J. Phys. Chem. C 2008, 112, 14417–14427
14417
Benzene and Its Dissociation Products on Ir{100} Shuichi Yamagishi,† Stephen J. Jenkins,*,‡ and David A. King‡ National Metrology Institute of Japan (NMIJ), National Institute of AdVanced Industrial Science and Technology (AIST), AIST Tsukuba Central 3, 1-1-1 Umezono, Tsukuba, Ibaraki 305-8563, Japan, and Department of Chemistry, UniVersity of Cambridge, Lensfield Road, Cambridge CB2 1EW, U.K. ReceiVed: May 7, 2008; ReVised Manuscript ReceiVed: July 7, 2008
Benzene forms a disorded overlayer when adsorbed on unreconstructed Ir{100} at low temperatures, but is known to dissociate yielding an ordered c(2 × 4) benzyne overlayer at moderate temperatures. Predosing the surface with a low coverage of atomic carbon, however, causes the benzyne overlayer to adopt a c(4 × 4) pattern instead. Here, we investigate the structure and energetics of these overlayers by means of density functional theory calculations, rationalizing the thermodynamic imperatives that drive the transitions between these various phases. 1. Introduction Adsorption of benzene on transition metal surfaces typically leads to a disordered overlayer, in which the molecules take on a flat-lying local geometry; where the ring plane is tilted, this may often be attributed to the inherent corrugation of the substrate.1,2 Ordered structures exist only for a relatively small number of cases, including adsorption on Ni{111} and Ru{0001}, both studied previously by ourselves within a periodic firstprinciples density functional theory (DFT) approach.3,4 The presence of coadsorbates can, however, induce order in otherwise disordered benzene overlayers or alter the arrangement of intrinsically ordered ones. Our earlier DFT calculations have elucidated the various ways in which coadsorption can critically affect the energetics of adsorbed benzene and drive changes in adsorption site and local electronic structure.5 An interesting exception to the general rules outlined above occurs when benzene is adsorbed on the metastable unreconstructed Ir{100} surface. Here, the overlayers are initially disordered following low-temperature deposition but undergo a spontaneous transition to a c(2 × 4) ordered phase when heated to around 500 K in a thermally programmed desorption (TPD) experiment.6,7 This transition is accompanied by the evolution of gaseous hydrogen, and consideration of the mass balance suggests that two hydrogen atoms are removed from each benzene molecule. Quantitative analysis of low-energy electron diffraction (LEED) results confirms that the molecules thus formed on the surface are indeed o-benzyne (C6H4) and that they bind primarily through σ bonds directed from each of their two adjacent radical C atoms toward the centers of two adjacent surface Ir atoms.6 Accordingly, the ring-plane normal might have been expected to be perpendicular to the surface normal, but in fact the LEED analysis very clearly indicates an angle close to 45°. Our DFT calculations have confirmed that this configuration does indeed yield the lowest energy, and the agreement between theoretically and experimentally determined structural parameters is correspondingly convincing.10,11 Intriguingly, however, coadsorption with small quantities of carbon leads to the formation of a c(4 × 4) periodicity upon benzene dehydrogenation, rather than the c(2 × 4) structure that * To whom correspondence should be addressed. † National Institute of Advanced Industrial Science and Technology. ‡ University of Cambridge.
ordinarily appears.6,12 Furthermore, the presence of glide symmetry, as inferred from the observed LEED pattern,13 strongly argues against a tilted geometry for the benzyne molecules in the coadsorbed case. Clearly, further investigation is highly desirable; hence the present study. 2. Density Functional Methodology Hafner and co-workers were, we believe, the first to report DFT calculations for benzene on a metal surface, with their studies on Al{111}.14 This work was swiftly followed by the first investigations of benzene adsorption on transition metal surfaces from the same group15 (Ni{100}, {110}, and {111}) and from ourselves3 (Ni{111}). Since that time, the theoretical database for benzene adsorption on transition metals has expanded to include studies on Ru{0001},4 Cu{110},16 Pt{111},17,18 Pd{111},18,19 and Rh{111}18 and even to encompass the determination of transition states for hydrogenation reactions on Ni{111},20 Pt{111},22,21 and Pd{111}.21 Meanwhile, a number of other aromatic adsorption systems have also been tackled, including phenol on Ni{111}23 and Pd{111},19 anisole on Pt{111},24 and o-toluic acid and 2-methylnicotinic acid on Rh{111}.25 These studies collectively provide a clear indication of the general suitability of DFT for calculations of this type, at least in terms of identifying adsorption sites, investigating adsorption geometry, and interrogating the adsorbate’s electronic structure. One should note, however, that accurate calorimetric adsorption heats reported by Campbell and co-workers26,27 for benzene and naphthalene on Pt{111} are somewhat higher than analogous calculated values.22,28 It therefore appears that DFT significantly underestimates the adsorption heat of aromatic compounds adopting a flat-lying geometry, at least on Pt{111}. This is remarkable, since DFT typically overestimates the covalent binding energy of nonaromatic molecular adsorbates; it has plausibly been suggested that deficiencies in the DFT treatment of van der Waals interactions may be responsible for the missing binding energy in the flat-lying aromatic systems.27 The extent to which this might also affect DFT energies for upright or semiupright aromatic radical species, such as benzyne10,11,29 or phenyl,29 remains unclear at the present time. Nevertheless, we believe the approach adopted here to provide an appropriate basis for at least a semiquantitative discussion, so long as these important caveats are borne in mind.
10.1021/jp804041j CCC: $40.75 2008 American Chemical Society Published on Web 08/23/2008
14418 J. Phys. Chem. C, Vol. 112, No. 37, 2008
Yamagishi et al.
In the present study, we have performed DFT calculations of Ir{100}/H, Ir{100}/C, Ir{100}/C6H6 and Ir{100}/(nC + mC6H4) by means of the CASTEP computer code,30 using ultrasoft pseudopotentials31 and a plane wave basis set of 320 eV cutoff. Electronic exchange and correlation were included through the generalized gradient approximation (GGA) in the Perdew-Wang (PW91) form,32 and the Brillouin zones of c(2 × 2), c(2 × 4), and c(4 × 4) unit cells were sampled via 6 × 6 × 1, 4 × 4 × 1, and 3 × 3 × 1 Monkhorst-Pack meshes33 of k-points, respectively. Adsorption was modeled on one side of a four-layer Ir slab, within a supercell of length equivalent to 10 atomic layers. Adsorbed species and the top two Ir layers were allowed to relax freely, according to the calculated forces. More details of the calculational method may be found in ref 10.
TABLE 1: Adsorption Energies for H2, C, and C6H6 (in eV)a site
EHad2
ECad
E Cads6 H6
atop bridge hollow
1.20 1.46 0.64
5.72 6.79 8.06
2.88
a For H2, the process is dissociative, but the energy is expressed per original gas-phase molecule; for C, the energy is relative to an isolated C atom; for C6H6, the energy represents adsorption of the intact molecule. The resulting overlayers are c(2 × 2) for H and C and c(4 × 4) for C6H6.
3. Adsorption Energies and Structural Results 3.1. H on Ir{100}. It is well-known that clean Ir{100} surfaces reconstruct to form a pseudohexagonal (1 × 5) overlayer34-37 and that adsorption of hydrogen induces lifting of this reconstruction to (1 × 1) and/or (1 × 3) surfaces.38-40 We, on the other hand, have actually calculated a c(2 × 2) overlayer on an unreconstructed substrate in order to represent a moderate-coverage case without the structural complexity of the (1 × 3) system. Our calculations should therefore be regarded as indicative only, at least as regards their direct relevance to the adsorption of hydrogen, and the details will certainly differ somewhat from experimental reality. The structure and energetics of c(2 × 2) H on Ir{100} were calculated for several geometries at 0.5 ML adatom coverage, and the bridge site was found to be the most favorable option, with a dissociative adsorption energy of EHad2 ) 1.46 eV per original hydrogen molecule (141 kJ mol-1 of H2). The adsorption energy has been defined according to the following equation
1 1 c(2×2) - EHad2 ) EIr/H - Ec(2×2) + EHg 2 + 2ER Ir 2 2
(
)
(1)
where Ec(2×2) and Ec(2×2) Ir Ir/H represent the total energies per supercell of clean-unreconstructed and H-adsorbed Ir surfaces, as calculated within a supercell of cross section equivalent to a c(2 × 2) primitive unit cell;41 E Hg 2 is the gas phase energy of a hydrogen molecule (calculated as -31.749 eV per molecule), and ER is the reconstruction energy per (1 × 1) cell for the (1 × 5) f (1 × 1) phase transition of the clean surface (calculated by Ge et al.42 to be 0.06 eV and by Ghosh et al.43 to be 0.05 eV; here, we have adopted the value of 0.06 eV, as the present calculational parameters are closer to those of the earlier work). The dissociative adsorption energy thus includes the energy required to lift the (1 × 5) reconstruction (over an area four times that of a (1 × 1) cell) as well as the dissociation energy of the molecule. Adsorption at the bridge site contradicts the assumption of hollow site adsorption made by Moritani et al.39 and by King and co-workers40 for the (1 × 3) structure. Nevertheless, the difference in adsorption energies suggests that the present assignment is quite secure (see Table 1). We also note that the zero-coverage desorption energy of deuterium (D2) from the (1 × 1) surface was previously determined38 by isosteric measurements as 98 ( 14 kJ mol-1 and by a second-order fit to desorption spectra as 111.5 kJ mol-1. Our adsorption energy is thus in reasonable agreement with the experimental results, albeit slightly overestimated; such a discrepancy is not unusual for DFT-PW91 calculations, and again one should recall that our substrate is unreconstructed. Considering the structure of the
Figure 1. DFT-calculated adsorption geometry for 0.5 ML H on Ir{100}. Note that only half of the conventional nonprimitive c(2 × 2) unit cell is depicted; the remainder may be inferred by translational symmetry. Units for the structural parameters are angstroms, and values in parentheses are the LEED-derived values for the (1 × 3) structure studied by Sauerhammer et al.40
bridge model (see Figure 1), the top two Ir layers show no buckling. The interlayer spacing between the first and the second layer (d12) is 1.86 Å, and that between the second and third layers (d23) is 1.95 Å (the DFT-calculated bulk value is 1.93 Å). The perpendicular distance between the H adatom and Ir surface atom is found to be 1.14 Å, and the Ir-H bond length is calculated to be 1.78 Å. 3.2. C on Ir{100}. It has been found through experiment44 that a well-ordered c(2 × 2) carbon overlayer may be formed on Ir{100} by heating a benzene overlayer to 700 K; the resulting adatoms are found, by quantitative LEED analysis, to occupy hollow sites. Although DFT results reported at the time44 amply support this assignment, we have nevertheless repeated almost identical calculations here. We make just two changes in order to bring the new results into methodological conformity with the others reported in the present work: we utilize a slightly less dense k-point sampling but allow two Ir layers to relax instead of one. We stress that the results reported here are very similar to those calculated in the earlier work, indicating that neither change is particularly drastic (i.e., both old and new calculations are rather well-converged with respect to k-point sampling and layer relaxation).
Benzene and Its Dissociation Products on Ir{100}
J. Phys. Chem. C, Vol. 112, No. 37, 2008 14419 0.125 ML. For these studies, we assumed adsorption only into the hollow site, prompted by the findings of Mittendorfer and Hafner for benzene adsorption on Ni{100}.15 Following their lead, we considered two orientations of the molecule: in orientation A two of the C-C bonds lie parallel to a 〈011〉 direction, whereas in orientation B two C-C bonds lie parallel to a 〈001〉 direction. Orientations A and B thus differ by a rotation of each molecule by 30° about a surface normal axis passing through its center of mass. In contrast to the earlier work, however, we determine orientation B to be marginally the more favorable, by 0.03 eV per molecule (Mittendorfer and Hafner determined a preference for orientation A on Ni{100} amounting to 0.04 eV per molecule15). The adsorption energy in orientation B on Ir{100} is 2.88 eV per molecule, evaluated by the simple formula c(4×4) -ECad6H6 ) EIr/C - (Ec(4×4) + ECg 6H6) + 8ER Ir 6H6
Figure 2. DFT-calculated adsorption geometry for 0.5 ML C on Ir{100}. Note that only one-quarter of the conventional nonprimitive c(2 × 2) unit cell is depicted; the remainder may be inferred by translational symmetry. Units for the structural parameters are angstroms, and figures in parentheses refer to LEED experiments.44
The structure and energetics of C on Ir{100} were thus calculated in a c(2 × 2) unit cell, and the hollow site was indeed found to be the most favorable option with a binding energy of -1 of C). The binding Ead C ) 8.06 eV per carbon atom (778 kJ mol energy has been determined according to the following formula: c(2×2) -ECad ) EIr/C - (Ec(2×2) + ECg) + 2ER Ir
(2)
where the various quantities are defined in similar fashion to their equivalents in the previous subsection (for reference, we calculate the energy of an isolated C atom as -148.110 eV). The comparison of adsorption energies in different adsorption sites is shown in Table 1. Considering the structure of the favored hollow model in detail (see Figure 2), the top Ir layer shows no buckling, but the second layer buckles very slightly in our calculation by 0.01 Å (according to the earlier LEED experiment,44 the surface layer shows no buckling and the second layer is buckled by 0.019 ( 0.035 Å). The DFT interlayer spacing between the first and second layers (d12) is 2.00 Å, and that between the second and third layers (d23) is 1.89 Å (compared with LEED values of 1.958 ( 0.035 and 1.873 ( 0.035 Å, respectively). Our calculations are thus in very good agreement with the experimental results as regards the substrate. The calculated perpendicular distance between the C adatom and the Ir surface atoms is found to be 0.68 Å, however, which is slightly smaller than the LEED result of 0.740 ( 0.040 Å. Nevertheless, the Ir-C bond length is calculated to be 2.05 Å, which is in excellent agreement with the LEED result of 2.054 ( 0.018 Å. 3.3. C6H6 on Ir{100}. Although benzene does not form ordered overlayers on Ir{100},6 we would still like to obtain information regarding its local bonding geometry and energetics. We have therefore performed calculations for a c(4 × 4) overlayer on the unreconstructed substrate, which we feel is probably representative of a generic coverage of benzene at
(3)
where ECg 6H6 is the gas phase energy of a benzene molecule (calculated as -1032.567 eV). The adsorption energy of benzene on Ir{100} is thus significantly higher than on Ni{100}, where the previous calculations15 indicated a value of 2.13 eV per molecule, despite a sizable downward correction in the present case for the lifting of the (1 × 5) reconstruction (without this correction, the adsorption energy relative to the (1 × 1) surface would be a massive 3.36 eV per molecule). Now, it will be recalled that recent evidence points toward a significant underestimate in DFT adsorption heats for flat-lying aromatic adsorbates on Pt{111}22,26-28 and that this has been attributed to poor description of van der Waals interaction between the molecule and the surface.27 While this seems entirely reasonable for the cases thus far investigated, where such interactions evidently comprise a significant fraction of the overall bonding, it is not clear to what extent the effect carries over in cases where the covalent contribution is much stronger, as in the present calculations. It may be the case, for example, that the typical DFT overestimate of covalent bonding interactions here compensates for the underestimate of van der Waals interactions, but it is probably unwise to speculate further without additional calorimetric information. Whatever the precise value of the adsorption heat, it is clearly very high in comparison to previously obtained values for benzene on other substrates. As regards the adsorption geometry in the hollow-B model (see Figure 3), we find the two C-C bonds lying along a 〈001〉 direction to be expanded to a length of 1.41 Å; the remainder are expanded slightly more, to a length of 1.46 Å (we calculate 1.38 Å for benzene in the gas phase). For ease of discussion, and by analogy with our previous description of benzene adsorption on Ni{111},3 we recognize three types of surface Ir atoms: those bonded to two C atoms (type I), those bonded to one C atom (type II), and those not bonded to benzene at all (type III). We find the IrI-C bond lengths to be 2.25 Å and the IrII-C bond lengths to be 2.12 Å. The first Ir layer is moderately buckled, with atoms of type I lying some 0.09 Å higher than those of type II, which in turn lie 0.05 Å above the average height for those of type III (these latter show a very slight buckling of around 0.01 Å between two symmetry-inequivalent subtypes). The benzene ring is also buckled, with those C atoms bonded to IrI lying 0.05 Å higher than those bonded to IrII; the C atoms lie on average 2.09 Å higher than the mean height of the first Ir layer. All C-H bonds remain close to their gas-phase length of 1.08 Å but are bent upward to make angles with the plane of the surface of 22.1° (for C bonded to IrI) and 31.5° (for C bonded to IrII).
14420 J. Phys. Chem. C, Vol. 112, No. 37, 2008
Figure 3. DFT-calculated adsorption geometry (hollow B) for 0.125 ML C6H6 on Ir{100}. Note that only 9/16 of the conventional nonprimitive c(4 × 4) unit cell is depicted; the remainder may be inferred by translational symmetry. Units for the structural parameters are angstroms.
Yamagishi et al.
Figure 4. DFT-calculated adsorption geometry for 0.25 ML C6H4 and 0.25 ML C coadsorbed on Ir{100}. Note that only 9/16 of the conventional nonprimitive c(4 × 4) unit cell is depicted; the remainder may be inferred by translational symmetry. Units for the structural parameters are angstroms.
+ (n + 6m)ECg 6H6) + 48ER (4) (6Ec(4×4) Ir
equilibrium with the carbon component of the benzyne molecules at 480 K. A more sophisticated analysis, presented in the later sections of this work, leads us to believe that the (2,2) model is, in fact, the preferred coadsorbed state formed under the reported experimental conditions. Considering the structure of the (2,2)-hollow model in more detail (see Figure 4), the top Ir layer shows no buckling (cf. c(2 × 2) overlayers for Ir{100}/H and Ir{100}/C described abovesin all three cases, this is a direct consequence of the surface symmetry). The second layer is buckled by 0.05 Å, however, and the distance between the Ir atoms in the first layer and the highest-lying Ir atoms in the second layer is 1.96 Å. The perpendicular distance between each C adatom (Ca) and the nearest Ir atoms in the first layer is found to be 0.50 Å, somewhat reduced from the value of 0.68 Å found in the Ir{100}/C-c(2 × 2) system; the Ir-Ca bond length is 2.02 Å. On the other hand, the perpendicular distance between the lowest-lying C atoms of benzyne (CR in the notation adopted in our previous studies10,11) and the first-layer Ir atoms is found to be 1.52 Å, with an Ir-CR bond length of 2.12 Å. The distance between the two CR atoms is 1.41 Å, showing a similar expansion from our calculated gas-phase value (1.24 Å) as noted previously in the c(2 × 4) pure benzyne phase.10
According to this formula, the adsorption energy for (n,m) ) (1,1) is ECad6H6 ) 1.19 eV, while for (1,2), (2,2), (4,2), and (6,2) the corresponding figures are 1.00, 0.93, 1.28, and 1.05 eV. These might seem, naively, to suggest that the (4,2) model would be favored over the other configurations. Such a view does not, however, account for the method by which the coadsorbed system is prepared; the C adatoms are, crucially, not in thermal
4. Thermodynamic and Kinetic Analyses 4.1. Underlying Theory and Assumptions. We begin by noting that the surface equilibrium energetics of a set of adsorbates x may best be studied through a free energy per cell supercell, F Ir/x , defined in terms of the internal energy per cell supercell, E Ir/x , as
3.4. C and C6H4 on Ir{100}. Detailed discussion of the c(2 × 4) pure benzyne phase has been provided in our previous work10,11 and need not be repeated here. We therefore concentrate on the c(4 × 4) phase of coadsorbed carbon and benzyne and begin by noting that both upright benzyne and carbon adatoms individually show strong preference for adsorption into hollow sites. Accordingly, we have only considered coadsorption models in which both species occupy hollow sites. Furthermore, we note that the presence of glide symmetry in observed LEED patterns13 strongly implies that there should be at least two carbon adatoms and two benzyne molecules within the primitive c(4 × 4) unit cell. We have, nevertheless, performed calculations for Ir{100}/(nC + mC6H4)-c(4 × 4) with (n,m) ) (1,1) and (1,2) in addition to (2,2), (4,2), and (6,2). The benzyne molecules are tilted in the (1, 1) model but upright in all the (n,2) cases. We define an adsorption energy with reference to a scheme in which gas phase C6H6 dissociates to produce adsorbed C and C6H4 species, together with H2 in the gas phase: c(4×4) -(n + 6m)ECad6H6 ) (6EIr/(nC+mC + 3(n + 2m)EHg 2) 6H4)
Benzene and Its Dissociation Products on Ir{100} cell cell FIr/x ) EIr/x -
∑ µini - µIrnIr
J. Phys. Chem. C, Vol. 112, No. 37, 2008 14421
(5)
i
where µi represents the chemical potential of species i and ni the number of particles of that species present in the system (note, however, that we restrict i to run only over the adsorbate species and include the Ir atoms in a separate term for later clarity). If the chemical potentials are known, the preference of the system for one structure or another can simply be judged on the basis of the lowest free energy, since variations in the numbers of particles present are automatically canceled by the terms within the summation. The internal energy, of course, is calculated within DFT, so the only remaining problem is to find these crucial chemical potentials. The chemical potential of Ir is the least problematic, since it may be determined with reference to the substrate energetics. The key is to realize that the surface must be in thermal equilibrium with its bulk, so that the surface chemical potential must equal the bulk chemical potential. The bulk chemical potential, in turn, is simply the total energy per atom in the bulk structure. For compatibility with the surface calculations, this must be the value calculated within DFT using comparable convergence parameters. Now, since some of the systems that we wish to consider are calculated within c(4 × 4) cells, while others are calculated within c(2 × 4) or c(2 × 2) cells, there may be small energy differences arising due not to physical causes but due to different Brillouin zone sampling. To some extent, these errors are systematic, however, and may be largely canceled by referencing each of our free energies to the free energy of the unreconstructed clean surface calculated within the appropriate cell. Thus, the free energies calculated within c(4 × 4) cells are referenced to the clean unreconstructed surface free energy calculated within a c(4 × 4) cell, while those calculated within c(2 × 4) cells are referenced to the same calculated within a c(2 × 4) cell and those calculated within c(2 × 2) cells are referenced to the same calculated within a c(2 × 2) cell. Relative to these reference energies (which would, of course, be in direct proportion to the cell area if our calculations were perfectly accurate) the adsorption-related free energy change per supercell becomes cell cell ∆FIr/x ) ∆EIr/x -
∑ µini
(6)
i
cell cell c(2×2) where ∆EIr/x ) EIr/x - EIrcell. Thus, explicitly, we have ∆EIr/x c(2×2) c(2×2) c(2×4) c(4×4) ) EIr/x - EIr , and similar for ∆EIr/x and ∆EIr/x . Such cell an approach has the added advantage that the terms in EIr/x and cell EIrcell featuring the chemical potential of Ir cancel in ∆FIr/x , so µIr need no longer be calculated at all. We will also take this opportunity to introduce the lowercell cell cell cell case symbols ∆f Ir/x , ∆eIr/x , f Ir/x , and eIr/x , intended to stand for precisely the same quantities as their upper-case counterparts but divided through by the supercell cross-sectional area c(2×4) expressed in units of (1 × 1) cells. For example, eIr/x ) EIr/ c(2×4) x /4 because the primitive c(2 × 4) surface unit cell has an area 4 times greater than the primitive (1 × 1) surface unit cell. In place of ni, the number of particles of type i in the supercell, we now have θi, the coverage in units of particles per (1 × 1) cell cell. Similarly, ∆f Ir/x is now the free energy change per (1 × 1) cell upon adsorption of the set of species x
∆f
cell cell Ir/x ) ∆eIr/x -
∑ µiθi
(7)
i
Calculated values of in Table 2.
cell ∆eIr/x
for various coverages θi are listed
cell TABLE 2: Energy per Supercell (eIr/x ) and Energy Difference per Supercell Relative to the Clean Surface cell (∆eIr/x ) for a Variety of Calculations with Different Coverages of H, C, C6H6, and C6H4 (θH, θC, θC6H6, θC6H4)a
label
θH
θC
θC6H6
θC6H4
cell eIr/x
cell
cell ∆eIr/x
0.000 0.000 0.000 0.000 c(2 × 2) -2248.040 0.000 0.000 0.000 0.000 c(2 × 4) -2248.042 0.000 0.000 0.000 0.000 c(4 × 4) -2248.007 a b c d e f
0.500 0.000 0.000 0.000 0.000 0.000
0.000 0.125 0.500 0.000 0.000 0.000
0.000 0.000 0.000 0.125 0.000 0.000
0.000 0.000 0.000 0.000 0.125 0.250
c(2 c(4 c(2 c(4 c(4 c(2
× × × × × ×
2) 4) 2) 4) 4) 4)
-2256.400 -2267.592 -2326.187 -2377.498 -2373.307 -2498.550
-8.360 -19.585 -78.147 -129.491 -125.300 -250.508
g h i j k l
0.000 0.000 0.000 0.000 0.000 0.000
0.125 0.125 0.125 0.250 0.500 0.750
0.125 0.000 0.000 0.000 0.000 0.000
0.000 0.125 0.250 0.250 0.250 0.250
c(4 c(4 c(4 c(4 c(4 c(4
× × × × × ×
4) 4) 4) 4) 4) 4)
-2397.077 -2392.871 -2518.070 -2537.597 -2575.690 -2614.608
-149.070 -144.864 -270.063 -289.590 -327.683 -366.601
a
All energies are expressed in eV.
Progress toward the chemical potentials for surface-adsorbed species may only be made if the system is held to be in thermal equilibrium with a gas of carbon- and hydrogen-containing species, however tenuous that gas may be. That is, we calculate the chemical potentials for appropriately chosen gas-phase species and take these as proxies for the chemical potentials of our corresponding surface species (justified by the assumption of thermal equilibrium). In the present case, we must expect the dominant gas-phase species to be benzene and molecular hydrogen. One complication, however, is that while the surface benzyne molecules may well be in thermal equilibrium with the gas phase, the carbon adatoms probably are not.45 It therefore makes most sense to treat the isolated carbon atoms as a distinct species, separate from the system’s complement of benzene, benzyne, and hydrogen. The free energy then becomes
1 cell cell ∆f Ir/x ) ∆eIr/x - µC6H6θC6H6 - µC6H4θC6H4 - µHθH - µCθC 2 (8) where µC and θC refer only to the carbon adatoms. The chemical potentials for the molecular species may be obtained with reference to the gas-phase thermodynamics. Dealing with each gas-phase species separately, we can write their (temperature- and pressure-dependent) chemical potentials as
µ(T, p) )
|
∂G ∂N T,p
(9)
where µ, G, and N should be regarded as representing the chemical potential, Gibbs free energy, and number of molecules of one or other gas-phase species (either benzene or molecular hydrogen). At this point, we recall that one may write infinitesimal changes in the Gibbs free energy at temperature T in terms of changes in the enthalpy, H, and the entropy, S
dG ) dH - T dS
(10)
Doing so, we find that the chemical potentials may be written as
14422 J. Phys. Chem. C, Vol. 112, No. 37, 2008
µ(T, p) )
|
|
∂H ∂S -T ∂N T,p ∂N T,p
Yamagishi et al.
(11)
Furthermore, in the case of an ideal gas, both the enthalpy and entropy are proportional to the numbers of molecules present. If we now explicitly identify H and S with molar enthalpy and molar entropy, respectively, we obtain
µ(T, p) )
1 (H(T, p) - TS(T, p)) NA
(12)
where NA is Avogadro’s number. Now, molar entropies for common gases are tabulated for a variety of temperatures at standard pressure (i.e., p° ) 100 000 Pa ) 1 bar). Molar enthalpies, on the other hand, are more usually tabulated in the form of differences from the value of the enthalpy at standard temperature (i.e., T° ) 298.15 K). The CRC Handbook,46 for instance, lists values of the molar enthalpy differences at standard pressure, ∆H(T° f T,p°), for both benzene and molecular hydrogen. In addition, for molecular hydrogen, it also quotes the increase in molar enthalpy in going from absolute zero temperature up to standard temperature (∆HH2(0 f T°,p°) ) 8.468 kJ mol-1). We thus have
HH2(T, p°) ) HH2(T°, p°) + ∆HH2(T° f T, p°)
(13)
HH2(T°, p°) ) HH2(0, 0) + ∆HH2(0 f T°, p°)
(14)
and
where both ∆HH2(0 f T°,p°) and ∆HH2(T° f T,p°) are known. We have made use of the fact that the enthalpy of a low-density gas at fixed temperature is practically independent of pressure to write HH2(0,p°) ) HH2(0,0). As for benzene, we must take a slightly more circuitous route, since the CRC Handbook46 does not list its change in enthalpy between absolute zero temperature and standard temperature. Instead, we make use of the enthalpy of formation of gaseous benzene at standard temperature and pressure (∆Hf(T°,p°) ) 82.880 kJ mol-1). That is to say, we write
HC6H6(T, p°) ) HC6H6(T°, p°) + ∆HC6H6(T° f T, p°) (15) with
HC6H6(T°, p°) ) 6HC(T°, p°) + 3HH2(T°, p°) + ∆Hf(T°, p°) (16) Here, HC(T°,p°) should be understood to represent the molar enthalpy of graphitic carbon at standard temperature and pressure. Fortunately, the change in enthalpy for graphite between absolute zero temperature and standard temperature is known (∆HC(0 f T°,p°) ) 1.050 kJ mol-1), and furthermore the zero temperature enthalpy of a solid, such as graphite, is again practically independent of pressure in the regime of interest. We therefore have
HC(T°, p°) ) HC(0, 0) + ∆HC(0 f T°, p°)
(17)
where ∆HC(0 f T°,p°) may be obtained from the CRC Handbook.46 The only unknown values entering into the equations above are now the enthalpies at zero temperature and pressure for graphitic carbon and gaseous molecular hydrogen. These are, of course, identical to the corresponding internal energies under the same conditions and therefore may be taken from our DFT calculations.47 Collecting all of this information, we now possess the molar enthalpies and molar entropies of benzene and molecular
TABLE 3: Key Thermodynamic Parameters for Benzene (C6H6) as Functions of Temperature, Ta T (K)
S(T,p°)
∆H(T,p°)
H(T,p°)
µ(T,p°)
298.15 300.00 400.00 500.00 600.00 700.00 800.00 900.00 1000.00
269.190 269.700 297.840 326.050 353.360 379.330 403.860 426.970 448.740
0.000 0.153 10.007 22.696 37.706 54.579 72.962 92.597 113.269
-99 491.447 -99 491.294 -99 481.440 -99 468.751 -99 453.741 -99 436.868 -99 418.485 -99 398.850 -99 378.178
-1031.996 -1032.001 -1032.296 -1032.619 -1032.971 -1033.351 -1033.757 -1034.188 -1034.641
a Units for the molar entropy, S, are J K-1 mol-1, while those for the molar enthalpy, H, and enthalpy difference, ∆H, are kJ mol-1. The chemical potential, µ, derived from these quantities is quoted in eV.
TABLE 4: Key Thermodynamic Parameters for Molecular Hydrogen (H2) as Functions of Temperature, Ta T (K)
S(T,p°)
∆H(T,p°)
H(T,p°)
µ(T,p°)
298.15 300.00 400.00 500.00 600.00 700.00 800.00 900.00 1000.00
130.680 130.858 139.217 145.738 151.078 155.607 159.549 163.052 166.680
0.000 0.053 2.960 5.882 8.811 11.749 14.702 17.676 20.680
-3054.788 -3054.735 -3051.823 -3048.906 -3045.977 -3043.039 -3040.086 -3037.112 -3034.108
-32.065 -32.067 -32.207 -32.355 -32.509 -32.668 -32.831 -32.999 -33.174
a Units for the molar entropy, S, are J K-1 mol-1, while those for the molar enthalpy, H, and enthalpy difference, ∆H, are kJ mol-1. The chemical potential, µ, derived from these quantities is quoted in eV.
TABLE 5: Temperature-Dependent Chemical Potentials, at Standard Pressure, for H2, C6H6, and C6H4 (Units Are eV) T (K)
µH2
µC6H6
µC6H4
298.15 300.00 400.00 500.00 600.00 700.00 800.00 900.00 1000.00
-32.065 -32.067 -32.207 -32.355 -32.509 -32.668 -32.831 -32.999 -33.174
-1031.996 -1032.001 -1032.296 -1032.619 -1032.971 -1033.351 -1033.757 -1034.118 -1034.641
-999.931 -999.934 -1000.089 -1000.264 -1000.462 -1000.683 -1000.926 -1001.119 -1001.467
hydrogen in the gas phase at standard pressure. These are tabulated in Tables 4 and 3, along with the standard-pressure chemical potentials derived from them. Once these are known, the chemical potentials at arbitrary pressure are easily obtained from
µ(T, p) ) µ(T, p°) + kT ln(p/p°)
(18)
This procedure provides us with values of the chemical potentials for benzene and hydrogen molecules, µC6H6 and µH2. Furthermore, we can assert that these must exist in thermal equilibrium with the reservoir of benzyne molecules at the surface, which condition implies
µC6H4 ) µC6H6 - µH2
(19)
All of the chemical potentials for molecular species at standard pressure are summarized in Table 5. The chemical potential for H atoms may furthermore be obtained as µH ) µH2/2. The only remaining unknown potential is therefore that corresponding to the carbon adatoms. Indeed, since these are
Benzene and Its Dissociation Products on Ir{100}
J. Phys. Chem. C, Vol. 112, No. 37, 2008 14423 cell cell ∆f Ir/i ) ∆eIr/i - θiµi(T, p) ) 0
(20)
Given the known pressure dependence of the gas-phase chemical potential, this condition may easily be rewritten to relate the partial pressure and temperature to calculable parameters of the system. Thus, the equilibrium isostere for 0.5 ML of atomic hydrogen may be derived from the c(2 × 2) DFT calculations as
1 1 c(2×2) - µH(T, p°) kT ln(p/p°) ) ∆eIr/H 4 2
(21)
and that for 0.125 ML of benzene may be derived from the c(4 × 4) calculations as
1 1 c(4×4) - µC6H6(T, p°) kT ln(p/p°) ) ∆eIr/C 6H6 8 8 Figure 5. Simulated thermal desorption spectra for hydrogen and benzene on Ir{100}, based upon desorption barriers (assumed constant) of 1.46 and 2.88 eV, respectively, with a 5 K s-1 heating rate. The relative peak areas reflect an initial 0.5 ML H adatom coverage and 0.125 ML C6H6 coverage.
not in thermal equilibrium, we cannot hope to determine this value with any precision. We can, however, set reasonable bounds on a range of values for this variable, by considering some equilibrium limits. We know, for instance, that µC should not far exceed the chemical potential of graphitic carbon; otherwise, there would be a strong driving force for the surface species to diffuse and form bulk graphite rather than remain evenly distributed. Furthermore, as a lower bound we may take the chemical potential of surface carbon in the zero coverage limit.48 It thus becomes possible to determine the free energy of any given structure, of whatever stoichiometry, for any value of µC within the limits just described. 4.2. Predicted Desorption Temperatures and Calculated Equilibrium Isosteres. We can utilize the calculated DFT energies together with the thermodynamic properties of the gasphase species to predict desorption temperatures for surface hydrogen and benzene in a number of different ways. First, we model the kinetics of desorption under conditions similar to a typical ultrahigh-vacuum thermally programmed desorption (TPD) experiment, where readsorption from the gas phase may be considered negligible. Assuming for simplicity that our calculated adsorption energies (1.46 eV for H2 and 2.88 eV for C6H6) can be interpreted as coverage-independent desorption barriers, we can apply simple second-order (H2) and first-order (C6H6) kinetic models with pre-exponential factors of 1013 s-1 per site (H2) and 1013 s-1 (C6H6). With a heating rate of 5 K s-1, the desorption peak for H2 occurs at 560 K, while that for C6H6 is at 1050 K (see Figure 5). The desorption temperature for H2 is rather higher than the experimental value of 450 K obtained by Ali et al.,38 reflecting the usual overestimate in covalent adsorption heats obtained by DFT-PW91. The desorption temperature for benzene is, however, extremely high when compared with values for other surfaces. This fact is, of course, rather important, as it implies that a significant coverage of benzene remains on the surface at sufficiently high temperatures for partial dissociation of a substantial fraction of molecules to occur. An alternative approach to understanding desorption behavior is to obtain the equilibrium conditions for constant coverage. These conditions occur when the change in free energy upon adsorption/desorption is zero. That is, if we allow only a single surface species i, we require:
(22)
Using these equations, we have calculated the equilibrium isosteres depicted in Figure 6. These curves indicate that hydrogen should persist indefinitely on the surface at adatom coverages above 0.5 ML up to temperatures of around 400-500 K under ultrahigh-vacuum conditions, while benzene would be stable at coverages in excess of 0.125 ML at temperatures up to 750-850 K in the same pressure regime. These temperatures are, of course, somewhat below the corresponding theoretical TPD peak positions because the isosteres relate to a situation where the surface is allowed to equilibrate; the kinetic experiment, on the other hand, is not performed at equilibrium. Nevertheless, the fact remains that even in these fully equilibrated circumstances benzene would remain on the surface at appreciable coverage up to rather high temperature, were it not for its experimentally observed dissociation to benzyne at temperatures above about 470 K. Note also that we have implicitly taken the clean surface to be unreconstructed, which is reasonable in light of the experimental procedure followed for preparation of the benzyne overlayer6 but which might not always be an appropriate assumption. 4.3. Thermodynamic Considerations in the Absence of Coadsorbed Carbon. Having ascertained the desorption temperatures for benzene and hydrogen, we now turn our attention to the issue of partial dissociation to form benzyne. We begin by noting a very general point, which is that we must be careful to distinguish between thermodynamic and kinetic factors controlling the dissociation temperature. It is entirely possible that dissociation may be thermodynamically favored but kineti-
Figure 6. Calculated isosteres for hydrogen and benzene on Ir{100}, based upon adsorption heats of 1.46 and 2.88 eV, respectively. The curves are for 0.5 ML H adatom coverage and 0.125 ML C6H6 coverage.
14424 J. Phys. Chem. C, Vol. 112, No. 37, 2008
Yamagishi et al.
TABLE 6: Temperature-Dependent Chemical Potentials, at pH2 ) 5 × 10-10 mbar and pC6H6 ) 1 × 10-7 mbar, for H2, C6H6, and C6H4 (Units Are eV) T (K)
µH2
µC6H6
µC6H4
298.15 300.00 400.00 500.00 600.00 700.00 800.00 900.00 1000.00
-32.793 -32.799 -33.183 -33.575 -33.973 -34.377 -34.784 -35.196 -35.615
-1032.588 -1032.596 -1033.090 -1033.611 -1034.162 -1034.740 -1035.344 -1035.974 -1036.625
-999.795 -999.797 -999.907 -1000.036 -1000.189 -1000.363 -1000.560 -1000.778 -1001.010
TABLE 7: Temperature-Dependent Chemical Potentials, at pH2 ) 5 × 10-10 mbar and pC6H6 ) 1 × 10-12 mbar, for H2, C6H6 and C6H4 (Units Are eV) T (K)
µH2
µC6H6
µC6H4
298.15 300.00 400.00 500.00 600.00 700.00 800.00 900.00 1000.00
-32.793 -32.799 -33.183 -33.575 -33.973 -34.377 -34.784 -35.196 -35.615
-1032.883 -1032.893 -1033.487 -1034.107 -1034.757 -1035.434 -1036.138 -1036.797 -1037.617
-1000.090 -1000.094 -1000.304 -1000.532 -1000.784 -1001.057 -1001.354 -1001.601 -1002.002
cally hindered on the time scale of a typical experiment. Kinetic factors include not only the obvious energy barrier to C-H bond scission itself but also the availability of appropriate surface sites and the time required for any necessary adsorption and desorption processes to occur. Our approach here is initially to consider the thermodynamic limit, and then ask to what extent that limit may be achieved in practice under experimental conditions. In the fully equilibrated thermodynamic limit, we explicitly allow the surface coverages of benzene, benzyne, and hydrogen to vary freely in pursuit of the lowest free energy. That is, the gas above the surface is viewed as an infinite reservoir for molecular hydrogen and benzene, while the surface permits infinitely rapid creation/annihilation of adsorbed benzyne. We can thus simply ask which of four models for the surface is thermodynamically favored at any given temperature and pressure. These models are (i) the 0.125 ML benzene c(4 × 4) structure, (ii) the 0.125 ML benzyne c(4 × 4) structure, (iii) the 0.25 ML benzyne c(2 × 4) structure, and (iv) the 0.5 ML hydrogen c(2 × 2) structure. These correspond respectively to structures “d”, “e”, “f”, and “a” listed in Table 2. The chemical potentials necessary for our analysis are tabulated as a function of temperature in Tables 6 and 7, in which the partial pressure of hydrogen in a typical ultrahigh-vacuum (uhv) chamber conducting this kind of experiment has been estimated as 5 × 10-10 mbar and that of benzene as 1 × 10-7 mbar during dosing and 1 × 10-12 mbar when not dosing. The relative stability of the models considered (embodied by the free energy difference, ∆f) is calculated according to eq 7 and depicted graphically in Figure 7. The most striking feature is that the c(2 × 4) benzyne structure is thermodynamically favored at all temperatures and pressures considered. In part, this is simply due to the fact that twice as many upright benzyne molecules can pack onto the surface as can intact flat-lying benzene molecules. In terms of experimental conditions, the fully equilibrated thermodynamic limit is an appropriate mimic of the situation during dosing, where the pressure of benzene is sufficiently large that the surface coverage of aromatic species can rapidly increase
Figure 7. Calculated free energy differences ∆f for various overlayers on Ir{100}, based on partial pressures of pH2 ) 5 × 10-10 mbar and pC6H6 ) 1 × 10-7 mbar consistent with benzene dosing.
Figure 8. Calculated free energy differences ∆f for various overlayers on Ir{100}, based on partial pressures of pH2 ) 5 × 10-10 mbar and pC6H6 ) 1 × 10-12 mbar consistent with ultrahigh-vacuum conditions.
to saturation on the time scale of the experiment. Thus, the data presented in Figure 7, relating to a reasonable dosing pressure of benzene, indicate that a surface saturated by benzyne in a c(2 × 4) structure is thermodynamically preferred at all temperatures below ∼1200 K. The fact that dissociation is not observed at low temperatures must therefore be due solely to the kinetics of C-H bond scission. We have not calculated barriers for this process, but it is known from experiment that benzene remains intact when dosed at 200 K, though not when dosed at 465 K;6 we can therefore surmise that the barriers involved must be in the region of 0.7-1.5 eV.49 In addition to formation of the benzyne overlayer by dosing benzene onto the unreconstructed surface at 465 K, however, it is also the case, as alluded to above, that the same c(2 × 4) LEED pattern can be obtained by dosing benzene onto the
Benzene and Its Dissociation Products on Ir{100}
J. Phys. Chem. C, Vol. 112, No. 37, 2008 14425
Figure 9. Calculated free energy differences ∆f for various overlayers on Ir{100}, based on partial pressures of pH2 ) 5 × 10-10 mbar and pC6H6 ) 1 × 10-12 mbar consistent with ultrahigh-vacuum conditions. The chemical potential for carbon adatoms is taken as (a) -156.184 eV for the carbon-rich limit and (b) -156.680 eV for the carbon-poor limit.
unreconstructed surface at low temperature and then heating to around 500 K.6 Under these circumstances, the fully equilibrated limit is less appropriate to understanding the behavior of the system. Specifically, the TPD experiments we wish to explain are completed on a time scale of minutes, implying that the 30 K temperature range wherein dissociation actually occurs is spanned in a matter of seconds. Can full thermal equilibrium between the gas-phase species and the surface be attained within this short time? The simple answer is no. Clearly two things need to occur concurrently to reach the fully equilibrated final state of the system (i.e., 0.25 ML benzyne) from the initial state (i.e., 0.125 ML benzene): not only must the hydrogen generated by benzene dehydrogenation desorb, but moreover the number of aromatic molecules at the surface must double through adsorption and subsequent dissociation of additional benzene. The hydrogen desorption step is not problematic, since we know empirically that large quantities of a surface species can desorb very rapidly indeed when equilibrium shifts to favor the gas phase. In contrast, however, the adsorption of gas-phase species when equilibrium favors the surface is limited by the pressure of the gas. Specifically, a pressure of 1 × 10-12 mbar for benzene (and this is an upper estimate when not dosing) would imply a maximum deposition rate of ∼10-6 ML s-1. It is therefore inconceivable that the coverage of aromatic molecules on the surface increases to any appreciable degree during a typical TPD experiment (or indeed over several hours under these conditions) unless the pressure is temporarily elevated, for example due to desorption from sample heating wires. We therefore suggest the following scenario: that once C-H bond scission becomes achievable, the hydrogen component of the system adapts rapidly to changes in temperature, maintaining in effect a quasiequilibrium situation appropriate to a fixed nonequilibrium coverage of benzene/benzyne. That is to say, the hydrogen component of the system is effectively in equilibrium with the gas phase at all times, while the carbon component is not. If we work on this basis, then it is clear that dehydrogenation of an initial c(4 × 4) benzene overlayer would lead to just half the surface being covered in islands of c(2 × 4) benzyne at
local 0.25 ML coverage; the remainder of the surface would either be bare or hydrogen covered, depending upon the surface temperature. We therefore consider a different set of four models to that examined above: (i) the 0.125 ML benzene c(4 × 4) structure, (ii) the 0.125 ML benzyne c(4 × 4) structure, (iii) a half-and-half mixture of the 0.25 ML benzyne c(2 × 4) and 0.5 ML hydrogen c(2 × 2) structures, and (iv) a half-and-half mixture of the 0.25 ML benzyne c(2 × 4) and clean unreconstructed surface structures. The first pair of models once again correspond to structures “d” and “e” in Table 2, while the third corresponds to an equal mixture of structures “a” and “f”; the fourth model corresponds to half the surface covered by structure “f”. In these “quasi-equilibrium” circumstances, the free energies depend only upon the calculated internal energies from DFT and the chemical potential of hydrogen; the results are presented in Figure 8. Notably, the benzene structure is now favored up to a temperature in the region of 580 K (plus or minus about 30 K if we allow the estimated hydrogen pressure to vary by an order of magnitude in either direction). Note the important point that follows from this result: even were C-H bond scission to become facile at low temperature, net dissociation of the surface benzene would not occur until the quasi-equilibrium limit favored benzyne. Taking the DFT results at face value, therefore, one would expect benzyne to be formed only above about 580 K, whereas experiment shows this to occur by around 500 K. Given the theoretical approximations involved up to this point, the disagreement between these two numbers is not, perhaps, too disturbing. What is evident, however, is that the formation of surface benzyne is not favored at all temperatures under uhv conditions and that the experimental observation of dissociation around 500 K in TPD could be representative of overcoming a purely kinetic limitation (i.e., C-H bond scission rate), a quasi-equilibrium thermodynamic limitation (i.e., benzene/benzyne free energy balance), or indeed both simultaneously. We defer calculation of the C-H bond scission barriers to future work and so cannot speculate further at this stage.
14426 J. Phys. Chem. C, Vol. 112, No. 37, 2008 4.4. Thermodynamic Considerations in the Presence of Coadsorbed Carbon. In section 3.4, we presented calculated adsorption heats, referenced to dissociation of gas-phase benzene and evolution of gas-phase hydrogen, for various models of coadsorbed carbon and benzyne. Labeling these models (n,m), where n and m respectively represented the number of carbon adatoms and benzyne molecules within each c(4 × 4) cell, we showed that the adsorption heat was greatest for the (4,2) model. The reason for this apparent stability, however, lies primarily in the strength of bonding between the adatoms and the surface. Since preparation of the experimentally observed overlayer is carried out with a small quantity of preadsorbed carbon and production of further carbon adatoms on the surface is kinetically unlikely at the temperatures employed, it is evident that such a phase could not cover more than a small fraction of the surface. Indeed, a more correct analysis, as described in section 4.1, must be based upon consideration of surface free energies and the recognition that carbon adatoms are not in equilibrium with the aromatic species at temperatures consistent with formation of the coadsorbed overlayer. Using the raw DFT energies listed in Table 2, together with the chemical potentials listed in Table 7, one need only assume a suitable value for the chemical potential of carbon adatoms in order to proceed. As mentioned above, we can estimate reasonable upper and lower bounds for this parameter, with reference to the energies of an isolated carbon atom and of an adsorbed carbon atom; the result is a range between -156.184 eV in the carbon-rich limit and -156.680 eV in the carbonpoor limit. Evaluating the free energy difference ∆f at these two extremes for the range of structures “g”-“l” listed in Table 2, we obtain the values presented graphically in Figure 9. It is immediately apparent from both tables that structures “k” and “l”, corresponding to models (4,2) and (6,2), are not only significantly unstable relative to other coadsorption models at all temperatures considered, but actually unstable with respect to the clean surface itself. That is to say, if impinging benzene molecules are permitted to dissociate only to form surface benzyne, but not to form additional surface carbon, then adsorption will be unfavorable at carbon precoverages above around 0.5 ML. In fact, the data in Figure 9 indicate that structures “i” and “j”, corresponding to models (1,2) and (2,2), are the most favorable; there is a marginal preference for the (2,2) model in the extreme carbon-rich limit and a slightly stronger preference for the (1,2) model in the extreme carbonpoor limit. Noting that diffraction studies indicate a glide symmetry for the coadsorbed phase, however, and that this is incompatible with the (1,2) model, we believe that the overall balance of evidence favors the (2,2) model for the experimentally observed phase. 5. Conclusions We have presented the results of DFT calculations for various combinations of H, C, C6H6, and C6H4 adsorbed and coadsorbed on Ir{100}. Through consideration of the free energies of different possible surface structures, as a function of the gasphase temperature and partial pressures of hydrogen and benzene, we conclude that dissociation to form adsorbed benzyne is thermodynamically favorable under all conditions studied. At low temperatures, however, dissociation is of course limited by the kinetics of C-H bond scission, but we demonstrate that it may also be limited by the rate of benzene adsorption on the time scale of a typical TPD experiment. Furthermore, we argue that free energy considerations, together with the experimental observation of glide symmetry, point
Yamagishi et al. toward a model for the coadsorbed phase of carbon and benzyne in which there are two adatoms and two aromatic molecules per primitive c(4 × 4) unit cell (i.e., per eight surface Ir atoms). Acknowledgment. S.J.J. thanks The Royal Society for a University Research Fellowship. The main calculations were carried out at the Cambridge University High Performance Computing Facility. References and Notes (1) Zebisch, P.; Stichler, M.; Trischberger, P.; Weinelt, M.; Steinruck, H.-P. Surf. Sci. 1998, 396, 61. (2) Terborg, R.; Polcik, M.; Hoeft, J. T.; Kittel, M.; Pascal, M.; Kang, J. H.; Lamont, C. L. A.; Bradshaw, A. M.; Woodruff, D. P. Surf. Sci. 2000, 457, 1. (3) Yamagishi, S.; Jenkins, S. J.; King, D. A. J. Chem. Phys. 2001, 114, 5765. (4) Held, G.; Braun, W.; Steinruck, H.-P.; Yamagishi, S.; Jenkins, S. J.; King, D. A. Phys. ReV. Lett. 2001, 87, 216102. (5) Yamagishi, S.; Jenkins, S. J.; King, D. A. J. Am. Chem. Soc. 2004, 126, 10962. (6) Johnson, K.; Sauerhammer, B.; Titmuss, S.; King, D. A. J. Chem. Phys. 2001, 114, 9539. (7) We know of studies on just one similar system, where heating a disordered benzene overlayer on Co{101j0} results in a p(3 × 1) periodicity attributed to dehydrogenation, resulting in either phenyl or benzyne. Photoemission and LEED experiments were not, however, wholly conclusive in determining the nature of the adsorbed species: see refs 8 and 9 for details. (8) Barnes, C. J.; Valden, M.; Pessa, M. Surf. ReV. Lett. 2000, 7, 67. (9) Pussi, K.; Lindroos, M.; Barnes, C. J. Chem. Phys. Lett. 2001, 341, 7. (10) Yamagishi, S.; Jenkins, S. J.; King, D. A. J. Chem. Phys. 2002, 117, 819. (11) Yamagishi, S.; Jenkins, S. J.; King, D. A. Chem. Phys. Lett. 2003, 367, 116. (12) Sauerhammer, B. PhD Thesis, University of Cambridge, 2002. (13) Lerotholi, T. J.; Held, G.; King, D. A., private communication. (14) Duschek, R.; Mittendorfer, F.; Hafner, J. Chem. Phys. Lett. 2000, 318, 43. (15) Mittendorfer, F.; Hafner, J. Surf. Sci. 2001, 472, 133. (16) Rogers, B. L.; Shapter, J. G.; Ford, M. Surf. Sci. 2004, 548, 29. (17) Morin, C.; Simon, D.; Sautet, P. J. Phys. Chem. B 2003, 107, 2995. (18) Morin, C.; Simon, D.; Sautet, P. J. Phys. Chem. B 2004, 108, 5653. (19) Orita, H.; Itoh, N. Appl. Catal., A 2004, 258, 17. (20) Mittendorfer, F.; Hafner, J. J. Phys. Chem. B 2002, 106, 13299. (21) Morin, C.; Simon, D.; Sautet, P. Surf. Sci. 2006, 600, 1339. (22) Saeys, M.; Reyniers, M. F.; Neurock, M.; Marin, G. B. J. Phys. Chem. B 2003, 107, 3844. (23) Delle Site, L.; Alavi, A.; Abrams, C. F. Phys. ReV. B 2003, 67, 193406. (24) Tan, Y. P.; Khatua, S.; Jenkins, S. J.; Yu, J.-Q.; Spencer, J. B.; King, D. A. Surf. Sci. 2005, 589, 173. (25) Barbosa, L. A. M. M.; Sautet, P. J. Catal. 2003, 217, 23. (26) Ihm, H.; Ajo, H. M.; Gottfried, J. M.; Bera, P.; Campbell, C. T. J. Phys. Chem. B 2004, 108, 14627. (27) Gottfried, J. M.; Vestergaard, E. K.; Bera, P.; Campbell, C. T. J. Phys. Chem. B 2006, 110, 17539. (28) Morin, C.; Simon, D.; Sautet, P. J. Phys. Chem. B 2004, 108, 12084. (29) Bocquet, M. L.; Lesnard, H.; Lorente, N. Phys. ReV. Lett. 2006, 96, 096101. (30) CASTEP 4.2, academic version, licensed under the UKCP-MSI agreement, 1999 2006. Payne, M. C.; Teter, M. P.; Allan, D. C.; Arias, T. A.; Joannopoulos, J. D. ReV. Mod. Phys. 1992, 64, 1045. (31) Vanderbilt, D. Phys. ReV. B 1990, 41, 7892. (32) Perdew, J. P.; Chevary, J. A.; Vosko, S. H.; Jackson, K. A.; Pederson, M. R.; Singh, D. J.; Fiolhais, C. Phys. ReV. B 1992, 46, 6671. (33) Monkhorst, H. J.; Pack, J. D. Phys. ReV. B 1976, 13, 5188. (34) Bickel, N.; Heinz, K. Surf. Sci. 1985, 163, 435. (35) Heinz, K.; Schmidt, G.; Hammer, L.; Mu¨ller, K. Phys. ReV. B 1985, 32, 6214. (36) According to a recent systematic classification of surface reconstructions, Ir{100}-(1 × 5) is an example of a “contractive symmetrybreaking reconstruction”; see ref 37 for details. (37) Jenkins, S. J.; Pratt, S. J. Surf. Sci. Rep. 2007, 62, 373. (38) Ali, T.; Walker, A. V.; Klo¨tzer, B.; King, D. A. Surf. Sci. 1998, 414, 304. (39) Moritani, K.; Okada, M.; Kasai, T.; Murata, Y. Surf. Sci. 2000, 445, 315. (40) Sauerhammer, B.; Johnson, K.; Greenwood, C.; Braun, W.; Held, G.; King, D. A. Surf. Sci. 2001, 488, 154.
Benzene and Its Dissociation Products on Ir{100} (41) Note that we explicitly adopt the convention, throughout this paper, that the subscript specifies not only the type of adsorbates present but also their quantity. For example, in the case of Ec(2×2) Ir/H , the “Ir/H” symbol indicates one H adatom per c(2 × 2) cell, as distinct from “Ir/2H” which would have indicated two. The coverage is thus implied by the combination of sub- and superscript. (42) Ge, Q.; King, D. A.; Marzari, N.; Payne, M. C. Surf. Sci. 1998, 418, 529. (43) Ghosh, P.; Narasimhan, S.; Jenkins, S. J.; King, D. A. J. Chem. Chem. 2007, 126, 244701. (44) Johnson, K.; Ge, Q.; Sauerhammer, B.; Titmuss, S.; King, D. A. Surf. Sci. 2001, 478, 49. (45) That this should be so is clear from consideration of the possible dehydrogenation pathways that transform benzene to benzyne and hydrogen (apparently facile at around 480 K) and those that transform benzyne to carbon and hydrogen (apparently kinetically hindered until above 530 K6). (46) Lide, D. R., Ed.; Chemical Rubber Company Handbook of Chemistry and Physics, 78th ed.; CRC Press: Boca Raton, FL, 1997.
J. Phys. Chem. C, Vol. 112, No. 37, 2008 14427 (47) We calculate the internal energy of graphite within DFT, employing a 8 × 8 × 3 k-point sampling of the Brillouin zone for a primitive unit cell, and a 320 eV cutoff, obtaining a value of-156.184 eV per carbon atom. Our calculated internal energy for a hydrogen molecule is-31.749 eV per molecule. (48) The upper boundmay be calculated within DFT as the internal energy per atom in graphitic carbon (i.e.,-156.184 eV). The lower bound is approximated as the difference between the DFT internal energies for a clean surface and a surface with a low coverage overlayer of pure carbon (we use a 0.125 ML c(4 × 4) carbon overlayer); this value is-156.680 eV. (49) The supposed range of 0.7-1.5 eV for CH bond scission barriers would correspond to a dissociation rate per bond no faster than once per hour at 200 K and no slower than once per 3 min at 465 K, assuming an attempt frequency of 1 ×1014 Hz, consistent with a typical C-H stretch frequency in the vicinity of 3000 cm-1.
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