for constructing a
model with the minimum number of parameters is surprisal
analysis, which has been used extensively in gas phase
dynamics,65 and has also proved useful in analyzing the dy-
namics of surface reactions.27,66,67 Surprisal analysis has
been discussed at length elsewhere,68–72 so only the primary
result will be stated here.
f
f
1
͑v
͑v
͓
1v
͑
2v2͔
f
,␪ ͒ϭN f
,␪ ͒exp ␭ cos ␪ ͒ϩ␭
f
1
0
2
f
f
cos ␪ ͒
͑
f
ϩN
f
͒,
͑15͒
͑v
60
ͫ
ͬ
cos 60͒
͑
The functional form for the ‘‘most random’’ possible
distribution subject to some ͑small͒ number of constraints is
where f ( ) is the same shifted Boltzmann as in Eq. ͑4͒. ␭ ,
v
60
1
␭2, N1 and N2 are not functions of the desorption angle, so
all of the velocity distributions of the high energy peak at all
desorption angles are fit with just four parameters. TOF
spectra at 1000 K with fits to Eq. ͑15͒ are shown in Figs. 9.
The temperature dependence of the surprisal parameters is
shown in Fig. 10.
The physical meaning of the constraints may be inter-
preted using detailed balance, although the conclusions must
be treated with caution, since measurements are made far
from equilibrium and the effects of the internal state distri-
butions are completely unknown. In general, at equilibrium,
the sticking coefficient as a function of velocity and incident
angle is given by
fm i͒ϭf i͒exp Ϫ
␭ A i͒ ,
͑12͒
͑
͑
͑
͚
0
n
n
ͫ
ͬ
n
where fm(i) is the measured distribution, the ␭ are the sur-
n
prisal parameters, the An are the constrained variables, and
f0(i) is the ‘‘prior’’ distribution, the most random possible
distribution in the absence of any constraint. Another useful
quantity is the information content of the distribution, or
‘‘surprisal’’ which is defined
fm i͒
͑
I i͒ϭϪln
ϭ␭ A ϩ␭ A ϩ••• .
͑13͒
͑
ͫ
ͬ
1
1
2
2
f0 i͒
͑
velocity distribution of desorbing molecules
s
,␪ ͒ϭ
f
͑16͒
͑v
velocity distribution of a gas at Ts incident on the surface
J. Chem. Phys., Vol. 104, No. 17, 1 May 1996
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
128.252.67.66 On: Tue, 23 Dec 2014 18:50:48

6830
Colonell, Gibson, and Sibener: NO reduction by H2 on Rh(111)
FIG. 10. Temperature dependence of the surprisal parameters used to fit the
high energy peak.
which, for the high energy peak becomes
2
s
,␪ ͒ϰexp ␭ cos ␪ ͒ϩ␭
1v
.
͑17͒
͑v
͓
͑
2v ͔
f
f
It is important to realize that this form only applies for the
energy range probed at a particular temperature, which may
be determined from the range of energies seen in the mea-
sured velocity distributions: about 200–900 meV at 700 K
and 200–1050 meV at 1000 K. Thus although the expression
FIG. 11. Panel ͑a͒: Dependence of the sticking coefficient via the high
energy channel on velocity, calculated for 700 K ͑solid line͒ and 1000 K
͑dashed line͒. The dashed vertical line marks the top of the velocity range
measured at 700 K. Panel ͑b͒: Same as ͑a͒ for sticking via the low energy
channel. As discussed in the text, the normalization of these curves is arbi-
trary: the absolute values of the sticking coefficients cannot be determined
from the data.
in Eq. ͑17͒ is not monotonic over all values of ͑since ␭
v
1
and ␭2 have opposite signs͒, the sticking coefficient is mono-
tonic over the velocity range observed at these temperatures.
The negative values of ␭ cause the sticking coefficient to
2
increase more slowly with normal velocity than a simple
constraint on the velocity.
scramble the energy among all the modes of the molecule.73
Thus the dynamics are not expected to be strongly tempera-
ture dependent.
The temperature dependence of the surprisal parameters
could be due to at least two causes. The most straightforward
is that the energy dependence of the reaction probability
changes as the temperature changes. A second possibility is
that different energy ranges are probed at different tempera-
Extracting information about the PES from the velocity
or energy dependence of the sticking coefficient is more dif-
ficult. This system does not obey normal energy scaling,
which argues against the dynamics being dominated by an
essentially one-dimensional barrier, or a distribution of one
dimensional barriers in the entrance channel for N2 sticking.
Total energy scaling, which is observed for the activated
tures, and that the dependence of s( ,␪ ) is somewhat dif-
v
f
ferent at different energies. If this is the case, we can patch
together s( ,␪ ) over the whole energy range from sticking
v
f
coefficients measured at different temperatures, as shown in
15
channel of N2 sticking on W͑100͒ and W͑110͒,13 also fails
panel ͑a͒ of Fig. 11. The solid line is s( ,0°) at 700 K and
v
to describe the data. The fact that the constraint on the total
energy is negative, so that energy in non-normal directions
actually hinders the reaction, is suggestive of a constrained
geometry near the transition state. If, for example, the reac-
tion can occur only in a specific point in the unit cell, veloc-
ity parallel to the surface might make it less likely for that
condition to be met. In this regard, it is important to remem-
ber that the energies of the desorbing molecules are much
higher than those of the Maxwell–Boltzmann distribution at
the surface temperature: Only a few percent have enough
energy to overcome the barrier. Thus we may be sampling
only the lowest possible barriers at the most optimal geom-
etries, rather than seeing an ‘‘average’’ barrier characteristic
of a large energy range on the PES.
the dashed line is s( ,0°) at 1000 K, calculated from the
v
surprisal parameters from the line fits in Fig. 10. The abso-
lute values of the sticking coefficients are not known: We
have no way of measuring the proportionality constant in Eq.
͑17͒, and the sticking coefficients have been arbitrarily set
equal at ϭ0.25 cm/␮s. The dashed vertical line shows the
v
top of the velocity range measured at 700 K ͑99% of the
intensity of the velocity distribution measured at 700 K and a
desorption angle of 2° is below this value͒. The curves are
quite similar below that point, but above it the 700 K curve is
much too steep to fit the data at 1000 K. What Fig. 11͑a͒
shows is that a single s( ,␪ ) could fit the data across the
v
f
whole temperature range, but that curve will have a more
complicated form than Eq. ͑17͒. Although temperature de-
pendence of the dynamics can not be ruled out, the strong
dependence of the reaction probability on normal velocity
suggests that the molecule does not interact much with the
surface during the reaction, since that would tend to
Surprisal analysis of the low energy peak
Surprisal plots of velocity distributions at 60° were
found to be linear for a constraint on the velocity and clearly
J. Chem. Phys., Vol. 104, No. 17, 1 May 1996
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
128.252.67.66 On: Tue, 23 Dec 2014 18:50:48

Colonell, Gibson, and Sibener: NO reduction by H2 on Rh(111)
6831
FIG. 12. Fits of the TOF spectra at ␪fϭ45° and ␪fϭ60° to the surprisal form in Eq. ͑18͒.
nonlinear for a constraint on 2. Since the angular distribu-
tion is cosine, there is no constraint on the angle, and the
expected form for the velocity distributions is
v
s
,␪ ͒ϰexp ␭ ͒.
͑ v
͑19͒
͑v
f
Figure 13 shows that ␭ has a fairly strong temperature de-
pendence. As mentioned earlier, this can be due to tempera-
ture dependence of the dynamics or be a result of the differ-
ent energy ranges probed at different temperatures. The latter
idea can be tested, to some extent, by attempting to construct
f
͒ϭNf
͒exp ␭ ͒,
͑v ͑ v
͑18͒
͑v
0
where N is a normalization constant, f ( ) is the prior dis-
v
0
tribution as defined in Eq. ͑14͒ and ␭ is the surprisal param-
eter. Fits of the data at 45° and 60° and a few temperatures
are shown in Fig. 12. As above, N and ␭ are not functions of
the desorption angle, so a single value of ␭ is determined for
each Ts . The fits are not quite as good as shifted Boltzmanns
͑which is why the latter were used in fitting the high energy
peak͒ but Eq. ͑18͒ describes the data quite well, and with
fewer parameters. The temperature dependence of the sur-
prisal parameter is shown in Fig. 13.
an s( ,␪ ) function which covers the entire energy range.
Panel ͑b͒ of Fig. 11 is analogous to panel ͑a͒: The solid line
v
f
is s( ) at 700 K and the dashed line is s( ) at 1000 K,
v
v
calculated from values of the surprisal parameter from the
line fit in Fig. 13. The dashed vertical line marks the top of
the energy range of the 700 K data. Again, the absolute val-
ues of the sticking coefficients are not known, and the stick-
ing coefficients have been arbitrarily set equal at ϭ0.15
v
As with the high energy peak, and with the same cave-
ats, the surprisal results may be interpreted using detailed
balance to extract the velocity dependence of the sticking
coefficient for this channel
cm/␮s. Unlike the case of the high energy peak, the two s( )
v
curves are substantially different even where the energy
ranges of the two measurements overlap, which suggests that
the dynamics are actually temperature dependent in this case.
J. Chem. Phys., Vol. 104, No. 17, 1 May 1996
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
128.252.67.66 On: Tue, 23 Dec 2014 18:50:48

6832
Colonell, Gibson, and Sibener: NO reduction by H2 on Rh(111)
channel appear to be temperature dependent; these properties
of the dynamics both suggest a strong interaction of the mol-
ecule with the surface during the reaction.
ACKNOWLEDGMENTS
J.I.C. acknowledges financial support from AT&T Bell
Laboratories through the Graduate Research Program for
Women. Acknowledgment is made to the donors of The Pe-
troleum Research Fund, administered by the ACS, for partial
support of this research. Additional support from the NSF
Materials Research Science and Engineering Center at The
University of Chicago is also gratefully acknowledged.
FIG. 13. Temperature dependence of the surprisal parameter used to fit the
low energy peak.
1 W. F. Egelhoff, in The Chemical Physics of Solid Surfaces and Heterge-
neous Catalysis, edited by D. A. King and D. P. Woodruff ͑Elsevier, New
York, 1982͒.
2 K. C. Taylor, Automobile Catalytic Converters, ͑Springer, Berlin, 1984͒.
3 R. M. Wolf, J. Siera, F. C. M. J. M. v. Delft, and B. E. Nieuwenhuys.
Faraday Discuss. Chem. Soc. 87, 275 ͑1989͒.
Although Fig. 11͑b͒ shows the sticking coefficient at 1000 K
to be smaller than at 700 K, this is strictly due to the arbi-
trary normalization shown: It could actually be larger or
smaller.
4 L. Bugyi and F. Solymosi, Surf. Sci. 258, 55 ͑1991͒.
5 R. Raval, M. A. Harrison, and D. A. King, in The Chemical Physics of
Solid Surfaces and Hetergenous Catalysis, edited by D. A. King and D. P.
Woodruff ͑Elsevier, New York, 1990͒.
The data show that the reaction probability ͑and, equiva-
lently, the sticking coefficient͒ for this channel is indepen-
dent of angle, so that it obeys total energy scaling instead of
normal energy scaling, and that it is less sensitive to the
energy at higher temperatures. These two facts suggest that
the molecule interacts strongly with the surface before it de-
sorbs ͑or sticks͒ so that the energy becomes scrambled
among the modes of the molecule. There may also be some
energy exchange with the surface. This would be easiest to
understand if the nitrogen molecule were trapped in a mo-
lecular chemisorbed state, and there were a barrier between
that state and dissociation, as has been suggested for N2 dis-
6 C. T. Rettner and H. Stein, Phys. Rev. Lett. 59, 2768 ͑1987͒.
7 C. T. Rettner and H. Stein, J. Chem. Phys. 87, 770 ͑1987͒.
8 R. P. Thorman and S. L. Bernasek, J. Chem. Phys. 74, 6498 ͑1981͒.
9 G. Haase and M. Asscher, Surf. Sci. 191, 75 ͑1987͒.
10 G. Haase, M. Asscher, and R. Kosloff, J. Chem. Phys. 90, 3346 ͑1989͒.
11 G. D. Billing, A. Guldberg, N. E. Henriksen, and F. Y. Hansen, Chem.
Phys. 147, 1 ͑1990͒.
12 N. E. Henriksen, G. D. Billing, and F. Y. Hansen, Surf. Sci. 227, 224
͑1990͒.
13
¨
H. E. Pfnur, C. T. Rettner, J. Lee, R. J. Madix, and D. J. Auerbach, J.
Chem. Phys. 85, 7452 ͑1986͒.
14 C. T. Rettner, H. Stein, and E. K. Schweizer, J. Chem. Phys. 89, 3337
͑1988͒.
15 C. T. Rettner, E. K. Schweizer, and H. Stein, J. Chem. Phys. 93, 1442
͑1990͒.
5
sociative chemisorption on Fe͑111͒ and W͑110͒.13 Another
16 G. Comsa and R. David, Chem. Phys. Lett. 49, 512 ͑1977͒.
17 G. Comsa and R. David, Surf. Sci. 117, 77 ͑1982͒.
18 H. A. Michelson, C. T. Rettner, D. J. Auerbach, and R. N. Zare, J. Chem.
Phys. 98, 8294 ͑1993͒.
possibility is that the molecule has multiple encounters with
a corrugated potential during the reaction.
19 L. K. Verheij, M. B. Hugenschmidt, A. B. Anton, B. Poelsema, and G.
Comsa, Surf. Sci. 210, 1 ͑1989͒.
CONCLUSIONS
20 C. A. Becker, J. P. Cowin, L. Wharton, and D. J. Auerbach, J. Chem.
Phys. 67, 3394 ͑1977͒.
We have reported measurements of the velocity distribu-
tions of product N2 molecules formed by the reduction of
NO by H2 on Rh͑111͒ in the low nitrogen coverage limit as
a function of surface temperature and desorption angle. The
N2 molecules desorb with average translational energies
three to four times that expected for molecules equilibrated
at the surface temperature. The angular and velocity distri-
butions are well fit by bimodal forms. The higher energy
component has a cos25͑⍜f͒ angular distribution, and its av-
erage energy depends on desorption angle. The low energy
component is cosine distributed, and its energy is indepen-
dent of angle. Both channels are substantially hyperthermal.
Surprisal analysis may be applied to both channels. The
high energy peak may be fit at all angles at a given surface
temperature with two dynamical parameters corresponding
to constraints on the normal velocity and the total energy.
The strong weighting toward large normal velocities and
negative constraint on the total energy may suggest a highly
geometrically constrained transition state with a high barrier.
The low energy peak may be fit with a single dynamical
constraint on the total velocity, and the dynamics of this
21 L. S. Brown and S. J. Sibener, J. Chem. Phys. 90, 2807 ͑1989͒.
22 T. Matsushima, K. Shobatake, and Y. Ohno, Surf. Sci. 283, 101 ͑1993͒.
23 Y. Ohno, T. Matsushima, and H. Uetsuka, J. Chem. Phys. 101, 5319
͑1994͒.
24 E. Poelmann, M. Schmitt, and H. Hoinkes, Surf. Sci. 287/288, 269 ͑1993͒.
25
¨
K.-H. Allers, H. Pfnur, P. Feulner, and D. Menzel, J. Chem. Phys. 100,
3985 ͑1994͒.
26
¨
K.-H. Allers, H. Pfnur, P. Feulener, and D. Menzel, Surf. Sci. 291, 167
͑1993͒.
27 J. I. Colonell, K. D. Gibson, and S. J. Sibener, J. Chem. Phys. 103, 6677
͑1995͒.
28 K. D. Gibson, J. I. Colonell, and S. J. Sibener, J. Chem. Phys. 103, 6735
͑1995͒.
29 K. D. Gibson, J. I. Colonell, and S. J. Sibener, Surf. Sci. Lett. 343, L1151
͑1995͒.
30 G. Comsa and R. David, Surf. Sci. Rep. 5, 145 ͑1985͒.
31 K. D. Gibson and S. J. Sibener, J. Chem. Phys. 88, 7862 ͑1988͒.
32 D. F. Padowitz and S. J. Sibener, Surf. Sci. 254, 125 ͑1991͒.
33 D. Bassi, in Atomic and Molecular Beam Methods, Vol. I, edited by G.
Scoles ͑Oxford University, New York, 1988͒.
34 L. Bugyi and F. Solymosi, Surf. Sci. 188, 475 ͑1987͒.
35 J. T. Yates, P. A. Thiel, and W. H. Weinberg, Surf. Sci. 84, 427 ͑1979͒.
36 T. W. Root, L. D. Schmidt, and G. B. Fisher, Surf. Sci. 134, 30 ͑1983͒.
37 D. J. Auerbach, C. T. Rettner, and H. A. Michelson, Surf. Sci. 283, 1
͑1993͒.
J. Chem. Phys., Vol. 104, No. 17, 1 May 1996
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
128.252.67.66 On: Tue, 23 Dec 2014 18:50:48

Colonell, Gibson, and Sibener: NO reduction by H2 on Rh(111)
6833
38 C. T. Rettner, D. J. Auerbach, and H. A. Michelson, J. Vac. Sci. Technol.
A 10, 2282 ͑1992͒.
57 M. F. H. v. Tol, P. T. Wouda, and B. E. Nieuwenhuys, J. Vac. Sci.
Technol. A 12, 2176 ͑1994͒.
39 J. Segner, C. T. Campbell, G. Doyen, and G. Ertl, Surf. Sci. 138, 505
͑1984͒.
58 H. Hirano, T. Yamada, K. I. Tanaka, J. Siera, P. Cobden, and B. E.
Nieuwenhuys, Surf. Sci. 262, 97 ͑1992͒.
40 H. H. Sawin and R. P. Merrill, J. Chem. Phys. 73, 996 ͑1980͒.
59 J. Siera, B. E. Nieuwenhuys, H. Hirano, T. Yamada, and K. I. Tanaka,
Catal. Lett. 3, 179 ͑1989͒.
41 V. A. Ukraintsev and I. Harrison, J. Chem. Phys. 98, 5971 ͑1993͒.
42
L. Bugyi, J. Kiss, K. Revesz, and F. Solymosi, Surf. Sci. 233, 1 ͑1990͒.
60 K. I. Tanaka, T. Yamada, and B. E. Nieuwenhuys, Surf. Sci. 242, 503
͑1991͒.
´ ´
43 C. T. Campbell and J. M. White, Appl. Surf. Sci. 1, 347 ͑1978͒.
44 L. A. DeLouise and N. Winograd, Surf. Sci. 159, 199 ͑1985͒.
45 H. A. C. M. Hendrickx and B. E. Niuwenhuys, Surf. Sci. 175, 185 ͑1985͒.
46 C.-T. Kao, G. S. Blackman, M. A. V. Hove, and G. A. Somorjai, Surf. Sci.
224, 77 ͑1989͒.
61 H. A. C. M. Hendrickx, A. Hoek, and B. E. Nieuwenhuys, Surf. Sci. 135,
81 ͑1983͒.
62 W. van Willigen, Phys. Lett. A 28, 80 ͑1968͒.
63 G. Doyen, Vacuum 32, 91 ͑1982͒.
47 T. W. Root, G. B. Fisher, and L. D. Schmidt, J. Chem. Phys. 85, 4679
͑1986͒.
64 G. Anger, A. Winkler, and K. D. Rendulic, Surf. Sci. 220, 1 ͑1989͒.
65 R. D. Levine and R. B. Bernstein, Molecular Reaction Dynamics and
Chemical Reactivity, ͑Oxford University, New York, 1987͒.
66 B. Halpern and M. Kori, Chem. Phys. Lett. 138, 261 ͑1987͒.
67 M. Kori and B. Halpern, Chem. Phys. Lett. 129, 407 ͑1986͒.
68 R. D. Levine, Ann. Rev. Phys. Chem. 29, 59 ͑1978͒.
69 R. D. Levine and J. L. Kinsey, in Atom–Molecule Collision Theory: A
Guide for the Experimentalist, edited by R. B. Bernstein ͑Plenum, New
York, 1978͒.
48 T. W. Root, G. B. Fisher, and L. D. Schmidt, J. Chem. Phys. 85, 4687
͑1986͒.
49 D. N. Belton and S. J. Schmieg, J. Catal. 144, 9 ͑1993͒.
50 W. C. Hecker and A. T. Bell, J. Catal. 92, 247 ͑1985͒.
51 F. Mertens and R. Imbihl, Nature ͑London͒ 370, 124 ͑1994͒.
52 A. Obuchi, S. Naito, T. Onishi, and K. Tamaru, Surf. Sci. 130, 29 ͑1983͒.
53 S. H. Oh, G. B. Fisher, J. E. Carpenter, and D. W. Goodman, J. Catal. 100,
360 ͑1985͒.
70 M. B. Faist, R. D. Levine, and R. B. Bernstein, J. Chem. Phys. 66, 511
͑1977͒.
54 T. W. Root, L. D. Schmidt, and G. B. Fisher, Surf. Sci. 130, 173 ͑1985͒.
55 J. Siera, P. Cobden, K. Tanaka, and B. E. Nieuwenhuys, Catal. Lett. 10,
335 ͑1991͒.
71 E. Pollak and R. D. Levine, Chem. Phys. 21, 61 ͑1977͒.
72 J. I. Steinfeld, J. S. Francisco, and W. L. Hase, Chemical Kinetics and
Dynamics ͑Prentiss Hall, Englewood Cliffs, 1989͒.
73 A. E. Depristo and A. Kara, Adv. Chem. Phys. 77, 163 ͑1990͒.
56 M. F. H. v. Tol, A. Gielbert, and B. E. Nieuwenhuys, Catal. Lett. 16, 297
͑1992͒.
J. Chem. Phys., Vol. 104, No. 17, 1 May 1996
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
128.252.67.66 On: Tue, 23 Dec 2014 18:50:48