Adsorption and Decomposition of CO on Stepped Fe (310) Surfaces

3692

J. Phys. Chem. C 2008, 112, 3692-3700

Adsorption and Decomposition of CO on Stepped Fe(310) Surfaces John M. H. Lo and Tom Ziegler* Department of Chemistry, UniVersity of Calgary, Calgary, Alberta, T2N 1N4 Canada ReceiVed: NoVember 19, 2007; In Final Form: December 19, 2007

First-principle DFT calculations for the chemisorption and reaction of CO on the stepped Fe(310) surface were performed. It is found that among the many possible adsorption sites CO is bound preferably to the hollow sites of the (100) terraces in a tilted geometry analogous to the adsorption of CO on the regular Fe(100) surface. The computed binding energy of 42.7 kcal/mol is similar to that for the CO adsorption on a more organized Fe(100) surface. An intriguing positive correlation of the CO adsorption energy with the surface coverage is noticed; the CO binding energy is increased to 44.2 kcal/mol when the surface coverage reaches 0.500 ML. Two CO decomposition pathways on Fe(310) have been explored. These processes do not show any significant contributions to the overall rate of CO dissociation at 0.250 ML because of their low exothermicity. Nevertheless, they become very prominent at 0.500 ML; it is estimated that the presence of 30% (by surface units) Fe(310) steps on the Fe(100) surface causes a 20% increase in the decomposition of adsorbed CO at 473 K.

1. Introduction The interaction of CO with transition-metal surfaces plays a fundamental role in many catalytic processes of industrial importance such as car exhaust catalysis and Fischer-Tropsch synthesis, and therefore has been the subject of numerous studies in the past few decades. The adsorption geometry and CO binding enthalpy have been reported for most of the transitionmetal elements1-4 and some bimetallic alloys.5-7 Iron is among the most explored surfaces because the CO activation on Fe is, on one hand, thought to be responsible for the embrittlement of steels, and on the other hand, is the key step that provides the reactive surface carbide species for hydrogenation reactions to form organic compounds in the Fischer-Tropsch synthesis. The structure of a CO monolayer on low-index Fe surfaces such as (100), (110), and (111) have been characterized experimentally using various techniques such as high-resolution electron energy loss spectroscopy (HREELS), X-ray photoelectron spectroscopy (XPS), temperature-programmed desorption (TDS), and low-energy electron diffraction (LEED).8-14 Although CO molecules prefer the upright configuration at the on-top positions on the compact (110) surface,9 they favor the chemisorption at the hollow sites on the more open (100) and (111) surfaces where high coordination can be achieved.12,13 In the latter cases, CO molecules adopt the tilted geometry in which both C and O are bonded to the surface Fe atoms. The additional surface-adsorbate interactions significantly weaken the CO bond strength in the precursor state, thereby reducing the dissociation energy of CO on the Fe(100) and (111) surfaces compared to Fe(110). This trend has been verified by the recent DFT calculations of Bromfield, Ferre´, and Niemantsverdriet,15 and Jiang and Carter,16 in which the activation energies for CO decomposition are 25.6 and 35.1 kcal/mol for the Fe(100) and Fe(110) surfaces, respectively. No theoretical reaction barrier is available for the CO dissociation on Fe(111), but a value of * Corresponding author. E-mail: [email protected].

20.0 kcal/mol has been estimated from the TDS measurement,17 which follows the predicted trend of reactivity: (111) > (100) > (110). The magnitude of the activation barrier for CO dissociation is a vital factor that influences the overall CO hydrogenation activity in the Fe-based Fischer-Tropsch synthesis because most of the representative kinetic expressions illustrate a strong dependence on the partial pressure of CO.18 Consistent evidence have been provided by the theoretical studies of Sorescu,19 Lo and Ziegler,20 and Gokhale and Mavrikakis,21 which show that the decomposition of CO is the rate-determining step for the process of methanation from synthesis gas. An efficient method of accelerating the CO decomposition is the use of corrugated or kinked surfaces. It was found from the TDS study of Ferrer et al.22 that a sputtered Fe(110) surface promotes the CO dissociation by 1.6 times compared to an annealed surface at 300 K. The phenomenon of lowering the activation barriers of small molecules by surface defects and steps has been noticed for the surfaces such as Ni{n(100) × (110)-(110)},23 Ru(109),24 Rh(211),25 Au(211),26 Pt(211),27 Pd(311),28 and Co(11 2h 4).29 For instance, the rate of methane dissociation on Pd(679), which is composed of 13% steps by area, is an order of magnitude faster than the process occurring on the flat Pd(111) surface.30 Presented here is a theoretical study of CO dissociation on the stepped Fe(310) surface. There are two main objectives in the following discussion. First, the adsorption sites on Fe(310) for CO are identified and characterized, and their selectivity is discussed from the electronic perspective. Second, the activation of CO on the stepped Fe(310) surface is explored, and the resulting dissociation channels and associated barriers are compared with those for the flat Fe(100) and Fe(110) counterparts. 2. Theoretical Method All first-principle calculations were performed in the framework of density functional theory in the generalized gradient approximation (GGA) as implemented in the Vienna ab initio

10.1021/jp711018y CCC: $40.75 © 2008 American Chemical Society Published on Web 02/16/2008

Adsorption and Decomposition of CO

J. Phys. Chem. C, Vol. 112, No. 10, 2008 3693

TABLE 1: Calculated Multilayer Relaxation in Interlayer Spacings dij and Registry Shifts aij at the Fe(310) Surfacea

a

model

d12

d23

d34

a12

a23

this work SJM45 SXFHW * 46 GKF47 SXFHW ** 46

-15.7 -16.1 ( 3.3 -17.7 ( 3.1 -13.3 -14.9

+9.2 +12.6 ( 3.3 +12.1 ( 1.8 +2.2 +8.0

-2.0 -4.0 ( 4.4 -5.5 ( 2.0 0.0 -1.4

+5.1 +7.2 ( 2.8 +6.6 ( 3.4 +1.7 +4.9

-0.3 +1.6 ( 2.8 -1.1 ( 3.1 -0.6 +0.4

All values are reported in % (note:

*

LEED experiment;

**

+2.8 ( 3.1 +1.4

DFT calculations).

Simulation Package (VASP).31-33 The Kohn-Sham equations describing the periodic Fe(310) system were solved iteratively with the electron-ion interaction represented by the nonlocal Vanderbilt-type ultra-soft pseudopotentials (usPPs),34 which takes into account the core-valence polarization of Fe.35 The resulting one-electron pseudo-orbitals were expanded using the plane wave basis sets with an energy cutoff of 400 eV. The energy contribution from exchange correlation was evaluated by the Perdew-Wang (PW91) functional within GGA.36 Spinpolarization was applied in all calculations to ensure the accurate description of the ferromagnetic properties of Fe bulk. For a better convergence of the electronic wave functions, a Methfessel-Paxton smearing function37 of 0.1 eV was utilized. The stepped Fe(310) surface was modeled by a periodic slab consisting of eight layers of Fe atoms in a p(2 × 2) supercell structure possessing four atoms per layer. The Brillouin zone was sampled by a 5 × 5 × 1 k-point mesh generated by the Monkhorst-Pack (MP) scheme.38 This k-point sampling yielded the PW91 equilibrium lattice constant of 2.85 Å, which differs slightly from the experimental value of 2.8665 Å,39 while the deduced magnetic moment of 2.27 µ0 is in good agreement with the experiment (2.22 µ0).40 Adsorption of CO was allowed on only one side of the slab, and a 10 Å vacuum layer was inserted between two repeating slabs in order to minimize the dipole-dipole interaction between supercells due to the CO adsorption. During the geometry optimization, the coordinates of the adsorbed CO molecule and the topmost four layers of Fe atoms were fully relaxed to account for the surface reconstruction. The ion optimization was performed using the Quasi-Newton RMM-DIIS algorithm41 with the convergence criterion of 0.01 eV/Å. To evaluate the adsorption energy of CO on Fe(310), the following equation was used

Eads ) Eslab + ECO - Eslab+adsorbate

a34 +1.1

(1)

in which ECO is the gas-phase energy of CO assuming that CO is encapsulated in a cubic unit cell of the dimension 10 × 10 × 10 Å3. The exothermic adsorption is illustrated by the positive value of Eads. The equilibrium geometries of adsorbed CO were verified by the harmonic vibrational frequency analysis. The normal modes were determined by the diagonalization of the Hessian matrix obtained via the finite difference method using the atomic displacement of (0.02 Å for each Cartesian coordinate of the adsorbate molecule. All surface Fe atoms were frozen in the frequency calculations. Utilizing these vibrational frequencies, the zero-point energy (ZPE) terms for different configurations were computed, and their adsorption energies were corrected accordingly. The climbing-image nudged elastic band (ciNEB) method of Jo´nsson and co-workers42-44 was used to map the minimum energy paths (MEPs) for the CO dissociation on Fe(310). In this approach, 8-10 intermediates (images) were generated by linear interpolation between the reactant (initial image) and product (final image) states, which were then simultaneously optimized along the MEP with the constraint that relaxation

was allowed solely on the hyperplanes orthogonal to the MEP. An advantage of the ciNEB method is that the image of highest energy always corresponds to the transition state of the MEP. A force tolerance of 0.03 eV/Å was applied in all ciNEB calculations. 3. Results and Discussion 3.1. Structure of Fe(310) Surface. A clean Fe(310) surface can be generated by cutting an ultrapure Fe sample prepared by strain-annealing, with the surface orientation precisely monitored by Laue photographs, followed by the prolonged high-temperature Ar+ bombardment to remove surface impurities such as sulfur and carbon.45 The Fe(310) surface can be described by a parallelogram mesh with unit vectors of lengths 2.87 and 4.75 Å defined along the (100) and (311) axes, respectively, and an interlayer spacing of 0.906 Å.45 Using an optimized bulk lattice constant of 2.85 Å, calculated unit vectors of lengths 2.86 and 4.74 Å and an interlayer distance of 0.90 Å were obtained. Because of the low packing efficiency (0.3725),45 the Fe(310) surface is subjected to a substantial anisotropic multilayer relaxation. In the LEED intensity analysis of Sokolov, Jona, and Marcus (SJM), it was observed that the top three layers undergo the perpendicular relaxation (i.e., along the (310) direction) in the contracted (16%), expanded (13%), and contracted (4%) pattern.45 The recent study of Wee et al.46 (SXFHW) reproduced the observed relaxation pattern for the top three layers of Fe(310) in spite of the fact that a larger contraction was suggested for d12 (18%) and d34 (6%). The FLAPW-GGA calculations of Geng et al.47 (GKF) yielded the same conclusion that the topmost layer of Fe(310) is contracted by 14%, which agrees well with the LEED experiment, although they underestimated the expansion of d23, the interlayer distance between the second and third surface layers. The calculated interlayer spacings in the present work are summarized in Table 1. As can be seen, the determined surface relaxations for the top three layers are consistent with the results of SJM within the experimental uncertainty, but are slightly too small compared to those obtained by SXFHW. The current DFT calculations predict the correct relaxation sequence of - + for the top three layers, and the results exhibit a superior accuracy compared to those of GKF and SXFHW. In the latter two cases, the Fe slabs employed were much larger than the 8-layer Fe slab considered here; GKF adopted a slab model made up of 15 layers of Fe atoms while SXFHW employed a 21-layer Fe(310) slab model. Both calculations only fixed the center layer and allowed the full relaxation for the remaining layers, while in this work only the top four layers were allowed to move in the geometry optimization. In addition to the interlayer relaxation, the present study also considered the parallel relaxation, or registry shift of the Fe(310) surface. According to the definition of SKM,45 the translational relaxations of various layers with respect to the bulk positions were computed and shown in Table 1. Opposite to the interlayer spacings, the registry shifts demonstrate the +

3694 J. Phys. Chem. C, Vol. 112, No. 10, 2008

Lo and Ziegler

TABLE 2: Calculated Magnetic Moments (in µB) in Each Layer of Fe(310) model this work GKF47

Fe(1) Fe(2) Fe(3) Fe(4) Fe(5) Fe(6) Fe(7) Fe(8) 2.89 2.85

2.72 2.65

2.36 2.33

2.50 2.43

2.47 2.34

2.38 2.23

2.66 2.27

2.93 2.22

- + pattern for a12, a23, and a34. Like the interlayer spacings, the computed registry shifts are in good agreement with the experiments. It is interesting that although experiments observed the positive shifts for a12 and a34 the results for a23 were not conclusive. SJM noticed a positive shift of 1.6% for a23, whereas SXFHW detected a negative shift of 1.1%, and the standard deviations in both cases were large. This ambiguity also occurs in the calculations of GKF and SXFHW; the former group obtained ∆a23 ) -0.6%, which disagrees with the finding of SJM from the LEED experiments (1.6%). Alternatively, the DFT calculations of SXFHW predicted ∆a23 ) +0.4%, which is opposite to the results of their own LEED measurements (-1.1%). Geng, Kim, and Freeman have associated the discrepancy of calculated interlayer distances with the errors in the registry shifts.47 Wee et al. also discussed the accuracy of DFT calculations on the structure of Fe(310),46 and they ascribed the possible errors to the use of finite slab thickness and the nonvanishing residual forces on the Fe ion cores. For the present study, the good consistency between the computed and measured ∆dij and ∆aij may be the result of the coincident cancellation of errors. It has been noticed in the calculations of GKF that the multilayer relaxation of Fe(310) influences up to the seventh layer of Fe atoms because of the small interlayer distance (>1 Å). This work considered only an eight-layer Fe slab, and just four layers were included in the relaxation calculations; larger discrepancies in ∆dij and ∆aij compared to those in the works of GKF and SXFHW were therefore anticipated. Nevertheless, these errors were compensated by the higher energy cutoff of plane wave basis sets than the ones used by GKF (177 eV) and SXFHW (340 eV), resulting in fairly good values of ∆dij and ∆aij. It is noteworthy that the computed ∆d45 (+4.9%; not included in Table 1) is far beyond the experimental value including the uncertainty46 (+1.1 ( 2.2%). This inconsistency is undoubtedly attributed to the frozen fifth layer of Fe atoms in the geometry optimization, which might create an upthrust on the fourth layer and lead to a large d45. The open Fe(310) surface is subjected to a magnetic moment enhancement because of the reduced coordination, and thus the localization of d bands near the surface.48 GKF have computed the local magnetic moments for each layer of Fe atoms in the Fe(310) slab;47 they observed the magnetic moment of 2.85 µB, which lies between the corresponding values for Fe(100)49 (2.97 µB) and Fe(111)50 (2.73 µB). Table 2 illustrates the magnetic moments obtained from the present calculations and the data from the work of GKF. The computed values are generally overestimated, but the largest difference for the top four layers is merely 0.07 µB. For the frozen layers, that is, the fifth to eighth layers, however, the discrepancy is remarkable. For instance, the magnetic moment for the seventh layer (Fe(7)) is overshot by 0.4 µB. These observations are not unexpected when considering the fact that the seventh and eighth layers, which constitute the “bottom surface” of an eight-layer Fe-slab, are susceptible to magnetic moment enhancement similar to those of the first and second layers. In the calculations of GKF where a 15-layer Fe slab was used, Fe(7) and Fe(8) in fact form the “core” of the slab, thereby possessing magnetic moments (∼2.2 µB) similar to that of bulk Fe.47

Figure 1. Illustrations of the stepped Fe(310) surface. The p(2 × 2) supercell is represented by the red parallelograms.

Figure 2. Adsorption sites on the stepped Fe(310) surface.

3.2. CO Adsorption on Fe(310) (0.250 ML). A perfect Fe(310) surface can be described as the replica of the units containing two-atom-wide (100) terraces separated by an oneatom-high (110) step; that is, Fe{ 2(100) + 1(110)}. Figure 1 shows the structures of the Fe(310) surface and the supercell that was employed in this work. Because of the different surface topologies of the (100) and (110) planes, a large number of sites for CO adsorption could be expected for Fe(310). Besides the on-top, bridge, 3-fold, and 4-fold hollow sites that are inherited from the Fe(100) and (110) surfaces, several additional sites that are unique to Fe(310) are identified in the step region. For instance, a new asymmetric 2-fold site located at the junction of Fe(100) and Fe(110) planes is found, while two types of 3-fold sites differing by the opposite orientations of adsorbed CO are noticed. The adsorption sites, and their nomenclatures that have been investigated in this work are depicted in Figure 2. It has been shown by infrared spectroscopy,14 and later by theoretical calculations,15,51 that CO molecules adopt a tilted geometry at the 4-fold sites of clean Fe(100), gaining an extra stability of 12 kcal/mol relative to the upright configuration. Therefore, three different tilted configurations were explored in the present work, in addition to the conventional upright configuration of CO (denoted by 4fv). The three tilted configurations correspond to CO tilted over the edge (4f), CO tilted across the terrace (4f2), and CO leaned against the (110) step (4f3), respectively. Their structures are illustrated in Figure 3. Because there is no available experimental data concerning the adsorbed CO monolayer on Fe(310), the present work only considered two simple situations: 0.250 and 0.500 ML surface coverage, corresponding to one and two CO molecules on a p(2 × 2) supercell, respectively. The computed binding energies and CdO bond distances for CO adsorbed at various sites of Fe(310) are listed in Table 3.



Figure 3. Adsorption modes of CO at hollow sites of the Fe(310) surface. Also included are 3f1 and lb configurations.

Figure 4. Adsorption modes of CO at hollow sites of the Fe(310) surface at 0.500 ML

TABLE 3: Adsorption Geometries and ZPE-Corrected Energies of CO on Fe(310) at 0.250 ML

bridge site on the step (as shown in Figure 3). The optimized lb conformation contains an asymmetric, nearly coplanar Fe2CO unit where the two Fe-C bonds are not equidistant. The Fe-C bonds to the bottom and top edges are 1.824 and 2.169 Å respectively. The resulting CdO bond is short (1.200 Å) and tilted upward by 22.5° from the [110] direction. These observations suggest that the adsorption of CO at the long-bridge site, as in the case of the 3-fold sites, is mainly due to the interaction of the filled 5σ-MO of CO and the empty d-band of a bottomedge Fe atom, while the back-donation involving the vacant CO 2π-MO’s only plays a minor role. The vibrational frequency calculations have been performed to identify the minimum configurations on the potential energy hyper-surface of adsorbed CO on Fe(310). Among the various structures, only two true local minima are found that correspond to the 4f and 4f2 tilted geometries (Figure 3) of CO at the hollow sites. The CO stretching frequencies of the 4f and 4f2 configurations are 1147 and 1189 cm-1, respectively. Both values show good agreement with the HREELS data of 1210 cm-1 deduced by Moon et al.12 for a low-coverage CO monolayer of similar geometry on Fe(100). The computed frequencies demonstrate a negative correlation with the bond distances and binding energies; a higher stretching frequency is associated with a shorter CdO bond and weaker adsorption enthalpy. This correlation infers a more pronounced backdonation effect on the 4f configuration that results in an enhanced surface-CO interaction but a weaker double-bond character of the CdO bond. 3.3. CO Adsorption on Fe(310) (0.500 ML). For the surface coverage of 0.50 ML, a p(2 × 1) adsorption pattern was assumed in all calculations. This structure consists of CO molecules occupying alternate adsorption sites along either the (100) terraces or (110) steps; however, two ordered configurations across the stepped Fe(310) are possible. One configuration forms rows of CO in the projected [015] direction, with each separated by 2 × 2.85 Å from the neighboring rows; meanwhile, the other configuration contains the adsorbed CO arranged in a zigzag mode along the [010] axis (Figure 4). Because of the fact that the spatial distance between two corresponding CO molecules on adjacent rows in [001] orientation (i.e., the dimension of the orthorhombic unit cell in Figure 1) remains the same in both configurations, they should be of similar stability. Therefore, only the latter surface configuration was employed in this study. The increase in surface coverage does not significantly affect the geometry of CO molecule in various adsorption configurations. As shown in Tables 3 and 4, excluding the 4f3 and sb configurations whose CO bonds are stretched by about 0.004 Å, the adsorbed CO molecules are generally compressed by 0.003 Å relative to those at 0.250 ML coverage. These changes

site

dC-O (Å)

Ead (kcal/mol)

1f 2f 2fe 3f1 3f2 4f 4f2 4f3 4fv lb sb

1.172 1.198 1.198 1.201 1.220 1.330 1.313 1.329 1.264 1.200 1.223

30.2 34.8 31.8 36.7 29.4 42.7 37.6 35.0 27.4 36.0 31.1

At lower surface coverage, the most stable sites on Fe(310) are the 4-fold sites on the (100) terrace at which CO is simultaneously bound to four Fe atoms. This site preference has been observed in the case of Fe(100) and is attributed to the effective overlap of the surface d-band and the 2π-MO of CO at the hollow site that leads to a large extent of backdonation. All three tilted configurations (i.e., 4f, 4f2, and 4f3) are energetically more stable than the vertical counterpart (4fv) in which the 4f configuration is most favorable and possesses the heat of adsorption of 42.7 kcal/mol, which is similar to that for CO adsorption on Fe(100) (46.7 kcal/mol).20 In this structure, CO is tilted from the surface normal by 55.3°; the value is comparable to the reported angle of 55 ( 2° measured by XPD.52 The other two tilted conformations are slightly less stable compared to the 4f mode, with the respective binding energies of 40.6 (for 4f2) and 35.0 kcal/mol (for 4f3). The strong adsorption enthalpies of these tilted conformations are associated with elongated CdO bonds. The CdO bond length of 1.330 Å for the 4f configuration is substantially longer than that for the 4fv (1.264 Å) and 1f (1.172 Å) configurations and free CO molecule (1.145 Å), suggesting a significant back-donation of the surface electron density to the antibonding 2π-MO’s of CO in a tilted geometry and thus a weaker CdO bond. The 3f1 and lb configurations are comparable in stability to the 4f2 configuration. For the 3f1 configuration, CO is located asymmetrically above a 3-fold site on the (110) step, and deviates from the centroid by 0.168 Å toward the Fe atom on the (100) bottom edge, forming an tilted angle of 12.4° from the (100) surface normal. The CdO bond in this configuration is only 1.201 Å and is much shorter than the 4f counterpart. The compressed CO bond indicates that the back-donation effect that stretches the CdO bond at hollow sites is not present in this case. This configuration, therefore, can be considered as equivalent to the 1ft configuration (1-fold terrace) where CO is σ-bonded to an Fe atom on the (100) terrace. The lb configuration is structurally related to the 3f1 configuration in a way that the CO molecule is shifted sideways to a neighboring long-


Lo and Ziegler

TABLE 4: Adsorption Geometries and ZPE-Corrected Energies of CO on Fe(310) at 0.500 ML site

dC-O (Å)

Eavg ad (kcal/mol)

E2nd ad (kcal/mol)

1f 2f 2fe 3f1 3f2 4f 4f2 4f3 4fv lb sb

1.170 1.197 1.195 1.198 1.217 1.329 1.310 1.333 1.261 1.197 1.226

29.8 34.4 31.7 36.8 30.6 44.2 38.2 36.2 26.7 36.4 31.9

31.6 34.9 32.7 36.8 29.2 45.6 38.8 37.2 25.8 36.7 31.2

are an order of magnitude smaller than the experimental error limit of 0.02 Å affordable in common characterization techniques such as near edge X-ray absorption fine structure (NEXAFS) spectroscopy;14 therefore, the influence of surface coverage on CO bond distances is considered negligible. The data reported in Tables 3 and 4 also reveal that the observed trend of relative stability for different adsorption configurations at 0.250 ML prevails at 0.500 ML. The 4f configuration at hollow sites is still the most energetically stable configuration for CO, possessing the adsorption enthalpy of 44.2 kcal/mol, which is slightly larger than the corresponding value at lower coverage. The calculated CO bond length remains essentially unchanged (1.329 vs 1.330 Å), while the tilted angle is moderately reduced (54.6° vs 55.3° ). The vibrational frequency analysis yields the CdO stretching frequency of 1132 cm-1 for this adsorption mode. The lower frequency, together with a larger CO binding energy, suggest that the 2π-MO’s of CO are more populated at 0.500 ML, leading to a weaker Cd O bonding character. The normal-mode calculations predict another stable adsorption mode corresponding to the 4f2 configuration at 0.500 ML. The CO molecule in this configuration is slightly contracted (-0.003 Å) and possesses a higher CdO stretching frequency (1209 cm-1), both of which infer a lesser extent of donation of surface electrons to the 2π antibonding orbitals of CO in this configuration, although surprisingly its adsorption energy is found to be increased by 0.6 kcal/mol. As in the case of lower coverage, only two true minima (4f and 4f2 configurations) are located for CO adsorption at 0.500 ML surface concentration, while all of the other configurations are either transition states or second-rank saddle points in the potential energy surface. The dependence of adsorption energies upon the surface coverage is intriguing; it is noticed that in general CO is more strongly bound to the Fe(310) surface when the surface coverage increases. For the adsorption of CO on flat surfaces such as Fe(100), raising the surface coverage is accompanied by a decrease in binding energy regardless of the adsorption sites. For example, the adsorption energy of CO at hollow sites on Fe(100) drops from 45.9 to 44.3 kcal/mol when the surface concentration is increased from 0.250 to 0.500 ML, and further increasing the surface coverage to 1.00 ML causes an additional reduction of 10.4 kcal/mol in the adsorption energy.15 The negative correlation can be ascribed to both electronic and spatial factors. On one hand, for the surface coverage beyond 0.250 ML, neighboring CO molecules compete for the electron density from the shared Fe atoms, which, as a consequence, weakens the resulting surface-CO interaction. On the other hand, the electrostatic repulsion between coadsorbed CO molecules is enhanced at high coverage because their intermolecular distance falls below 4 Å. However, both factors are insignificant in the

case of the Fe(310) surface. Because CO molecules are adsorbed on alternate sites on a terrace or step at 0.500 ML coverage, there is no direct sharing of surface Fe atoms between two adjacent CO, and thus the electron donation is not greatly affected relative to the situation at 0.250 ML coverage. Moreover, the shortest separation between coadsorbed CO molecules is about 4.7 Å, which is much longer than the van der Waals diameter of CO (∼3.16 Å);53 therefore, the destabilization effect due to electrostatic repulsion is minimal. The increase in CO binding energies at higher surface coverage may be related to the closure of the stepped Fe(310) surface. It has been known that the instability of stepped surfaces originates from the unsaturation of metal atoms at the topmost layer; half of the bonds of these atoms to the neighboring atoms are broken when a surface is generated. In order to regain the stability, the surface may undergo substantial reconstruction and relaxation. The process of CO chemisorption on Fe(310) can be considered as increasing the coordination of surface Fe atoms through the formation of Fe-C and Fe-O bonds, which stabilizes the Fe(310) surface. Because the counteracting influence such as electrostatic repulsion or the competition of surface d-band electrons is not significant, increasing the surface coverage of CO leads to a better saturation of coordination of Fe(310), resulting in a greater stabilization of CO-adsorbed Fe(310) and larger binding energies of CO. 3.4. Density-of-State Analysis. It has been found that the adsorption enthalpies of CO on the flat Fe(100) and stepped Fe(310) are similar. In order to understand the bonding interaction of CO with these surfaces, the densities of state (DOS) of Fe(100) and Fe(310) were computed, and those corresponding to the d-band of the topmost layer of these surfaces are depicted in Figure 5. One can see that the surface DOS of Fe(310) is almost identical to that for Fe(100) except that the latter one is more spread at a high-energy range (>5 eV). Alternatively, the energy band near the Fermi level for Fe(310) is more occupied than Fe(100), and a larger extent of band localization, at -1 and -3 eV, respectively, relative to Fe(100) is observed because of the reduction of coordination of the surface Fe atoms.47,54,55 Hammer and Nørskov have suggested the d-band model56,57 that successfully accounted for the trends of adsorption energies of H2,56 CO,58 methyl,59 and oxygen60 on various transitionmetal surfaces. In this model, the interaction between adsorbate molecules and the metal surface is determined mainly by the positions of the molecular bonding b and antibonding a states relative to the metal d-band d, and their coupling matrix element V. The resulting perturbational expression for the energy shift of the metal d-states due to their coupling with the adsorbate orbitals is given by58

∆)

V2 b/a - d

(2)

For the present study of CO chemisorption on Fe(310), only the filled 5σ and empty 2π orbitals were considered because they are mainly responsible for the bonding to metal surfaces.61 Upon adsorption, these CO orbitals interact with the metal d-states leading to the formation of 5σ-d, 2π-d bonding orbitals and their antibonding counterparts as illustrated in Figure 6. For the 5σ-d interaction, the bonding state lying at -7 eV are filled while the antibonding state around the Fermi level is almost fully occupied, thus giving rise to an overall weak stabilization effect. Alternatively, the 2π-d bonding and antibonding states sandwich the Fermi level and the antibonding


Figure 5. d-Band density-of-state (DOS) plots for the Fe(100) and Fe(310) surfaces. All energies are plotted with respect to the Fermi level (F ) 0).

state at ∼3 eV is unfilled. Therefore, the net result of the 2π-d interaction is attractive causing the downshift of the metal d-states. Note that the CO 5σ and 2π orbital energies are approximately constant when switching from Fe(100) to Fe(310) because the same type of adsorption sites and configurations were considered, while the parameter V 2 is small compared to b/a - d.56 Therefore, it may be concluded that the 2π-d interaction should play a more dominant role in ∆, and the position of the center of the d-band d of these surfaces would determine the magnitude of ∆ = V 2/(2π - d) and thus the strength of the surface Fe-CO bonds. The higher the d-band, the smaller the denominator 2π - d and the larger the resulting stabilization ∆. The magnitude of d for Fe(100) and Fe(310) could be readily obtained from Figure 5. One may see that Fe(310) has an d value slightly lower than that of Fe(100), although both are located at ∼ -1 eV. This number agrees with the reported value of -0.92 eV.59 In consequence, the d-band model suggests that the adsorption energy of CO on Fe(310) should be smaller than that when it is adsorbed on Fe(100). The present calculations confirm this preference and predict that the difference in CO binding energies on these two surfaces is merely 0.4 kcal/mol. In addition to the trend of relative stability of CO chemisorption on Fe(310) and Fe(100), the DOS analysis also reveals the nature of interactions between CO and the metal surfaces. Figure 6 shows the projected DOS for CO on Fe(100) and Fe(310) in the 4f and 4f2 configurations. There are several noteworthy features in these plots. First, it is clear that the CO adsorption on Fe is generally strong, as reflected by the significant downshift of the 2π orbitals on CO below the Fermi level. A substantial amount of surface electron density is


Figure 6. Density-of-state (DOS) plots for CO on Fe(100) and Fe(310) surfaces at 0.250 ML. All energies are plotted with respect to the Fermi level. The σ- and π-type orbitals are represented by the red and green line, respectively.

transferred to the antibonding 2π orbitals of CO, giving rise to the elongated CdO bond distances. Second, the projected DOS plots for CO in 4f and 4f2 configurations on Fe(310) (structures 2 and 3, as shown in Figure 6) are noticeably different, but the latter one resembles closely that of CO on Fe(100) adopting the tilted geometry (structure 1). These observations are in line with the fact that structure 3 (as illustrated in Figure 3) can be considered similar to structure 1; the CO molecule in this geometry is tilted in the direction along the flat (001) terrace (Figure 1), whereas in the structure 2, the CO molecule is bent toward the (310) step. Two peaks exist at -6.7 and -7.2 eV for structure 1 corresponding, respectively, to the 5σ and 1π orbitals of CO. This feature prevails in the DOS for structure 3, although the 1π peak is slightly split, yielding a new peak at -7.3 eV. This could be ascribed to the fact that CO in this configuration is bonded asymmetrically to a Fe-Fe bridge; the Fe-O bond to the edge Fe atom is shorter than the counterpart by 0.3 Å. The nonequivalent interaction of CO with the two bridge Fe atoms thus leads to the small splitting of the resulting 1π peak. For the structure 2, however, the DOS is completely different where its 1π appears as a doublet about -7.1 eV, indicating that the two degenerate 1π orbitals of CO interact differently with the Fe atoms on the top edge. Moreover, the splitting of the 1π peak may result from the unsaturation of coordination of the edge Fe atoms that significantly alters the overall surface band structure of Fe(310), and in turn the metal-CO bonds. Increasing the surface coverage does not induce significant changes in the DOS of structures 2 and 3. One may see from Figures 6 and 7 that both the 1π and 5σ peaks are not shifted


Lo and Ziegler TABLE 5: Adsorption of C and O on Fe(310) at 0.250 ML (min ) Minimum; TS ) Transition State; SP ) Higher-Order Saddle Point)

Figure 7. Density-of-state (DOS) plots for CO on the Fe(310) surface at 0.500 ML. All energies are plotted with respect to the Fermi level. The σ- and π-type orbitals are represented by the red and green line, respectively.

at 0.500 ML, which is consistent with the approximately constant CO binding energies for these two configurations at different surface concentrations (Tables 3 and 4). The 1π peaks of structures 2 and 3 are similar to those at 0.250 ML; however, the 5σ peak of the structure 3 at -6.5 eV becomes less populated, suggesting the electron transfer from the CO 5σ orbital to the empty Fe d-states. Another interesting feature is noticed for structure 2 where peaks appears at -3 eV. On one hand, the enhanced occupation reflects a notable increase in the extent of back-donation from the surface Fe atoms to the antibonding 2π orbitals of CO in structure 2 due to the increased surface coverage. On the other hand, the reduced coordination of the edge Fe atoms causes more localization of these bands for structure 2 compared to structure 3. 3.5. Activation of CO on Fe(310). It has been proposed in a previous work by Lo and Ziegler20,62 that the CO dissociation is the likely rate-determining step in the Fe-catalyzed FischerTropsch synthesis utilizing syngas as the source of carbon. In order to accelerate the overall process of hydrocarbon formation, locating alternative paths for generating active carbon in subsequent hydrogenation reactions has therefore become of importance. One solution to this issue is the presence of steps on the surface of the catalyst. The DFT calculations performed by Ge and Neurock29 have demonstrated that the activation barrier of CO can be remarkably reduced from 218 kJ/mol on flat Co(0001) to only 123 kJ/mol on the stepped Co(10 1h 2) surface. Moreover, the same reaction taking place on the stepped Ni(531) surface is nearly barrierless while a barrier of 1.05 eV is found when it is performed on Ni(111).63 Hence, in order to

Eads (kcal/mol)

species

sites

stability

C

3f1 3f2 4f

160.2 125.8 181.7

TS SP min

O

3f1 3f2 4f

155.3 118.2 149.6

min TS min

acquire insight into the dependence of the activation of CO on the surface structures of Fe, the dissociation channels of CO on the stepped Fe(310) were computed, and the results were compared with those obtained for the corresponding processes on the flat Fe(100) and Fe(110) surfaces. Because of the fact that both C and O prefer the adsorption on metal surfaces with high coordination,15,16 there are only a number of adsorption sites of Fe(310) that C and O may reside on. In this work, the adsorption modes of these atoms on the 3f1, 3f2, and 4f sites were studied. It can be seen from Table 5 that C and O favor the hollow sites on Fe(310) at which they are simultaneously bonded to four surface Fe atoms; their resulting binding energies are similar to those for the corresponding adsorption on Fe(100)15 and Fe(110).16 For O atoms, there is an additional, energetically more stable adsorption mode at the 3f1 sites. Its stability relative to the 4f adsorption mode is possibly attributed to the relief of electrostatic repulsion between the electronegative O and the Fe surface when O is adsorbed at a 3-fold site instead of a 4-fold site. Having determined the most preferred sites at which C and O are adsorbed, possible CO dissociation channels could then be constructed. Because only the 4f and 4f2 configurations for adsorbed CO correspond to the true minima of the potential energy surface, two reaction paths exist leading to the decomposition of CO on Fe(310). Both channels are shown in Figure 8. The first path (pathway 1) considers the activation of CO in the 4f configuration in which the O atom migrates over the 2-fold edge and occupies a 3f1 site on the (110) step. At 0.250 ML its associated activation energy is found to be 21.6 kcal/ mol, which is lower than the corresponding value (25.6 kcal/ mol) for the CO dissociation on Fe(100) at the same coverage.62 The lower barrier is due to the high unsaturation of the edge Fe atoms that activate the adsorbed CO at the 4f configuration, as reflected by a long CdO bond distance of 1.330 Å. The transition-state structure resembles the reactant state, with the stretched CdO bond of only 1.803 Å. It is noted that this process is exothermic, but the reaction energy (∆Hrxn) is only 4.3 kcal/ mol. The small energy gain is likely a consequence of the strong

Figure 8. Channels for CO dissociation on Fe(310) at 0.250 ML coverage.


J. Phys. Chem. C, Vol. 112, No. 10, 2008 3699 TABLE 6: Dissociation of CO on the Fe(310) and Fe(100) Surfaces20 (All ZPE-Corrected Energies Are Given in kcal/mol) coverage 0.250 0.500

Figure 9. Channels for CO dissociation on Fe(310) at 0.500 ML coverage.

repulsion between C and O atoms coadsorbed at the neighboring hollow and 3-fold sites that destabilizes the product state. The second path (pathway 2) concerns the dissociation of CO on the (100) terrace originating from the 4f2 configuration of CO. In this channel, the CO molecule in a tilted geometry is activated and the O atom diffuses subsequently to an adjacent hollow site. This process is identical to the one occurring on Fe(100); therefore, their resulting reaction barriers are very similar. The difference between these barriers is only 0.7 kcal/ mol, although the calculated barrier of 26.3 kcal/mol is larger than that for pathway 1 by almost 5 kcal/mol. The CdO bond at the transition state is much elongated (2.066 cf. 1.313 Å) and is less stabilized because the O atom deviates slightly (∼0.03 Å) from the reaction axis (along which two adjacent hollow sites are linked) and is coordinated asymmetrically to the FeFe bridge. Moreover, the energy gain of pathway 2 is only 4.8 kcal/mol; the small exothermicity is possibly caused by the destabilization of O at the hollow site relative to the 3-fold site (Table 5). The surface coverage dependence of the activation energies for these pathways is intriguing. For the CO decomposition on regular surfaces such as Fe(100), the correlation is positive; the higher the surface coverage, the larger the reaction barrier. This trend, nevertheless, is not observed in the present case. The activation energy for pathway 1 increases marginally to 22.9 kcal/mol, whereas the barrier for pathway 2 is reduced significantly to 21.6 kcal/mol when the surface coverage reaches 0.500 ML. The smaller barriers compared to those for the same processes on Fe(100) can be ascribed to the less compact packing of surface Fe atoms on Fe(310) that affords a larger extent of relaxation during the course of CO dissociation, giving rise to a better stabilization of the transition-state species and lowering of the reaction barrier. The noticeable decrease in the activation energy for pathway 2, although not fully understood, may result from the fact that the associated transition state (Figure 9) contains a Fe-O bond with an bottom-edge Fe atom, which is more favorable than the Fe-O bonds with the topedge Fe atoms, thereby lowering the energy of the transitionstate structure and the reaction barrier. The pathway 1 at 0.500 ML is a thermally neutral process, with an energy gain of only 1.2 kcal/mol, because the O atom adsorbed at the 3f1 site induces a remarkable electrostatic repulsion with the CO molecules adsorbed at the hollow sites of the nearby terrace. Alternatively, pathway 2 turns to be highly exothermic at 0.500 ML; the heat of reaction rises to 12.0 kcal/ mol, contrary to the observation that the process is endothermic on the Fe(100) surface at the same coverage. An explanation accounting for this unusual behavior is that, as illustrated in Figure 9, although steric interactions do not play an important role for the two CO molecules adsorbed respectively on different

surface

configuration

Ef

Eb

∆Hrxn

Fe(310) Fe(310) Fe(100) Fe(310) Fe(310) Fe(100)

4f 4f2 4f 4f 4f2 4f

21.6 26.3 25.6 22.9 21.6 25.3

25.8 31.1 33.9 24.1 33.6 27.5

4.2 4.8 8.3 1.2 12.0 2.2

terraces in a supercell the product state acquires an extra stability from the increased saturation of coordination of the surface Fe atoms. The impacts of structural defects, in particular the stepped surfaces, on the rate of CO decomposition on iron catalyst can be seen clearly from Table 6, which summarizes the computed CO activation barriers for both Fe(100) and Fe(310) surfaces. It is assumed that the adsorption of CO on both Fe(100) and Fe(310) possesses small barriers (

Adsorption and Decomposition of CO on Stepped Fe (310) Surfaces

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