THE JOURNAL OF CHEMICAL PHYSICS 126, 044710 共2007兲
Theory of C2Hx species on Ptˆ110‰ „1 Ã 2…: Reaction pathways
for dehydrogenation
A. T. Anghel, D. J. Wales, S. J. Jenkins, and D. A. King
Department of Chemistry, Cambridge University, Lensfield Road, Cambridge CB2 1EW, United Kingdom
共Received 5 September 2006; accepted 4 December 2006; published online 31 January 2007兲
A complete reaction sequence for molecular dissociation at a surface has been characterized using
density functional theory. The barriers for sequential ethane dehydrogenation on Pt兵110其 are found
to fall into distinct energy sets: very low barriers, with values in the range of 0.29– 0.42 eV, for the
initial ethane dissociation to ethene and ethylidene at the surface; medium barriers, in the range of
0.72– 1.10 eV, for dehydrogenation of C2H4 fragments to vinylidene and ethyne; and high barriers,
requiring more than 1.45 eV, for further dehydrogenation. For dissociation processes where more
than one pathway has been found, the lowest energetic route links the most stable reactant adsorbed
state at the surface to a product state involving the hydrocarbon moiety adsorbed in its most stable
configuration at the surface. Hence there is a clear link between surface stability and kinetics for
these species. © 2007 American Institute of Physics. 关DOI: 10.1063/1.2429068兴
INTRODUCTION
A large number of industrially relevant processes, such
as catalytic steam cracking of ethane,1 alkene
hydrogenation,2,3 Fischer-Tropsch synthesis,4,5 and catalytic
hydrocarbon oxidation, are crucially influenced by the stability and reactivity of C2Hx hydrocarbon fragments at metal
surfaces. These processes are selectively catalyzed by a
small group of transition metals and alloys, including platinum and bimetallic alloys such as platinum-gold, platinumiridium, and platinum-rhenium. Adsorption is often accompanied by the evolution of hydrogen, C–H bonds being much
more easily broken than C–C bonds.6–8 The relevant catalytic cycles must therefore involve a sequence of at least
three key reaction steps, the first of which is the dissociative
chemisorption of the hydrocarbon at a specific surface site,
where C–H bond scission preferentially proceeds. This step
may be reversible or irreversible depending on the metal, the
nature of the reacting hydrocarbon, and the reaction conditions employed. The second step is fragmentation or skeletal
rearrangement of the dehydrogenated intermediates thus
formed, whose relative probabilities determine the product
distribution. The final step is rehydrogenation or desorption
of chemisorbed species, thereby restoring vacant surface
sites to complete the catalytic cycle.
Significant progress has been made in understanding the
interaction of C2Hx fragments with metal surfaces using experimental techniques.6 However, there still remains much to
be done. Furthermore, the large number of possible structures has, hitherto, made comprehensive theoretical studies
of C2Hx dehydrogenation pathways and products difficult. It
has only recently become possible to study these systems
using theoretical tools, thanks to continued increases in
available computer power and improved geometry optimization techniques. However, there are still relatively few theoretical studies on these systems. In the present contribution
we attempt to quantify a complete catalytic reaction sequence for molecular adsorption at a metal surface.
0021-9606/2007/126共4兲/044710/13/$23.00
Our previous study determined the most stable geometries for each C2Hx 共x = 0 − 5兲 stoichiometric species chemisorbed on the missing-row reconstructed Pt兵110其 共1 ⫻ 2兲
surface.9 We found that the preferred geometry in each case
is one that completes the tetravalency of the carbon atoms
while maximizing the number of platinum atoms involved.
In general, more hydrogenated compounds tend to bind most
strongly in the vicinity of the ridge, with the trough preferred
only by C–CH and C–C species. Analysis of the thermodynamic stability of C2Hx surface species through a free energy
approach provided further insight, agreeing with prior UHV
experimental findings that ethene and ethylidyne are favored
at low temperatures, with ethynyl and eventually ethynylene
becoming dominant at around 400 and 600 K, respectively.
We have also reported two distinct pathways for dissociation
of gaseous ethane and two pathways for further dehydrogenation of chemisorbed ethyl on Pt兵110其,10 and the results
have been benchmarked against experimental information
from a supersonic molecular beam study.11 In this article we
describe a complete reaction sequence for hydrocarbon dissociation at a metal surface. We report density functional
theory 共DFT兲 results for single dehydrogenation pathways
for C2Hx 共x = 0 − 4兲 dissociation on Pt兵110其.
COMPUTATIONAL DETAILS
The electronic structure was treated with DFT using the
PW-91 exchange-correlation functional, as implemented in
15
CASTEP.
The parameters and computational model employed are the same as those described in detail
elsewhere.9,10,16 The Pt兵110其 surface was modeled by a sixlayer slab with the missing-row reconstruction on one face
only. A 0.25 ML adsorbate coverage was achieved by placing
a single hydrocarbon molecule in a 共2 ⫻ 2兲 unit cell with
respect to the reconstructed surface. The top three surface
layers and the hydrocarbon fragments were allowed to relax
during geometry optimization. Since calculation of the
Hessian 共second derivative兲 matrix is undesirable for large
126, 044710-1
© 2007 American Institute of Physics
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J. Chem. Phys. 126, 044710 共2007兲
FIG. 1. Path5 involves a 1, 2-H shift between the two
carbons of H2C – CH2, thereby converting ethene into
ethylidene.
systems, such as the ones investigated here, a hybrid
eigenvector-following scheme was employed17–19 to refine
initial guesses for transition state geometries obtained by
constrained minimization. Once the smallest nonzero eigenvalue ␭min and the corresponding eigenvector emin have been
found, an uphill eigenvector-following step is taken in this
direction while minimizing in the orthogonal subspace. The
process is repeated until we have a stationary point with a
sufficiently small root-mean-square 共rms兲 force. The two
downhill paths for this transition state are then calculated by
energy minimization following small initial displacements
parallel and antiparallel to the eigenvector corresponding to
the unique negative eigenvalue.17–19
of 0.29 and 0.33 eV, respectively.10 Overall these four pathways can be summarized by the following scheme:
RESULTS
1,2-H shift between ethene and ethylidene
Two pathways, Path1 and Path2, for gaseous ethane dissociation to chemisorbed ethyl, H2C – CH3, at a ridge site and
H at a neighboring surface site have been previously
reported.10 These processes involve activation energies of
0.38 and 0.42 eV and sample the corrugation of the surface.
The ethyl moiety can itself dissociate to give chemisorbed
ethene 共H2C – CH2兲 and H 共pathway Path3兲 or ethylidene
共HC – CH3兲 and H 共pathway Path 4兲 with activation barriers
FIG. 2. Reactant 共ethene兲, transition state 共TS兲, and product 共ethylidene兲
structures for Path5. All bond lengths are in Å.
C2H6共gas兲 + 2 ⴱ H2C – CH3 + H,
共1兲
H2C – CH3 + ⴱ HC – CH3 + H,
共2兲
H2C – CH3 + ⴱ H2C – CH2 + H.
共3兲
Here ⴱ denotes an empty surface site, and in the product state
the hydrocarbon fragment and H are coadsorbed on the surface. In the current study we report subsequent dissociation
and interconversion pathways, labeled Path5 to Path21 in
Fig. 1–19 and in Table I1. For simplicity, only the repeating
unit cell is shown in the following illustrations of the reaction pathways, where the color scheme is gray for platinum,
green for carbon, and black for hydrogen.
A pathway, labeled Path5, for the conversion of ethene to
ethylidene on Pt兵110其 has been characterized, and is shown
in Fig. 1. The mechanism involves a 1,2-H shift between the
two carbon centers, which can be summarized by the equation
H2C – CH2 HC – CH3 .
共4兲
Figure 2 gives the structural details for key stationary points
on the reaction pathway. Here, the reactant and product states
correspond to the most stable configuration for ethene and
ethylidene adsorption at the surface, as found in our previous
study.9 The pathway involves the diffusion of the C–C backbone in ethene along the 关11̄0兴 surface direction in such a
way that one C atom approaches a ridge bridge site. The
hybridization of the other carbon atom changes to sp3 during
a simultaneous process of bond breaking away from the surface and bond formation to the H atom being transferred
from the other C center. The transition state structure is unusual in that the H atom being exchanged is pointing away
from and does not interact with the surface. Hence this process is not surface mediated, which accounts for the high
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C2Hx species in dehydrogenation by Pt
FIG. 3. Path6 and Path7 for ethylidene, HC – CH3, dissociation.
activation barrier of 2.31 eV. We further note that, as described in the following sections, it requires less energy to
activate both ethene and ethylidene toward dehydrogenation
than for these species to undergo an interconversion. Interestingly, a 1,2-H shift process converting methylcarbene to
ethylene in the gas phase is also found to be relatively
unfavorable.20 This is because gaseous methylcarbene has a
triplet ground electronic state,21,22 while gaseous ethylene
has a singlet 1A1g ground electronic state,20 implying that a
1,2-H shift isomerization involving the ground electronic
states does not show the large energy release normally asso-
ciated with gaseous 1,2-hydrogen shifts. Furthermore, the
lowest triplet electronic state for gaseous ethylene lies just
above the 1A1g ground electronic state,20 suggesting that
interconversion in the gas phase is more likely to occur via
electronically excited potential energy surfaces.
Pathways for ethylidene and ethene dehydrogenation
Adsorbed ethylidene and ethene can dehydrogenate to
species of C2H3 stoichiometry, as shown in the reaction
scheme below. Dehydrogenation of ethylene to ethylidyne
FIG. 4. Transition state 共left兲 and product state 共right兲
geometries for ethylidyne dehydrogentation in Path6
and Path7. The reactant state for both pathways corresponds to HC – CH3 adsorbed at the same ridge bridge
site as shown in Fig. 2. Bond lengths are in Å.
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Anghel et al.
FIG. 5. Path8 and Path9 for ethene, H2C – CH2, dissociation. The reactant state for both pathways corresponds to H2C – CH2 adsorbed at the same ridge bridge
site.
共C – CH3兲 is expected to be a multistep process, as it involves
forming a new H–Pt bond at the expense of breaking two
C–H bonds, two H–Pt bonds, and one C–Pt bond. However,
ethylidene can dehydrogenate to form either vinyl,
HC – CH2, and H or ethylidyne, C – CH3, and H:
HC – CH3 + ⴱ C – CH3 + H,
共5兲
HC – CH3 + ⴱ HC – CH2 + H,
共6兲
H2C – CH2 + ⴱ HC – CH2 + H.
共7兲
Two pathways for ethylidene, HC – CH3, dissociation from
its most stable surface adsorbed state have been identified
and are shown in Fig. 3. Structural details are given in Fig. 4.
Path6 corresponds to ethylidene dehydrogenation to a vinyl
共HC – CH2兲 species, while Path7 corresponds to dehydrogenation to ethylidyne, C – CH3. The geometry of the vinyl and
ethylidyne fragments in the two product states corresponds
to their most stable adsorption structures, as described in our
previous study.9 Path6 requires the C–C axis in ethylidene to
rotate such that the –CH3 fragment can tilt down and approach the surface via the breaking H atom at a ridge-atop
site. Two bonds between the hydrocarbon and the surface are
being formed in this process: a C–Pt and a H–Pt bond. Path7
involves diffusion of the hydrocarbon fragment from a ridge
bridge to a threefold hollow site via the unsaturated C atom,
with a simultaneous elongation of the breaking C–H bond
over a ridge-atop site. The product state, however, features
the coadsorbed H atom at a ridge bridge site.
Two very similar pathways have been found for ethene
dissociation from its most stable adsorbed geometry at the
surface, labeled Path8 and Path9 in Fig. 5. The product and
transition state 共TS兲 structures are given in Fig. 6. In these
pathways the hydrocarbon fragment diffuses along the 关11̄0兴
direction in such a way that one C atom bridges two neighbouring ridge surface sites. The second carbon lies above a
ridge surface site. On approaching the TS, the molecular
FIG. 6. Transition state 共left兲 and product state 共right兲
geometries for ethene dehydrogenation in Path8 and
Path9. The reactant state for both pathways corresponds
to H2C – CH2 adsorbed over a neighboring ridge site, as
shown in Fig. 2. Bond lengths are in Å.
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J. Chem. Phys. 126, 044710 共2007兲
FIG. 7. Path10 and Path11 for ethylidyne 共C – CH3兲 dissociation. The reactant state for both pathways corresponds to C – CH3 adsorbed at the same threefold site.
C–C axis has rotated by approximately 45° around the axis
perpendicular to the surface plane. The degree of unsaturation in the hydrocarbon fragment increases. The geometry of
the vinyl 共HC – CH2兲 product for the two pathways corresponds to the most stable geometry found in our previous
study.9 The location of the coadsorbed H atom in the product
state differs between the two pathways: for Path8 it is a
bridge site between a ridge and a second-layer surface atom,
while for Path9 it lies at a bridge site between two neighboring ridge atoms, as shown in Fig. 6. It is likely that the
transition state is actually the same for these two paths, and
the alternative sites for the H atom in the product reflect the
finite step size used to characterize the downhill paths.
Adsorbed vinyl species were found experimentally to be
the favored products upon dosing ethene in the surface temperature range of 160– 200 K on open surfaces such as
Pt兵110其 共1 ⫻ 1兲, Ni兵100其, Ni兵110其, and Pd兵100其.23–27 It is possible that a similar dehydrogenation pathway to the ones
found on Pt兵110其 共1 ⫻ 2兲 also exits for these surfaces. This
process is of significant industrial importance, since it has
been suggested that the selective catalytic conversion of ethylene to functionalized olefins such as vinyl chloride, vinyl
acetate, and vinyl alcohols on supported metal catalysts may
involve the formation of a surface vinyl intermediate,
HC – CH2.28
Pathways for vinyl and ethylidyne dehydrogenation
Although we have searched for conversion mechanisms
between adsorbed ethylidyne and vinyl on Pt兵110其, no such
pathways were found. However, we have characterized four
distinct pathways for dehydrogenation of these species to
FIG. 8. Transition state 共left兲 and product state 共right兲
geometries for ethylidyne dehydrogenation in Path10
and Path11. The reactant state for both pathways corresponds to C – CH3 adsorbed in its most stable site 共see
Ref. 9兲. Bond lengths are in Å.
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J. Chem. Phys. 126, 044710 共2007兲
FIG. 9. Path12 and Path13 for vinyl
共HC – CH2兲 dissociation. The reactant
state for both pathways corresponds to
HC – CH2 adsorbed at the ridge site.
ethyne and vinylidene, summarized by the reaction scheme
below. Ethylidyne 共C – CH3兲 dehydrogenation to ethyne
共HC–CH兲 is thought to be a multistep process, but pathways
for dehydrogenation to vinylidene 共C – CH2兲 and H have
been characterized by our study. Ethylidyne 共C – CH3兲 dissociates from its most stable adsorbed geometry9 via two different processes, labeled Path10 and Path11 in Fig. 7. The
structures of the TS and product states are given in Fig. 8.
The barrier in Path10 is 0.88 eV. Here the –CH3 fragment
tilts down and approaches the surface at a ridge site via one
H atom, leading to an extension of the breaking C–H bond. A
new C–Pt bond is being formed, but there is no change in the
position of the unsaturated -C atom. The product state features the vinylidene fragment in a geometry close to its most
stable adsorbed state at the surface,9 while the coadsorbed H
atom is at a ridge bridge site.
Path11 in Fig. 7 is unusual, leading to a product state
that features the –CH2 fragment pointing away and not interacting with the surface, while the coadsorbed H atom lies
at a ridge bridge site. The geometry of the vinylidene fragment in this structure was previously found to be 0.52 eV
higher than in its most stable configuration.9 The corresponding activation barrier is 2.03 eV.
C – CH3 + ⴱ C – CH2 + H,
共8兲
HC – CH2 + ⴱ C – CH2 + H,
共9兲
HC – CH2 + ⴱ HC – CH + H.
共10兲
Vinyl 共HC – CH2兲 in its most stable adsorbed state9 dissociates to vinylidene, C – CH2, and H via Path12, as shown in
Fig. 9 and 10. The product state features the vinylidene frag-
FIG. 10. Transition state 共left兲 and product state 共right兲
geometries for vinyl dehydrogenation in Path12 and
Path13. The reactant state for both pathways corresponds to HC – CH2 adsorbed at its most stable site 共see
Ref. 9兲. Bond lengths are in Å.
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J. Chem. Phys. 126, 044710 共2007兲
FIG. 11. Path14, Path15, and Path16
for HC–CH dissociation. The reactant
state for all three pathways corresponds to HC–CH adsorbed at a ridge
site.
FIG. 12. Transition state 共left兲 and product state 共right兲 geometries for ethyne dehydrogenation in Path14, Path15, and Path16. Bond lengths are in Å.
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FIG. 13. Path17 and Path18 for vinylidene dissociation. The reactant state for both pathways corresponds to C – CH2 adsorbed at the ridge site.
ment adsorbed in its most stable geometry.9 The activation
barrier for this process is calculated as 0.93 eV. The same
vinyl structure can dehydrogenate to ethyne and H via
Path13 in Fig. 9. This process entails a higher activation
barrier of 1.27 eV. The ethyne fragment in the product state
is not in its lowest energy geometry but 0.29 eV higher.9
Pathways for ethyne and vinylidene dehydrogenation
Three pathways for ethyne 共HC–CH兲 dehydrogenation
have been characterized, and are labeled Path14, Path15, and
Path16 in Fig. 11. The TS and product structures are shown
in Fig. 12. All three pathways have the same reactant state,
which corresponds to the most stable adsorbed ethyne geom-
etry at the surface, as previously reported.9 Each of the three
processes is believed to require bonding of the hydrocarbon
moiety to the surface at the TS to be mediated through a
three-centered C–H–Pt orbital, and involves ␴ electron donation from the C–H bond to a mainly s-character metal
orbital. Vinylidene was found to dissociate from its most
stable adsorbed state, described in Ref. 9, via two pathways
labeled Path17 and Path18 in Fig. 13. The TS and product
structures are given in Fig. 14. The acetylidene fragment in
the product state for both pathways bonds to the surface at
sites involving the ridge and second layer. The position of
the coadsorbed H atom differs, with preferential stabilization
of the ridge bridge site in Path17. We note that the reactant
FIG. 14. Transition state 共left兲 and product state 共right兲
geometries for vinylidene dehydrogenation in Path17
and Path18. The reactant state for both pathways corresponds to C – CH2 adsorbed at its most stable site 共see
Ref. 9兲. Bond lengths are in Å.
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C2Hx species in dehydrogenation by Pt
FIG. 15. Path19 for diffusion of acetylidene, C–CH.
vinylidene and ethyne states in Fig. 11 and 13 are almost
isoenergetic on the surface, in agreement with our previous
results.9
C – CH2 + ⴱ C – CH + H,
共11兲
HC – CH + ⴱ C – CH + H.
共12兲
The high activation barriers, in the range of
1.37– 1.59 eV, found for vinylidene and ethyne dehydrogenation 共11兲 and 共12兲 suggest that high surface temperatures
are required for these processes to be observed under experimental conditions. This conclusion agrees with experimental
results for a variety of metal surfaces. On Pt兵110其, C2H2 was
found to decompose to give C–CH at 400 K.11 Similarly, a
number of experimental techniques found that ethylene adsorption on Pt兵111其 共Ref. 14 and 29–42兲 and acetylene adsorption on Pd兵111其 共Ref. 43兲 produce chemisorbed C–CH
only above 400 K.
Pathways for acetylidene diffusion
and dehydrogenation
The acetylidene 共C–CH兲 fragment in the product states
for C2H2 dissociation in Path14 and Path18 is adsorbed at
surface sites involving the ridge and second layer. However,
the most stable acetylidene structure adsorbed at the surface
was previously found9 to involve second- and third-layer surface sites. Hence we investigated two possibilities: breaking
the C–H bond in acetylidene adsorbed at a ridge site and
diffusion of acetylidene from the ridge to the trough, followed by C–H bond breaking:
C – CH + ⴱ C – CH + ⴱ ,
共13兲
C – CH + ⴱ C – C + H.
共14兲
We have identified a diffusion pathway for acetylidene
diffusion between two trough surface sites, as shown in Fig.
15. The activation barrier from the reactant state is only
0.21 eV. However, the product state is significantly lower in
energy than the reactant state. The latter structure corresponds to the most stable C–CH structure found in our previous study.9 We expect that pathways for acetylidene diffusion from the ridge to the trough involve similar barriers,
which would be easily surmountable at the surface temperatures required for formation of acetylidene. Hence, diffusion
to the trough is not believed to be rate determining for further dissociation at the surface. Once at the trough, acetylidene can undergo further dehydrogenation via pathway
Path20 in Fig. 16 from its most stable adsorbed state. The
geometries of the TS and product states are given in Fig. 17.
This pathway leads to the formation of dicarbide in its most
stable adsorbed state at the surface.9 Here the C–C structure
is also stabilized over the trough.9
Pathways for C–C bond scission in acetylidene
We have characterized a pathway for C–C bond scission
in acetylidene, Path21, as shown in Fig. 18 and 19. The
reactant C–CH state is 0.52 eV higher in energy than its most
stable configuration at the surface. However, this structure is
ideally suited for diffusion of the CH moiety away from the
trough and rearrangement of the C entity within the trough.
Harris et al. found that upon exposing the products of ethane
dissociative chemisorption to deuterium on Pt兵110其 at 370 K,
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J. Chem. Phys. 126, 044710 共2007兲
FIG. 16. Path20 for acetylidene,
C–CH, dissociation.
no deuterated methane was produced, indicating that C–C
bond scission does not occur at the temperatures
investigated.11 Our results agree with this study, since the
reactant state required for C–C scission is thermodynamically disfavored and the process is kinetically hindered. We
conclude that this process is unlikely to play any significant
part in the reaction scheme for ethane dissociation on
Pt兵110其.
DISCUSSION
As we see from Table I, the barriers for sequential ethane
dehydrogenation on Pt兵110其 fall into distinct sets: low barriers, with values in the range of 0.29 to 0.42 eV, for the initial ethane dissociation to ethene and the ethylidene at the
surface; medium sized barriers, in the range of
0.72– 1.10 eV, for dehydrogenation of C2H4 fragments to vinylidene and ethyne; and high barriers, of more than
1.45 eV, for further dehydrogenation. However, the hydrogenation barriers are not so clearly divided. Interestingly, for
FIG. 17. Transition state 共left兲 and product state 共right兲 geometries for
acetylidene dehydrogenation in Path20. Bond lengths are in Å.
dissociation processes where more than one pathway has
been identified, the route involving the lowest barrier links
the most stable reactant adsorbed state at the surface to a
product state involving the hydrocarbon moiety adsorbed at
its most stable configuration. There is a clear link between
surface stability and kinetics for these species. Connecting
all these mechanisms together provides information on the
processes that govern the chemistry of adsorbed C2Hx fragments on Pt兵110其. Adsorbed ethyl is predicted to be rapidly
consumed at low surface temperatures by dehydrogenation to
ethene and ethylidene. To estimate relevant surface temperatures corresponding to the barriers that we have found, we
assume a frequency factor of 1013 s−1 and calculate the temperature corresponding to a rate of 0.1 s−1. The latter value
should be appropriate for an experimental time scale on the
order of minutes. With these parameters we expect ethene to
build up in significant amounts on the surface only over a
narrow, relatively low temperature range around 230 K,
since ethylidene hydrogenation back to ethyl can also take
place.
At higher temperatures, estimated around 270 K from
the barrier of order 0.75 eV, the vinyl formed from ethene
dehydrogenation will rehydrogenate. Hence, at such temperatures we expect ethene to be present on the surface. At
higher surface temperatures around 320 K ethylidyne and
vinylidene are expected to coexist on Pt兵110其. Above about
400 K ethyne will also form on the surface and is expected
to coexist with vinylidene. Both these species will dehydrogenate to acetylidene, with barriers of over 1.37 eV. Hydrogenation of acetylidene back to C2H2 involves much lower
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FIG. 18. Path21 for C–CH dissociation to CH and C.
The C–CH reactant is adsorbed in its most stable state,
which is the reactant in Path19.
barriers. However, at the high temperatures required for
C2H2 dissociation, the H atoms thus formed are expected to
desorb, hence driving the formation of more unsaturated species, such as acetylidene. In effect there will be virtually no
H atoms on the surface for rehydrogenation. Higher temperatures are required to give dicarbide. However, we note that
desorption of hydrocarbon fragments and hydrogen from the
surface can significantly alter the product distribution. Only a
detailed kinetic model that explicitly includes a treatment of
surface temperature activation of reactive pathways and accounts for hydrocarbon and hydrogen desorption from the
surface can therefore describe the product distribution for
sequential dehydrogenation of ethane on Pt兵110其 共1 ⫻ 2兲.
We now provide a qualitative comparison between our
results and those from experiment. Stuck et al.12 found that
the calorimetric differential heat on adsorbing ethene on
Pt兵110其 drops in several steps with increasing coverage at
300 K. They ascribed these steps to formation of both C2H2
and C2H3 on the surface, based on combined electron energy
loss spectroscopy and comparison with thermal desorption
results by Yagasaki et al.13 at 300 K. The -CH2 wag and
scissor modes were observed in this study at 990 and
1420 cm−1, respectively, which was interpreted as indicating
that the C2H2 surface species observed is in fact vinylidene,
with no ethyne being formed. The proportion of C – CH2
compared to C – CH3 was found to be higher at lower coverages, as expected for an adlayer containing a mixture of species. Our conclusions based on the computed dissociation
barriers are in full agreement with the results of Stuck et al.12
since much higher barriers are required for the formation of
ethyne on the surface.
A recent molecular beam study by Harris et al.11 found
that the stable product of ethane dissociative adsorption at
Pt兵110其 共1 ⫻ 2兲 has C2H2 stoichiometry at all coverages in
the surface temperature range of 350– 400 K. Further analysis suggested that a pure vinylidene adlayer was formed. Under these conditions adsorbed atomic hydrogen resulting
from hydrocarbon dissociation desorbs as soon as it is
formed at surface temperatures above 370 K. Temperature
programed reaction studies have shown that vinylidene decomposes to acetylidene above 400 K, with a reactionlimited peak temperature of 430 K. Here the formation of
FIG. 19. Reactant 共left兲, transition
state 共middle兲, and product state
共right兲 geometries for C–C bond
cleavage in acetylidene in Path21.
Bond lengths are in Å.
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J. Chem. Phys. 126, 044710 共2007兲
Anghel et al.
TABLE I. Properties of all the stationary points considered in the present work. Energies are in eV, and the lowest minimum for a given stoichiometry was
chosen as the arbitrary zero in each case. ER is the energy of the adsorbed reactant state, ETS is the energy of the TS, and EP is the energy of the adsorbed
product state. ⌬EPR and ⌬ERP are the barriers for the forward and reverse reactions, respectively. The final column gives the unique negative Hessian
eigenvalue at the transition state in eV/ Å2, which indicates the curvature of the corresponding reaction path at this point. The convergence condition for the
self-consistent-field calculations in CASTEP was 5 ⫻ 10−8 eV/ atom, and the rms force was generally reduced to 0.0028 eV/ Å or less for every stationary point.
For these thresholds the energy difference found for equivalent stationary points obtained in different runs was of the order of 0.01 eV or less.
Path
R
P
ER
⌬ERP
ETS
⌬EPR
EP
Eigenvalue
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
C2H6 gas
C2H6 gas
C 2H 5
C 2H 5
H2C – CH2
HC – CH3
HC – CH3
H2C – CH2
H2C – CH2
C – CH3
C – CH3
HC – CH2
HC – CH2
HC–CH
HC–CH
HC–CH
C – CH2
C – CH2
C–CH
C–CH
C–CH
C 2H 5 + H
C 2H 5 + H
HC – CH3 + H
H2C – CH2 + H
HC – CH3
HC – CH2 + H
C – CH3 + H
HC – CH2 + H
HC – CH2 + H
C – CH2 + H
C – CH2 + H
C – CH2 + H
HC – CH + H
C – CH + H
C – CH + H
C – CH + H
C – CH + H
C – CH + H
C–CH
C–C+H
C–H+C
0.22
0.18
0.46
0.46
0.00
0.27
0.27
0.00
0.00
0.05
0.00
0.16
0.17
0.00
0.00
0.00
0.03
0.02
1.09
0.00
0.52
0.38
0.42
0.33
0.29
2.31
0.75
0.90
0.72
0.73
0.83
2.03
0.77
1.10
1.45
1.55
1.59
1.37
1.55
0.21
1.63
1.71
0.60
0.60
0.79
0.75
2.31
1.02
1.17
0.72
0.73
0.88
2.03
0.93
1.27
1.45
1.55
1.59
1.40
1.57
1.30
1.63
2.23
0.60
0.51
0.64
0.75
2.04
0.72
1.26
0.43
0.40
0.69
1.44
0.41
0.72
0.47
0.54
0.77
0.80
0.50
1.30
1.09
1.39
0.00
0.09
0.15
0.00
0.27
0.30
−0.09
0.29
0.33
0.19
0.60
0.52
0.55
0.98
1.00
0.82
0.59
1.07
0.00
0.54
0.84
−4.5
−4.1
−3.7
−3.3
−14.8
−3.7
−6.4
−4.0
−4.0
−3.3
−9.4
−6.6
−5.1
−5.3
−4.9
−8.4
−4.2
−5.8
−2.7
−11.9
−16.6
product mixtures below 300 K observed by Stuck et al.12
was reinterpreted in terms of the presence of coadsorbed hydrogen on the surface at these temperatures, which was previously shown to inhibit the decomposition of HC – CH3 and
H2C – CH2 on Pt兵111其.14 Our results suggest that it is unlikely
for vinylidene to form alone on the surface over such a wide
and relatively low temperature range. However, only a full
kinetic analysis can rule this possibility out. We further note
that the supersonic molecular beam experimental method
employed by Harris et al.11 relies on imparting translational
and vibrational energy to gaseous ethane before it reaches
the surface, in order for dissociation to occur at a significant
rate. This observation implies that formation of C – CH2 under supersonic molecular beam conditions takes place at
lower surface temperatures than otherwise required, providing that all processes leading to formation of C2H2 are fast,
and that incomplete thermal accommodation of the internal
energy initially available in the hydrocarbon moiety to the
surface occurs.
CONCLUSIONS
A complete reaction sequence for molecular dissociation
at a surface has been obtained using a density functional
treatment of the electronic structure and hybrid eigenvectorfollowing geometry optimization.17–19 The barriers for sequential ethane dehydrogenation on Pt兵110其 are found to fall
into distinct energy sets: low barriers, with values in the
range of 0.29– 0.42 eV, for the initial ethane dissociation to
ethene and the ethylidene at the surface; medium barriers, in
the range of 0.72– 1.10 eV, for dehydrogenation of C2H4
fragments to vinylidene and ethyne; and high barriers, requiring more than 1.45 eV, corresponding to further dehydrogenation. For dissociation processes where more than one
pathway has been identified, the route involving the lowest
barriers links the most stable reactant adsorbed state to a
product state involving the hydrocarbon moiety adsorbed in
its most stable configuration. Hence there is a clear link between surface stability and kinetics for these species.
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