Plane-Wave Density Functional Theory Investigations of the

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Plane-Wave Density Functional Theory Investigations of the Adsorption and Activation of CO on Fe5C2 Surfaces Dan C. Sorescu U.S. Department of Energy, National Energy Technology Laboratory, Pittsburgh, PennsylVania 15236 ReceiVed: December 24, 2008; ReVised Manuscript ReceiVed: February 19, 2009

A systematic analysis of the adsorption properties of CO on a set of seven low Miller index surfaces ((010) 0.25, (111j) 0.00, (110) 0.00, (111) 0.00, (111j) 0.50, (110) 0.50, and (100) 0.00)) of the Ha¨gg iron carbide (Fe5C2) phase has been performed. Calculations were based on spin-polarized plane-wave density functional theory (DFT) within the generalized gradient approximation (GGA). Three general groups of adsorption configurations have been identified corresponding to CO binding exclusively to surface Fe atoms (Fe-only states), to mixed Fe and C(s) atoms (mF-C states), and exclusively to surface C(s) atoms (0F-C states), respectively. Among these, the most stable adsorption configurations correspond to adsorption at Fe-only sites with maximum binding energies ranging from 44.4 to 48.5 kcal/mol, depending on the crystallographic orientation. A diverse bonding scheme for CO was found to exist with formation of one up to six different bonds to the Fe atoms. In the case of CO adsorption at mixed mF-C states or exclusively on top of C(s) atoms, lower adsorption energies are observed ranging from 18.5 to 35 kcal/mol. Despite the lower binding energies, adsorption at mF-C states is shown to lead to significant weakening of the CO bonds, as reflected by large bond elongations and red shifts of the vibrational frequencies. The analysis of the dissociation properties of CO indicates that the most stable adsorption configurations at Fe-only sites have also large activation energies for dissociation, in excess of 40 kcal/mol. Decrease of the activation energy of dissociation was found to take place only for a limited number of cases in which the molecule adsorb in a lying down configuration, where both the C and O ends are bonded to the surface by a total of at least five bonds. Molecular dissociation from mixed mF-C states requires significantly lower activation energies, consistent to the weakening of the CO bonds observed in adsorption studies. In such instances activation energies as low as 15.6 kcal/mol have been determined. Formation of small carbon chains is preferential upon molecular dissociation from such states. 1. Introduction It is well-documented that Fe-based catalysts can be used effectively in Fischer-Tropsch (FT) synthesis (FTS) for conversion of syngas (CO and H2) to liquid fuels.1-3 Relative to other FT catalysts like Co or Ru, Fe catalysts have the advantage of a relatively low cost, flexibility in product distribution, and suitability to convert low H2/CO ratio syngas obtained from coal or biomass feedstocks.4 In practical applications, the R-Fe2O3 (hematite) oxide is generally used as the starting catalyst. As this phase is (almost) inactive for FT synthesis, the catalyst is subject first to an activation treatment that can be done in different reducing atmospheres such as H2, CO, or synthesis gas.4-7 The oxide reduction was found to take place in two steps.5,7 The first one corresponds to a facile reduction of R-Fe2O3 to Fe3O4 (magnetite) and does not depend on the activation gas used. The second one is a slow reduction of Fe3O4 to either metallic iron (H2 reduction) or to iron carbide phases (under CO or syngas treatment). Under FTS conditions several carbide phases such as ε-Fe2C, ε′-Fe2.2C, χ-Fe5C2, and θ-Fe3C have been detected.8 However, among various carbide phases there seems to exist some consensus that the active phase in FTS is the monoclinic χ-Fe5C2 (Ha¨gg) phase.5,9-14 As a result, characterization of the surface properties of the Ha¨gg iron carbide surface, previously indicated as the “true Fischer-Tropsch catalyst”,9 and of its interactions with atomic or molecular species such as H, CO, CHx, CxHy, or OH is of outmost importance for understanding and further optimization of the FTS process. 10.1021/jp811381d

Despite its importance, a detailed experimental characterization of the surface properties of the χ-Fe5C2 phase is not yet available. Initial progress, however, into description at the atomic level of the catalytic properties of χ-Fe5C2 has been obtained based on theoretical calculations.15-18 In particular, Cao et al. have used density functional theory (DFT) calculations to investigate the adsorption properties of CO,15 H2,16 or coadsorbed CO and H217 on the (001), (100), and (110) surfaces of Fe5C2. Similarly, a report about ketene hydrogenation on Fe5C2(001) has also been published by the same group of authors.18 However, no motivation has been provided in these studies for the specific choice of these particular surface orientations. Recently, a systematic theoretical analysis of the surface stabilities of χ-Fe5C2 has been reported.19 On the basis of DFT calculations it was determined that among a set of 14 low Miller index surfaces, which are symmetric and maintain the Fe5C2 stoichiometry of the bulk, the (010) Miller index plane is the most stable surface, whereas the (101) surface is the least stable. Additionally, it was found that several surface orientations have surface energies in a narrow energy range, which leads to difficulty in identification of the most suitable surface for FTS applications. On the basis of these findings it was concluded that several different Ha¨gg iron carbide surfaces can play an important role in FTS process and, consequently, caution should be considered both in selection of the surface models used in calculations as well as in identification of the representative active catalyst surfaces.19

This article not subject to U.S. Copyright. Published 2009 by the American Chemical Society Published on Web 04/29/2009

Adsorption and Activation of CO on Fe5C2 Surfaces In light of these new findings related to complexity of various surface orientations of the Ha¨gg Fe carbide phase, in the present work we focus on description of the adsorption and reaction properties of CO on a set of seven most stable surfaces of χ-Fe5C2 crystal. The computational methodology considered in this study is similar to the one used by us to analyze the adsorption properties of CO on the Fe(110), Fe(100), Fe(211), Fe(710), Fe(310), and Fe(111) series of flat, stepped, and kinked surfaces20-22 or the adsorption and hydrogenation reactions of CHx (x ) 0, 4) species on the Fe(100) surface.21 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 and dissociation properties of CO on various surfaces of iron carbide are given in section 3. Finally, we summarize the main conclusions in section 4.

J. Phys. Chem. C, Vol. 113, No. 21, 2009 9257 TABLE 1: Comparison of the Calculated Lattice Parameters and the Average Magnetic Moment Per Iron Atom Obtained in This Work for the Monoclinic χ-Fe5C2 Phase with Other Previous Experimental and Theoretical Valuesa method b

a (Å)

11.588 11.580 (-0.07) US-PW91d 11.510 (-0.67) US-PBEd 11.496 (-0.79) US-RPBEd 11.568 (-0.17) FP-LAPW-PW91e 11.504 (-0.17) exptl PAW-PBEc

b (Å)

c (Å)

4.579 4.508 (-1.55) 4.477 (-2.23) 4.485 (-2.03) 4.523 (-1.22) 4.524 (-1.20)

5.059 4.994 (-1.29) 4.952 (-1.29) 4.962 (-1.92) 5.002 (-1.13) 5.012 (-0.93)

β (deg) 〈m〉Fe (µB) 97.746 96.638 (-0.11) 97.6 (-0.11) 97.6 (-0.05) 97.7 (-0.05) 97.6 (-0.11)

1.72-1.75 1.73 1.70 1.76 1.83 1.71

a

2. Computational Method Spin-polarized density functional theory calculations were performed to investigate the stability properties of different iron carbide surfaces and their interactions with molecular (CO) and atomic (C, O) species. This has been done using Vienna ab initio simulation package (VASP)23 in conjunction to 3D periodic slab models. The electron-ion interaction is described by the projector augmented wave (PAW) method of Blo¨chl24 in the implementation of Kresse and Joubert.25 As shown before25 this method provides an improved description of the magnetic transition metals. For the treatment of exchange and correlation the generalized gradient approximation (GGA) with the Perdew, Burke, and Ernzerhof (PBE) functional, hereafter denoted as GGA-PBE,26 was used together with the spin interpolation for the correlation energy introduced by VoskoWilk-Nusair (VWN).27 Solution of the Kohn-Sham equations was done using a plane-wave basis set with a cutoff energy of 400 eV, whereas the sampling of the Brillouin zone was performed using a Monkhorst-Pack scheme.28 Electron smearing was employed via the Methfessel-Paxton technique,29 with a smearing width consistent to σ ) 0.1 eV, and all energies were extrapolated to T ) 0 K. The climbing image nudged elastic band method (CI-NEB)30,31 has been used to determine the minimum reaction pathway for dissociation of CO on various surfaces. The nature of different local minima or transition states on the potential energy surface has been tested based on vibrational frequencies of the adsorbed atomic or molecular species in the frozen phonon mode approximation. In these calculations the Hessian matrix has been determined using a finite difference approach with a step size of 0.02 Å for displacement of individual atoms along each Cartesian coordinate. 3. Results and Discussion 3.1. Calculations of Bulk Ha¨gg Fe5C2. The monoclinic bulk structure of the χ-Fe5C2 phase has C2/c crystallographic symmetry and contains 20 Fe and 8 C atoms per unit cell. There are three different types of iron atoms in the unit cell with the Wyckoff positions Fe1(x1, y1, z1) (8f), Fe2(x2, y2, z2) (8f), and Fe3(0, y3, 0.25) (4e), and a single type of carbon site C(x4, y4, z4) (8f). Optimization of the unit cell has been done using a 2 × 6 × 6 Monkhorst-Pack grid of k-points. On the basis of a Murnaghan equation of state analysis32 the corresponding optimized lattice parameters found are a ) 11.580 Å, b ) 4.508 Å, c ) 4.994 Å, β ) 97.64°, and a bulk modulus B0 ) 227.8 GPa. These crystallographic parameters are compared with

The values given in parentheses represent the percentage deviation relative to experimental measured values. b The experimental values for lattice parameters are from ref 33, and that for the average magnetic moment per Fe atom is from ref 34. c Values determined in this work. d Theoretical values reported in ref 19 based on DFT calculations using ultrasoft pseudopotentials and PW91, PBE, and RPBE exchange correlation functionals. e Data from ref 35.

experimental values and to other theoretical results in Table 1. As can be seen the agreement with experimental data is very good, with a maximum deviation of -1.55% observed in the case of b lattice parameter. This level of agreement is also similar to the one reported in ref 19 based on RPBE exchange correlation functional and ultrasoft (US) pseudopotentials (see Table 1), but it is superior to the PW91 and PBE sets of results reported in the same reference. Beside the crystallographic parameters we have also analyzed the magnetic structure of the unit cell. We found that overall the bulk crystal is ferromagnetic with a total magnetic moment per formula unit (Fe5C2) of 8.41 µB. A detailed analysis of the magnetic moments distribution indicates that the three nonequivalent iron atoms Fe1, Fe2, and Fe3 have different magnetic moments with values of 2.126, 1.698, and 1.020 µB, respectively, whereas the C atom carries a magnetic moment of opposite sign of about -0.1 µB. The average magnetic moment over all Fe atoms inside the unit cell is 1.73 µB. This value is in excellent agreement with experimental results ranging from 1.72 to 1.75 µB, determined from saturation magnetization experiments. We note that calculations35 based on full-potential linearized augmented plane wave (FP-LAPW) with PW91 functional (see Table 1) indicated a similar but slightly smaller value for the average magnetic moment, i.e., 1.71 µB, whereas the US-RPBE result19 of 1.83 µB clearly overestimates the corresponding experimental values. Overall, the results obtained in this section indicate that PAWPBE computational method is able to provide a very good representation of both the structural and magnetic properties of bulk Fe5C2. Additionally, as we have shown in our previous investigations,20,21 the same theoretical level can be used to describe accurately the properties of the CO molecule and its interactions with Fe surfaces. 3.2. Low Miller Index Surfaces of χ-Fe5C2. As indicated in the Introduction section a systematic analysis of various low Miller index surfaces of Ha¨gg Fe carbide was considered before by Steynberg et al.19 based on US-PBE calculations. In this case the analysis was performed for surfaces that were both stoichiometric to the bulk and have a symmetric termination with equivalent top and bottom planes of the slab.

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TABLE 2: Calculated Surface Energies for Different Low Miller Index Surfaces of χ-Fe5C2 surface energy (J/m2) surface symmetric surfaces (010) 0.25 (111j) 0.00 (110) 0.00 (111) 0.00 (111j) 0.50 (110) 0.50 (001) 0.00 (100) 0.25 (011) 0.00 (101j) 0.00 (111) 0.50 (011) 0.25 (010) 0.00 (101) 0.00 asymmetric surfaces 15. (100) 0.00

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.

a

PAW-PBE

US-PBEa

2.16 2.20 2.37 2.40 2.43 2.44 2.53 2.52 2.52 2.66 2.67 2.66 2.66 2.86

2.47 2.56 2.71 2.78 2.80 2.84 2.88 2.89 2.90 2.97 3.01 3.05 3.08 3.28

2.16

Data from ref 19.

In this study we analyzed a similar set of surface orientations as the one described in ref 19, and the corresponding results for surface energies are presented in Table 2. Here the notation used is consistent with the one introduced in ref 19. Specifically, for each surface the first group of indices given in parentheses indicates the corresponding Miller index, whereas the second group of indices provides the fractional distance relative to the unit cell origin in a direction perpendicular to the Miller surface where the cleavage plane has been taken. For each surface the Monkhorst-Pack grid considered corresponds to a separation resolution of ∼0.04 Å-1 and a vacuum width of 14 Å. The calculation of the surface energies has been done using the method proposed by Boettger36 based on a set of slab energies with increasing number of layers. In our calculations, we have used slab models with a number of formula units (Fe5C2) ranging typically from 4 to 12 per supercell. As can be seen from the data presented in Table 2, the relative stability order of various low Miller index surfaces is basically consistent to that determined by Steynberg et al.,19 but our values are systematically smaller by 0.3-0.4 J/m2 than values reported in ref 19. The exact source of these differences is hard to identify, as various parameters such as the optimized geometries and the corresponding surface area, the convergence parameters, the set of pseudopotentials, and even the supercell sizes have some influence upon the final results. Nevertheless, the order of stability for various surface orientations is confirmed, particularly for the set of low-energy surfaces. Some small variations take place in the relative order of different surfaces (see, for example, entries 7-9 and 12 and 13). However, the corresponding surface energies in these instances are all very close to each other making a clear differentiation of their stabilities a difficult task. Overall, among this set of surfaces our calculations indicate that the (010) 0.25 and (111j) 0.00 surfaces are the most stable, with surface energies of 2.16 and 2.20 J/m2, respectively. We also note that the surface energies determined in this study for the most stable surfaces of χ-Fe5C2 are close and slightly larger than the values obtained for the cementite (Fe3C) phase of iron carbide, consistent with the increased stability of the cementite phase. Specifically, the surface energies for a set of seven low index Miller surfaces of cementite were found to range from 2.0 to 2.5 J/m2 as determined by DFT calculations by Chiou and Carter.37 Among

these surfaces the most stable is (001) with a surface energy of 2.05 J/m2. This value is lower than any of the surface energies of χ-Fe5C2 phase determined in this study. We note that Steynberg et al.19 have attempted to correlate the calculated surface energies with various surface properties such as the number of dangling bonds, surface atom density, relative ruggedness of surfaces, surface relaxation, or the total spin density changes, but only approximate correlations were identified. Overall, it was concluded that an accurate correlation of surface properties with optimized surface energy was not possible and a large set of crystallographic surfaces have closed separated energies. Finally, as indicated in the Introduction section, previous theoretical studies15,16 of the elementary adsorption properties of CO and H2 on Fe5C2 considered the case of (100), (110), and (001) surfaces without providing motivation for this particular selection of surfaces. As can be seen from the data provided in Table 2 both the (110) 0.00 and (001) 0.00 surfaces have surfaces energies larger than either the (010) 0.25 or (111j) 0.00 surfaces, and this relative difference is particularly important for the case of the (001) 0.00 surface. The case of the (100) 0.00 surface is a special one as this surface has a nonsymmetric termination, with one side terminated by an Fe layer while the opposite side is terminated by a layer containing both Fe and C atoms. As mentioned earlier in this section the focus in this work is primarily related to the case of stoichiometric symmetric surfaces. We have analyzed, however, the (100) 0.00 surface and determined the existence of a low surface energy. Given this finding and for comparison with previous results reported in ref 15 we have included this surface in the set of surfaces for which the adsorption and dissociation properties of CO have been further determined. 3.3. CO Adsorption on Low Miller Index Surfaces of χ-Fe5C2. Having established the stability order for various low Miller index surfaces, in this section we consider the analysis of the adsorption properties of CO on these surfaces. This has been done for the case of the first seven most stable and symmetric surfaces identified in the previous section, i.e., (010) 0.25, (111j) 0.00, (110) 0.00, (111) 0.00, (111j) 0.50, (110) 0.50, and (100) 0.00 surfaces. For various adsorption configurations identified on these surfaces we report in Table 3 the corresponding adsorption energies. These have been determined based on the equation Eads ) Emolec + Eslab s E(molec+slab), where Emolec is the energy of the isolated molecule 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. In this sign convention positive adsorption energies correspond to stable configurations. Here, the energy Emolec of the isolated adsorbate was determined from calculations performed on a single molecule in a cubic cell with sides of 12 Å. In the adsorption studies both the adsorbate and the top half of the slab have been allowed to relax during optimizations. Pictorial views of the most representative adsorption configurations indicated in Table 3 are provided in Figures 2-4, while additional configurations are given in the Supporting Information. In Table 3, for easy identification of various configurations on different surfaces we use a nomenclature based on two indices of the form (n) m. Here the first index (n) given in parentheses refers to one of the seven surfaces indicated above. The second index refers to a specific configuration illustrated in one of Figures 2-4, a function of the crystallographic orientation. In a number of instances we also make

Adsorption and Activation of CO on Fe5C2 Surfaces

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TABLE 3: Calculated Equilibrium Distances and Adsorption Energies for CO Adsorbed on Different Surfaces of χ-Fe5C2a configuration/bonding typeb (1) (1) (1) (1) (1) (1) (1) (1)

1 2 3 4 5 6 7 8

(1) 9 (1)10 (1)11

1F 1F 1F 1F-t 1F-t 2F 2F 4F 4F 5F 0F-C

r(Fe-C)

r(Fe-O)

r(Cs-C)

r(C-O)

Eads

ν(C-O)

1.163 1.171 1.171 1.183 1.188 1.183 1.181 1.207

28.3 44.7 44.6 45.8 42.1 43.7 43.8 46.4

2000 1947 1944 1867 1844 1822 1873 1697

1.338

1.214 1.284 1.174

42.7 43.3 27.7

1652 1329 2046

1.507 1.528 1.482

1.174 1.176 1.170 1.203 1.202 1.243 1.239 1.315

46.2 43.4 41.7 44.7 35.8 25.3 27.8 25.0

1930 1920 1957 1731 1723 1507 1529 1188

1.451

1.333

26.8

1194

1.376 1.435 1.345

1.187 1.203 1.204 1.298 1.182

43.7 47.8 22.9 35.0 22.8

1854 1750 1819 1319 1979

1.504 1.455 1.399 1.475

1.177 1.176 1.174 1.194 1.206 1.313 1.317 1.334 1.319

48.5 43.6 30.1 44.8 47.3 24.2 28.8 28.0 34.3

1914 1899 1929 1802 1713 1176 1240 1242 1207

1.182 1.178 1.207 1.210

47.5 45.6 35.8 48.0

1869 1894 1682 1684

1.497 1.486

1.311 1.269 1.233

35.2 18.3 25.2

1183 1408 1574

1.416 1.424 1.524 1.481 1.326

1.169 1.185 1.206 1.241 1.236 1.256 1.270 1.288 1.356 1.187

35.4 44.6 37.6 38.2 45.2 32.4 30.1 26.0 28.3 33.7

1953 1868 1709 1521 1557 1530 1463 1304 1118 2000

1.176 1.181 1.205 1.206 1.303 1.284

44.3 43.8 44.4 44.4 40.6 29.2

1900 1860 1701 1701 1224 1272

(a) (010) 0.25 1.781 1.784 1.782 1.820 1.759 1.792, 2.210 1.785, 2.239 1.885, 2.038,2.347 2.371 1.980, 1.983, 2.243, 2.254 1.869, 1.958, 1.979 2.147, 2.255 (b) (111j) 0.00

(2) (2) (2) (2) (2) (2) (2) (2)

1 S1 S2 2 S3 3 4 5

1F 1F 1F 3F 3F 3F-C 3F-C 4F-C

1.768 1.770 1.767 1.887, 2.090, 2.092 1.926, 1.955, 2.330 2.018, 2109, 2.154 2.020, 2.127, 2.191 1.482, 1.965, 2.052 2.116 1.964, 2.004, 2.184

(2) 6

5F-C

(3) (3) (3) (3) (3)

1 2 3 4 5

2F 3F 1F-C 4F-C 0F-C

1.775, 2.259 1.841, 2.087, 2.206 2.153 1.915, 2.236, 2.255

(4) (4) (4) (4) (4) (4) (4) (4) (4)

1 S1 S2 2 3 4 5 6 S3

1F 1F 1F 2F 3F 3F-C 4F-C 5F-C 5F-C

1.770 1.775 1.753 1.841, 2.062 1.956, 1.971, 2.179 1.939, 2.122 2.029, 2.036, 2.090 1.953, 2.130, 2.163 1.927, 2.211, 2.259

(5) (5) (5) (5)

1 S1 2 3

2F 2F 3F 4F

1.778, 2.278 1.787, 2.380 1.971, 2.010, 2.093 1.932, 2.044, 2.232

(5) 4 (5) 5 (5) 6

5F 3F-C 3F-C

1.937, 1.989, 2.019 1.858, 2.117 2.176, 2.203, 2.203

(6) (6) (6) (6) (6) (6) (6) (6) (6) (6)

1 2 S1 S2 3 4 S3 5 6 S4

1F 2F 2F 3F 4F 3F-C 3F-C 4F-C 5F-C 0F-C

1.784 1.766, 2.333 1.922, 1.943 1.885, 1.946 1.898, 1.923, 2.230 1.898, 2.280 1.917, 2057 1.928, 2.041, 2.179 1.940, 2.097, 2.277

(7) (7) (7) (7) (7) (7)

1 2 3 4 5 6

1F 1F-t 3F 3F 5F 6F

2.178 2.090, 2.146 (c) (110) 0.00

2.005 (d) (111) 0.00

2.017 1.962 2.128, 2.229 1.994 2.262 (e) (111j) 0.50

2.333 2.048, 2.288 2.085 (f) (110) 0.50

2.217 2.140 2.142 2.044 2.011 2.027, 2.102

(g) (100) 0.00 1.783 1.794 1.913, 1.971, 2.269 1.909, 1.981, 2.274 1.899, 2.028, 2.040 2.192, 2.127 2.094, 2.107, 2.297, 2.249, 2.245 2.024

a The bond distances are in units of angstroms, the chemisorption energies are in kcal/mol, and vibrational frequencies are in cm-1. b Each set of configurations is denoted with two symbols corresponding to the surface number (given in parentheses) and to configuration index as represented in Figures 2-4. Those configurations indicated with an additional symbol S are given in the Supporting Information. The bonding symbols 1F-6F refer to the number of bonds formed between the adsorbing CO molecule and the Fe surface atoms. The mixed symbols 0F-C indicates the case when the CO molecule is bonded exclusively on top of a surface C(s) atom. Configurations mF-C, m g 1 correspond to the case when the CO molecule is bonded to mFe atoms and a surface C(s) atom. The 1F and 1F-t notations are used for bonding at one-folded sites in vertical, respectively, tilted configurations relative to surface normal.

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Figure 1. Side and top views of the slab models used to describe the chemisorption properties of CO on different crystallographic surfaces of χ-Fe5C2: (a) (010) 0.25, (b)(111j) 0.00, (c) (110) 0.00, (d) (111) 0.00, (e) (111j) 0.50, (f) (110) 0.50, and (g) (110) 0.00. The notation used to specify the Miller indexes is consistent to the one introduced in ref 19. The Fe atoms are represented in light brown while the C atoms are in green. For the top view representations only the atoms in the top layers were included for improved clarity.

Figure 2. Representative adsorption configurations of CO on the (010) 0.25 surface of χ-Fe5C2. The corresponding index for each configuration is consistent to the data entry in Table 3a. The top, left-side panel provides a top view of the surface atoms. Different rows of surface Fe atoms four- (4f), five- (5f), or six-fold (6f) coordinated to other Fe atoms in the top layer are also indicated.

reference to additional configurations presented in the Supporting Information. Such configurations were denoted with (n) Sm symbols. 3.3.1. (010) 0.25 Surface. The adsorption properties of CO on the (010) 0.25 surface have been studied using a slab model containing 40 Fe and 16 C atoms as represented in Figure 1a. The top layer of the surface presents a complex pattern of Fe and C atoms as can be seen in the detailed top view of the surface provided in the first panel of Figure 2. Specifically, in the middle region of the supercell, the surface contains both Fe and C atoms. For clarity, hereafter we will denote such surface C atoms as C(s). These C(s) atoms are slightly above, respectively, slightly below and four-fold coordinated to Fe atoms in the top layer. In other regions of the surface unit cell,

toward the left and right boundaries, only Fe atoms are present in the top layer. Hereafter we denote this as the Fe-only region. As a result of this pattern, diverse types of Fe-Fe or Fe-C(s) coordinations are observed along the surface. Specifically, by moving from the middle row of Fe atoms to the left or right boundaries, Fe atoms which are four-fold (4f), five-fold (5f) and six-fold (6f) coordinated to other Fe atoms in the surface layer can be identified. The (4f) and (5f) Fe atoms are also bonded to C(s) atoms positioned either above or below the Fe plane. For simplicity we will denote herewith these Fe surface atoms as Fe(4f), Fe(5f), and Fe(6f), respectively. As a result of these topographic and compositional differences it is expected that the adsorption properties of the CO molecule will be different at different locations within the surface unit cell.

Adsorption and Activation of CO on Fe5C2 Surfaces On the (010) 0.25 surface we have identified 11 different adsorption configurations that can be grouped in five different bonding types. These configurations are indicated in Table 3 as (1)1-(1)11 states and are also illustrated in Figure 2. The first three groups are represented by configurations where CO binds directly to Fe atoms, and this can take place through formation of one (1F) (configurations (1)1-(1)5), two (2F) (configurations (1)6 and (1)7), four (4F) (configurations (1)8 and (1)9), and five (5F) (configuration (1)10) bonds to Fe atoms, respectively. The fifth group contains configurations where CO binds directly on top of the C(s) atom. In such case (see configuration (1)11 in Figure 2) no bonding to the surface Fe atoms takes place, and as a result we will indicate this type of bonding as 0F-C. A closer inspection of the binding energies for the 1F group of configurations (see Table 3a) indicates the presence of some important differences. For example, when CO adsorbs on top of an Fe atom, in the middle portion of the supercell (configuration (1)1), the corresponding binding energy is 28.3 kcal/ mol. Similar configurations as (1)2 or (1)3 states positioned close to the unit cell boundaries, in the middle of the Fe-only region, have significantly larger adsorption energies of 44.5-44.7 kcal/ mol. In these cases molecular bonding takes place at Fe(6f) sites. In the Fe-only region, beside the vertical 1F state the CO molecule can also adsorb in a tilted, one-fold configuration (denoted as 1F-t). This is, for example, the case of (1)4 (Eads ) 45.8 kcal/mol) and (1)5 (Eads ) 42.1 kcal/mol) structures adsorbed at Fe(6f) sites which have tilt angles relative to surface normal of 27.3° and 10.9°, respectively. Two-fold (2F) tilted binding configurations were also observed but only in the Fe-only surface region. Here, molecular bonding involves the Fe(5f) and Fe(6f) type of sites (see (1)6 and (1)7 structures) and the corresponding binding energies have identical values of 43.8 kcal/mol. In the Fe-only region adsorption can also take place in a pseudo-4F configuration with formation of four Fe-C bonds as can be seen for (1)8 and (1)9 states. The adsorption at the (1)8 site is the most stable among all the other states on the (010) 0.25 surface and has a binding energy of 46.4 kcal/mol. The CO molecule is bonded in this case to three Fe(6f) and one Fe(5f) type of surface atoms. Due to the nonplanar shape of the surface the four Fe-C bonds are not identical, and their bond lengths range from 1.885 to 2.371 Å. The second type of 4F configuration (see (1)9 in Figure 2), involves CO bonding to a pair of Fe(6f) (r(Fe-C) ) 1.980, 1.983 Å) and Fe(5f) (r(Fe-C) ) 2.243, 2.254 Å) atoms. In this case the adsorption energy decreases somewhat to 42.7 kcal/mol. In the Fe-only regions of the surface the CO molecule can also adsorb in a lying down tilted configuration (see panel (1)10 in Figure 2) with an adsorption energy of 43.3 kcal/mol. In this case both ends of the molecule are bonded to surface Fe atoms by three Fe-C and two Fe-O bonds. The corresponding bond lengths are indicated in Table 3a. For consistency in notation we denote this state as a 5F configuration based on the total number of bonds formed between the CO molecule and the Fe atoms. Finally, CO adsorption can take place directly on top of the C(s) atom (see structure (1)11 in Figure 2), at a C(s)-CO separation of 1.338 Å. As in this case no Fe atoms are involved in molecular bonding, we indicate this state as being of 0F-C type. The corresponding binding energy in this case is 27.7 kcal/ mol, among the smallest found on this surface. Overall, the above-presented results indicate that the strongest binding energies take place in the region of the surface

J. Phys. Chem. C, Vol. 113, No. 21, 2009 9261 containing only Fe atoms (Fe-only region). In this case there is a relatively small range of variation in binding energies from 42.1 to 46.4 kcal/mol despite the fact that diverse 1F, 2F, 4F, or 5F bonding configurations can be formed. The weakest adsorption configurations are seen in the surface region containing both Fe and C(s) atoms in the top layer. Here, CO adsorption on top of Fe atom (1(1) state) or on the C(s) atom ((1)11 state) leads to similar binding energies of 27.7-28.3 kcal/mol. In Table 3a we also indicate the corresponding ν(C-O) vibrational frequencies for each of the adsorption states identified. We observe that the highest vibrational frequencies of 2000 and 2046 cm-1 take place for the adsorption states with the smallest binding energies. As the adsorption energies increase, a corresponding red shift of the vibrational frequencies takes place. The lowest vibrational frequencies of 1697 (1652) and 1329 cm-1 are observed for the 4F (1)8 and (1)9 states and for the lying down 5F (1)10 configuration. These variations of the vibrational frequencies are consistently reflected in the corresponding CO bonds, which increase in length from 1.163 Å for the (1)1 state, to 1.181 for (1)7, and further to 1.284 Å for the (1)10 state. These results indicate important weakening of the CO bond, and as result it is expected that both the 4F and 5F states will play an important role in molecular dissociation on this surface. 3.3.2. (111j) 0.00 Surface. The adsorption properties of CO on the (111j) 0.00 surface have been investigated using the slab model represented in Figure 1b containing 40 Fe and 16 C atoms. The surface of this crystallographic orientation contains both Fe and C(s) atoms in the top layer, but the surface corrugation is such that no C(s) atoms are at a height above the neighbor Fe atoms. By inspecting the top view representation of the atomic structure given in Figure 1b it can be observed that for each surface unit cell there are two C(s) atoms positioned at the boundaries of this unit which are five-fold coordinated to other Fe surface atoms. A systematic analysis of CO binding properties on this surface indicates the existence of five main groups of configurations which are represented in Figure 3 (see configurations (2)1-(2)6)) and in Figure S1 of the Supporting Information (configurations (2)S1-(2)S3). The adsorption energies and characteristic geometric parameters for these configurations are detailed in Table 3b. The first group of adsorption configurations contains the (2)1, (2)S1, and (2)S2 individual configurations, corresponding to 1F type of bonding, on top of Fe atoms. In these cases the adsorption energies are among the largest on this surface with values of 46.2, 43.4, and 41.6 kcal/mol, respectively. Despite the apparent similarity of these 1F adsorption configurations there are also variations in the specific binding energies due to the different bonding environment of each adsorption state. For example, in the case of the most stable (2)1 structure, the CO molecule adsorbs on an Fe atom which is five- and, respectively, two-fold coordinated to other surface Fe and C(s) atoms, and these two C(s) atoms are located in a top and, respectively, in a subsurface layer. For the less stable case of (2)S2 configuration, CO is also one-fold bonded to an Fe atom, but this Fe atom is four-fold and, respectively, two-fold coordinated to other surface Fe and C(s) atoms, and these two C(s) atoms are both positioned in the top layer. The second group of binding states is represented by 3F configurations on Fe atoms like (2)2 and (2)S3 states which have smaller adsorption energies of 44.7 and 35.8 kcal/mol, respectively. In both these cases CO bonding to the surface takes place through formation of three Fe-C bonds.

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Figure 3. Representative adsorption configurations of CO on (111j) 0.00, (110) 0.00, and (111) 0.00 surfaces of χ-Fe5C2. The corresponding index for each configuration is consistent to the data in Table 3, sections b, c, and d, respectively.

Beside these adsorption configurations involving only Fe atoms, three other groups of binding states have been identified, which involve bonding to mixed Fe and C(s) atoms. Such states can have a number of three (3F-C), four (4F-C), or five (5F-C) bonds to Fe atoms in addition to a C-C(s) bond to the carbide C(s) atom. These states are illustrated in panels (2)3-2(6) of Figure 3, while specific bond lengths for each configuration are detailed in Table 3b. Overall, it can be seen that despite the relative large number of bonds of the CO molecule to the surface, the corresponding binding energies of 25.0-27.8 kcal/mol are smaller than those determined on Fe sites, for 1F and 3F configurations, respectively. The corresponding vibrational frequencies for various adsorption configurations are also indicated in Table 3b. We observe that there exist significant red shifts among 1F, 3F, and the mixed 3F-C, 4F-C, or 5F-C states, with the lowest vibrational frequencies being observed for the mixed bonding mF-C, m ) 3-5 states. For example, the CO vibrational frequencies change from a high of 1957 cm-1 as seen for the 1F (2)S2 structure to a low of 1188 and 1194 cm-1 for the 4F-C (2)5 and 5F-C (2)6 adsorption states. These variations are also reflected in geometric changes, as the CO bond lengths increase from a 1.170 Å for 1F (2)S2 structure to 1.315 and 1.333 Å for the 4F-C (2)5 and 5F-C (2)6 states. Overall, the above results indicate that the most stable adsorption configurations are seen when CO bonding takes place on Fe sites as 1F or 3F states. However, bonding to mixed Fe and C(s) atoms leads to adsorption configurations where the C-O bond is significantly weakened as reflected by both large bond elongations and red shifts of the CO stretching frequency. 3.3.3. (110) 0.00 Surface. The (110) 0.00 surface of Fe5C2 (see Figure 1c) presents a different pattern for the Fe and C(s) atoms. In this case the C(s) atoms in the surface layer are fourfold coordinated to other Fe atoms and are positioned in an alternate structure above and, respectively, below the plane of Fe atoms. Additionally, different from the case of the (010) 0.25 surface which is almost flat, the (110) 0.00 surface is highly corrugated. Adsorption of the CO molecule on this surface can take place by direct bonding only to Fe atoms, by bonding to mixed Fe

and C(s) atoms, or on top of a given C(s) atom, respectively. Pictorial views of these configurations are presented in panels (3)1-3(5) of Figure 3. Binding to Fe atoms was found to be possible either as a two-fold (2F) tilted configuration (see (3)1) or as a three-fold (3F) state (see (3)2), with respective adsorption energies of 43.7 and 47.8 kcal/mol. We observe that these values of the adsorption energies are similar to the corresponding ones obtained on (010) 0.25 or (111j) 0.00 surfaces. We have also attempted to identify 1F type of adsorption configurations, on top of the Fe sites which were found to be also very stable on (010).25 and (111j) 0.00 surfaces, but for the current surface these were found to be either unstable or to correspond to a transition state on the potential energy surface. In the case of CO bonding to mixed Fe and C(s) surface sites, two different states have been identified characterized by a single Fe-C bond (see (3)3), respectively, by three Fe-C and one Fe-O bond (see (3)4), in additional to the C(s)-CO bond. The binding energies of these configurations of 22.9 and 35.0 kcal/ mol are also lower than those obtained when adsorption takes place exclusively on Fe sites. Besides bonding on Fe sites or mixed Fe and C(s) sites, direct bonding on top of a single C(s) atom is also possible on the (110) 0.00 surface without formation of other bonds to Fe atoms. Such a configuration, denoted in our nomenclature as 0F-C, is illustrated in panel (3)5 of Figure 3 and has a relatively small adsorption energy of 22.8 kcal/mol. In Table 3c, besides the geometric and energetic parameters, we also report the vibrational frequencies of CO for various adsorption configurations described above. The highest vibrational frequencies observed in this case correspond to 0F-C bonding configuration. By increasing the number of bonds to Fe atoms, the CO stretching frequency is red-shifted from 1854 cm-1 for 2F state to 1750 cm-1 as we see for the 3F state. This downward shift is even more pronounced in the case of bonding to mixed Fe and C(s) atoms, particularly when the number of Fe-C bonds increases. For example, the 4F-C configuration is characterized by a low vibrational frequency of 1319 cm-1, consistent with the largest CO bond elongation of 1.298 Å among all the other adsorption states.



Figure 4. Representative adsorption configurations of CO on (111j) 0.50, (110) 0.50, (100) 0.00 of χ-Fe5C2. The corresponding index for each configuration is consistent to the data in Table 3, sections e, f, and g, respectively.

The above results reconfirm that preferential adsorption of CO takes place on Fe atoms, whereas adsorption on or around the C(s) sites is significantly weaker than the one on Fe sites. However, bonding to mixed Fe and C(s) sites with formation of multiple Fe-C bonds leads to large red shifts in vibrational frequencies and correspondingly an important weakening of the CO bond. As indicated in the Introduction section, the adsorption of CO on the (110) surface has also been studied by Cao et al.15 using DFT calculations with ultrasoft pseudopotentials within GGA approximation. On the basis of a slab model with five iron layers and three carbon layers these authors have identified at low coverages two types of 3F adsorption configurations with energies of 53.9 and 51.4 kcal/mol and two types of C(s)-CO bonding states with energies of 38.0 and 26.7 kcal/mol, respectively. No bridge configurations, like the 2F structure (3)1, or adsorption states on top of the C(s) atoms, like 0F-C structure (3)5 identified here, have been reported in that study. For the common set of adsorption configurations identified both in ref 15 and in this work we observe that our calculated binding energies are systematically smaller than those reported previously.15 Several reasons can be responsible for such differences. Among these we note the different exchange correlation functionals and pseudopotentials sets used in the two calculations. Additionally, there are important differences between the slab models used in the two sets of calculations. For example, our slab model contains 3 times more layers than the one used in ref 15. This number was necessary in order to achieve the convergence in surface energy with the increase in the number of layers in the slab. 3.3.4. (111) 0.00 Surface. The structural and energetic properties of CO adsorbed on the (111) 0.00 surface are indicated in Table 3d while representative atomic configurations are represented in Figure 3, panels (4)1-(4)6, and in Figure S2 of the Supporting Information (panels (4)1-(4)S3). On this surface, molecular bonding exclusively to Fe atoms can take place as 1F, 2F, and 3F binding configurations with maximum adsorption energies of 48.5 (configuration 4(1)), 44.8 (configuration 4(2)), and 47.3 kcal/mol (configuration 4(3)), respectively. We note, however, that due to the differences in the local

surface environment and surface topography some noticeable differences appear even for the same type of binding states, as function of the specific location within the surface unit cell. For example, in the case of the 1F states the adsorption energies decrease from a maximum of 48.5 kcal/mol observed for the (4)1 state to 43.6 kcal/mol for the (4)S1 and further down to 30.1 kcal/mol for the (4)S2 configurations, respectively. Besides adsorption exclusively to Fe atoms, CO bonding to mixed Fe and C(s) atoms is also possible. Specifically, we identified several different types of adsorption configurations with a total of three (configuration (4)4), four (configuration (4)5), and five (configurations (4)6 and (4)S3) bonds formed between the C and O ends of the molecule and the surface Fe atoms, in addition to the C(s)-CO bond. For these structures the adsorption energies range between 24.2 kcal/mol (for (4)4) and 34.3 kcal/mol (for (4)S3), appreciably lower than the binding values on Fe-only sites. Similar to the other surfaces analyzed above, for the group of adsorption configurations 3F-C, 4F-C, and 5F-C involving bonding to mixed Fe and C(s) atoms, the CO bonds are significantly elongated to 1.313-1.334 Å. These values can be compared to the case when adsorption takes place at Fe-only sites, where the same bonds vary only from 1.174 to 1.206 Å. Additionally, for the mF-C (m ) 3, 5) states above, important downward shifts of the vibrational frequencies are observed, ranging from 1204 to 1242 cm-1. 3.3.5. (111j) 0.50 Surface. On the (111j) 0.50 surface a diverse set of adsorption configurations has been found involving bonding exclusively to Fe atoms or to mixed Fe and C(s) atoms. In the first category of states, binding configurations with a total of two ((5)1 and (5)S1), three ((5)2), four (5(3)), and five (5(4)) bonds between the C and O ends of the molecule to the surface Fe atoms can be formed as it is illustrated in Figure 4 and Figure S2 of the Supporting Information. Among these states the 2F and the 4F structures (see entries (5)1 and (5)3 in Table 3e) have the highest binding energies with values of 47.5 and 48.0 kcal/mol. Due to the increased roughness of this surface, a new 5F bonding state (see (5)4 in Figure 4) is possible with formation of three Fe-C and two Fe-O bonds. The increased bonding in

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this case does not lead, however, to higher binding energies but to increased elongation of the CO bond. For example, the binding energy of the 5F state is slightly smaller than the one of the 3F (5)2 configuration. We note, however, that the increased in bonding leads to a systematic increase in CO bond length, which varies from 1.178 (1.182) Å for 2F configurations, to 1.207 Å for 3F, and further to values of 1.210 and 1.311 Å for 4F and 5F structures, respectively. Correspondingly, there is a continuous red shift of the vibrational frequency from a high of 1894 cm-1 for 2F (5)S1 to a low value of 1183 cm-1 for the 5F (5)4 bonding configuration. Bonding of CO to mixed Fe and C(s) atoms was found to be possible in diverse types of configurations. For example, for the (5)5 configuration (see Figure 4) there are two Fe-C and one Fe-O bonds, whereas for the (5)6 state there are three Fe-C bonds, in addition to the C(s)-CO bond. The corresponding adsorption energies in these two cases are 18.3 and 25.2 kcal/mol, significantly smaller than those obtained when binding takes place exclusively on Fe atoms. However, despite these lower adsorption energies, significant weakening of the CO bonds takes place, reflected by increased CO bond elongation to values of 1.269 (1.233) Å for (5)5 ((5)6) and by corresponding red shifts to 1408 (1574) cm-1 of the corresponding vibrational frequencies. 3.3.6. (110) 0.50 Surface. The results of the adsorption calculations of CO on the (110) 0.50 surface are summarized in Table 3f, while the corresponding atomic configurations are presented in Figure 4, panels 6(1)-6(6), and in Figure S3 of the Supporting Information. Similar to the case of the (111j) 0.50 surface, the adsorption on (110) 0.50 can take place under a variety of adsorption configurations involving either Fe-only sites, mixed Fe and C(s) atoms, or only C(s) sites. Among these states, the most stable adsorption configurations are on Fe sites. In this case several different binding configurations have been identified containing a total of one, two, three, and four bonds between the C and O ends and the surface Fe atoms (see panels 6(1)-6(3) in Figure 4 and panels 6(S1) and 6(S2) in Supporting Information Figure S3. In particular, a bridge 2F tilted configuration (see panel 6(2) in Figure 4) and a 4F state (panel 6(3) in Figure 4) with three Fe-C and one Fe-O bonds were found to have the largest adsorption energies of 44.6 and 45.2 kcal/mol, respectively. A large variety of different adsorption configurations is also present in the case when mixed Fe and C(s) sites are involved. As illustrated in panels (6)4-(6)6 of Figure 4 and (6)S3-(6)S4 of Supporting Information Figure S3, configurations with a total number of bonds to Fe atoms ranging from three to five in addition to the C(s)-CO bond can be formed. Similar to other surfaces, the adsorption energies (26.0-32.4 kcal/mol) of these mF-C states are smaller than those involving bonding only to Fe sites. Finally, we note that CO adsorption can take place directly on top of the C(s) surface atom without involvement of any other bonds to the surface Fe atoms. Such a configuration is illustrated in panel (6)S4 of Supporting Information Figure S3 and has an intermediate binding energy of 33.7 kcal/mol. 3.3.7. (100) 0.00 Surface. The set of six crystallographic surfaces of χ-Fe5C2 investigated above are all stoichiometric and symmetric. In this subsection we expand our investigations to the case of the (100) 0.00 surface which has a nonsymmetric termination for the top and bottom planes (see Figure 1g). The motivation for selection of this surface is twofold. First, as indicated in section 3.2 this surface has one of the lowest surface energies among various crystallographic surfaces of Fe5C2, and

Sorescu consequently, it might be observed in practical experimental cases. Additionally, this surface orientation has been also considered in a previous report related to adsorption properties of CO of Fe5C2.15 We note, however, that in the current study the analysis of the adsorption properties of CO has been done using a slab model containing 3 times more layers (see Figure 1g) than the one used in ref 15 which contained five layers of Fe and two layers of C atoms. A similar difference in the slab sizes exists for the (110) 0.00 surface. As illustrated in section 3.2 this increased number of layers was considered in order to achieve convergence of surface energy properties. The results of our adsorption investigations for the (100) 0.00 surface are summarized in Table 3g while the corresponding adsorption configurations are illustrated in panels 7(1)-7(5) of Figure 4. For comparison with results provided in ref 15 we analyze here only the adsorption configurations on the Feterminated side of the slab (top side of the slab in Figure 1g). The most stable adsorption configurations identified on this surface correspond to on-top (configuration 7(1)) and to a threefold binding (configurations 7(2) and 7(3)) states, with almost identical energies of 44.3 and 44.4 kcal/mol, respectively. These configurations have been also identified before,15 but the corresponding binding energies were found to have larger values of 51 and 50.7 kcal/mol, respectively. Beside these 1F and 3F states, in this study we have also identified two new other binding configurations which were not observed before.15 Both these states involves adsorption of the CO molecule in the surface trough, in tilted configurations relative to the surface normal (see panels 7(5) and 7(6) in Figure 4). As a result of tilting, both the C and O ends of the molecule are involved in bonding to the surface Fe atoms. Specifically, in the case of the 7(5) structure three Fe-C and two Fe-O bonds are formed, whereas in the case of 7(6) configuration there are five Fe-C and one Fe-O bonds. The individual lengths of these bonds are indicated in Table 3g. The adsorption energies of these tilted states have values of 40.6 (for 7(5)) and 29.2 kcal/mol (for 7(6)), both of them being smaller than those observed for either the 1F or 3F states described above. Despite lower adsorption energies, both these 5F and 6F states are characterized by significant elongations of the corresponding CO bonds to values of 1.284 Å for 7(6) and 1.303 Å for 7(5), indicating important weakening of these bonds. Overall, the increase of the CO bond lengths takes place in the order 1F < 3F < 6F < 5F. This trend is correlated with a decrease of the vibrational frequencies, which changes from 1900 cm-1 for 7(1), to 1701 cm-1 for 7(3), 1272 cm-1 for 7(6), and 1224 cm-1 for 7(5). As a result, it is expected that configurations like 7(5) characterized by significant weakening of the CO bond represent intermediates for dissociation of CO on the (100) 0.00 surface. 3.3.8. Comparison of the Adsorption Energies and Vibrational Frequencies of CO on Different χ-Fe5C2 Surfaces. The overall results for the adsorption energies and the corresponding vibrational frequencies of the CO molecules adsorbed on different surfaces of χ-Fe5C2 are compared in Figure 5. Given the diversity of bonding environments this comparison is done here as a function of the total number of bonds formed between the CO molecule and the surface atoms. In this analysis, we make distinction between configurations where bonding involves only Fe atoms (1F-6F configurations), or mixed Fe and surface C(s) atoms (1F-C, 3F-C, 4F-C and 5F-C configurations), or it takes place on top of C(s) atoms (0F-C configuration). From the data presented in Figure 5 it is clear that adsorption energies of CO are the highest when bonding involves only the Fe atoms. In the case of 1F-4F states the adsorption energies



Figure 5. Comparison of the adsorption energies (top panel) and vibrational frequencies (lower panel) of CO on different surfaces of χ-Fe5C2 (indicated in legend) together with representative values obtained on bare Fe(110) and Fe(100) surfaces. Notations 1F-6F and mF-C, m ) 0-5 refer to CO bonding exclusively to Fe atoms by one to six different bonds or by bonding to mFe atoms and a surface C(s) atom. Further details of the notation are provided in text. In the case of bare Fe surfaces the acronyms used refer to the tilt hollow (TH), on-top (OT), and tilt bridge (TB) adsorption configurations.

were found to be distributed in the range of 35.8-48.5 kcal/ mol with the majority of the adsorption sites having values in excess of 45 kcal/mol. When CO adsorption takes place at mixed mF-C, m ) 1, 3-5 states or on sites involving only the C(s) atoms (0F-C state) the corresponding adsorption energies are much lower ranging from 18.3 to 35 kcal/mol. As the maximum values of the most stable adsorption configurations for the 1F-4F states are very close, with values ranging from 46.1 to 48.0 kcal/mol, a general trend to establish the most stable adsorption configurations is not easily identifiable. We observe that either of the 1F, 2F, 3F, or 4F states can be preferred depending on the specific crystallographic surface. Further increase, however, in the number of bonds of CO to the surface leads to noticeable lower adsorption energies as is the case of 5F and 6F structures. The adsorption energies determined here, particularly those on Fe-only sites can be compared with those obtained on bare Fe surfaces.20,38 We include in this comparison only the results obtained on the two most stable Fe surfaces, i.e., Fe(110) and Fe(100), obtained at the same theoretical level PAW-PBE as the one used in this paper. These values are indicated in the left side of the top panel in Figure 5. Specifically, on the Fe(110) surface, the most stable adsorption configuration at low coverages corresponds to on-top (OT) binding (Eads ) 44.2 kcal/mol). On the Fe(100) surface three different adsorption configurations have been identified, corresponding to OT (Eads ) 34.1 kcal/ mol), a tilted-bridge (TB) (Eads ) 36.1 kcal/mol), and a tilt state at the four-fold hollow site (TH) (Eads ) 48.9 kcal/mol). From the data in Figure 5 it is clear that the adsorption energies on χ-Fe5C2 are consistent with those obtained on Fe surfaces, as the corresponding results for 1F, 2F, 3F, and 4F states are practically bracketed by the values obtained for Fe(100) (OT) and Fe(100) (TH). In the bottom panel of Figure 5 we illustrate the variation of the ν(CO) stretching frequency on different crystallographic surfaces of Fe5C2 as a function of the bonding type. In this case more clearly defined variation trends are noticeable. Specifically,

for the Fe-only bonding configurations the vibrational frequencies are observed to systematically decrease when going from the 1F to 5F and 6F configurations. Such variations indicate a continuous weakening of the CO bond with the increase in the number of bonds to surface Fe atoms. A similar trend is observed for the case of bare Fe(110) and Fe(100) surfaces, represented on the left side of the lower panel in Figure 5. In this case the corresponding vibrational frequencies were found to decrease from a high value of 1928 cm-1 for the OT site on Fe(110) to a low value of 1189 cm-1 for HF configuration on the Fe(100) surface. A similar behavior of the CO vibrational frequencies is observed in the case of mF-C, m ) 0, 1, 3-5 states. In these cases the highest vibrational frequencies are observed for the 0F-C states with a maximum value of 2046 cm-1 on the (010) 0.25 surface. By increasing the number of bonds to Fe atoms, large red shifts of ν(CO) take place, leading to vibrational frequencies as low as 1118 cm-1 as determined for the 5F-C configuration on the (110) 0.50 surface. The overall picture emerging from the set of results presented above is that the CO molecules preferentially adsorb on sites involving binding to Fe-only atoms (1F-4F states). However, the largest bond weakening effects are observed in the case of bonding to mixed type of Fe and C(s) atoms leading to formation of mF-C (m ) 3-5) states or when bonding on Fe-only sites takes place with formation of a large number of bonds, as is the case of 5F and 6F states. The variation of the calculated vibrational frequencies with CO bond lengths is detailed in Supporting Information Figure S4. As indicated in this figure there is an inverse proportional dependence of the vibrational frequencies with the increase in CO bond length. Correlated with the weakening of the CO bond is the total amount of charge carried out by the CO molecule. It is well-known39,40 that in the case of CO bonding to metallic surfaces the electronic transfer can be described in terms of direct donation from the CO 5σ to the metal d states and back-

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Figure 6. Variation of the total Bader charges (in electron units) of the CO molecule relative to the isolated gas-phase molecule for different adsorption configurations indicated in text in the case of (a) (010) 0.25, (b) (111j) 0.00, and (c) (110) 0.00 surfaces.

donation from the metal to the CO 2π* orbitals. When the net charge transfer is such that the back-donation from the metal d orbitals in the antibonding orbitals of CO is dominant, it is expected that CO bond weakening is facilitated. In order to analyze the charge transfer upon adsorption we have determined the variation of the total charge of the CO molecule relative to the isolated gas-phase case for a number of adsorption configurations in the case of the three most stable surfaces, i.e., (010) 0.25, (111j) 0.00, and (110) 0.00. In these cases the electronic charge density decomposition was done using the algorithm introduced by Henkelman et al.41 for evaluation of the Bader charges.42 As can be seen from the results in Figure 6, there is a general trend of increase in the total amount of charge transferred to the CO molecule with the increase in the total number of bonds. Specifically, on the (010) 0.25 surface where bonding to Feonly atoms is predominant there is a significant charge transfer from the surface to CO when going from 1F to 5F bonding states, whereas in the case of direct bonding on top of the C(s) atom (0F-C) this transfer is less significant. For the other two (111j) 0.00 and (110) 0.00 surfaces, a similar trend is seen independent of the type of bonding to Fe-only or to mixed Fe and C(s) sites. The largest electronic transfer is seen for the

Sorescu configurations with large number of bonds as is the case of 4F-C and 5F-C states on (111j) 0.00 or 4F-C state on (110) 0.00. Overall, on the basis of these results it is expected that the largest weakening effects of CO bond will be observed for those configurations which have a large number of bonds to the surface. Additionally, this effect is even more accentuated if bonding to surface C(s) atoms is involved as is the case of 4F-C and 5F-C bonding states on (111j) 0.00 and (110) 0.00 states. As a result, it is expected that direct dissociation of CO from bonding states involving only few Fe atoms like 1F-4F will take place only by overcoming large activation energies. Significantly smaller activation energies should be, however, observed for those adsorption states which have a large number of bonds, such as the 5F state on (010) 0.25 or when mixed bonding to both Fe and C(s) is possible. These expected trends are put to test in the next sections where we analyze the dissociation energies of CO on various crystallographic surfaces of χ-Fe5C2. 3.4. CO Dissociation on Low Miller Index Surfaces of χ-Fe5C2. In this section we focus on the analysis of the dissociation properties of CO on various low Miller index surface of χ-Fe5C2. Such properties have been determined by calculating the minimum energy potential pathways for dissociation of CO starting from different local minima on the surface. Due to the lack of surface symmetry in a number of instances we had to evaluate different possible reaction pathways starting from the same initial adsorption configuration but reaching different final dissociated states. In this section we make reference only to the reaction pathways with the lowest activation energies. 3.4.1. (010) 0.25 Surface. As was shown in section 3.3.1, the most stable adsorption configurations of CO on the (010) 0.25 surface correspond to the 1F and 4F bonding states, and in this section we focus first on analysis of dissociation properties starting from these configurations (see Figure 7, panels a and b). In the case of the pathway initiated at the 1F state, see image no. 0 in Figure 7a, the overall reaction is endothermic by 14.1 kcal/mol and has a large activation energy of 44.8 kcal/mol. Upon dissociation both the C and O species are adsorbed on the surface at three-fold sites (see image no. 8). In the transition state, corresponding to image no. 6, the C and O atoms are separated by 1.810 Å and they share bonding with one of surface Fe atoms. In the case of the second pathway having as initial state the 4F configuration (see Figure 7b) the reaction profile is slightly more complex. In the initial state the CO molecule is pointing vertical to the surface (see image no. 0 in Figure 7b). From here the molecule tilts first toward the surface and reaches an intermediate local minimum corresponding to image no. 3. In this state both ends of the molecule are bonded to the surface by three Fe-C and two Fe-O bonds, respectively, and the CO bond is elongated to about 1.343 Å. Further elongation of the CO bond leads to molecular dissociation when the separation between the C and O atoms reaches a value of 2.008 Å. In the final state the C and O atoms are adsorbed at four-fold and threefold hollow sites, respectively. The overall reaction is endothermic by only 1.5 kcal/mol, and its activation energy decreases somewhat to 40.0 kcal/mol. As mentioned in previous sections, configurations which present significant weakening of the CO bond such as the 5F state on (010) 0.25 can play an important role in the dissociation process as smaller activation energies from such states are



Figure 7. Minimum energy pathways for CO dissociation on the (010) 0.25 surface for the case of adsorption configurations (a) (1)4 1F-t, (b) (1)8 4F, and (c) (1)10 5F indicated in Table 3a.

expected. Indeed, when the reaction is initiated from such a 5F state (see Figure 7c) the corresponding activation energy decreases even more to 36.9 kcal/mol, the smallest among all the other dissociation pathways determined. We note that the difference between this activation energy and the one determined for dissociation started at 4F state (represented in Figure 7b) is 3.1 kcal/mol. This value is practically equal with the difference of the adsorption energies among 4F and 5F states. These results indicate that during the dissociation process initiated at the most stable 4F state the molecule first evolves to an intermediate local minimum represented by the 5F state (image no. 3 in Figure 7b) from where final dissociation takes place. 3.4.2. (111j) 0.00 Surface. The results of the adsorption analysis on the (111j) 0.00 surface presented in section 3.3.2 indicated that the 1F adsorption state on Fe atoms is the most stable, whereas the mixed 3F-C bonding state leads to the most

weakened CO bond. In this section we compare the corresponding minimum reaction pathways for dissociation from both these two states. The minimum energy pathway for CO dissociation starting from the 1F state is represented in Figure 8a. The overall reaction is endothermic by 24.7 kcal/mol and has an activation energy of 41.6 kcal/mol. Upon dissociation, the C atoms move to a nearby three-fold site, whereas the O atoms end up in a bridge configuration. Similar to the dissociation of the 1F state on the (010) 0.25 surface, in the current case the activation barrier of CO is substantial. In Figure 8, panels b and c, we present the minimum energy pathways for both (2)5 and (2)6 3F-C bonding states determined before. In the case of the first pathway, the molecule is initially bonded to three Fe and one C(s) and the CO bond points away from the surface. From here, the molecule initially tilts

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Figure 8. Minimum energy pathways for CO dissociation on the (111j) 0.00 surface for the case of adsorption configurations (a) (2)1 1F, (b) (2)3 3F-C, and (c) (2)4 3F-C indicated in Table 3b. The intermediate minima represented by image no. 3 in panels b and c correspond to configurations (2)5 4F-C and (2)6 5F-C described in text and in Table 3b.

toward the surface until a new Fe-O bond is formed, corresponding to the small local minimum indicated by image no. 3 in Figure 8b. From this state further elongation leads to the transition state (image no. 6 in Figure 8b) at a separation of 1.793 Å between C and O atoms. Following the transition state the O atom moves away to a three-fold site while the C atom belonging to the CO molecule remains bonded to a C(s) atom and to other three Fe atoms. The overall reaction is slightly exothermic by -2.5 kcal/mol but has a significantly lower activation energy of 15.6 kcal/mol than the one determined for the 1F state. This activation energy is also smaller than the binding energy of CO in the initial configuration ((2)5 state) of 25.3 kcal/mol. These results indicate that dissociation process is favored relative to desorption as the energy increases.

A similar situation is observed for the second minimum energy pathway represented in Figure 8c, corresponding to dissociation of a CO molecule from the (2)6 state. In this case the reaction proceeds with a more complex molecular motion composed by a tilt toward the surface and a simultaneous rotation relative to the original C(s)-C direction. As a result the system evolves to an intermediate local minimum (see image no. 3 in Figure 8c) in which the O end of the CO molecule is bonded to two nearby Fe atoms. From this state further elongation of the CO bond to 1.868 Å leads to reaching the transition state from where the O atom moves away to a bridge site. The overall barrier for this process is 22.2 kcal/mol. This value is larger than the barrier obtained for the dissociation from



Figure 9. (a and b) Minimum energy pathways for CO dissociation on the (110) 0.00 surface starting from (a) (3)2 3F and (b) (3)4 4F-C configurations indicated in Table 3c. (c and d) Minimum energy pathways for CO dissociation on the (111) 0.00 surface for the case of adsorption configurations (c) (4)4 3F-C and (d) (4)6 5F-C indicated in Table 3d.

(2)5 state, but nevertheless it remains significantly smaller than the one of the most stable 1F state. Overall the above results confirm the initial expectations that dissociation energies for CO bonded initially to mixed Fe and C(s) atoms are significantly smaller than those when adsorption takes place at Fe-only sites, such as the 1F state on this surface. 3.4.3. (110) 0.00 Surface. In the case of the (110) 0.00 surface we have analyzed the dissociation pathways corresponding to the most stable (3)2 state and to the most activated (3)4 state. The potential profiles for these two pathways are represented in Figure 9, panels a and b, respectively. In the case of the first pathway the CO molecule is initially positioned at a 3F site (see Figure 9a). From here the molecule can dissociate with formation of an adsorbed C atom at a fourfold site and of an O atom at a three-fold site. The barrier height for this process is 43.8 kcal/mol, and the overall reaction is endothermic by 23.1 kcal/mol. In the transition state the O atom is bridge-bonded to two Fe atoms, and the corresponding C-O separation is 1.826 Å. In the case of the second pathway (see Figure 9b) the CO molecule is initially bonded by three Fe-C, one Fe-O, and one C-C(s) bonds. The transition state of the reaction is similar to the one identified for the (3)2 configuration as the O atom is bridge-bonded to two Fe atoms, and the C-O separation is 1.884 Å. In the dissociated state (see image no. 8 in Figure 9b) the C atom of the CO molecule is bonded to three other Fe atoms and with a nearby C(s) atom, whereas the O is three-fold bonded to Fe surface atoms. Despite the similarity of this transition state to that observed for the first pathway, in the current case the overall activation energy for dissociation is reduced to 31.5 kcal/ mol and the reaction becomes exothermic by -7.1 kcal/mol. These results clearly show that even when similar reaction pathways take place as is the case of the reactions presented in Figure 9, panels a and b, CO bonding to a surface C(s) has an important effect in weakening the CO bond and in lowering the corresponding dissociation barrier. 3.4.4. (111) 0.00 Surface. As indicated in section 3.3.4, on the (111) 0.0 surface there exist several types of 3F-C, 4F-C,

and 5F-C mixed binding states in which the CO bond is significantly weakened. In this case we have analyzed the dissociation only for the 3F-C and 5F-C states characterized by the lowest CO vibrational frequencies and potentially having the largest weakening of the CO bonds. In Figure 9c the minimum energy pathway for dissociation from the (4)4 3F-C state is represented. Here, in the initial state the C end of CO is bonded to two Fe atoms and a nearby C(s) atom, whereas the O end is bonded to a surface Fe atom. In this state the CO bond has a significant elongation of 1.313 Å. Upon dissociation the O atom moves to a nearby bridge site. The activation energy for this process is 27.0 kcal/mol, and the overall reaction is exothermic by -14.1 kcal/mol. The second reaction channel investigated corresponds to dissociation of the CO molecule from a 5F-C state (configuration (4)6 in Figure 3). In the initial state the CO molecule is bonded to the surface by three Fe-C, two Fe-O, and one C-C(s) bonds. This multicenter bonding leads again to a significant elongation of the CO bond to 1.334 Å. The energy profile for dissociation of CO starting from this state is presented in Figure 9d. In the transition state the O atom is approximately positioned in a bridge configuration at a C-O separation of 1.851 Å. From here it moves upon dissociation to a nearby threefold adsorption configuration. The activation energy for this process decreases to 19.8 kcal/mol while the overall reaction is exothermic by -12.9 kcal/mol. 3.4.5. (111j) 0.50 Surface. In the case of the (111j) 0.50 surface we have analyzed the dissociation of a CO molecule for the case of the most stable adsorbed state, i.e., configuration (5)3 in Figure 4, as well as for states which present significant red shifts of the vibrational frequencies such as the (5)4 and (5)5, which are expected to have low activation energies for dissociation. The reaction profile corresponding to dissociation of the CO from the (5)3 state is represented in Supporting Information Figure S5. Here, in the initial state the CO molecule is bonded to four Fe atoms through the C end while the O end points vertically away from the surface. From this state the molecule

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Figure 10. (a and b) Minimum energy pathways for CO dissociation on the (111j) 0.50 surface for the case of adsorption configurations (a) (5)4 5F and (b) (5)5 3F-C indicated in Table 3e. (c) Minimum energy pathway for CO dissociation on the (110) 0.50 surface for the case of 6(6) 5F-C configuration indicated in Table 3f.

rotates itself toward the surface, leading to formation of two new Fe-O bonds (see image no. 3 in Supporting Information Figure S5). Further increase in the CO bond to 2.02 Å leads to the transition state, from where the O atom moves further to a pseudo-four-fold adsorption configuration. The overall reaction is endothermic by 13.5 kcal/mol and has a large activation energy of 42.1 kcal/mol. This high activation energy for dissociation is in line with values presented above for other surfaces of Fe5C2 for the case of the most stable adsorption configurations. In the case of the (5)4 5F state, both ends of the molecule are involved in bonding to the Fe atoms with formation of three Fe-C and two Fe-O bonds. Such a double end bonding leads to a significant CO bond elongation to 1.311 Å and a low vibrational frequency of 1183 cm-1. This initial weakening of the CO bond has also implications upon the corresponding dissociation properties. Indeed, as indicated in Figure 10a, where the minimum energy pathway for dissociation is presented, the overall barrier is only 18.6 kcal/mol, significantly smaller than the one obtained when the molecule initially adsorbs at the most stable (5)3 state, described above. A similar weakening of the CO bond is also observed for the case when CO binds to mixed Fe and C(s) atoms. For example, as indicated in Figure 10b where the minimum energy pathway for dissociation of CO from state (5)5 3F-C is represented, the corresponding barrier is also relatively small with a value of 19.1 kcal/mol. Overall, the current set of results indicates that dissociation of CO is significantly facilitated for bonding configurations involving mixed Fe and C(s) sites or even on Fe-only sites when multiple (five) bonds exist between the C and O ends and the Fe atoms. 3.4.6. (110) 0.50 Surface. As seen from the results obtained in previous sections the activation energy for CO dissociation is significantly facilitated in those cases when the CO molecule is bonded simultaneously to multiple Fe and C(s) atoms. As a result of this multicenter interaction, weakening of the bond takes place which in turn leads to significant red shifts in the

corresponding vibrational frequencies. The ensemble of results obtained so far suggest that those configurations which present the largest red shifts of the vibrational frequencies are also characterized by smallest activation energies for dissociation. In the case of the (110) 0.50 surface we have tested this aspect for the case of the (6)6 5F-C adsorption configuration characterized by a low vibrational frequency of 1118 cm-1. The minimum energy reaction pathway for dissociation of CO in the (6)6 state is represented in Figure 10c. As seen from this figure the calculated results confirm the existence of a relatively small activation energy of only 20.8 kcal/mol. The small activation energy quoted here is done by comparison to those obtained for dissociation of CO from the most stable states. For example, on the current surface dissociation of the most stable adsorption state (6)4 4F requires an activation energy of 58.4 kcal/mol (results not shown). Such results clearly indicate that a significant lowering of the dissociation barrier takes place when CO is bonded to both C(s) and several surface Fe atoms instead of simple binding exclusively to Fe atoms. 3.4.7. (100) 0.00 Surface. In the case (100) 0.00 no stable adsorption configurations involving binding to C(s) atoms were determined. Instead the most stable adsorption states were found to take place at 1F and 3F sites. Such states, however, are expected to have large activation energies for dissociation. In order to further clarify this aspect we present in Figure 11a the minimum energy pathway for CO dissociation initially adsorbed at a 3F site. Upon dissociation, the system leads to formation of C and O species adsorbed at three-folded sites. As can be seen in Figure 11a the corresponding barrier for dissociation is substantial, with a value of 42 kcal/mol, and the overall reaction is endothermic by 5.4 kcal/mol. Significantly smaller activation energies, however, are expected to take place for those adsorption configurations which present large red shifts in the vibrational frequencies such as the 5F state identified on this surface. In order to illustrate this point we present in Figure 11b the minimum energy pathway for dissociation of CO, initially adsorbed at a 5F site. In this configuration both ends of the molecule are bonded to the



Figure 11. (a and b) Minimum energy pathways for CO dissociation on the Fe-terminated (100) 0.00 surface for the case of adsorption configurations (a) (7)3 3F and (b) (7)5 5F indicated in Table 3g.

Figure 12. Comparison of the dissociation energies for a CO molecule adsorbed on different surfaces of χ-Fe5C2 (indicated in legend). In each case the type of molecular bonding to the surface is indicated involving only Fe atoms (1F, 3F, 4F, 5F) or mixed Fe and C(s) atoms (3F-C, 4F-C, 5F-C).

surface with formation of three Fe-C and two Fe-O bonds. As a result the CO bond is elongated to 1.303 Å and has a low stretching frequency of 1224 cm-1. The transition state is reached when the separation between the C and O atoms is 2.02 Å, from where the system evolves to dissociated C and O species adsorbed at two different three-folded sites. The barrier for this process is 26.9 kcal/mol, significantly smaller than the one determined for dissociation initiated at the most stable 3F site. The results obtained for the (100) 0.00 surface further confirm that the most stable adsorption configurations of CO are also characterized by large barriers for dissociation. Significant reduction of the dissociation barriers are observed, however, for those binding states where the CO molecule is lying down on the surface, such that both ends of the molecules are involved in multiple bonds to the surface atoms. 3.4.8. Comparison of the Dissociation Energies of CO on Different χ-Fe5C2 Surfaces. The ensemble of results obtained in previous sections related to activation energies for dissociation of CO on different crystallographic surfaces of the χ-Fe5C2 phase are compared in Figure 12. In each instance the initial state of the CO molecule is indicated as a function of the type and total number of bonds made to the surface atoms. Specifically, in the case when bonding involves only Fe atoms this is indicated using notation mF, with m ) 1, 3, 4, 5, whereas in the case when molecular bonding involves both Fe and C(s) atoms the corresponding notation has the form mF-C, with m ) 3, 4, 5. As indicated in previous sections the main configurations we focused upon are either the most stable adsorption states or those with the largest red shifts of the CO vibrational frequencies. This latest category of states was selected because they are the best candidates for smaller activation energies for dissociation.

Given the focus of our investigations, in Figure 12 we have not included dissociation from all the other binding configurations identified such as the 2F or 0F-C, as such states are either not the most stable or the most reactive on χ-Fe5C2 surfaces. From the data presented in Figure 12 it is clear that independent of the crystallographic surface orientation, when CO adsorbs on Fe-only sites in one of the 1F, 3F, 4F configurations, the corresponding activation energies for dissociation are substantial, with values in excess of 40 kcal/mol. As such states are the most stable on Fe5C2 surfaces it can be concluded that they also have the largest activation energies for dissociation. The activation energies decrease, however, in the particular cases when the CO molecule adsorbs in tilted configurations that allow formation of multiple bonds of both C and O ends, as is the case of the 5F states. In such instances the activation energies decrease to 18.6-36.9 kcal/mol a function of the specific crystallographic orientation. The second important category of adsorption configurations are the mF-C states involving simultaneous bonding to mixed Fe and surface C(s) atoms. The results of the adsorption investigations (see Figure 5) have indicated that these binding configurations are less stable than those involving Fe-only atoms. However, these states are characterized by important elongations of the CO bonds and, correspondingly, by large red shifts of the vibrational frequencies, indicative of significant weakening of the CO bonds. The data in Figure 12 confirm that the activation energies for dissociation from these states, ranging from 15.6 to 31.5 kcal/mol, are significantly smaller than those obtained for 1F-4F states where bonding takes place exclusively on Fe atoms.

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These results suggest that the mF-C configurations represent the precursor states for CO dissociation on Fe5C2 surfaces. Upon CO dissociation from such states the resultant C(s)-C fragments remain adsorbed on the surface. Such fragments can be, however, involved in additional adsorption and dissociation processes of other CO molecules. It is clear, however, that extensive increase in the length of the C(s)-Cx, x ) 1, 2, ..., chains beyond few units will lead to formation of graphitic type of carbon, which in turn will determine a significant decrease in the catalytic properties for CO dissociation reaction. However, if the iron carbide surface is exposed not only to CO but to H2 as well, as is the case of FTS applications, then the polymeric carbon chains can interact with the adsorbed H, leading to formation and chain growth of hydrocarbon species. As a result, under exposure to a combined CO + H2 atmosphere, it is expected that formation of light polymeric carbon chains containing few C-C units becomes favorable. In summary, on (010) 0.25, (111j) 0.5, and (100) 0.00 surfaces the favored pathways of CO dissociation correspond to dissociation starting from 5F type of sites where the tilted adsorption configuration of CO allows formation of multiple bonds of both C and O ends of the molecule. On the set of (111j) 0.00, (110) 0.00, (111) 0.00, and (110) 0.50 surfaces the preferred dissociation pathways involve, however, the mF-C states where CO bonding takes place with large elongations and red shifts of the vibrational frequencies. A direct comparison of the variation of dissociation energies to the corresponding binding energies is provided in Supporting Information Figure S6. As can be seen from this figure only a qualitative correlation can be established. In a number of instances important differences exist between the activation energies corresponding to similar binding energies as is the case of the data at about 25 and 35 kcal/mol, respectively. The lack of a direct dependence between the adsorption and dissociation energies is not, however, unexpected. Indeed, as dissociation of CO on Fe5C2 surfaces takes place with a late transition state and significant molecular reorientation relative to the surface and bond elongation are involved prior to dissociation, the thermodynamic parameters for the transition state are more related to the chemisorption properties of the product state instead of the initial adsorption state. As a result the obtained correlation is only qualitative in nature. The ensemble of CO dissociation energies on χ-Fe5C2 surfaces determined above can be also compared against the corresponding dissociation energies on bare Fe surfaces. In doing this comparison we make reference to our recent study20 in which we have analyzed extensively the dissociation properties of CO on a large number of flat, stepped, and kinked Fe surfaces at low coverages. An important conclusion of that study is that among the set of surfaces (110), (100), (211), (710), (310), and (111) important variations of the dissociation barriers exist. In particular, the largest activation energy of 35.6 kcal/mol has been determined in the case of a p(2 × 2) CO overlayer. Such activation barriers, however, decrease significantly in the case of stepped or kinked surfaces. For example, on the Fe(100) surface the activation energy of dissociation is only 24.7 kcal/ mol and corresponds to dissociation of a CO molecule initially adsorbed at the hollow site in a tilted configuration. Such a configuration allows bonding of the C end of CO to five Fe atoms (four in the top layer and one in the second layer) while the O end is bonded to two Fe atoms. Consistent to notation used in this study such a state would be denoted as a 7F state. The smallest activation energies for dissociation of CO on bare Fe surfaces have been determined, however, for kinked

Sorescu Fe(710) and Fe(310) surfaces. The corresponding barriers in these cases are 15.4 and 16.4 kcal/mol, respectively. Such low barriers were determined for the case when the CO molecule is initially adsorbed at a four-fold site positioned at the bottom of the step.20 In such configurations there are five Fe-C bonds and three Fe-O bonds between the molecule and the Fe atoms. Consequently, consistent with the nomenclature used in this paper, such states can be denoted with symbol 8F, based on the total number of bonds to the surface atoms. The most representative activation energies of CO on bare Fe surfaces are compared to those obtained on Fe5C2 surfaces in Figure 12. From this figure it can be seen that the activation energies are the largest for those configurations with the smallest number of bonds to the surface, as is the case of 1F states on both Fe and Fe5C2 surfaces. Second, by increasing the number of bonds to the surface the activation energy for CO dissociation drops significantly. This is, for example, the case of Fe(100) or kinked Fe(710) and Fe(310) surfaces where the adsorption configurations with seven and, respectively, eight bonds to the surface are also characterized by the lower dissociation energies. Similarly, on Fe5C2 surfaces, important decreases in activation energies of dissociation take place with the increase in the number of bonds to the surface. Despite these similarities there are also a number of noticeable differences, particularly related to the outcome of the dissociation process. In the case of bare Fe surfaces dissociation will lead to formation of adsorbed C atoms. Such atoms can either diffuse into the surface or in the presence of a H2 atmosphere can be hydrogenated to form methane as we have shown in a previous studies.20,21 On Fe5C2 surfaces where dissociation from mF-C type of states is preferential this leads to formation of C(s)-C units. Such carbon units are expected to grow on the surface in the absence of H2, but they will be involved in hydrocarbon condensation if H2 is present. The different types of carbon species indicated above have been also observed in experimental studies. For example, Xu and Bartholomew6 have identified, based on temperatureprogrammed hydrogenation (TPH) and Mo¨ssbauer spectroscopy studies, six different surface and bulk carbonaceous species on the iron catalyst under realistic FTS conditions. Among these, the two most reactive were denoted as the CR and Cβ species which correspond to adsorbed atomic carbon, respectively, to lightly polymerized hydrocarbon or carbon surface species. The CR species resulted from CO dissociation on the Fe surface can dissolve into iron to form iron carbides. In contradistinction, on iron carbide surfaces, the atomic carbon at the surface is converted to Cβ species, a polymeric carbonaceous specie containing few (two to three) C atoms. The existence and stabilization of Cβ species on the surface of χ-Fe5C2 was also confirmed by Herranz et al.5 based on a series of temperatureprogrammed surface reactions with hydrogen (TPSR-H2), temperature-programmed surface desorption with argon (TPD-Ar), X-ray diffraction, and Mo¨ssbauer spectroscopy studies. Our theoretical results indicate the existence of a favorable channel for formation of Cβ species as a result of CO dissociation from mixed mF-C sites and correspondingly supports the abovepresented experimental findings. 4. Conclusions We have performed plane-wave DFT calculations using the GGA-PBE method to determine the stability properties of different surfaces of χ-Fe5C2. The adsorption properties of CO in the regime of low coverages have been calculated for the set of top seven most stable Fe5C2 surfaces, and the minimum

Adsorption and Activation of CO on Fe5C2 Surfaces energy potential pathways for CO dissociation reaction leading to formation of adsorbed C and O species have been determined. The main conclusions of this study can be summarized as follows: (a) The stability properties for a set of 14 different crystallographic surface orientations with symmetric termination of the top and bottom planes and with the bulk stoichiometry have been determined for the χ phase of Fe5C2. Among these, the six most stable surfaces were found to be (010) 0.25, (111j ) 0.00, (110) 0.00, (111) 0.00, (111j) 0.50, and (110) 0.50, with surface energies in the range of 2.47-2.84 J/m2. The stability order determined in this study agrees with previous findings obtained by Steynberg et al.19 Additionally, we have included in our investigations the case of the (100) 0.00 surface which has an asymmetric crystallographic termination of the upper and lower planes as this surface has a low surface energy of 2.16 J/m2. (b) The adsorption properties of CO in the regime of low coverages have been analyzed for the set of six most stable symmetric surfaces of χ-Fe5C2 and on the asymmetric (100) 0.00 surface. The results obtained indicate that the CO molecule preferentially adsorbs on sites involving binding to Fe atoms. For the ensemble of surfaces analyzed, a large diversity of binding configurations has been found to exist with formation of one up to six total bonds with Fe atoms. Among these states however, the most stable are the 1F-4F states, with maximum binding energies ranging from 44.4 to 48.5 kcal/mol. A second category of distinct adsorption states corresponds to the case when the CO molecule is bonded to both Fe and surface C(s) atoms. Such states, generically denoted as mF-C, m ) 1, 3-5, can have a total of one up to five different bonds to surface Fe atoms, in addition to a C-C(s) bond to a surface C(s) atom. Finally, direct bonding of CO on top of a C(s) atom (0F-C states) has been also identified, particularly on (010) 0.25, (110) 0.00, or (110) 0.50 surfaces where C(s) atoms are positioned in the top layer. Overall, the adsorption at mF-C (m ) 0, 1, 3-5) states are characterized by lower adsorption energies ranging from 15.6 to 31.5 kcal/mol. (c) The vibrational analysis performed in the phonon mode approximation for each of the adsorption configurations identified has evidenced important differences among different bonding states. Specifically, in the case of binding configurations involving Fe atoms a systematic decrease of the vibrational frequencies was found to take place when going from 1F to 5F and 6F configurations, indicating a continuous weakening of the CO bond with the increase in the number of bonds formed to the Fe atoms. Similarly, in the case of mF-C states a red shift change of the vibrational frequencies was determined when going from the 0F-C states to states with a large number of bonds like 5F-C configurations. Among various adsorption states the largest bond weakening was observed for either mixed configurations (mF-C states, m ) 3, 5) or for states involving a large number of bonds to surface Fe atoms (like 5F and 6F states). The weakening of the CO bonds was found to be associated with a charge transfer from metal to the CO molecule. (d) The bond dissociation energies of CO for the most stable adsorption configurations were also found to be the

J. Phys. Chem. C, Vol. 113, No. 21, 2009 9273 highest. These activation energies, however, decrease significantly with the increase in the total number of bonds to the surface atoms. Among these, the lowest activation energies were found to take place for configurations like 5F, 3F-C, or 5F-C. Dissociation reaction initiated from the mixed mF-C states leads to preferential formation of small C(s)-C chain units, in agreement with experimental observation of polymeric carbonaceous species containing few (two to three) C atoms.6 Acknowledgment. We gratefully acknowledge the computational resources provided by the Pittsburgh Supercomputer Center and the 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. Supporting Information Available: Pictorial views of additional CO adsorption configurations and representative minimum energy potential pathways for CO dissociation on different surfaces of χ-Fe5C2. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) (a) Fischer, F.; Tropsch, H. Brennst. Chem. 1923, 4, 276. (b) Anderson, E. B. The Fischer-Tropsch Synthesis; Academic Press: New York, 1984. (2) Fischer-Tropsch Synthesis, Catalysts and Catalysis; Davis, B. H., Occelli, M. L., Eds.; Studies in Surface Science and Catalysis, Vol. 163; Elsevier Science: Amsterdam, 2006. (3) Davis, B. H. Catal. Today 2009, 141, 25. (4) Dry, M. E. The Fischer-Tropsch Synthesis. In Catalysis; Anderson, J. R., Boudart, M., Eds.; Springer-Verlag: New York, 1981; Vol. 1. (5) Herranz, T.; Rojas, S.; Pe´rez-Alonso, F. J.; Ojeda, M.; Terreros, P.; Fierro, J. L. G. J. Catal. 2006, 243, 199. (6) Xu, J.; Bartholomew, C. H. J. Phys. Chem. B 2005, 109, 2392. (7) Li, S.; Meitzner, G. D.; Iglesia, E. J. Phys. Chem. B 2001, 105, 5743. (8) Emmett, P. H., Ed. Crystallite Phase and Their Relationship to Fischer-Tropsch Catalysis; Reinhold: New York, 1956. (9) Riedel, T.; Schulz, H.; Schaub, G.; Jun, K.-W.; Hwang, J.-S.; Lee, K.-W. Top. Catal. 2003, 26, 1. (10) Davis, B. H. Catal. Today 2003, 84, 83. (11) Ning, W.; Koizumi, N.; Chang, H.; Mochizuki, T.; Itoh, T.; Yamada, M. Appl. Catal., A 2006, 312, 35. (12) Caceres, P. G. Mater. Charact. 2006, 56, 26. (13) Datye, A. K.; Jin, Y.; Mansker, L.; Motjope, R. T.; Dlamini, H.; Coville, N. J. Stud. Surf. Sci. Catal. 2000, 130, 1139. (14) Bukur, D. B.; Okabe, K.; Rosynek, M. P.; Li, C.; Wang, D.; Rao, K. R. P. M.; Huffman, G. P. J. Catal. 1995, 155, 353. (15) Cao, D.-B.; Zhang, F.-Q.; Li, Y.-W.; Jiao, H. J. Phys. Chem. B 2004, 108, 9094. (16) Cao, D.-B.; Zhang, F.-Q.; Li, Y.-W.; Jiao, H. J. Phys. Chem. B 2005, 109, 833. (17) Cao, D.-B.; Zhang, F.-Q.; Li, Y.-W.; Jiao, H. J. Phys. Chem. B 2005, 109, 10922. (18) Cao, D.-B.; Zhang, F.-Q.; Li, Y.-W.; Jiao, H. J. Mol. Catal. A: Chem. 2007, 272, 275. (19) Steynberg, P. J.; van den Berg, J. A.; van Rensburg, W. J. J. Phys.: Condens. Matter 2008, 20, 064238. (20) Sorescu, D. C. J. Phys. Chem. C 2008, 112, 10472. (21) Sorescu, D. C. Phys. ReV. B 2006, 73, 155420. (22) Sorescu, D. C.; Thompson, D. L.; Hurley, M. M.; Chabalowski, C. F. Phys. ReV. B 2002, 66, 035416. (23) (a) Kresse, G.; Furthmu¨ller, J. Comput. Mater. Sci. 1996, 6, 15. (b) Kresse, G.; Furthmu¨ller, J. Phys. ReV. B 1996, 54, 11169. (24) Blo¨chl, P. E. Phys. ReV. B 1994, 50, 17953. (25) Kresse, G.; Joubert, D. Phys. ReV. B 1999, 59, 1758. (26) Perdew, P.; Burke, K.; Ernzerhof, M. Phys. ReV. Lett. 1996, 77, 3865. (27) Vosko, S. H.; Wilk, L.; Nusair, M. Can. J. Phys. 1980, 58, 1200. (28) Monkhorst, H. J.; Pack, J. D. Phys. ReV. B 1976, 13, 5188. (29) Methfessel, M.; Paxton, A. T. Phys. ReV. B 1989, 40, 3616. (30) Jońsson, 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.

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JP811381D

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