Plane-Wave DFT Investigations of the Adsorption ... - ACS Publications

10472

J. Phys. Chem. C 2008, 112, 10472–10489

Plane-Wave DFT Investigations of the Adsorption, Diffusion, and Activation of CO on Kinked Fe(710) and Fe(310) Surfaces Dan C. Sorescu U.S. Department of Energy, National Energy Technology Laboratory, Pittsburgh, PennsylVania 15236 ReceiVed: January 28, 2008; ReVised Manuscript ReceiVed: April 7, 2008

The adsorption, diffusion, and dissociation properties of CO on kinked Fe(710) and Fe(310) surfaces have been analyzed using spin-polarized plane-wave density functional theory (DFT) calculations within the generalized gradient approximation (GGA). Several one-, two-, three- and 4-fold binding configurations have been identified among which the preferential adsorption takes place at a 4-fold hollow site near the top of the step while the one with the smallest activation energy for dissociation is located at a 4-fold site near the bottom of the step. In the case of the individual atomic species, the adsorption takes place preferentially at the hollow site for the C atom and at the pseudo 3-fold site on the step for the O atom. By the increase in coverage, there is an overall decrease of the adsorption energies for either molecular (CO) or atomic (C,O) species. The diffusion barriers among different local minima at the steps or on the terraces of both surfaces have been determined, and their values were found to be smaller than the barriers for CO dissociation. The most activated configuration at the bottom of the step can be populated by direct diffusion over the step, from the upper terrace, or by reorientation of the CO molecule within the same hollow site. This last process requires an activation energy of 6.5 kcal/mol on Fe(710) and 9.3 kcal/mol on the Fe(310) surface. The barrier heights for dissociation of CO molecules on Fe(710) (Fe(310)) were found to vary between 15.4 and 20.5 (16.7 and 20.9) kcal/mol depending on the specific location of the hollow site relative to the step edge and to the particular molecular orientation within a given hollow site. For the set of crystallographic Fe surfaces (110), (100), (211), (710), (310), and (111), we found that dissociation on Fe(710) and Fe(310) requires the smallest activation energies in the regime of low coverages. The analysis of the activation properties of CO on this six-member set of flat, stepped, and kinked surfaces indicates the existence of a direct correlation between the apparent activation energy and the rebonding energy of the noninteracting products of the reaction. 1. Introduction Characterization of the elementary surface reactions of CO on iron catalysts is a topic of primary importance with significant relevanceforkeytechnologicalapplicationssuchasFischer-Tropsch (FT) synthesis of aliphatic hydrocarbons, electrochemistry, or corrosion.1–4 In the particular case of syngas FT conversion, generically represented as CO + (1 + n/2)H2 f CHn + H2O, adsorption and dissociation of CO on the iron surface followed by hydrogenation, chain growth reactions, and the formation of hydrocarbon and water species are of paramount importance.5 Additionally, understanding the nature of the deposited C and O species is also essential because significant transformations of the iron surface by carburization and oxidation processes can take place. In all of these instances, some of the key scientific questions are identification of the active surface sites, the nature of the adsorbed molecular and atomic species, and description of the barrier heights for different surface reactions. Understanding these processes is essential in order to determine the relationship between the intrinsic catalyst surface structure and the corresponding catalytic activity. Several previous experimental studies focused on a description of the adsorption and dissociation processes of CO on iron surfaces among which the most detailed have been obtained on single crystals using surface science techniques. Here we will restrain ourselves to mention only the results connected to topics covered in this study. Particularly, work done in Bernasek’s6,7 and Madix’s8 groups indicated that below 440 K CO adsorption on the Fe(100) surface takes place molecularly with sequential

filling of three states corresponding to three types of binding configurations of the CO molecule. On the basis of vibrational frequency analysis, it was suggested that these three states correspond to one- (1F), two- (2F), and, respectively, 4-fold (4F) binding configurations of the CO molecule on the surface.7b Among these, the most tightly bound molecular state, denoted CO(R3), is the precursor to dissociation at 440 K and corresponds to CO adsorbed at the (4F) hollow site in a tilted configuration.7 In recent years, with the advancement of computational methods and computer hardware, various aspects of the chemisorption and reaction properties of molecular CO and atomic (C, O) species with iron surfaces have become available. In particular, several density functional theory calculations including our own studies, in conjunction with cluster or slab models, have focused on description of the adsorption properties of CO on low-index (100),9–11 (110),12,13 and (111)14 Fe surfaces or the initial stages of oxidation of (100) and (110) surfaces of iron.15 Similarly, the interaction of atomic C with Fe(100),16,17 Fe(110),17 or bulk bcc iron16,17 or of the atomic O with Fe(110) and Fe(100) surfaces,18 have been considered. Recently, we have reported upon the chemisorption properties of CHx(x ) 0,4) species on the Fe(100) surface.16 We have shown that the presence of the C atom at either the hollow or subsurface sites increases the stability of the other atomic (C,H,O) and molecular or radical species (CO, CHx (x ) 1,4)) adsorbed on the surface. Another major finding of that study was that for the ensemble of surface processes involving the

10.1021/jp8008145 CCC: $40.75  2008 American Chemical Society Published on Web 06/20/2008

CO on Kinked Fe(710) and Fe(310) Surfaces dissociation of CO and H2 species on the Fe(100) surface followed by hydrogenation reactions of CHx(x ) 0,3) species with formation of CH4, the CO dissociation is the ratedetermining step. The findings of our study have been systematically analyzed recently by Lo and Ziegler.19a The same group of authors have further developed a kinetic model for the methanation process on the Fe(100) surface,19a while in a subsequent study they have reported upon the formation and reactivity properties of the C2 hydrocarbon species on Fe(100).19b As seen from the above examples, a great majority of previous experimental and theoretical studies have focused on descriptions of the chemisorption properties on low-index (110), (100), and (111) Fe surfaces. Noticeably missing are published papers related to the case of high-index stepped or kinked surfaces. The lack of such studies considering the influence of surface corrugation upon chemisorption properties is surprising because several stepped surfaces such as (211) and (310) have surface energies in between those of the low-index (100) and (111) surfaces.20 As a result, such stepped surfaces are expected to play an important role in practical cases involving polycrystalline iron systems. A few noticeable exceptions are the experimental work by Schmiedl et al.21 focused on the structural, thermodynamic, and kinetic properties of hydrogen on Fe(211) and the theoretical analysis by Jenkins related to characterization of the adsorption properties of C, N, and O atoms on Fe(211).22 The importance of the surface steps upon various processes involved in FT synthesis such as the chemisorption and dissociation of CO species has been evidenced already for several other metallic systems. For example, Zubkov et al.23 have shown that the step sites on the Ru(109) surface facilitate both adsorption and dissociation of the CO species. Furthermore, a mobile carbon species has been identified, and it was inferred that FT catalytic chemistry can be related to the properties of this mobile carbon at the step defect sites. In the case of the stepped Co(0001) surface, Gong et al.24 have demonstrated that CO dissociation is much more favored than that on the flat (0001) surface. In this case, the stepped surface was also found to favor the first step in O removal, that is O + H f OH; but no similar trend was observed for the second step, corresponding to the OH + H f H2O reaction. Similarly, Ge and Neurock25 have determined that stepped Co{101j2} and Co{112j4} surfaces are much more active for CO dissociation than flat Co{0001} or corrugated Co{112j0} surfaces. It was further shown that the activation energies for CO dissociation on both of these stepped surfaces are lower than those in the gas-phase, a fact that allows spontaneous dissociation of molecules from the gas phase and explains the observed high reactivity for CO dissociation on the stepped surfaces. This selective set of examples clearly indicates the important role played by metallic stepped surfaces upon catalytic activity, particularly related to CO activation. In the present work, we extend our previous set of studies related to chemisorption properties on the Fe(100) surface10,16,26 to the case of kinked or stepped surfaces. Specifically, we present the results of a density functional theory analysis of the adsorption and chemisorption properties of atomic (C, O) and molecular (CO) species on Fe(710) and Fe(310) surfaces and compare these results to those obtained on Fe(100) and to other surfaces with low surface energies such as Fe(110), Fe(211), and Fe(111). Selection of the two main Fe(710) and Fe(310) surfaces allows the analysis of the chemisorption properties on surfaces with single steps separated by terraces with (001) orientation of different lengths. Indeed, as illustrated in Figure 1a, the Fe(710) surface can be seen as a Fe(100) stepped surface with a step height of one atomic layer and with

J. Phys. Chem. C, Vol. 112, No. 28, 2008 10473

Figure 1. Pictorial view of the slab models used to describe the chemisorption properties of Fe(710) (a and b) and Fe(310) (c and d) surfaces. For visualization purposes, the slabs have been extended by two units in both directions of the surface. Panels a and c correspond to side views of the slab models, and panels b and d represent the corresponding top views. For the top view representations, only the atoms in top layers are shown for improved clarity. The Fe atoms positioned at the bottom of the steps are depicted in a different (blue) color for increased clarity. The positions of various 4F, 2F, and 3F sites referenced in the text are also indicated.

three rows of atoms in the top layer separating the neighbor steps. At the other extreme is the Fe(310) surface (see Figure 1c), which can be seen as a stepped Fe(100) surface in which adjacent steps are separated by only one row of surface atoms. We note that recently Jenkins and Pratt27 have introduced a systematic terminology for the description of various facets of fcc, bcc, and hcp crystals based on close-packed chains of atoms rather than planes of atoms. According to this terminology, in the case of bcc iron, Fe(110) is the only flat surface among various crystallographic orientations, Fe(211) is considered a stepped surface, whereas other surfaces like Fe(100), Fe(111), Fe(710), or Fe(310) considered in this study should be denoted as kinked surfaces. Where necessary, we will use this terminology in the current work. The organization of the paper is as follows: In section 2, we describe the computational methods used in this study. The results of total energy calculations to describe the adsorption, diffusion, and dissociation properties of atomic and molecular species on Fe(710) and Fe(310) surfaces are given in Section 3 together with a discussion of the activation properties on other representative iron surfaces, that is, Fe(110), Fe(100), Fe(211), and Fe(111). Finally, we summarize the main conclusions in Section 4. 2. Computational Method Plane-wave density functional theory calculations were performed in this study using the Vienna ab initio simulation

10474 J. Phys. Chem. C, Vol. 112, No. 28, 2008

Sorescu

TABLE 1: Calculated Magnetic Moments (in Bohr Magneton Units, µB) of the Fe Atoms at Different Surface Sites for the Bare Slabs of Fe(710) and Fe(310) Surfaces as Determined Based on PAW-PBE Calculationsa surface

S(1)

S(2)

S(3)

S(4)

S(5)

S(6)

S(7)

S(8)

Fe(710) Fe(310)

2.89 2.87 (2.86)b

2.93 2.67 (2.67)

2.94 2.27 (2.33)

2.69 2.39 (2.43)

2.35 2.30 (2.34)

2.32

2.33

2.46

a Sites S(1)-S(4) and S(5)-S(8) correspond to the Fe atoms in the top and, respectively, in the subsurface layers for the case of the Fe(710) surface, as indicated in Figure 1a. In the case of Fe(310) surface atoms, S(1) and S(2) belong to the top surface layers and S(3)-S(5), to subsequent deeper layers as detailed in Figure 1c. b The values in parentheses were obtained based on FLAPW+GGA calculations given in ref 39.

package (VASP)28 in conjunction with periodic slab models. The electron-ion interaction was described using the projector augmented wave (PAW) method of Blo¨chl29 in the implementation of Kresse and Joubert.30 This method is known to improve the description of magnetic transition metals.30 For the treatment of exchange and correlation, we have used the generalized gradient approximation (GGA) with the Perdew, Burke, and Ernzerhof (PBE) functional, hereafter denoted as GGA-PBE31 together with the spin interpolation for the correlation energy introduced by Vosko-Wilk-Nusair (VWN).32 The calculations were spin-polarized to account for the magnetic properties of iron. Slab models with periodic boundary conditions have been used to describe the adsorbate-surface system. The electron pseudo-orbitals were expanded over a plane-wave basis set with a cutoff energy of 400 eV. The sampling of the Brillouin zone was performed using a Monkhorst-Pack scheme.33 Electron smearing was employed via the Methfessel-Paxton technique,34 with a smearing width consistent with σ ) 0.1 eV, and all energies were extrapolated to T ) 0 K. The minimization of the electronic free energy was performed using an efficient iterative matrix-diagonalization routine based on a sequential band-by-band residuum minimization method (RMM)28 or alternatively based on preconditioned band-by-band conjugategradient (CG) minimization.35 The optimization of different atomic configurations was performed by conjugate-gradient minimization of the total energy. Where necessary, the vibrational frequencies of the adsorbed atomic or molecular species have been evaluated in the frozen phonon mode approximation. In these cases, the Hessian matrix has been determined based on a finite difference approach with a step size of 0.02 Å for the displacements of the individual atoms of the adsorbate along each Cartesian coordinate. The minimum reaction pathways and the activation energies for various diffusion and dissociation reactions analyzed in this study were determined using the climbing image nudged elastic band method.36,37 The corresponding transition-state structures have been further verified by vibrational frequency calculations. Tests of Bulk and Surface Properties. On the basis of a k-point mesh of 15 × 15 × 15, we have determined the optimized equilibrium constant for bulk bcc iron as 2.833 Å and the corresponding bulk modulus B0 as 1.71 Mbar. These values compare well with experimental values of 2.87 Å and 1.68 Mbar, respectively.38 For the optimized bulk structure, the magnetic moment per atom and the corresponding saturation magnetizations are 2.20 µB and 1791 Gs. These values compare equally well to the corresponding experimental data38 of 2.22 µB and 1759 Gs, respectively. The chemisorption properties of (710) and (310) surfaces have been obtained using slab models as represented in Figure 1. Specifically, in the case of (710) the neighbor steps are separated by three rows of atoms along the (001) terrace. The supercell contains two surface units along the direction to

minimize the lateral interactions between adsorbates in the neighboring unit cells. In this model, there are 38 Fe atoms distributed over 19 layers with the top 11 layers of the slab being allowed to relax. A vacuum width of 12 Å separates the neighbor slabs. Finally, for the Fe(310) surface we have used a 2 × 2 slab model as represented in Figure 1c. This model contains 44 Fe atoms distributed over 11 layers and has a vacuum width of 12 Å. In this case, the top six layers of the slab were allowed to relax. For these surfaces, we determined the corresponding surfaces energies of 2.50 J/m2 for Fe(710) and 2.52 J/m2 for Fe(310). These values are in between the surface energies determined for Fe(100) (2.47 J/m2)16,20 and Fe(111) (2.58 J/m2).20 The presence of the surface steps in combination with terraces of different lengths introduces anisotropies of the individual magnetic moments on Fe(710) and Fe(310) surfaces. This information is detailed in Table 1 where we present only the results corresponding to the Fe atoms in the top surface layers. Here the sites S(1)-S(8) for Fe(710) and S(1)-S(5) for Fe(310) correspond to the numbers indicated in Figure 1a and c. Relative to the magnetic moment of the Fe atom in bcc bulk of 2.2 µB, the magnetic moments of the surface atoms are increased significantly to values as high as 2.94 µB for Fe(710) and 2.87 µB for Fe(310) surfaces, respectively. For both surfaces, there are also important variations of the magnetic moments when moving along the surface terrace from the top of the step to the internal edge atom. Specifically, in the case of Fe(710), at the middle of the terrace the corresponding magnetic moments reach maximum values of 2.93 µB for site S(2) and 2.94 µB for site S(3), practically identical to the one we determined previously for the case of the Fe(100) surface of 2.94 µB at the PAW-PBE level.16 Near the top of the step, the magnetic moment of the S(1) atom decreases slightly to 2.89 µB. The smallest value of the magnetic moment is observed for the case of the internal edge atom, that is, the S(4) atom on Fe(710), which is also the one with the largest coordination numbers among various terrace atoms. In the subsurface layer, the magnetization for S(5)-S(8) atoms decreases to values ranging from 2.32 to 2.46 µB. In the case of the Fe(310) surface, similar trends of the magnetic moments are observed. The atom S(1) at the top of the step has a magnetic moment of 2.87 µB, similar to the one of the atom S(1) on Fe(710), whereas the internal edge atom S(2) has the smallest magnetic moment of 2.67 µB among the terrace surface atoms. This value of the magnetic moment is also very close to the one for the internal edge atom on Fe(710) of 2.69 µB. Consequently, it can be concluded that the two S(1) and S(2) terrace atoms of the Fe(310) surface practically have the same magnetic moments as atoms S(1) and S(4) positioned at the extremities of the (001) terrace on Fe(710). As a final note, we provide in parentheses in Table 1 the magnetic moments for Fe(310) as determined based on FLAPW calculations by Geng et al.39 using a larger slab of 15 layers. The agreement between the two sets of values is very good

CO on Kinked Fe(710) and Fe(310) Surfaces particularly in the case of top layer atoms, whereas slight differences are observed for subsurface sites S(3)-S(5). The results for the magnetic moments of both Fe(710) and Fe(310) presented above suggest that the coordination numbers of various atoms play important roles in establishing the magnitude of these magnetic moments. Atoms S(1)-S(3) on Fe(710), or S(1) on Fe(310), with the largest magnetic moments are also characterized by four nearest neighbors (NN). The same number, 4 NN, is valid for the top surface atoms of the Fe(100) surface, which have a large magnetic moment of 2.94 µB as calculated at the PAW-PBE level (or 3.05 µB at the US-PW91 level).16 In contradistinction, the internal edge atoms, that is, S(4) on Fe(710) and S(2) on Fe(310), have six NN and correspondingly smaller magnetic moments. Tests of the Adsorbate Properties. Further evidence for the accuracy of the current plane-wave DFT method is provided by analyzing the structural and vibrational frequencies and bond dissociation energies of gas-phase CO. These calculations have been done by optimizations of the isolated molecular species in a cubic box of 12-Å sides. In this case, spin-unpolarized calculations have been performed for the CO molecular system, whereas spin polarized calculations were done for the O and C species. For comparison, we have also considered the results of ab initio molecular orbital calculations using the Gaussian 03 package40 at the PBEPBE/aug-cc-pvtz level. The calculated bond distance r(C-O), vibrational frequency ν(C-O), and bond dissociation energy (De) were found to be 1.1434 Å, 2125 cm-1, and 265.9 kcal/mol using the VASP GGA-PBE level and 1.1374 Å, 2123 cm-1, and 268.1 kcal/mol at the PBEPBE level, respectively. As can be seen, the current GGA-PBE results are very close to those obtained using Gaussian calculations and large basis sets. Relative to the experimental data (rexp(CO) ) 1.1282 Å, νexp(C-O) ) 2170 cm-1, Dexp(CO) ) 261.8 kcal/ mol), 41 both sets of calculated results provide an acceptable good approximation for geometric and energetic parameters. Here, the experimental dissociation energy Dexp includes a zeropoint energy correction using the experimental vibrational frequencies. Larger differences from experimental results are observed, however, for the calculated vibrational frequencies because of omission of the anharmonic effects in either the plane-wave or the molecular orbital calculations. Nevertheless, overall the current plane-wave GGA-PBE computational method is able to provide a good description of both the bulk bcc phase of Fe and its surfaces and of the molecular species of interest considered in this study. 3. Results and Discussions The absorption energies of various molecular and atomic species were obtained based on the equation Eads ) Emolec + Eslab - E(molec+slab), where Emolec is the energy of the isolated adsorbate (atomic or molecular species) in its equilibrium position, Eslab is the total energy of the slab, and E(molec+slab) is the total energy of the adsorbate/slab system. A positive Eads corresponds to a stable adsorbate/slab system. The energy of the isolated adsorbate was determined from calculations performed on a single molecule in a cubic cell with sides of 12 Å. 3.1. Adsorption of Atomic C and O Species on the Fe(100) Surface. Because of the similarities of the Fe(710) and F(310) surfaces to those of the Fe(100) surface, we will mention very briefly the main results obtained on this latest system as obtained from our previous studies.10,16 It has been found that in the regime of low coverages, that is θ ) 0.25 ML, corresponding to one adsorbate atom per 2 × 2 surface cell, the most stable adsorption configurations for the C and O atomic species are at

J. Phys. Chem. C, Vol. 112, No. 28, 2008 10475 TABLE 2: Calculated Equilibrium Distances and Adsorption Energies for C and O Species Adsorbed on (a) Fe(100), (b) Fe(710), and (c) Fe(310) Surfacesa r(FeI-X)b

r(FeII-X)b

Eads

(a) Fe(100) C(4F) O(4F)

1.949 2.096

1.969 2.122

190.3 147.0

(b) Fe(710) C(4F,1) C(4F,2) C(4F,3) C(3F,s1) O(4F,1) O(4F,2) O(4F,3) O(3F,s1) O(3F,s2)

1.938, 1.940, 1.946,1.947 1.939, 1.939, 1.953, 1958 1.950, 1.951, 1.953, 1.955 1.817, 1.817 2.051, 2.054, 2.064, 2.067 2.064, 2.064, 2.078, 2.089 2.009, 2.010, 2.112, 2.113 1.873, 1.875 1.863, 1.913

1.979 1.970 1.977 1.808 2.143 2.128 2.116 1.960 1.915

189.0 188.9 189.8 165.2 146.8 148.3 146.0 149.5 136.9

(c) Fe(310) C(4F) C(3F,s1) O(4F) O(3F,s1) O(3F,s2)

1.941, 1.942, 1.953, 1.955 1.813, 1.814 1.999, 1.999, 2.108, 2.113 1.876, 1.879 1.862

1.974 1.799 2.124 1.936 1.910, 1.913

188.8 164.6 143.6 148.8 137.0

configuration

a The bond distances are in units of angstroms, and chemisorption energies, in kcal/mol. The symbols 4F, 3F, and 2F denote four-, three-, and 2-fold sites. The labels of specific sites on (710) and (310) surfaces are indicated in Figure 1. b FeI and FeII denote the iron atoms in the top and subsurface layers of the (001) terrace, and X in the table heading stands for C or O chemical symbols, respectively.

the 4-fold (4F) hollow sites. The adsorption at the other surface sites such as on-top (1F) or bridge sites (2F) was found to be energetically less favorable than that at the hollow site. By increasing the coverage, the adsorption energies decrease monotonically for both C and O species. For reference, we detail in Table 2 the corresponding binding energies at θ ) 0.25 ML and the geometric parameters for both C and O species while in Table S1 of the Supporting Information section we indicate the corresponding vibrational frequencies for the most-stable configurations. 3.2. Adsorption of the Atomic C and O Species on the Fe(710) Surface. As illustrated in Figure 1a and b, several different adsorption sites are available on the terrace and at the step of the Fe(710) surface. Specifically, on the (001) terrace there are three independent 4F sites, denoted (4F,1), (4F,2), and (4F,3), where the first of them (4F,1) is the closest to the upper step edge and the last one (4F,3) is the closest to the bottom, internal step edge. Despite the apparent similitude of the hollow sites along the (001) terrace, we note that they are not equivalent. Specifically, the number of nearest neighbors (NN) and nextnearest neighbors (NNN) for the top-layer atoms are 4 NN and 4 NNN for the Fe atom at the top of the step (site S(1) in Figure 1a), 4 NN and 5 NNN for the Fe atom in the middle of the 001 terrace (sites S(2) and S(3)), and 6 NN and 5 NNN for the Fe atom at the bottom of the step (site S(4)). As indicated before, the differences in coordination number lead to different magnitudes of the corresponding magnetic moments and consequently to different chemical environments for the adsorbates. At the surface step, two different types of threefoldcoordinated sites can be distinguished, hereafter denoted as (3F,s1) and (3F,s2) (see Figure 1b). The (3F,s1) and (3F,s2) sites involve two, respectively, one Fe atom at the top edge of the step and one, respectively, two Fe atoms at the bottom of the step. The adsorption energies of the individual C and O atomic species at various sites are detailed in Table 2, and


Figure 2. Adsorption configurations of the O atom (colored in red) on Fe(710) (a-f) and Fe(310) (g-i) surfaces. Panels a-c indicate adsorption at hollow (4F,1), (4F,2), and (4F,3) sites on the (001) terrace of the Fe(710) surface, while panels d-f correspond to adsorption at step (3F,s1) or (3F,s2) or at mixed (4F,1)-(3F,s1) sites on the same surface. Adsorption at hollow (4F) and threefold (3F,s1) and (3F,s2) step sites on the Fe(310) surface are depicted in panels g-i.

representative pictorial views for the case of the O atoms are presented in Figure 2a-e. By inspecting the adsorption energies of C species at the (4F,1), (4F,2), and (4F,3) sites on the Fe(710) it can be seen from Table 2b that the corresponding values change very little and they follow the results obtained on Fe(100) closely. For the O atom, a similar situation is found with a slight preference for the (4F,2) site at the middle of the terrace. At the surface steps, however, the stability behavior is different for the C and O species. In the case of the C species, only adsorption at the step (3F,s1) site was found to correspond to a local minimum, a fact confirmed by the corresponding set of vibrational frequencies (see Table S1 in the Supporting Information), which are all positively defined. In this case, the C atom is bonded to two Fe atoms at the top of the step (r(C-Fe) ) 1.817 Å) and one at the bottom of the step (r(C-Fe) ) 1.808 Å). The adsorption at the other (3F,s2) site was found to be unstable, and the C atom moves away from this site to a nearby (4F,3) configuration. Relative to the terrace hollow sites, the binding at the step (3F,s1) site was found to be significantly less stable by about 24 kcal/mol. These results clearly indicate the preference of the C atom to adsorb at the hollow sites of the (001) terrace, which allows coordination to four Fe atoms in the first surface layer and one in the second layer. For the O species, both (3F,s1) or (3F,s2) sites are local minima, but the former site is favored by 12.6 kcal/mol relative to the latter one. The (3F,s1) step site is also favored when compared to various hollow terrace sites, but the difference in stability relative to these sites is less significant, with values in the range of 1.2-3.5 kcal/mol. It is interesting that in the case of the Fe(110) surface, where a similar pseudo-threefold hollow site exists, O adsorption at this site is not stable and the atom moves away to a long bridge position.17 In the case of Fe(710), such a long bridge site, positioned at the intersection of the step and the lower terrace planes, is sterically inaccessible to the adsorbing O. As a result, an O atom positioned at such a bridgelike site at the bottom of the step is unstable and the atom moves away to nearby (3F,s2) or (4F,3) sites. The effect of coverage increase upon adsorption properties of C and O species is detailed in Table 3, entries b and e, as a function of the occupation of different surface sites. In the case of the C atom, adsorption at different (4F) hollow sites remains the preferred configuration even at higher coverages. Specifi-

Sorescu cally, for a local coverage of 0.5 ML the C atoms adsorb on the hollow sites of the terrace in a c(2 × 2) pattern. Configurations such as C(4F,2)-C(4F,3) and C(4F,2)-C(4F,1) on the same terrace have the largest adsorption energies of 191.5 and 190.3 kcal/mol, respectively, followed closely by states such as C(4F,1)-C(4F,3), where one C atom is at the top of the step and the other one at the bottom of the step, with a binding energy of 189.4 kcal/mol. We also tested the case when adsorption takes place at nearby hollow sites (separated by the surface lattice constant). In such cases, (see C(4F,3)-C(4F,3) entry in Table 3b) because of the repulsive interactions the binding energy decreases relative to the c(2 × 2) configuration. This decrease is even more accentuated for the step sites where adsorption at nearby 3F sites (entry C(3F,s1)-C(3F,s1)) is significantly less favorable with a binding energy of 158.9 kcal/mol. Finally, by occupation of all hollow sites of the Fe(710) terrace (see entry C(4F,all) in Table 3b) the binding energy decreases to 181.5 kcal/mol. The above results clearly indicate that the adsorption energy of the C species adsorbed on the hollow sites first increases with coverage up to 0.5 ML, followed by a decrease above this coverage. This effect is similar to the one we16 and other authors17 observed before for the case of the Fe(100) surface (see also section a in Table 3). In the case of the O species, the increase in coverage leads to a different pattern in occupation of various surface sites. As shown above, at low coverages the most stable configurations are the step (3F,s1) followed by the terrace (4F,2) sites. By increasing the coverage, it was found that the most stable state corresponds to a mixed O(3F,s1)-O(4F,1) configuration (see Figure 2f) with a binding energy of 149.7 kcal/mol. In this case, the two O atoms are placed in a diagonal position relative to each other at a separation of 3.716 Å, such that only a single surface Fe atom is shared by both of them. Other hollow-hollow (O(4F,2)-O(4F,3), O(4F,1)-O(4F,2)) with a c(2 × 2) pattern or step-hollow (O(3F,s1)-O(4F,3)) combinations are also possible as detailed in Table 3e, but their binding energies are slightly smaller with values ranging from 146.0 to 146.6 kcal/ mol. Finally, occupation of the nearby states of the same type such as O(3F,s1)-O(3F,s1) or O(4F,2)-O(4F,2), leads to an accentuated decrease in binding energy due to the repulsive nature of the lateral interactions between the O atoms at a separation of about 2.833 Å. This effect is even more prominent, for example, when all hollow and step sites are occupied (see entry O(4F,all)-O(3F,all) in Table 3) because the corresponding binding energy decreases further to 135.2 kcal/mol. Overall, the above results indicate that at low coverages the terrace hollow sites are preferentially occupied by C atoms while the step (3F) sites are favored by O atoms. Preferential locations of the adsorbate species are observed by the increase in coverage. Specifically, for C atoms the c(2 × 2) structure on the terrace hollow sites is preferred. In the case of O atoms, a mixed step-terrace site occupation (O(3F,s1)-O(4F,1)) in a diagonal relative position where a single Fe atom is shared by the two adsorbates, was found to be the most stable. A further increase in coverage above 0.5 ML leads to a decrease in binding energies for both C and O species because of steric repulsions. 3.3. Adsorption of Atomic C and O Species on the Fe(310) Surface. On the Fe(310) surface, successive steps are separated by a single row of Fe atoms and as a result a single hollow site exists. Hereafter, we denote this site using a single (4F) index (see Figure 1d). The steps of this surface, however, are similar to those of Fe(710) and, consequently, two different threefold symmetry sites, hereafter denoted as (3F,s1) and (3F,s2), can be identified (see Figure 1d).

CO on Kinked Fe(710) and Fe(310) Surfaces


TABLE 3: Variation of the Adsorption Energies for C, O, and CO Species as a Result of Simultaneous Binding at Different Sites on Fe(100), Fe(710), and Fe(310) Surfacesa configuration

Eadsa

(a) C/Fe(100) (4F)-(4F) [c2] (4F, all)

191.6 176.3

(d) O/Fe(100) (4F)-(4F) [c2] (4F, all)

146.1 138.0

(g) CO/Fe(100) (4F)-(4F) [c2, pl]b (4F)-(4F) [c2,ap] (4F)-(4F) [sd, pl] (4F)-(4F) [sd, ap]

50.1 48.8 45.3 45.2

configuration (b) C/Fe(710) (4F,2)-(4F,3) [c2] (4F,2)-(4F,1) [c2] (4F,1)-(4F,3) (4F,3)-(4F,3) (3F,s1)-(3F,s1) (4F,all) (e) O/Fe(710) (3F,s1)-(4F,1) (4F,2)-(4F,3) [c2] (3F,s1)-(4F,3) (4F,1)-(4F,2) [c2] (4F,2)-(4F,2) (4F,1)-(4F,1) (4F,3)-(4F,3) (3F,s1)-(3F,s1) (4F,all)-(3F,all) (h) CO/Fe(710) (4F,1,1)-(4F,2,-1) (4F,1,1)-(4F,3,1) (4F,1,1)-(4F,2,1) (4F,2,1)-(4F,3,1) (4F,1,1)-(4F,3,-1) (4F,1,1)-(4F,1,1) (4F,1,1)-(3F,s1) (4F,1,1)-(4F,1,-1) (4F,3,1)-(3F,s1)

Eads 191.5 190.3 189.4 187.3 158.9 181.5 149.7 146.6 146.3 146.0 142.4 141.0 139.5 141.9 135.2 49.4 48.7 48.3 48.2 46.1 45.4 45.3 44.0 42.2

configuration

Eads

(c) C/Fe(310) (4F)-(4F) [far] (4F)-(4F) (3F,s1)-(4F) (4F,all)

189.5 187.3 175.0 187.7

(f) O/Fe(310) (3F,s1)-(4F) (4F)-(4F) [far] (3F,s1)-(3F,s1) (4F)-(4F) (4F,all)-(3F,1,all)

144.7 143.4 141.8 137.3 131.9

(i) CO/Fe(310) (4F,1)-(4F,1) [far] (4F,1)-(4F,-1) [far] (4F,1)-(4F,1) [sd] (4F,1)-(3F,s1) (4F,1)-(4F,-1) [sd] (4F,-1)-(4F,-1)

49.3 45.7 45.5 44.2 40.2 37.2

a The binding energies are given in units of kcal/mol. For each configuration, we indicate the specific sites occupied by the adsorbates. b The list of acronyms used is as follows: [c2] denotes a c(2 × 2)-like configuration of the two adsorbates on Fe(100) or on the terrace of the Fe(710) surface, sd indicates a side-by-side configuration of CO molecules in neighbor hollow sites, pl indicates parallel orientations pointing to the same direction, ap indicates antiparallel orientations pointing in opposite directions, (4F,all) and (3F,all) indicate occupation of all fourand, respectively, threefold sites on the surface. The acronym far used in the case of Fe(310) refers to binding configurations on successive terraces such that no surface Fe atoms are shared in adsorbate bonding.

As in the case of the Fe(710) surface, we note that the four atoms surrounding the (4F) site are not equivalent because they have different coordination numbers. Specifically, the Fe atoms at the top of the step on Fe(310) (denoted with S(1) in Figure 1c) have 4 NN, whereas the atoms at the bottom of the step (denoted with S(2) in Figure 1c) have 6 NN. In Table 2c, we present the set of adsorption energies on the Fe(310) surface together with representative bond distances for C and O species. A pictorial view corresponding to adsorption of the O atom at different sites on this surface is provided in Figure 2g-i. The results obtained in this case present similar trends to those observed on the Fe(710) surface. Specifically, the hollow (4F) site is preferred by the C atom, whereas the step (3F,s1) is favored by the O atom. The existence of various local minima was also confirmed based on the positive nature of all vibrational values (see the Supporting Information, Table S1). The increase in the local coverage of C atoms to 0.5 ML leads first to occupation of the hollow sites. However, in contradistinction to Fe(710), on the Fe(310) surface a c(2 × 2) adsorption pattern for either C or O atoms is not possible because of the limited size of the terrace in the latest case. As a result, on Fe(310) the most stable configuration of the two C atoms corresponds to occupation of two hollow sites belonging to different terraces (entry C(4F)-C(4F) [far] in Table 3c) followed by occupation of two nearby hollow sites on the same terrace (entry C(4F)-C(4F) in Table 3c). We note that this latest configuration is practically identical to the C(4F,3)-C(4F,3) state identified on Fe(710), a fact also demonstrated by the identity of the corresponding sets of binding energies. Finally, in the case of O species, the systematic analysis of various

combinations of adsorption sites (see Table 3f) shows that at 0.5 ML the most stable state is a mixed O(3F,s1)-O(4F) state. This state has a binding energy of 144.7 kcal/mol, similar to the value of 146.6 kcal/mol found for the O(3F,s1)-O(4F,3) state on Fe(710). As in the case of the Fe(710) surface, the increase in surface coverage with full occupation of (4F) and (3F,s1) sites leads to a decrease in binding energies to 131.9 kcal/mol. Overall, the set of results presented in this section indicates that the adsorption properties for the C or O species on the Fe(310) surface are similar to those observed on Fe(710) corresponding to the step (3F,s1) and (3F,s2) sites and to the hollow (4F,3) site at the bottom of the step. The main difference between the two surfaces, however, comes from the small terrace length of the Fe(310) surface, which does not allow adsorption at the hollow sites in a c(2 × 2) pattern with the increase in coverage. The c(2 × 2) pattern proved to be essential in order to maximize the adsorption energy at 0.5 ML on either Fe(100) or on the terrace sites of Fe(710). However, on both surfaces further increase in coverage above 0.5 ML leads to a continuous decrease in binding energies for either the C or O species. 3.4. Adsorption, Diffusion, and Dissociation of Molecular CO on Fe(100). The adsorption, diffusion, and dissociation properties of CO on Fe(100) have been analyzed previously by us10 based on plane-wave DFT calculations using the PW91 exchange-correlation functional42 and ultrasoft pseudopotentials (USPP). Among the various possible surface sites, that is, ontop, bridge, and hollow, the most stable adsorption configuration was found to be the hollow (4F) site (also called the CO(R3) state). In this state, the molecule adsorbs in a tilted configuration,


Sorescu

TABLE 4: Calculated Equilibrium Distances and Adsorption Energies for CO Adsorbed on (a) Fe(100), (b) Fe(710), and (c) Fe(310) Surfacesa r(FeI-C)b

r(FeII-C)b

1.955, 1.955, 2.227, 2.230 1.976, 1.976, 2.196, 2.196

2.082 2.069

(b) Fe(710) (4F,1, 1) (4F,1,-1) (4F,1, 0) (4F,2, 1) (4F,2,-1) (4F,3, 1) (4F,3,-1) (4F,3, 0) (2F,1) (1F,1) (3F,s1)c (2F,s1)c (1F,s1)c (1F,s2)c

1.954, 1.961, 2.189, 2.199 1.957, 1.957, 2.228, 2.233 1.945, 1.950, 2.203, 2.205 1.958, 1.969, 2.221, 2.234 1.953, 1.948, 2.260, 2.246 1.966, 1.955, 2.215, 2.210 1.981, 1.982, 2.205, 2.210 1.931, 1.957, 2.209, 2.235 2.170, 1.808 1.781 1.963, 1.965 2.288 1.788

2.096 2.102 2.133 2.076 2.086 2.143 2.080 2.117

(c) Fe(310) (4F,1) (4F,-1) (3F,s1) (2F,s1) (1F,s1) (1F,s2)

1.960, 1.961, 2.197, 2.201 1.971, 1.973, 2.216, 2.217 1.971, 1.968 2.273 1.794

configuration (a) Fe(100) (4F) (4F)-(4F)

r(FeI-O)b

r(C-O)

Eads

1.320 1.318

48.9 49.1

2.086, 2.092 2.121, 2.121 2.133, 2.087 2.133, 2.113 2.120, 2.122 2.118, 2.112 2.257, 2.262, 2.150 2.183, 2.045

1.332 1.321 1.322 1.321 1.319 1.332 1.335 1.323 1.196 1.175 1.211 1.198 1.180 1.193

48.9 46.7 45.8 46.4 46.6 47.1 41.6 45.8 36.2 34.9 40.8 41.1 38.4 40.3

2.082, 2.083 2.236, 2.258, 2.194

1.331 1.329 1.210 1.200 1.179 1.193

48.2 40.9 39.9 41.6 37.1 40.5

2.106 1.806 1.787 2.135 2.095 2.097 1.809 1.778

a

The bond distances are in units of angstroms, and chemisorption energies, in kcal/mol. The notation used to specify various configurations is indicated in Figure 1. b FeI and FeII denote the iron atoms in the top and subsurface layers of the (001) terrace plane. c The acronyms (3F,s1), (2F,s1), (1F,s1), and (1F,s2) denote three-, two-, and one-fold-coordinated configurations on the step plane corresponding to Figure 3e-h.

in agreement with extensive experimental data obtained in Bernasek’s group.6,7 To allow direct comparison with the results determined for stepped surfaces, we provide in Table 3 updated results obtained at the PAW-PBE level for the geometric and energetic parameters while vibrational frequencies are detailed in the Supporting Information, Table S1. Specifically, we found that at the 4F site the CO molecular axis is tilted relative to the surface normal by 49.3° (vs the experimental value of 45° ( 10°),6e while the CO bond is significantly elongated to 1.320 Å relative to the gas phase result of 1.143 Å. Correspondingly, the CO vibrational frequency calculated in the frozen phonon mode approximation is significantly red-shifted to 1189 cm-1, indicating an important weakening of the CO bond. At θ ) 0.25 ML coverage, a binding energy of 48.9 kcal/mol has been determined, which increases slightly to 49.9 kcal/mol at 0.50 ML for the c(2 × 2) overlayer structure. The calculated PAW-PBE binding energy is slightly larger than our previous result of 46.7 kcal/mol determined using USPP-PW91 calculations.10 In our previous study,10 we have also shown that on the Fe(100) surface CO diffusion can readily take place for (1F) f (2F) and (2F) f (4F) pathways, with activation energies of less than 1.8 kcal/mol. This indicates that independent of the initial adsorption site of CO on the surface the molecules will end up at the most stable hollow sites. Once adsorbed at these hollow sites, the diffusion is significantly hindered because of larger activation energies. For example, for the diffusion pathway between (4F) and (2F) an activation energy of 13.1 kcal/mol has been determined. From the 4F tilted configuration, the CO molecule can dissociate through a transition state in which the C atom remains in its original 4F potential well and the O atom moves close to the bridge site. From this configuration, the system further evolves to a state in which C and O species are adsorbed in

neighbor hollow sites. On the basis of PAW-PBE calculations in connection to the CI-NEB method (results not shown), we determined that at θ ) 0.25 ML the overall CO dissociation reaction is exothermic with an energy change of -10.4 kcal/ mol and an activation energy of 24.7 kcal/mol. This activation energy is only slightly larger than our previous result of 24.5 kcal/mol, obtained based on USPP-PW91 calculations.10 In a recent theoretical study, Bromfield et al.11 have investigated using PAW-PW91 calculations the dependence on coverage of CO dissociation. It was determined that by increasing the coverage from 0.25 to 0.5 ML the reaction changes from exothermic to slightly endothermic, with a total energy change of about 2.3 kcal/mol. In this study, we have analyzed both the stability and the dissociation properties for the CO-c(2 × 2) overlayer using the PAW-PBE method. As indicated in Table 3g (see entry (4F)-(4F) [c2, pl]), the c(2 × 2) overlayer with CO molecules in a parallel configuration is the most stable relative to other possible orientations. For the parallel c(2 × 2) overlayer, we have further analyzed the dissociation properties and found that dissociation of one of the two CO molecules in the supercell is still an exothermic process but the total energy change is very small: only -0.93 kcal/mol. This significant variation in reaction energy from -10.4 kcal/mol at 0.25 ML to -0.93 kcal/mol at 0.5 ML, together with a corresponding increase in the activation energy for dissociation to 26.7 kcal/mol, indicates that CO dissociation becomes less favorable by the increase in coverage. 3.5. Adsorption Properties of CO on Fe(710). The results of CO adsorption on the stepped Fe(710) surface are summarized in Table 4b, and pictorial views of representative configurations are given in Figure 3a-h. In the case of the (001) terrace of the Fe(710) surface, special attention was paid to the analysis of the binding properties at the hollow sites, which are the most stable sites. As indicated in Figure 1b, on the Fe(710) terrace



Figure 3. Representative adsorption configurations of CO on Fe(710) (a-h) and Fe(310) (i-l) surfaces. In each case, top and side views are indicated. Panels a-d correspond to configurations (4F,1,1), (4F,3,1), (4F,3,-1), and (2F,1) on the (001) terrace of the Fe(710). Panels e-h correspond to configurations (3F,s1), (2F,s1), (1F,s1), and (1F,s2) at the step sites. Panels i-l illustrate configurations (4F,1) (i), (4F,-1) (j), (3F,s1), and (1F,s2) on the Fe(310) surface.

there are three hollow sites between successive steps where CO molecules can adsorb with different orientations relative to the step edge. To describe these individual adsorption configurations we adopt hereafter a three-indices notation of the form (4F, m, n), with m ) 1,2,3 and n ) -1,0,1. Here, the first two indices, that is, (4F,1), (4F,2), and (4F,3), denote the position of the hollow site counted from the top of the step along the terrace, similar to the notation introduced in Section 3.2. The third index refers to the specific orientation of the adsorbed CO molecule with its molecular axis perpendicular or parallel to the step edge. The indices n ) +1 or n ) -1 denote configurations with the molecular axis perpendicular to the step edge and pointing toward the upper step edge in the direction (see Figure 1a), respectively, in the reverse direction toward the bottom step edge. A configuration with the molecular axis parallel to the step edge is denoted with an index n ) 0. Using

this notation, a CO molecule adsorbed at a 4F hollow site near the top edge and with its molecular axis oriented toward the external step edge is denoted as (4F,1,1) (see Figure 3a) while a molecule bonded in the hollow site at the bottom of the step and with its molecular axis oriented in the reverse direction toward the internal step edge is denoted as (4F,3,-1) (see Figure 3c). By comparing the values given in Table 4b, it can be seen that the majority of hollow configurations have binding energies spread in the 45.8-48.9 kcal/mol range. Among these, the most stable states are the (4F,1,1) and (4F,3,1) (see Figure 3b) with binding energies of 48.9 and 47.1 kcal/mol, respectively. The less stable hollow configuration (Eads ) 41.6 kcal/mol) is the (4F,3,-1) state at the bottom of the step where the CO molecule points toward the nearby step. Because of the nonequivalent nature of the individual Fe rows along the (001) terrace, there

10480 J. Phys. Chem. C, Vol. 112, No. 28, 2008 are noticeable differences in binding energies even when the CO molecule adsorbs at a given hollow site but has different orientations relative to the step edge. For example, in the case of configurations (4F,1,1), (4F,1,-1), or (4F,1,0) that can exist within the same (4F,1) hollow well, the corresponding binding energies vary in the 45.8-48.9 kcal/mol range. This anisotropic behavior is even more accentuated for the (4F,3) hollow site near the bottom of the step where the binding energies range from 41.6 to 47.1 kcal/mol. A common element for all of the hollow sites described above is the tilted adsorption configuration, which allows simultaneous bonding to the surface atoms of both C and O ends. The corresponding Fe-C or Fe-O bond distances are indicated in Table 3b. As a result of the bonding at both molecular ends, significant elongation of the C-O bond in the 1.319-1.335 Å range takes place. The highest bond elongation is seen in the case of the (4F,3,-1) structure where the O atom interacts simultaneously with two Fe atoms on the lower terrace (r(Fe-O) ∼ 2.26 Å) and one at the top of the step (r(Fe-O) ) 2.15 Å). As noted above, this triple bonding of the O end leads to the highest destabilization of the CO molecule among various 4F configurations on the Fe(710) surface. The weakening of the CO bond is also reflected by the downward shift of the corresponding stretching frequency. Indeed, as indicated in Table S1, the ν(C-O) vibrational frequencies decrease from the gas phase value of 2125 to 1147 cm-1 for (4F,1,1) or 1175 cm-1 for (4F,3,1) structures, while an even larger decrease to 1091 cm-1 takes place for the most elongated structure at (4F,3,-1). In addition to the hollow (4F) site, CO adsorption can also take place on top or at a bridge configuration. However, in these last two cases the corresponding binding energies are significantly smaller than those at hollow sites. For example, in the case of a bridge tilted state at the top of the step (see configuration (2F,1) in Figure 3d) the binding energy decreases to 36.2 kcal/mol while a (1F,1) on-top configuration at the top of the step (not shown), perpendicular to the (001) terrace plane, has a binding energy of 34.9 kcal/mol. As a result, these configurations are expected to play a less-important role, particularly in the regime of low coverages. On the step plane of the Fe(710) surface, several types of adsorption configurations have been identified, namely, a threefold (3F,s1) (see Figure 3e, a twofold (2F,s1) (see Figure 3f), and two types of one-fold (1F,s1) (see Figure 3g) and (1F,s2) (see Figure 3h) configurations. In the (3F,s1) configuration, the molecule is bonded to two Fe atoms at the top and one at the bottom of the step. At this site, however, two different orientations of the molecule were found, characterized by tilt angles θ(Fe(b)-C-O) of 133° and 170° respectively, where Fe(b) is the iron atom at the bottom of the step. The adsorption energies of these two structures were found to be practically degenerate with a value of 40.8 kcal/mol. As a result, we present in Figure 3e only one of these structures for which the θ(Fe(b)-C-O) tilt angle is 133°. A similar binding energy (Eads ) 41.1 kcal/mol) is observed for the (2F,s1) state where CO bonding involves one Fe atom at the top and, respectively, one at the bottom of the step. Finally, in the case of the (1F) states bonding can take place either at the top (configuration (1F,s1)) or at the bottom (configuration (1F,s2)) of the step. The binding energies in these cases are slightly smaller than that at 3F site, with values of 38.4 kcal/mol for (1F,1) and 40.3 kcal/mol for (1F,2), respectively. We have verified through normal-mode analysis that all of these configurations correspond to local minima on the potential energy surface (see Table S1).

Sorescu The effect of local coverage increase upon binding properties of CO on the Fe(710) surface is detailed in Table 3h. A local surface coverage of 0.5 ML has been considered by analyzing different combinations of surface sites and molecular orientations. The corresponding results indicate a distribution of binding values ranging from 42.2 to 49.4 kcal/mol. Among these, those configurations with a diagonal relative position of the molecules such as CO(4F,1,1)-CO(4F,2,-1), similar to the c(2 × 2) on Fe(100), are preferred. Overall, it can be concluded that on Fe(710) several different adsorption configurations are possible, among which the most stable are the hollow (4F) sites on the terrace followed by the (3F), (2F), and (1F) configurations on the step plan. The nonequivalence of different rows of Fe atoms along the terrace leads to a distribution in the binding energies with the most stable at the top of the step and the most activated at the bottom of the step. Interestingly, we found that when adsorption takes place at the hollow sites, the stability properties depend not only on the location of the site from the step edge but also on the relative orientation of the CO molecule with respect to the step edge. The increase in coverage leads to a preferential occupation of the hollow terrace sites in a diagonal pattern where a single Fe atom is shared by two added molecules, similar to the c(2 × 2) overlayer observed on the Fe(100) surface.16 3.6. Adsorption Properties of CO on Fe(310). The results of CO adsorption on Fe(310) surface are detailed in Table 4c, and the most important adsorption configurations are represented in Figure 3i-l. Similar to the Fe(710) case, on the Fe(310) surface the most stable site is the hollow 4F where the molecule adsorbs in a tilted configuration. However, the specific binding energy at this site depends on the molecular orientation. In the case of (4F,1) configuration (see Figure 3i) where the O atom binds to two Fe atoms at the top of the step (r(Fe-O) bonds of 2.082 and 2.083 Å) the adsorption energy is the highest and has a value of 48.2 kcal/mol. This binding energy is almost at the midpoint between the values obtained for (4F,1,1) and (4F,3,1) configurations on the Fe(710) surface. In the case of the opposite orientation of the CO molecule on Fe(310), corresponding to state (4F,-1) (see Figure 3j) the O end is bonded to two Fe atoms at the bottom (r(Fe-O) bonds of 2.236 and 2.258 Å) and, respectively, one at the top (r(Fe-O) bond of 2.194 Å) of the step. In this case, the binding energy decreases to 40.9 kcal/mol. This value is close to that of configuration (4F,3,-1) on the Fe(710) surface of 41.6 kcal/mol. On the step plane of the Fe(310) surface, the binding configurations of CO molecules are similar to those identified on the Fe(710) surface, namely, a threefold (3F,s1), a twofold (2F,s1) state, and two different one-fold configurations where bonding involves an Fe atom at the top (1F,s1), respectively, and at the bottom (1F,s2) of the step. Among these, we illustrate for reference in Figure 3k and l the (3F,s1) and (1F,s2) states. The similarity between the step configurations on Fe(710) and Fe(310) is also reflected in their corresponding binding energies and geometric parameters, which have close values. The analysis of the surface sites’ occupation with the increase in coverage is complicated by the relative large number of different sites and molecular orientations within these sites that need to be considered. In Table 3i, we summarize the main results of our analysis for the case when two CO molecules are adsorbed on the surface. Overall, we obtained a relatively broad distribution of binding energies spread over 12 kcal/mol. Among these, the most stable states correspond to adsorption of CO molecules at the hollow sites placed on successive terraces (see entries (4F,1)-(4F,1)[far] and (4F,1)-(4F,-1) [far] in Table



Figure 4. Potential energy surfaces for CO diffusion on (a and b) Fe(710) and (c) Fe(310) surfaces. The indicated pathways connect the following configurations: (4F,1,1) T (3F,s1) T (4F,3,1) T (4F,2,1) T (4F,1,1) on Fe(710) in panel a, (4F,1,1) T (2F,1) T (2F,s1) T(4F,3,-1) T(4F,3,0) T(4F,3,1) in panel b on Fe(710), and (4F,1) T (2F,s1) T (4F,-1) T (4F,1) on Fe(310) in panel c.

3I followed by the case when adsorption takes place at nearby hollow sites on the same terrace (entry (4F,1)-(4F,1) [sd] in Table 3i or mixed (4F,1)-(3F,s1) states. It is worthwhile to point out that the calculated binding energies for the CO pairs (4F,1)-(4F,1) and (4F,1)-(3F,s1) on Fe(310) are very close to those of configurations (4F,1,1)-(4F,1,1) and (4F,1,1)-(3F,s1) on Fe(710). This fact further supports the similarity in the adsorption behavior of the two sets of molecular configurations, that is, (4F,1) on Fe(310) to (4F,1,1) on Fe(710) and (3F,s1) on Fe(310) to (3F,s1) on Fe(710). 3.7. Minimum Energy Pathways for Diffusion of a CO Molecule on Fe(710) and Fe(310) Surfaces. As was shown in previous sections, CO adsorption at the hollow sites is preferred on both Fe(710) and Fe(310) surfaces. Consequently, it is important to determine the minimum energy pathway for CO diffusion among such hollow sites. A first set of results corresponding to CO diffusion on the Fe(710) surface is presented in Figure 4a. Here the minimum energy pathways for diffusion have been obtained using the CINEB calculations. The overall process is initiated from a hollow site at the top of the step. From the upper terrace, the CO molecule diffuses over the step to the lower terrace and then moves further along the (001) terrace. This pathway involves

diffusion among the following local minima: CO(4F,1,1) T CO(3F,s1) T CO(4F,3,1) T CO (4F,2,1) T CO(4F,1,1). The calculated results indicate that similar activation energies exist for diffusion out of the hollow sites with values between 13.1 and 13.6 kcal/mol. Practically, from the most stable (4F,1,1) configuration at the top of the step the molecule can diffuse either on the terrace to the (4F,2,1) state or across the step to a (3F,s1) configuration. A slightly larger barrier is observed in the middle region of the terrace for diffusion among (4F,3,1) T (4F,2,1) configurations. Finally, we observe that the atomic configuration (4F,3,1) at the bottom of the step is readily available from the step sites because the activation for pathway (3F,s1) f (4F,3,1) is only 2.9 kcal/mol. In Figure 4b, we analyze the minimum energy pathways that connect the most stable (4F,1,1) and (4F,3,1) configurations on Fe(710) to the most activated (4F,3,-1) state at the bottom of the step. From the energy diagram in Figure 4b, it can be seen that the overall diffusion pathway from (4F,1,1) to (4F,3,-1) involves going through additional local minima corresponding to the bridge tilted configuration (2F,1) and to the step twofold coordinated configuration (2F,s1). As a result, the potential energy profile has several barriers among which the largest is the one corresponding to the initial step from (4F,1,1) to (2F,1)


Sorescu

Figure 5. Potential energy surfaces for CO dissociation on the Fe(710) surface (a and b) corresponding to reactions (a) CO(4F,1,1) f C(4F,1) + O(3F,s1) and (b) CO(4F,3,-1) f C(4F,3) + O(3F,s1), and on the Fe(310) surface (c and d), corresponding to reactions (c) CO(4F,1) f C(4F) + O(3F,s1) and (d) CO(4F,-1) f C(4F) + O(3F,s1).

with a barrier height of 13.2 kcal/mol, while further diffusion from (2F,s1) to the (4F,3,-1) state requires overcoming a small barrier of 4.3 kcal/mol. The second possibility to access the (4F,3,-1) state is by direct orientational interconversion within the same hollow site, that is, (4F,3,1) f (4F,3,-1). This process is also indicated in Figure 4b and involves going through a rotated (4F,3,0) state parallel to the step edge. The overall activation energy in this case is only 6.5 kcal/mol. On the basis of these sets of results, it can be concluded that the activated (4F,3,-1) state can be populated more easily by direct orientational interconversion within the same hollow site, corresponding to the process (4F,3,1) f (4F,3,-1), than diffusion of the molecule over the step from the upper to the lower terrace, that is, (4F,1,1) f (4F,3,-1). A final point we considered in our analysis was to determine the changes in the activation energy for diffusion on the Fe(310) surface. The results represented in Figure 4c indicate the same trend, namely, that interconversion within the hollow site between (4F,1) and (4F,-1) states requires a smaller activation energy of 9.3 kcal/mol than direct diffusion over the step. Overall, the results obtained indicate that on Fe(710) the largest barriers are observed for diffusion out of the hollow sites with values in the 13.1-14.1 kcal/mol range. These values are similar to the diffusion barrier of 13.1 kcal/mol determined previously by us for the Fe(100) surface.10 Diffusion out of various local minima on the step plane to the adjacent hollow sites on the lower terrace require significantly smaller activation energies of 2.9-4.3 kcal/mol. Finally, the most activated state (4F,3,-1) at the bottom of the step can be accessed from the either of the two most stable adsorption configurations, that is, (4F,1,1) and (4F,3,1). However, among these the interconversion (4F,3,1) f (4F,3,-1) is preferred with an activation energy of 6.5 kcal/mol. This finding is also valid on Fe(310) where the

interconversion process (4F,1) f (4F,-1) has a smaller activation energy than diffusion over the step. 3.8. CO Dissociation on Fe(710) and Fe(310) Surfaces. From the analysis presented in Sections 3.5 and 3.6, it follows that upon adsorption at 4F sites in a tilted configuration the CO bond is significantly elongated and weakened. As a result, these states are important candidates for molecular dissociation, similar to the case of the the Fe(100) surface where molecular dissociation starts from the tilted CO(R3) configuration. In the case of Fe(710), we have analyzed two different dissociation pathways, which are presented in Figure 5a and b. The first one, hereafter denoted as reaction R1, corresponds to dissociation of a CO molecule initially positioned on the upper terrace at the most stable (4F,1,1) configuration. From this state, upon further elongation of the C-O bond, the system evolves to a state in which the C atom remains localized in the original potential well while the O atom moves to a step (3F,s1) configuration. The minimum energy reaction profile together with representative configurations corresponding to the initial, transition, and final states are represented in Figure 5a. The second case analyzed, hereafter denoted as reaction R2, corresponds to dissociation of the CO molecule initially positioned in the hollow site at the bottom of the step, in the (4F,3,-1) configuration. As mentioned in Section 3.5, in this state there is an additional weakening and elongation of the CO bond due to a three-center bonding of the O atom to both top and bottom atoms of the step. Upon dissociation, the C atom remains located in the original hollow site at the bottom of the step while the O atom migrates to a nearby (3F,s1) site. The corresponding reaction profile in this case is presented in Figure 5b. As can be seen from Figure 5a and b, there are important differences between the activation energies of these two

CO on Kinked Fe(710) and Fe(310) Surfaces reactions with values of 20.5 and 15.4 kcal/mol, respectively, and between the exothermicity of the reactions with values of -10.5 and -27.6 kcal/mol, respectively. In the transition states of these two reactions, the C-O bond distances are elongated to 1.889 and 1.775 Å, respectively. The large difference between the final state potential energies is due to the difference in the repulsive interactions between the chemisorbed C and O atoms positioned at different separations in the two reactions. Indeed, for reaction R1 where the C and O atoms in the product state share two Fe atoms, the distance between chemisorbed C and O atoms (see image no. 8 in Figure 5a) is 2.797 Å while in the case of R2 reaction where only one Fe atom is shared between the C and O atoms (see image no. 8 in Figure 5b) the same distance is 3.065 Å. The effect of repulsive interactions can also be seen by comparing the energies of the final states for reactions R1 and R2 to the energies of the C and O atoms calculated in separated unit cells. We find that in the case of reaction R1 the energy of the C and O atoms when they are in the same cell is 13.1 kcal/mol larger than that in separated cells, whereas for reaction R2 the same difference is only 4.2 kcal/ mol. This data clearly indicates significantly smaller repulsive interactions for the R2 reaction relative to R1. The calculated activation energies for dissociation at step sites are also significantly different from those obtained on the Fe(100) surface. Specifically, the R1 and R2 reactions have activation energies smaller by 18% and 34% relative to the barrier height of 24.7 kcal/mol on the Fe(100) surface, indicating a clear preference for dissociation of CO at step sites. A final issue analyzed here was to determine the influence of coverage effects upon the activation energy of CO dissociation. Specifically, we have considered the case when reaction R1 takes place in the presence of a second undissociated CO molecule adsorbed at the bottom of the step in the CO(4F,3,1) state. Our calculations (not shown) indicate that in this case the activation energy for the dissociation of the first CO molecule is relatively little influenced as its activation barrier increases slightly to 20.9 kcal/mol. However, the reaction becomes less exothermal with respect to chemisorbed CO, by -3.1 kcal/mol. A similar effect has been observed in the case of reaction R2. In this latest case when a second undissociated molecule is adsorbed at the top of the step in the CO(4F,1,1) configuration, the activation energy for dissociation of the initial CO molecule changes little but the overall reaction becomes less exothermic, with a value of -22.8 kcal/mol. This effect is similar to the one indicated in Section 3.4 for the Fe(100) surface where the increase in CO coverage was found to decrease the exothermic character of the dissociation reaction. Similar to Fe(710), in the case of the Fe(310) surface we have analyzed two minimum energy pathways for CO dissociation starting from the 4F hollow sites. The first one, corresponding to reaction CO(4F,1) f C(4F) +O(3F,s1) (see Figure 5c) has as starting configuration the state CO(4F,1), which is the most stable on the Fe(310) surface while the last configuration corresponds to a C atom adsorbed at the same hollow site as the initial CO molecule and an O atom adsorbed at a nearby (3F,s1) step site. This reaction is exothermic by -10.7 kcal/mol and has an activation energy of 20.9 kcal/mol, values almost identical to those determined for the similar process CO(4F,1,1) f C(4F,1) + O(3F,s1) on Fe(710). The second dissociation process investigated was CO(4F,-1) f C(4F) + O(3F,s1) for which the corresponding minimum energy path is represented in Figure 5d. This reaction is also exothermic by -26.3 kcal/mol and has a barrier height of 16.7 kcal/mol. Both of these sets of values are almost identical

J. Phys. Chem. C, Vol. 112, No. 28, 2008 10483 to those determined on the Fe(710) surface in the case of the CO(4F,3,-1) f C(4F,3) + O(3F,s1) process (see Figure 5b). Overall, the results presented in this section indicate that in the case of the Fe(310) surface both the binding energies and the dissociation energies of the CO molecule have values similar to those determined on the Fe(710) surface when the same type of surface sites and molecular orientations are considered. A common characteristic of the Fe(710) and Fe(310) stepped surfaces is that the calculated activation energies for CO dissociation are smaller than those obtained on the Fe(100) surface. Additionally, by comparing the activation energies for dissociation with those for diffusion determined in previous section, it can be observed that the calculated activation energies for diffusion on both Fe(710) and Fe(310) surfaces are smaller than those for dissociation. These findings suggest that by increase in temperature both the most stable and the most activated sites are populated prior to the onset of the molecular dissociation. 3.9. Comparison of the Adsorption and Dissociation Properties of CO on Different Fe Surfaces. In our previous analysis16 of the adsorption and dissociation of CO and H2 species on the Fe(100) surface, followed by hydrogenation reactions of CHx (x ) 0,3) species with formation of CH4, it was found that the rate-determining step is represented by dissociation of adsorbed CO with formation of adsorbed C and O species. Consequently, it is important to understand the effect of different iron surface orientations upon the activation properties of CO. In this section, we expand our analysis by considering not only the case of kinked Fe(100), Fe(710), and Fe(310) surfaces but also other orientations, namely, the Fe(110), Fe(211), and Fe(111) surfaces. This selection is motivated by the fact that this set of surfaces has energies in a relatively close range of values, and as a result they might be present in the case of the polycrystalline Fe system. In this section, we will analyze the properties of these surfaces following the stability order for their surface energies (γ), that is, γ (110) < γ (100) < γ (211) < γ (310) < γ (111).20 As indicated early in this manuscript, the surface energy of the (710) surface was found to be practically identical to the one for the (211) surface determined by Błon´ski et al.20 We note that a similar trend in the stability of (110), (100), (211), and (111) surfaces has been determined earlier by Pratt et al.43 These authors have also determined that the stepped (321) surface is slightly less stable than the (211) surface. (110) Surface. In the case of bcc Fe, the most stable surface orientation is the (110) surface with a calculated surface energy of 2.37 J/m2.20 As demonstrated by both previous experimental44 and theoretical12 studies, at low coverages the CO molecule adsorbs preferentially in an on-top position. In the regime of low coverages (θ ) 0.25 ML) the p(2 × 2) overlayer was found theoretically12 to be slightly more stable than the experimentally suggested c(2 × 4) ordered structure.44 On the basis of PAWPBE calculations, a binding energy of 43.35 kcal/mol has been determined for the on-top site.12 From this state, the molecule dissociates with an activation energy of about 35.1 kcal/mol with formation of C and O species, each of them being adsorbed at long-bridge sites. The overall reaction was found to be endothermic by 11.5 kcal/mol. In the transition state, the C-O bond (r(C-O) ) 1.74 Å) is laying almost parallel to the surface above a short-bridge site. In order to extract the quantities of interest for this study, as will be described later in this section, we have reanalyzed the adsorption and dissociation properties of CO on the (110) surface for the case of the p(2 × 2) overlayer. Similar to the approach

10484 J. Phys. Chem. C, Vol. 112, No. 28, 2008 used in ref 12, our slab model contains seven layers, among which the top three layers were allowed to relax while the rest were kept frozen at bulk optimized positions. Our results indicate an adsorption energy of CO at the on-top site of 44.2 kcal/mol, an activation energy for dissociation of 35.6 kcal/mol, and an overall reaction endothermicity of 11.5 kcal/mol, in close agreement with the corresponding results reported by Jiang and Carter.12 (100) Surface. The second most stable surface orientation of Fe is (100) with a surface energy of 2.47 J/m2. As discussed in Section 3.4, in the regime of low coverages (θ ) 0.25 ML) the most stable state adsorption configuration is the hollow site where the molecule adsorbs in a stretched (r(CO) ) 1.320 Å) tilted configuration with a binding energy of 48.9 kcal/mol. The CO dissociation reaction on Fe(100) is exothermic by -10.3 kcal/mol and has an activation energy of 24.7 kcal/mol. At the transition state, the C-O separation is significantly elongated to 1.933 Å relative to gas phase value, indicating the existence of a late transition state. We note that this calculated activation energy for CO dissociation is in excellent agreement with the experimental value of 25.1 kcal/mol reported by Benziger and Madix based on temperature-programmed desorption.45 (211) Surface. The more open (211) surface has a surface energy of 2.50 J/m2,20 slightly higher than that of the Fe(100) surface. As indicated by Błon´ski et al.,20 an accurate description of the lattice relaxations of this surface should be done by considering slab models with as many as 15 layers. In this study, we have analyzed the adsorption and dissociation properties of CO on this surface at low coverages using a slab model with 15 layers, extended in a (2 × 2) supercell along the and crystallographic directions. We have identified two main binding configurations for the adsorption of CO on this surface. One of them corresponds to the on-top adsorption (see Figure 6a) with a binding energy of 39.7 kcal/mol (r(Fe-C) ) 1.780 Å and r(C-O) ) 1.176 Å) while the second one corresponds to a tilted state (see Figures 6b) with a binding energy of 45.2 kcal/mol. In the tilted state, there is an important weakening of the CO bond relative to the on-top configuration as indicated by its elongation to a value of 1.283 Å. The increased binding and elongation of the CO molecule in this tilted state can be understood because the C atom is simultaneously bonded to two Fe atoms in the top layer (r(FeI-C) of 1.980 and 2.140 Å) and two in the second layer (r(FeII-C) of 1.962 and 2.055 Å) while the O atom binds to one of the top-layer Fe atoms (r(FeI-O) ) 2.037 Å). Starting from the most stable tilted configuration identified above, we have further analyzed the minimum energy pathway for CO dissociation on the (211) surface. The corresponding energy profile is indicated in Figure 6c. The molecule dissociates with an activation energy of 23.6 kcal/mol with formation of an adsorbed C atom at a bridge site (r(FeI-C) of 1.891 and 1.882 Å) and of an O atom at a pseudo threefold site. Specifically, the O atom is bonded to two Fe atoms in the top layer (r(FeI-O) of 1.874 and 1.842 Å) and one in the second layer (r(FeII-O) ) 1.970 Å). In the transition state, the C-O separation is 1.932 Å while a single Fe atom is shared by both C and O atoms. The overall CO dissociation reaction is found to be exothermic by -5.6 kcal/mol. We note that the presence of the tilted adsorption configuration on the (211) surface leads to a significant decrease in the activation energy relative to the one on the close-packed (110) surface, while the dissociation reaction itself changes its character from endothermal on Fe(110) to exothermal on Fe(211).

Sorescu

Figure 6. Top and side views of the most stable adsorption configurations of CO on the Fe(211) surface at the on-top (a) and the bridgetilted (b) states. Panel c represents the minimum energy pathway for CO dissociation on the Fe(211) surface starting from the bridge-tilted configuration with formation of an adsorbed C atom at a bridge site and of an O atom at a pseudo threefold step site.

(710) and (310) Surfaces. The Fe(710) and Fe(310) surfaces considered earlier in the present work with surface energies of 2.50 and 2.52 J/m2 come next in terms of stability after Fe(100) and Fe(211) surfaces. As we have shown in previous sections of this work, on these surfaces two important types of configurations have been identified, denoted as the most stable and, respectively, the most activated. The first type corresponds to adsorption on Fe(710)(Fe(310)) at the (4F,1,1)((4F,1)) site located at the top of the step where the CO molecule points toward the step edge while the second one denoted as (4F,3,-1) ((4F,-1)) corresponds to adsorption at the bottom of the step with CO oriented toward the internal step edge. Both of these sets of configurations are tilted relative to the terrace plane. Dissociation of CO at these states requires activation energies of 20.5 (20.9) and 15.4 (16.7) kcal/mol, respectively. Both reactions are exothermic by -10.5 (-10.7) and -27.6 (-26.3) kcal/mol, respectively. Moreover, as shown in Section 3.7 the most activated states on either Fe(710) and Fe(310) can be populated by surface diffusion prior to the onset of dissociation. (111) Surface. The last surface orientation considered in this section is the Fe(111) surface. It has the largest surface energy of 2.58 J/m2 and as a result is the least stable among the various surface orientations considered in this section. The adsorption properties of CO on this surface have been analyzed previously by Chen et al.14 based on plane-wave DFT calculations with the PBE exchange correlation functional. Using a p(3 × 3)slab model with seven layers, three main adsorption configurations have been identified in the regime of low coverages (θ ) 1/3), that is, an on-top, a shallow-hollow, and a bridge-like configuration, respectively. Among these, the most


Figure 7. Top and side views of the adsorption configurations of CO on the Fe(111) surface corresponding to the on-top (a), shallow-hollow (b), and shallow-bridge (c) states. Panel d indicates the minimum energy pathway for dissociation of CO initiated from the bridge configuration with formations of the C and O atoms adsorbed at bridge sites where they are bonded to two Fe atoms in the top and two in the second layers, respectively. Another possible final state for the C atom can involve bonding to the four Fe atoms indicated in pink, among which one is in the top, two are in the second, and one is in the third layer, respectively.

stable was found to be the shallow-hollow site with a binding energy of 56.5 kcal/mol followed closely by the bridge-like with a binding of 54.2 kcal/mol. In this latest case, the molecule adopts a tilted state relative to the surface plane, whereas in the other two cases, that is, on-top and shallow-hollow, the molecule adsorbs perpendicular to the surface. The dissociation properties of CO on (111) have not been considered in the previous study,14 but it has been suggested that instead of the direct dissociation of CO molecule from the shallow-hollow site, the molecule will diffuse first to the tilted bridge-like site from where further dissociation might take place with a smaller barrier. To test these assumptions and to determine the corresponding activation energies for dissociation of CO on the Fe(111) surface, we have reviewed the adsorption properties of CO on this surface. We have used a similar p(3× 3) slab as indicated by Chen et al.14 but we have increased the number of layers in the slab to 10. All calculations have been done using a (4 × 4 × 1) k-point mesh. A pictorial view of the adsorption configurations determined, that is, on-top, shallow-hollow, and bridge-like are presented in Figure 7a-c. For these configurations, we have determined a stability order similar to the one determined by Chen et al.14 but our calculated binding energies are systematically smaller than those reported in the indicated study. Specifically, we obtained adsorption energies of 29.8 kcal/mol for the on-top, 48.2 kcal/mol for the shallow-bridge, and 44.8 kcal/mol for the bridge-like configurations, respectively. We note that the binding energy for the shallow-bridge configuration on Fe(111) obtained in this study

J. Phys. Chem. C, Vol. 112, No. 28, 2008 10485 is slightly smaller than the one we determined for the (4F) tilted configuration on the Fe(100) surface of 48.9 kcal/mol and this stability order is consistent with the observed experimental data. Indeed, in the regime of low coverages, the desorption temperature for the shallow-bridge state on Fe(111) was found to be centered at 420 K,46 whereas the corresponding desorption temperature for the tilted R3 state on Fe(100) was found to be slightly larger with a value of 440 K.6 These experimental findings indicate an increased stability of the binding sites on Fe(100) versus those on Fe(111), in agreement with our set of calculated binding energies. Despite the lower binding energy at the bridge state, the CO bond in this state is weakened relative to the vertical shallow-bridge configuration. This fact is due to simultaneous bonding of both C and O ends of the molecule in the bridge state, leading to a stretched bond of 1.246 Å. This value can be compared against the smaller CO bond length of 1.195 Å observed at the shallow-bridge state. Having determined the important adsorption sites of CO on Fe(111), we have further analyzed the minimum energy pathway for dissociation. Previous experimental studies47,48 have indicated a complex situation in which intersite conversion takes place prior to dissociation. For example, Bartosch et al.47 have indicated that the deep-hollow state can convert into the shallowhollow state with subsequent dissociation at 345 K while Whiteman et al.48 proposed a mechanism in which CO, initially bonded at a deep-hollow site, converts to a bridge-bonded site and subsequently dissociates at 320 K. In this work, we have analyzed the dissociation pathways started either from the shallow-hollow or from the bridge-like configurations. The minimum energy pathway for CO dissociation initiated from the most activated bridge configuration is represented in Figure 7d. In the transition state (see image no. 5 in Figure 7d) the C and O atoms occupy bridge-like configurations between the top layer Fe atoms and share one of these atoms. The corresponding CO separation in this state is 1.802 Å. Following the transition state, the O atom moves away to an intermediate local minimum (image no. 8 in Figure 6d) involving bonding to two Fe atoms in the top layer and one in the second layer. From this state, the system evolves to the final more stable minimum (image no. 14 in Figure 7d) in which both C and O atoms adsorb at bridge sites with simultaneous bonding to two Fe atoms in the top layer and two in the second layer. The overall reaction is exothermic by -6.5 kcal/mol while the activation energy for dissociation is 24.4 kcal/mol. We note that from the intermediate minimum indicated by image no. 8 the system can evolve toward a different final state of the C and O adsorbed atoms. Specifically, we found that such a favorable state is formed when the O is at the bridge state while the C atom is bonded to the four Fe atoms colored in pink in image no. 14 of Figure 7d, one in the first, two in the second, and one in the third layer, respectively. However, the overall minimum energy pathway starting from the bridge configuration and leading to such a final state involves the same transition state as the one indicated above (see image no. 5 in Figure 7d). Finally, we have analyzed the minimum energy pathway for direct CO dissociation starting from the shallow-hollow site (not shown). Again, the system evolves practically through the same transition state as the one illustrated by image no. 5 in Figure 7d, and the final C and O states of the reaction are the same to those represented by image no. 14 in the same figure. The activation energy for this dissociation process was found to increase to 27.8 kcal/mol with an exothermicity of the reaction of -3.1 kcal/mol.


Sorescu

Figure 8. Comparison of the adsorption, dissociation, and reaction energies of CO on Fe(110), Fe(100), Fe(211), Fe(710), Fe(310), and Fe(111) surfaces. For Fe(710) and Fe(310), the two sets of data correspond to dissociation at the most stable, respectively, at the most activated sites while for Fe(111) the indicated data corresponds to reactions initiated at the hollow-shallow and bridge sites, respectively. For each reaction, the corresponding atomic configuration in the transition state is represented in the lower panel.

Given the lower activation energy determined for dissociation initiated from the more activated bridge state than the one from the shallow-hollow state, it follows that the first process is the preferred one in agreement with the proposed mechanism of Whiteman et al.48 We also note that our calculated activation energy of 24.4 kcal/mol for dissociation initiated from the bridge-bonded configuration is also in very good agreement with the value of 20 ( 5 kcal/mol determined by Whiteman et al.48 based on temperature-programmed electron energy-loss spectroscopy (TP-EELS). CO Bond Activation on Various Crystallographic Fe Surfaces. The ensemble of the most important results related to adsorption and dissociation of CO on (110), (100), (211), (710), (310), and (111) surfaces is presented in a comparative way in Figure 8. We focus here only on the results obtained at low CO coverages. For each surface, three main quantities are indicated, namely, the CO binding energy of the initial unreacted state given in parentheses, the activation energy for CO dissociation relative to the initial adsorbed state, and the overall reaction energy relative to the initial unreacted state. The reference zero energy state is taken as the total energy of the isolated slab and isolated molecule for each individual surface. In the particular case of Fe(710) and Fe(310) surfaces, we indicate two situations: the first corresponds to the reaction profile starting from the most stable adsorbed state, and the second profile corresponds to the most activated state, namely, the state with the lowest activation energy of dissociation. For Fe(111), both reactions initiated at the shallow-hollow and bridge sites are indicated. By inspecting the most stable adsorption configurations of CO on Fe surfaces with different crystallographic orientations, it can be observed that the binding energies vary in a relatively small range from 44.2 to 48.9 kcal/mol. However, significant differences can be observed among the corresponding activation energies of dissociation and the overall reaction energies. Specifically, on the closed-packed Fe(110) surface the dissociation of CO is endothermic and has an activation energy (Eact) of 35.6 kcal/mol, which is the highest among all surfaces

considered in this study. In the case of the other more open surfaces, the dissociation reactions become exothermic with a corresponding decrease of the activation energies. For example, important decreases take place on either Fe(100) (Eact ) 24.7 kcal/mol) and Fe(111) (Eact ) 24.4 kcal/mol) surfaces. However, the largest decrease of the activation barrier is observed for the case of stepped Fe(710) and Fe(310) surfaces with barriers as low as 15.4 and 16.7 kcal/mol, respectively. These low barriers are associated with an increase in the exothermic character of the reactions by -27.6 kcal/mol for Fe(710) and -26.3 kcal/ mol for Fe(310). If an Arrhenius law for the reaction rate per site is considered and assuming that the attempt frequency is independent of the reaction pathway or the crystallographic orientation, then the ratio between the reaction rates at step relative to the terrace sites can be estimated based on the relation r(step)/r(terrace) ) exp(E(terrace) - E(step) )/kBT. This amounts to a a about 15 orders of magnitude for ratio r(710)/r(110) or 6 orders of magnitude for r(710)/r(100). Clearly, the reactivity at the step sites is significantly larger than that on either of the (110) or (100) surfaces. Overall, these results clearly indicate that activation of CO on Fe increases on the open surfaces while steps provide an effective environment in facilitating CO dissociation. In Figure 8 we also present the atomic configurations corresponding to the transition state for each of the individual reactions considered. From these panels, it can be clearly seen that two distinctive situations exist. In the case of the group of surfaces Fe(110), Fe(100), Fe(710), and Fe(310), hereafter denoted as group G1, the C and O atoms share two surface Fe atoms while a single Fe atom is shared in the case of Fe(211) and Fe(111) surfaces, hereafter denoted as group G2. As a result of this bonding difference, it is expected that the interaction energies between the C and O atoms in the first category of transition states will be larger than those in the second one. We will provide later in this section a more quantitative description of these interactions. A common element of the dissociation reactions described above is that in the transition state the CO bond is significantly



TABLE 5: Summary of the Calculated Energies for CO Adsorption and Dissociation on Various Fe Surfacesa ∆Eads,CO ∆Eads,C ∆Eads,O ∆ETS Erebond Eint,TS Nshared

Fe(110)

Fe(100)

Fe(211)

Fe(710)

Fe(310)

Fe(111)

-44.2 -178.5 -147.8 -8.6 -60.5 51.8 2

-48.9 -190.3 -147.0 -24.2 -71.4 47.2 2

-45.2 -178.1 -143.0 -21.6 -55.2 33.6 1

-41.6 -189.8 -149.5 -26.2 -73.4 47.2 2

-40.7 -188.8 -148.8 -23.9 -71.6 47.7 2

-44.8 -175.9 -141.4 -20.5 -51.3 30.9 1

a All calculated energies are given in units of kcal/mol. When several reaction pathways are possible on a given surface, only the one with the lowest activation energy is indicated. The adsorption energies for chemisorbed CO, ∆Eads,CO, and the effective reaction barrier ∆ETS are given with respect to the isolated surface and the isolated gas phase CO while the atomic chemisorption energies for C (∆Eads,C) and O (∆Eads,O) are given with respect to the isolated surface and the isolated atomic species. A negative sign indicates in this case that the corresponding state is lower in energy than the reference state. Erebond indicates the sum of the atomic adsorption energies for the reaction products calculated in separate unit cells relative to the gas-phase CO molecule. Eint,TS represents the strength of the intramolecular interaction in the transition state. Nshared is the number of shared nearest-neighbor Fe atoms by CO in the transition state.

elongated to 1.74-1.93 Å relative to the gas-phase equilibrium value. In turn, this indicates that along the reaction coordinate the transition state is located at the exit channel, corresponding to a late transition state.25,49 For such reactions, it has been established25,49–51 that there is an apparent linear relationship between the dissociation barrier and the chemisorption energy of the product state. For example, Hammer50 has demonstrated that dissociation energies of NO on flat and stepped Ru(0001) are governed by the rebonding energies, which are a measure of the noninteracting reaction products. A similar conclusion has been reached by Gajdosˇ et al.51 who have determined a linear dependence of the transition-state energies on the sum of the adsorption energies of the isolated atoms in the product state, for the dissociation of NO on a series of close-packed transitionmetal surfaces. In this study, we are interested to determine if a similar relationship can be established for the case of CO dissociation on various Fe surfaces. Following Hammer50 and Gajdosˇ et al.,51 a common way to compare the activation energies of a given reaction on different surfaces is to express the potential energy parameters with respect to a common reference state represented by the total energy of the isolated molecule in the gas phase and the corresponding isolated surface. Accordingly, an apparent activation energy of the transition state, ∆ETS, can be defined with respect to the energy of the isolated surface and isolated CO molecule in the gas phase, based on the relation

∆ETS)Erebond+ Eint,TS

(1)

Erebond ) ∆Eads,C + ∆Eads,O + ∆Ezero

(2)

where

is the rebonding energy for the reaction products and Eint,TS is the interaction between the C and O atoms in the transition state. In eq 2, the rebonding energy is expressed as a function of the individual chemisorption energies of the atomic C and O species, that is, ∆Eads,C and ∆Eads,O, calculated in separated units cells while the term ∆Ezero) EC(gas) + EO(gas) - ECO(gas) ) 265.945 kcal/mol is used to shift the energy zero to the gasphase CO molecule. We note that the rebonding energy as defined in eq 2 is also a measure of the overall reaction energy with respect to molecular CO. A summary of the above introduced quantities for each of the Fe surfaces considered in this study together with the corresponding adsorption energies for the initial undissociated state ∆Eads,CO are presented in Table 5. For surfaces where several reactions are possible, we indicate only the data corresponding to the minimum energy pathways. As indicated before in this section, the adsorption energies have a small range

Figure 9. Variation of the apparent activation energy (ETS) with the rebonding energy (Erebond) of the noninteracting chemisorbed C and O species on the Fe(110), Fe(100), Fe(211), Fe(710), Fe(310), and Fe(111) surfaces. The continuous line is a linear square fit of the calculated values for Fe(110), Fe(710), Fe(100), and Fe(310) surfaces while the dashed line is a constrained linear fit of the data for Fe(211) and Fe(111) surfaces with the same slope as the continuous line.

of variation. However, the most important changes are observed in the adsorption energies of the final states for either C or O species. For various surfaces, we present in Figure 9 the variation of the apparent activation energies ∆ETS with the rebonding energy for the reaction products. As seen in this figure, there is a clear linear dependence on the form ∆ETS )A + B · Erebond, with A ) 74.46 kcal/mol and B ) 1.375 for the group G1 which includes (110), (100), (710), and (310) surfaces. However, the activation energies for the second group G2, which include (211) and (111) surfaces, are not positioned on the same line as the first group of surfaces. This behavior can be related to the different nature of the transition states for the G1 and G2 groups of surfaces. Indeed, as indicated earlier in this section (see also Figure 8), for the G1 group of surfaces there are two Fe atoms shared by the C and O atoms in the transition state while a single Fe atom is shared in the transition state for the group G2. In turn, these characteristics lead to different interaction energies between the C and O species in the transition state. Indeed, as can be seen in Table 5 where the interaction energy Eint,TS between the C and O atoms in the transition state is indicated, we observe that within a given group of surfaces the interaction energies have similar values and the interaction energies are larger for the group with more shared Fe atoms in the transition state. Overall, the results for CO activation energies on various flat and stepped Fe surfaces considered in this study indicate that

10488 J. Phys. Chem. C, Vol. 112, No. 28, 2008 two distinct groups of surfaces can be identified, which are characterized by a distinct number of Fe atoms shared in the transition state. Within a given group, a linear dependence can be established between the apparent activation energy for CO dissociation and the rebonding energy, which is a measure of the chemisorption properties of the noninteracting reaction products. This is particularly the case for the G1 group containing the Fe(110), Fe(100), Fe(710), and Fe(310) surfaces. If we assume the universality of the linear dependence determined for group G1 to group G2, containing Fe(211) and Fe(111) surfaces, then a tentative linear dependence of the form ∆ETS )A′ + B · Erebond (A′ ) 52.24 kcal/mol) can be determined, which is represented as a dotted line in Figure 9. However, a more accurate determination of the dependence of ∆ETS on Erebond for the group G2 of surfaces will require inclusion of other Fe surfaces for which the transition state is characterized by a single shared Fe atom between the C and O atoms. Finally, we remark that similar findings related to the existence of groups of pathways having similar values of Eint,TS have been established before by Hammer50 for the case of NO dissociation on flat and stepped Ru surfaces. 4. Conclusions Plane-wave DFT calculations using the GGA-PBE method have been performed in order to determine the adsorption and diffusion properties of CO on stepped Fe(710) and Fe(310) surfaces. The minimum energy pathways for dissociation of CO on these surfaces have also been calculated and the corresponding results were discussed in connection with those determined on other flat, kinked, or stepped surfaces, namely, Fe(110), Fe(100), Fe(211), and Fe(111). The main conclusions of this study can be summarized as follows: (a) At low coverages, C adsorption takes place preferentially at the hollow 4F sites while the step 3F sites are favored by O atoms on both Fe(710) and Fe(310) surfaces. On Fe(710), the increase in the local C coverage to about 0.5 ML takes place with formation of a c(2 × 2) structure on the terrace hollow sites while a mixed step-terrace occupation at (3F,s1)-(4F,1) sites is preferred in the case of O atoms. By increasing the local coverage, the corresponding adsorption energies generally decrease because of steric repulsions. The adsorption properties for C or O species on the Fe(310) surface are similar to those observed on Fe(710) when bindings at either hollow or step sites are considered. However, because of the limited size of the terrace between successive steps on the Fe(310) surface, formation of a c(2 × 2) pattern at the hollow sites is not possible. (b) On Fe(710) several four-, three-, two-, and one-fold adsorption configurations for CO have been identified among which the most stable corresponds to adsorption at a hollow (4F) site at the top of the step (Eads ) 48.9 kcal/mol) while the most activated was also found at a hollow site but at the bottom of the step (Eads ) 41.6 kcal/mol). The differences in bonding environment for different rows of surface atoms were found to lead to a distribution in the binding energies for CO. As a result, both the location of the specific hollow sites relative to the step edge as well as the relative molecular orientation within a given hollow site were found to influence the adsorption properties. By increasing the local coverage to θ ) 0.5 ML, the most stable configuration corresponds to a diagonal occupation of the hollow terrace sites with a single shared Fe atom, in a pattern similar to the c(2 × 2) overlayer on the Fe(100) surface. The adsorption properties on the Fe(310) surface follow the same trends as those observed on Fe(710) with the most stable configuration corresponding to adsorption at a hollow site with CO pointing to the

Sorescu top of the step while the most activated corresponds to adsorption at the bottom of the step with CO pointing toward the step. (c) Minimum energy pathways for CO diffusion on Fe(710) surfaces have been mapped, and the largest diffusion barriers were found to vary in the 12.7-14.1 kcal/mol range. The most activated state (4F,3,-1) at the bottom of the step was found to be accessible from either of the two most stable adsorption configurations (4F,1,1) and (4F,3,1) by overcoming diffusion barriers of 13.2 and 6.5 kcal/mol, respectively. On Fe(310) direct interconversion between the most stable (4F,1) configuration and the most activated (4F,-1) state can be achieved by overcoming a barrier of 9.3 kcal/mol. (d) On Fe(710) and Fe(310) surfaces, the most efficient dissociation pathways were determined for the case when the CO molecule is adsorbed initially at a hollow site near the bottom of the step with the O end oriented toward the step. Dissociation from such states can take place with barriers as low as 15.4 and 16.7 kcal/mol for Fe(710) and Fe(310), respectively. Upon dissociation, the resulted O atom adsorbs on the step plane at a 3F site while the C atom remains adsorbed in the original hollow site on the lower terrace, at the bottom of the step. (e) The study of the adsorption properties of CO at low coverages has been further extended to other Fe(211) and Fe(111) surfaces, where data of interest for the current work were not available. On the Fe(211) surface, the most stable adsorption configuration corresponds to a tilted state with a binding energy of 45.2 kcal/mol. From this state, CO dissociates with an activation energy of 23.6 kcal/mol with formation of an adsorbed C atom at a bridge site and of an O atom at a threefold site. On Fe(111), we revisited the adsorption configurations for CO and determined that the two most stable adsorption configurations correspond to a shallow-bridge (Eads ) 48.2 kcal/mol) and bridge-like (Eads ) 44.8 kcal/mol) sites. The activation energies for CO dissociation from these sites have values of 27.8 and 24.4 kcal/mol, and the corresponding dissociation pathways involve similar transition states. (f) For the ensemble of Fe(110), Fe(100), Fe(211), Fe(710), Fe(310), and Fe(111) surfaces at low coverages, the CO dissociation was found to proceed through a late transition state with extensive elongation of the CO bond in the transition state. Relative to gas-phase CO, the dissociation reactions were found to be exothermic on all of these surfaces. The highest activation energy for CO dissociation is found on Fe(110), and the smallest activations were seen on stepped Fe(710) and Fe(310) surfaces. The activation properties of CO on flat and stepped Fe surfaces were found to be primarily influenced by the rebonding energy of the noninteracting reaction products while the repulsion interactions in the transition states are correlated with the number of Fe atoms shared by C and O atoms in this state. On the basis of these characteristics, two distinct groups of surfaces have been identified with two (for Fe(110), Fe(100), Fe(710), and Fe(310)) and, respectively, with one (for Fe(211) and Fe(111)) Fe atom shared in the transition state. A linear dependence between the apparent activation energy for CO dissociation and the rebonding energy has been established within the Fe(110), Fe(100), Fe(710), and Fe(310) groups of surfaces. Acknowledgment. We gratefully acknowledge the computational resources provided by Pittsburgh Supercomputer Center and ARL MSRC supercomputer center. Disclaimer. Reference in this work to any specific commercial product is to facilitate understanding and does not necessarily imply endorsement by the United States Department of Energy.

CO on Kinked Fe(710) and Fe(310) Surfaces Supporting Information Available. List of vibrational frequencies obtained for the atomic (C and O) and molecular (CO) species adsorbed on Fe(100), Fe(710), and Fe(310) surfaces as determined within frozen phonon approximation at the PAW-PBE level. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Handbook of Heterogeneous Catalysis; Ertl, G., Kno¨zinger, H., Weltkamp, J., Eds.; VCH: Weinheim, Germany,1997. (2) Corrosion of Stainless Steels, 2nd ed.; Sedriks, A. J., Ed.; WileyInterscience: New York, 1996. (3) (a) Fischer, F.; Tropsch, H. Brennst. Chem. 1923, 4, 276. (b) Anderson, E. B. The Fischer-Tropsch Synthesis; Academic Press: New York, 1984. (4) Fischer-Tropsch Synthesis, Catalysts and Catalysis (Studies in Surface Science and Catalysis); Davis, B. H., Occelli, M. L., Eds.; Elsevier Science: Amsterdam, 2006; Vol. 163. (5) (a) Bian, G.; Oonuki, A.; Koizumi, N.; Nomoto, H.; Yamada, M. J. Mol. Catal. A 2002, 186, 203. (b) Luo, M.; Davis, B. Fuel Proc. Technol. 2003, 83, 49. (c) Ngantsoue-Hoc, W.; Zhang, Y.; O’Brien, R. J.; Luo, M.; Davis, B. H. Appl. Catal., A 2002, 236, 77. (6) Bernasek, S. L. Annu. ReV. Phys. Chem. 1993, 44, 265. (7) (a) Moon, D. W.; Dwyer, D. J.; Bernasek, S. L. Surf. Sci. 1985, 163, 215. (b) Moon, D. W.; Bernasek, S. L.; Lu, J. P.; Gland, J. L.; Dwyer, D. L. Surf. Sci. 1987, 184, 90. (c) Moon, D. W.; Cameron, S.; Zaera, F.; Eberhardt, W.; Carr, R.; Bernasek, S. L.; Gland, J. L.; Dwyer, D. J. Surf. Sci. 1987, 180, L123. (d) Lu, J.-P.; Albert, M. R.; Bernasek, S. L. Surf. Sci. 1989, 217, 55. (e) Moon, D. W.; Bernasek, S. L.; Dwyer, D. J.; Gland, J. L. J. Am. Chem. Soc. 1985, 107–4363. (f) Lu, J.-P.; Albert, M. R.; Bernasek, S. L. J. Phys. Chem. 1990, 94, 6028. (8) (a) Madix, R. J.; Benziger, J. Surf. Sci. 1980, 94, 119. (b) Benziger, J. B.; Madix, R. J. Surf. Sci. 1982, 115, 279. (c) Burke, M. I.; Madix, R. J. Surf. Sci. 1990, 237, 20. (9) Nayak, S. K.; Nooijen, M.; Bernasek, S. L.; Blaha, P. J. Phys. Chem. B 2001, 105, 164. (10) Sorescu, D. C.; Thompson, D. L.; Hurley, M. M.; Chabalowski, C. F. Phys. ReV. B 2002, 66, 035416. (11) Bromfiled, T. C.; Ferre´, D. C.; Niemantsverdriet, J. W. ChemPhysChem. 2005, 6, 254. (12) Jiang, D. E.; Carter, E. A. Surf. Sci. 2004, 579, 167. (13) Stibor, A.; Kresse, G.; Eichler, A.; Hafner, J. Surf. Sci. 2002, 507, 99. (14) Chen, Y.-H.; Cao, D.-B.; Jun, Y.; Li, Y.-W.; Wang, J.; Jiao, H. Chem. Phys. Lett. 2004, 400, 35. (15) Eder, M.; Terakura, K.; Hafner, J. Phys. ReV. B 2001, 64, 115426. (16) Sorescu, D. C. Phys. ReV. B 2006, 73, 155420. (17) Jiang, D. E.; Carter, E. A. Phys. ReV. 2005, 71, 045402. (18) Błon´ski, P.; Kiejna, A.; Hafner, J. Surf. Sci. 2005, 590, 88. (19) (a) Lo, J. M. H.; Ziegler, T. J. Phys. Chem. C 2007, 111, 11012. (b) Lo, J. M. H.; Ziegler, T. J. Phys. Chem. C 2007, 111, 13149. (20) Błon´ski, P.; Kiejna, A. Surf. Sci. 2007, 601, 123. (21) Schmiedl, R.; Nichtl-Pecher, W.; Hammer, L.; Heinz, K.; Mu˝ller, K. Surf. Sci. 1995, 324, 289. (22) Jenkins, S. J. Surf. Sci. 2006, 600, 1431. (23) (a) Zubkov, T.; Morgan, G. A.; Yates, J. T., Jr.; Ku˝hlert, O.; Lisowski, M.; Schillinger, R.; Fick, D.; Ja¨nsch, H. J. Surf. Sci. 2003, 526, 57. (b) Zubkov, T.; Morgna, G. A.; Yates, J. T., Jr Chem. Phys. Lett. 2002, 362, 2002.

J. Phys. Chem. C, Vol. 112, No. 28, 2008 10489 (24) Gong, X.-Q.; Raval, R.; Hu, P. Surf. Sci. 2004, 562, 247. (25) Ge, Q.; Neurock, M. J. Phys. Chem. B 2006, 110, 15368. (26) Sorescu, D. C. Catal. Today 2005, 105, 44. (27) Jenkins, S. J.; Pratt, S. J. Surf. Sci. Rep. 2007, 62, 373. (28) (a) Kresse, G.; Furthmu¨ller, J. Comput. Mater. Sci. 1996, 6, 15. (b) Kresse, G.; Furthmu¨ller, J. Phys. ReV. B 1996, 54, 11169. (29) Blo¨chl, P. E. Phys. ReV. B 1994, 50, 17953. (30) Kresse, G.; Joubert, D. Phys. ReV. B 1999, 59, 1758. (31) Perdew, P.; Burke, K.; Ernzerhof, M. Phys. ReV. Lett. 1996, 77, 3865. (32) Vosko, S. H.; Wilk, L.; Nusair, M. Can. J. Phys. 1980, 58, 1200. (33) Monkhorst, H. J.; Pack, J. D. Phys. ReV. B 1976, 13, 5188. (34) Methfessel, M.; Paxton, A. T. Phys. ReV. B 1989, 40, 3616. (35) Kresse, G.; Hafner, J. Phys. ReV. B 1993, 47, R558. (36) Jo´nsson,H. ; Mills, G.; Jacobsen, K. W. In Classical and Quantum Dynamics in Condensed Phase Simulations; Berne, B. J., Ciccotti, G., Coker, D. F., Eds.; World Scientific: Singapore, 1998; p 385. (37) Henkelman, G.; Uberuaga, B. P.; Jo´nsson, H. J. Chem. Phys. 2000, 113, 9901. (38) Kittel, C. Introduction to Solid State Physics; Wiley: New York, 1996. (39) Geng, W. T.; Kim, M.; Freeman, A. J. Phys. ReV. B 2001, 63, 245401. (40) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, Jr. J. A.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03, Revision B.05; Gaussian, Inc.: Pittsburgh, PA, 2003. (41) CRC Handbook of Chemistry and Physics, 81st ed.; Lide, D. R. , Ed.;CRC Press: Boca Raton, FL, 2000. (42) Perdew, J. P.; Chevary, J. A.; Vosko, S. H.; Jackson, K. A.; Pedersen, M. R.; Singh, D. J.; Fiolhais, C. Phys. ReV. B 1992, 46, 6671. (43) Pratt, S. J.; Jenkins, S. J.; King, D. A. Surf. Sci. 2005, 585, L159. (44) Erley, W. J. Vac. Sci. Technol. 1981, 18, 472. (45) Benziger, J.; Madix, R. J. Surf. Sci. 1980, 94, 119. (46) Seip, U.; Tsai, M.-C.; Christmann, K.; Ku¨ppers, J. K.; Ertl, G. Surf. Sci. 1984, 139, 29. (47) Bartosch, C. E.; Whitman, L. J.; Ho, W. J. Chem. Phys. 1986, 85, 1052. (48) Whitman, L. J.; Gurney, B. A.; Richter, L. J.; Vilarrubia, J. S.; Ho, W. J. Vac. Sci. Technol., A 1987, 5, 538. (49) Liu, Z. P.; Ju, P. J. Chem. Phys. 2001, 114, 8244. (50) Hammer, B. Surf. Sci. 2000, 459, 323. (51) Gajdosˇ, M.; Hafner, J.; Eichler, A. J. Phys.: Condens. Matter 2006, 18, 41.

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