QTAIM analysis of the effect of late transition metal doping on methane selectivity in Fischer–Tröpsch catalysis

Computational and Theoretical Chemistry 1063 (2015) 1–9

Contents lists available at ScienceDirect

Computational and Theoretical Chemistry journal homepage: www.elsevier.com/locate/comptc

DFT/QTAIM analysis of the effect of late transition metal doping on methane selectivity in Fischer–Tröpsch catalysis Peter C. Psarras, David W. Ball ⇑ Department of Chemistry, Cleveland State University, Cleveland, OH 44115, United States

a r t i c l e

i n f o

Article history: Received 3 February 2015 Received in revised form 7 April 2015 Accepted 7 April 2015 Available online 16 April 2015 Keywords: Fischer-Tröpsch Methane selectivity Catalysis Density functional theory

a b s t r a c t The effect of late transition metal substitution into Fe(1 0 0), Ni(1 1 1), and Co(0 0 0 1) surface analogs has been investigated density functional theory (DFT) methods. The surface was modeled using a 7-atom cluster, with perimeter atoms saturated with hydrogen atoms to approximate surface coordination and mitigate dangling bond artifacts. All calculations were performed at the B3PW91 level of theory with the LANL2DZ basis. Eight surface adsorbates were studied: C, CH, CH2, and CH3 represented the hydrogenating steps on surface carbide, while C+CH, CH+CH, C+CH3, and CH2+CH2 represented four competitive coupling pathways. A review of the effect of Cu, Ag, Au, and Pd on the reaction energies and barriers associated with these critical steps is discussed. QTAIM is employed to develop a picture of the electronic environment associated with methane selectivity. Attention is focused on the charge trends for the involved surface atoms and coupling species. Our results suggest that promising candidates for the reduction of FT methane selectivity include Au and Pd on Ni, Au and Ag on Co, and Cu, Ag, and Pd on Fe. Ó 2015 Elsevier B.V. All rights reserved.

1. Introduction Fischer–Tropsch synthesis has endured a long and industrious career as the premier chemical method for the synthesis of hydrocarbons from non-petroleum-based precursors. Historically, a collection of factors has dictated interest in the FT process, including foreign policy, availability of precursor(s), availability of alternate fuel sources and reserves, and environmental considerations [1]. As the current administration places increasing emphasis on energy independence and large reserves of natural gas await harvest to be monetized via gas-to-liquid (GTL) technologies [2], FT interest has seen a slight resurgence. Although these contributions continue to play a large role, FT interest is ultimately tied to the economic viability of processing versus the cost of crude oil. Improving catalytic efficiency will make FT technology more economically viable and a larger player in the global energy market. Additionally, these results may be extended to the design of new catalytic materials for other applications such as carbon capture or reduction of CO2 to fuel. Though controversy surrounds the exact mechanism of chain growth [3–8], the process is simple in theory in that a mixture of CO and H2 synthesis gas (syngas) is reacted over a supported transition metal catalyst to produce a variety of hydrocarbons with product selectivities based upon catalyst choice (typically Fe, Co, or alloys thereof). Nearly 60% of operating capital is devoted to ⇑ Corresponding author. http://dx.doi.org/10.1016/j.comptc.2015.04.004 2210-271X/Ó 2015 Elsevier B.V. All rights reserved.

the preparation and purification of the syngas precursor [9]. Such processes involve the removal of sulfur species (which are catalytic poisons) and the partial oxidation of CH4 to CO. With such a large contribution of capital devoted to the feedstock preparation, CH4 presence in FT product-streams defines counter-productivity. According to the Anderson–Schulz–Flory (ASF) distribution [10], FT products are dictated by a single parameter a, the chain growth probability. Yet major deviations are observed in C1, C2 and C3 species. Isotopic labeling has suggested that C2 species are reabsorbed to the surface and become re-incorporated into longer chain hydrocarbons [11]. Various theories surround the deviation at C1 (methane), ranging from errors in quantification methods to the hydrogenolytic cleavage of a-olefins, though the exact source of additional methane remains unclear. Though the role of promotion in FT synthesis is well documented in terms of catalytic activity, effects of promotion on product selectivities are less certain. [12–22] Evidence suggests that a Bronsted–Evans–Polanyi (BEP) relationship exists between the effective barrier to methanation and carbon binding strength. It is important to clarify that the presence of carbon in this study is not intended to suggest a particular mechanism. Rather, carbon is used as a simple descriptor to methane selectivity, as studies by Cheng et al. have illustrated that carbon binding strength can accurately reproduce methane selectivity trends over FT metals [23]. A classic volcano curve of carbon binding strength against methane selectivity reveals an important consideration akin to the Sabatier principle: catalytic surfaces should not bind the

2

P.C. Psarras, D.W. Ball / Computational and Theoretical Chemistry 1063 (2015) 1–9

adsorbate too weakly, nor too strongly, as the adsorbate species is either non-activated or acts as a surface poison, respectively [24]. Naturally, a tightly bound surface species may reduce methane selectively but the trade-off is unfavorable: catalytic poisoning and, in the case of the FT surface, carbide build-up. The role of a promoter is to shift the parent surface to a more favorable portion of the volcano curve, i.e. higher activity/lower methane selectivity; thus, a deeper understanding of the electronic environments associated with methane selectivity is needed to design more efficient FT catalysts. In this study, the effect of late transition metal promotion (Cu, Ag, Au, and Pd) on three active FT catalytic surface analogs (Ni(1 1 1), Fe(1 0 0), and Co(0 0 0 1)) is investigated. Initially, adsorption data for two sets of adsorbates is presented, i.e., species involved in surface carbide hydrogenation and carbon–carbon coupling reaction pathways, respectively:

surface þ CðgÞ CðadsÞ

ð1Þ

CðadsÞ þ HðadsÞ CHðadsÞ

ð2Þ

CHðadsÞ þ HðadsÞ CH2ðadsÞ

ð3Þ

CH2ðadsÞ þ HðadsÞ CH3ðadsÞ

ð4Þ

CH3ðadsÞ þ HðadsÞ CH4ðgÞ

ð5Þ

CðadsÞ þ CHðadsÞ C2 HðadsÞ

ð6Þ

CHðadsÞ þ CHðadsÞ C2 H2ðadsÞ

ð7Þ

CH3ðadsÞ þ CðadsÞ C2 H3ðadsÞ

ð8Þ

CH2ðadsÞ þ CH2ðadsÞ C2 H4ðadsÞ

ð9Þ

Of the nine possible carbon–carbon coupling pathways involved in the C1–C2 transition, the four pathways listed in Eqs. (6)–(9) been found to occur at the fastest rates [25]. Next, transition states (TS) are sought for each of the aforementioned reactions, and barriers for these steps are presented. Promising candidates can be revealed through the comparison of (i) carbon binding strengths over the proposed surface analogs, as well as (ii) barriers for the hydrogenating and coupling steps, respectively. The quantum theory of atoms in molecules (QTAIM) approach, or Bader analysis [26], is a valuable tool for analyzing charge distribution data from DFT calculations [27–30]. However, this tool has not been used extensively in the study of FT reactivity. Bader analysis will be employed to reveal how promoter substitution changes the surface electronic environment, and how promotion influences electronic redistribution upon adsorption. 2. Computational methodology All geometry optimizations and frequency calculations for the reactants, products, and transition state species were performed in the Gaussian 03/09 platform [31]. All calculations were processed on the Oakley Cluster at the Ohio Supercomputing Center in Columbus, OH, project PFS-0213. The exchange–correlation term was treated with the Becke 3-parameter formulation [32]/ Perdew and Wang [33] (B3PW91) hybrid functional. The exchange functional was defined as a linear combination of Hartree–Fock, local, and gradient-corrected exchange terms; this functional was then mixed with the PW91 correlation functional of Perdew and Wang. This functional was chosen for its superior performance when compared to many non-hybrid DFT functionals, for its accuracy in predicting geometries, and for its appearance in similar

studies [34–36]. Electronic orbitals were described with the LANL2DZ [37] basis set, which includes relativistic effects required for larger atoms (Z > 36) and treats core electrons with a non-explicit effective core potential (ECP). The efficiency of calculation was greatly increased by treating core electrons (those that are not involved in bonding) by only their collective effect on valence electrons. Seven-atom clusters were used to approximate local surfaceadsorbate interactions. A number of studies have used small, non-periodic clusters as effective surface analogs [38–43]. These idealized clusters lack important surface features (such as sub-layer atoms) and require perimeter treatment of dangling bonds; however, errors created by such factors are expected to be similar on all clusters and should largely cancel upon inter-cluster comparisons. Insights into catalysis can thus be acquired through analysis of the cluster trends. Each cluster was designed based on experimental crystal structures for the most active surface for each considered FT catalyst: Ni(1 1 1), Fe(1 0 0), and Co(0 0 0 1). Clusters were allowed to optimize within the aforementioned basis and level of theory. Perimeter atoms were then saturated with atomic hydrogen to mediate dangling bonds and drive the perimeter coordination number to five (CN = 5). This saturation assists to remove severely undercoordinated atoms in reference to the central cluster atom, i.e., CN = 6. Such discrepancies have lead to adsorbate migration to, and in some cases past, the coordinatively unsaturated atoms at the cluster perimeter. A diagram of the pure and promoted surface analog is provided in Fig. 1. Surface positions were numbered with 1 at the center, 2 held by the promoter, and positions 3–7 follow counter-clockwise around the perimeter. All clusters were tested for proper spin configuration, where the correct spin state was determined variationally. All adsorbates were placed centrally atop the cluster and allowed to optimize freely while all surface coordinates were held constant. With the exception of carbon chemisorption Eq. (1), surface adsorbed species (and not free gaseous species) were used in calculating free energy changes, obviating the need for basis set superposition error correction (BSSE). Though calculations were conducted at 0 K, all energies were reported as a sum of electronic and thermal free energies with zero-point energy correction, calculated from the corresponding partition functions at ambient conditions (see the method described in ref [58]). Adsorption energies were calculated via:

Dr G  ¼

X

ðeo þ Gcorr Þproducts 

X

ðeo þ Gcorr Þreactants

ð10Þ

where eo + Gcorr is the sum of electronic (zero-point corrected) and thermal free energies. The B3PW91 functional has been shown to systematically underestimate barrier heights [34], though this effect is considered relative and should vanish when trends are considered. Transition state searches were performed via the Berny algorithm (i.e., a Hessian-guided maximization of energy along the imaginary mode). Carefully calculated, chemically rational TS geometries for all adsorbates over pure Ni were first sought, as TS searching over this surface proved less computationally intensive than over Co and Fe, respectively. These TS geometries served as initial guesses for all other surface-analogs. Transition states were confirmed by the presence of a single imaginary frequency corresponding with a mode that connects reactant and product geometries. Activation barriers were calculated via:

DGz ¼

X

ðeo þ Gcorr Þtransition

state



X

ðeo þ Gcorr Þreactants

ð11Þ

Bader charge assignment and analysis of critical point data was performed with the AIMALL suite of programs (v. 13.11.04) [44]. The atomic integration method and atomic integration parameters were automatically determined by AIMALL, where appropriate

3

P.C. Psarras, D.W. Ball / Computational and Theoretical Chemistry 1063 (2015) 1–9

Fig. 1. Seven-atom surface analogs: pure (left) and with promoter substitution (right). Position 1 is in center, position 2 is held by the promoter, and positions 3–7 follow counter-clockwise around the perimeter.

reconfiguration was automatically implemented for ‘‘difficult’’ atoms as required to achieve results having reasonable numerical accuracy (±0.001 atomic units (a.u.) for atomic charge assignments) [45–47].

3. Results and discussion 3.1. Surface geometry The surface geometries of 15 unique clusters were examined to estimate the effect of two factors: (1) the accuracy of our computational method in predicting nearest-neighbor (NN) distances on pure surfaces and (2) the effect of promoter insertion on these distances. Results are listed in Table 1. For pure surfaces (Ni(1 1 1), Co(0 0 0 1) and Fe(1 0 0)), average distances are calculated from 12 NN, of which 6 are between the central surface atom and each of 6 perimeter atoms and 6 from the NN of each perimeter atom with its neighbor. Co(0 0 0 1) NN distances were predicted best, with an overestimation of 0.86% when compared to an experimental distance of 2.507 Å [48]. Ni(1 1 1) and Fe(1 0 0) were underestimated by 2.8% (exp. 2.492 Å) [49] and overestimated by 3.4% (exp. 2.482 Å) [50], respectively. Surface readjustment can play a large role in the local electronic environment experienced by any set of adsorbates. Promoters with larger van der Waals radii (silver and gold, for example) will force an extended NN distance in the immediate vicinity due to internuclear repulsions, and this may or may not directly affect the distance between neighboring (native surface) atoms. This effect was measured by considering 3 averages: (1) the total NN distance NN ), (2) the average distance of atoms coordinated to average (d NP ), and (3) the average of NN distances that the promoter (d NQ ). These averages are compared to the exclude the promoter (d experimental NN distance and presented as a percentage difference (positive if the spacing increases, negative it the spacing decreases). Total NN distance averages may be misleading as large

local displacements created by promoters are counter-balanced by the induced closer proximity of their next-nearest neighbors (NNN). In many cases, the total average NN distance for promoted surfaces deviated by less than 1% from experimental measurements. The effect of promotion on the creation of space immediNP . For all ately surrounding the promoter was quantified by the d 3 surfaces considered, silver created the largest positive displacement of its nearest neighbors (+6.1% on Ni(1 1 1), +6.6% on Co(0 0 0 1), and +9.4% on Fe(1 0 0)), followed closely by gold (+4.0% on Ni(11), +4.2% on Co(0 0 0 1), and +6.7% on Fe(1 0 0)). This can be attributed to the large van der Waals radii associated with silver (1.72 Å) and gold (1.66 Å). Copper had the unique effect of allowing the NN spacing to decrease when placed as a substitute on Ni(1 1 1) and Co(0 0 0 1), again a function of its smaller van der Waals radius (1.40 Å). Though palladium has a van der Waals radius comparable in size to gold, it was considered least invasive in terms of geometric rearrangement, with an effect of roughly 1% on Ni(1 1 1) and Co(0 0 0 1) and less than 1% on Fe(1 0 0). It has been suggested that the effect of electronegativity (EN) differences between surface and promoter may also influence NN spacing [51]. The promoters Cu and Ag have similar Pauling EN values to the 3 surface metals, ranging from 1.83 (Fe) to 1.93 (Ag), while Pd and Au are considerably more EN, at 2.20 and 2.54, respectively. Lower-EN promoters would effectively push electron density into their nearest (more EN) neighbors, while greater-EN promoters would pull this NN electronic density away. It is possible that geometric effects are a combination of EN and promoter size effects, though a lack of trends associated with these descriptors suggests additional factors. One possible explanation involves an enthalpic collapse of the each cluster system driven by an attempt to resolve dangling bonds and varying degrees of unsaturation. Further investigation of geometric vs. electronic effects will be pursued in the discussion on Bader charges, Section 3.4. The creation (or in some cases elimination) of space due to promoter substitution was also quantified in terms of the remaining surface. Metal–metal spacing (where metal is the native surface

Table 1 Optimized nearest-neighbor (NN) distances as represented by percentage difference of 3 averages against the experimental spacing [48–50]: (1) the average of all nearest NN ), (2) the average spacing between the promoter and atoms coordinated to the promoter (d NP ), and (3) the average NN distances that exclude the neighbor atomic spacings (d promoter Positive and negative percentages indicate an increase and decrease in spacing, respectively. Distance

Percent change {(calculated[B3PW91/LANL2DZ) – experimental)/experimental}  100% Ni

NiCu

NiAg

NiAu

NiPd

Co

CoCu

 d NN  d

2.80

2.60

0.28

0.29

1.10

0.90

1.40

NP

–

1.90

6.10

4.00

1.20

–

1.30

6.60

4.20

 d NQ

–

2.80

2.40

2.00

1.80

–

1.40

1.43

0.60

CoAg 0.70

CoAu 0.80

CoPd

Fe

FeCu

FeAg

FeAu

FePd

0.50

3.40

2.10

4.40

5.00

3.10

1.10

–

3.00

9.40

6.70

6.50

1.00

–

1.80

2.70

4.00

3.90

4

P.C. Psarras, D.W. Ball / Computational and Theoretical Chemistry 1063 (2015) 1–9

metal Ni, Fe, or Co) was compared on all clusters. When compared to the NN distance on un-promoted clusters, the effect of promotion on nickel spacing was considered negligible with average separations ranging from 0.1% to 0.9%. Though our model overestimates Co(0 0 0 1) spacing by roughly 0.8%, all promoters had the effect of reducing cobalt-cobalt spacing from 1.4% to 2.2%. Promoters added to the iron cluster decreased spacing relative to pure Fe(1 0 0), though the NN distance remained overestimated by upwards of +4%. The spacing configuration is presented to illustrate how the ensemble effect, that is, the arrangement of the atoms in a molecule or cluster, correlate with the thermodynamic trends to be presented in the following section. 3.2. Adsorbate chemisorption on Ni(1 1 1), Co(0 0 0 1), and Fe(1 0 0) 3.2.1. Carbon chemisorption Previous studies of carbon chemisorption on transition metal surfaces suggest that both Co and Ni would benefit from strengthening of the carbon-surface bond [23], while Fe should become more catalytically active with a weakening of the carbon-surface bond, albeit at a slight increase to methane selectivity. Further, it has been suggested that a Brønsted-Evans-Polanyi (BEP) relationship exists between carbon binding strength and the effective barrier to methanation, Eeff:;CH4 , defined as the difference between the energy associated with the rate-limiting-step (RLS) in methane formation (here regarded as the transition state (TS) in hydrogenation of a surface methyl group) and the binding energy of carbon. The BEP relationship assigns a linear correspondence between thermodynamic and kinetic descriptors, in our case carbon binding energy and barrier height. It is assumed that because the TS more closely resembles the final state (FS) than the initial state (IS), then changes in the (IS) should have negligible effect on the TS and the barrier height will be relative to carbon binding strength. Results for carbon chemisorption are displayed in Table 2. In the convention of calculating adsorption energies as described in Eq. (10), stronger energies are more negative. As one moves from right to left in the transition metals, the d-band center model predicts an increase in binding strength [52]. Results confirm this prediction with binding energy increasing on the order of Ni (513 kJ/mol) < Co (580 kJ/mol) < Fe (709 kJ/mol). Comparison against the literature shows that binding energies are severely underestimated in our cluster model, in some cases on the order of 50 kJ/mol [53]. Previous studies [40,53] have reported an approximate difference of 40–44 kJ/mol between chemisorption on cobalt and nickel (D 33 kJ/mol reported here). Though the cluster model appears to fail quantitatively, it shows promise in preserving trends. Promotion had a subtle effect on nickel, strengthening the carbon-surface bond in all cases. Silver had the most notable effect, increasing the binding strength by 18 kJ/mol. When comparing relative electronegativities of the promoter atoms, the similarity to Ni (jENNi  ENpromoter j) increases on the order of

Table 2 Calculated adsorption energies for carbon over pure and promoted FT surface analogs. System

Nickel Cobalt Iron

Carbon Eads (kJ/mol) Pure

+Cu

+Ag

+Au

+Pd

Literaturea

513 580 709

523 562 691

531 587 780

515 578 675

522 589 707

595b 635b 745c

a Literature values obtained for cluster calculations on un-promoted Ni and Co, and periodic calculations on un-promoted Fe(111). b = Ref. [53]. c = Ref. [66].

Cu < Ag < Pd < Au. Though Pd and Au had a similar negligible effect on binding strength, Ag proved more effective than Cu and thus binding strength on nickel surfaces does not appear to be a function of promoter electronegativity. It has been reported elsewhere that cobalt is not easily influenced by promotion [54]. This phenomenon is captured in the relatively small change in carbon adsorption energies on promoted Co clusters. Cobalt saw favorable promotion from Ag and Pd, with moderate increases to carbon adsorption energies (+7 and +9 kJ/mol, respectively). Iron was most influenced by promotion, with changes in adsorption energies for carbon ranging from 34 to +71 kJ/mol. Strong-binding iron already exhibits lower methane selectivity compared to cobalt and nickel, though weakening of the iron-carbon bond should increase catalytic activity and possibly reduce the build-up of detrimental surface carbide. Copper is a common promoter on iron FT catalysts as it assists in reducing surface Fe atoms to increase the number of active sites [9]. Our results show a decrease in carbon binding strength (18 kJ/mol) on Fe6Cu over pure Fe(1 0 0). Our results also suggest that silver would not favorably promote iron catalysts due to a substantial increase in carbon binding strength (+71 kJ/mol). As was the case with cobalt, carbon optimized to similar sites on all iron clusters, though the peculiar case surrounding Fe6Au should be stated here. Au substitution on Fe forced an almost soup-bowl like optimization of the 7-atom cluster, where the optimization patterns seemed funneled toward the center of the cluster. As a result, many adsorbates preferred to settle in a bridge created by the artificial partial collapse of two adjacent 3-fold hollows. The authors have agreed to include the Fe6Au results in this study, though the geometry of the Fe6Au cluster was deemed unique enough to consider the associated results with caution. 3.2.2. Adsorption of –CHx, x = 1–3, –C2Hy, y = 1–4 Adsorption energies were obtained for the remaining species involved in surface carbide hydrogenation, as well as for the (4) competitive carbon–carbon coupling pathways. As was the case with carbon, adsorbates were placed using optimized geometries on pure Ni(1 1 1) as a guide. Adsorbates were allowed to freely optimize about the fixed surface potential. Migrations from the preoptimized placement were more substantial than in the single-carbon optimizations, with the extent of migration loosely tied to adsorbate size. Because no restrictions were placed on adsorbate location, specific binding site energies could not be obtained for comparison. As observed with carbon chemisorption, our calculated binding energies underestimate bulk calculations, where here we define bulk as a periodically-modeled surface. However, comparisons with DFT bulk values can be difficult for a number of reasons. First, our calculations are on frozen surface analogs. On most plane-wave slab models, the top few layers (and, at times, all layers) are allowed to relax to account for surface readjustment upon adsorption. This necessarily lowers the total energy of the surface-adsorbate complex as the surface atoms are free to seek lower energy coordinates. As described previously, this effect could not be incorporated into small cluster calculations as it has been shown that such relaxations are severely exaggerated. However, it is reasonable to assume that this unphysical representation should have similar manifestations on all systems and any error would likely cancel out. Secondly, the binding sites of our cluster model are unique to bulk surface binding sites because there is no atomic sublayer and thus no hcp hollow. On a crystal surface, the fcc hollow is void of a sublayer (second layer) atom directly beneath the hollow and is considered closest to our cluster hollows for sake of comparison. Bridging sites and top sites are considered less susceptible to sublayer effects as the proximity of the top layer atoms should dominate in bonding and orbital overlap. Thus, in

5

P.C. Psarras, D.W. Ball / Computational and Theoretical Chemistry 1063 (2015) 1–9

comparing our calculated values with literature bulk values, likesites were sought, but not always available. A summary of calculated adsorption energies is presented in Table 3. All systems present the same trends as observed in the literature [40,53,55,3,56,57]: adsorption energies tend to decrease with increasing n for CHn, n = 0–3, and adsorption energies are far stronger for the coupling adsorbates where one carbon is devoid of hydrogen (here, this corresponds with C2H3 and C2H) when compared with adsorption energies for C2H2 and C2H4. Both of these phenomena are a likely result of increased bonding and hybridization of the surface-directed carbon, where addition of hydrogen both changes the hybridization state of the carbon bonding orbitals to involve more p-character effectively raising the energy of the bond, and makes less electronic density available to invest in the surface-carbon bond. Binding strengths of all adsorbates generally followed the trend observed for carbon chemisorption with adsorption energies increasing on the order of Ni < Co < Fe. This is in agreement with the notion that chemisorption energies of these species should decrease (weaken) with increasing d-band occupation [59]. A suggested mechanism for FT polymerization, [3–8,11] involves the coupling of surface CH2 groups. We can assign stabilities to surface species by the convention that stronger binding energies lend to a greater stabilization of the adsorbate on surface and, presumably, greater residence time at any given temperature. This last presumption invokes the BEP relationship as described in Section 1. Hence, the IS energies presented in Table 3 govern adsorbate residence times. In this description, methylene stability increases on the order of Ni < Co < Fe, a familiar trend that aligns with decreasing hydrogenating character. Promotion had a very subtle effect on methylene chemisorption on nickel clusters, with copper yielding the only effect considered relevant (43 kJ/mol). Cobalt was likewise invulnerable to promotion effects, with the exception of silver, which stabilized methylene over cobalt by 90 kJ/mol. This result, however, should be considered in context of binding location, as CH2 appeared to favor the top binding site and may have experienced some stabilization from the perimeter saturating hydrogen atoms. All other methylene groups adsorbed on bridge sites over cobalt, and their relative binding energies, fell within a fairly narrow range of energies (268 to 283 kJ/mol). Promotion effects on iron were far more erratic, both in terms of methylene adsorption energies and binding site preference. Methylene experienced the strongest binding on promoted Fe clusters, with the exception of Au-promoted Fe, which resulted in a drastic destabilization in adsorption energy (+281 kJ/mol). As

mentioned in the previous section, this could be due to the unique geometry of the Fe6Au cluster. Another interesting adsorbate to monitor was CH3, as this represents the ultimate species in the transition from surface carbide to methane. The surface-methyl has two fates (oxygenated paths excluded): (1) hydrogenation to methane and (2) coupling to another carbon species. Cobalt systems proved weakest in methyl binding, followed by nickel and iron. Our results did not coincide with the literature values reported, which predict the weakest methyl binding on Fe, not Ni. Because this species is the direct precursor to methane, it is reasonable to assume that increasing binding strength to methyl groups may help reduce methane release, assuming once again that changes in methyl binding had no effect on the barrier to methane formation. This is a reasonable assumption considering that the TS involved in this step is far closer to the FS than IS [23]. Using methyl binding as a possible descriptor for methane selectivity, Ag promotion yielded favorable results on nickel and cobalt, (15 and 49 kJ/mol, respectively). Promotion on Fe reduced methyl binding in all cases, a result that is favorable in context of the previously described volcano curve of catalytic activity. Invariably, we must simultaneously consider promotive effects on the binding strengths of the carbon-coupling adsorbates. Trends for coupling species follow the trend previously reported for carbon chemisorption, with energies increasing on the order of Ni < Co < Fe. With few exceptions, C2H4 was the most unstable coupling intermediate on all surfaces, followed by C2H2. The stability of these species is of interest due to the proposed reincorporation of C2 species into longer chain hydrocarbons. Isotopic labeling studies have shown that 13C2Hx, x = 2,4 is found terminally incorporated into higher weight FT fractions, suggesting that these C2 species are re-adsorbed to the surface to serve as primers for the building of longer chain hydrocarbons [60]. This also explains the early negative deviation of C2 species observed in the (ASF) product distribution. Stabilities of these species were comparable on unpromoted Co and Ni, and no general trends could be assigned for promotion. Ethylene binding was generally far stronger over Fe, which would support iron’s superior tendency for chain growth. 3.3. Reaction barriers In an attempt to link thermodynamic properties to kinetic trends, we have proposed a number of assumptions based on the validity of a BEP relationship between adsorption energies and barrier heights. There was great motivation to make these

Table 3 Calculated adsorption energies for the eight adsorbates under study over pure and promoted FT surface analogs. Adsorbate

Eads (kJ/mol) Ni

C CH CH2 CH3 C2H C2H2 C2H3 C2H4 a b c d e f g

= Ref. [65]. = Ref. [66]. = Ref. [55]. = Ref. [3]. = Ref. [56]. = Ref. [40]. = Ref. [57].

513 397 245 117 359 105 339 85

Co +Cu

+Ag

+Au

+Pd

523 404 288 110 347 145 350 57

531 407 263 132 371 97 350 90

515 392 250 118 359 80 331 79

522 402 255 107 380 131 362 65

580 430 268 90 371 158 370 66

Fe +Cu

+Ag

+Au

+Pd

562 479 276 101 383 115 395 123

587 491 358 139 349 172 411 106

579 483 275 71 338 174 417 71

589 442 283 94 353 173 382 53

709 552 446 270 592 334 562 254

Literature +Cu

+Ag

+Au

+Pd

Ni

Co

Fe

691 562 365 133 512 251 489 112

780 685 516 231 493 253 615 238

675 220 165 48 422 122 346 8

707 422 300 145 399 170 419 102

595a 289e 260e 162e 180f 79f 518f 70f

635a 577d 375d 182d

747b 590c 349c 147c 581g 203c 548g 51c

6

P.C. Psarras, D.W. Ball / Computational and Theoretical Chemistry 1063 (2015) 1–9

assumptions, as thermodynamic properties are far easier, and faster, to calculate. To validate these BEP assumptions and to further investigate the effect of promotion on all surfaces under study, activation energies were calculated for the transition states linking reactions (2)–(9). The B3PW91 functional was chosen in part due to its strong accuracy for application to transition state geometries and energies [61]. However, it has also been reported that B3PW91, and many other hybrid density functionals, generally underestimate barrier heights. Unfortunately, there is no perfect functional designed for both accurate reaction energies and activation energies. This phenomenon is a result of the significance of the fraction of HF exchange: higher values of HF exchange are needed for accurate TS energies, but this compromises the accuracy of calculated reaction energies. As we could not change the functional ‘‘mid-method’’, we should expect an underestimation in our barrier calculations. A study comparing energetics for various functionals reported that similar functionals could expect a mean signed error of 3.6% to 4.1%, while mean unsigned errors in reaction energetics were more reasonable, between 1.3% and 2.8% (mean unsigned errors are presented for reaction energetics as the reaction could be written in either direction) [61]. Results are presented in Table 4. As indicated, our approach has generally underestimated barriers when to compared to other literature bulk DFT values, though there was some conflict between reported values for certain reaction transitions. However, DFT values over pure surfaces are provided to illustrate the relative trends, not for direct quantitative comparison. Differences in binding locations, surface index, and surface context preclude the direct comparison of these values. A comparison of our barriers to hydrogenation over pure FT surface-analogs fits within the respective profiles of hydrogenating character: the more hydrogenating catalysts (Ni and Co) have lower barriers for these steps than Fe. Trends within the hydrogenating steps on each metal show that the no single step is considered rate-limiting. For nickel, hydrogenation of the surface methyl has the largest barrier (74 kJ/mol), while for cobalt and iron the largest barriers belong to the hydrogenation of surface methylene (95 kJ/mol) and surface methylidyne (118 kJ/mol), respectively. Since hydrogenation of a surface methyl group results in the formation of methane, it would be desirable to increase the barrier involved in this step, so long as such an increase is not equally distributed amongst other favorable steps such as those involved in chain growth. Hence, the promotive effect on barrier heights must be examined on both hydrogenating steps and coupling steps simultaneously. Promoters considered favorable will lower barriers to the coupling reactions and increase barriers to

hydrogenation. Further, when results appear ambiguous, reaction kinetics would suggest that increases to coupling barriers should be considered more detrimental than decreases to hydrogenation barriers. No catalyst was considered unanimously effective nor ineffective over the eight reactions considered. The clusters Ni6Au and Ni6Pd were considered strong candidates because they both lowered all barriers to coupling while simultaneously raising the barrier to methane formation. Ni6Ag could be considered moderately effective as it raised many barriers to methanation, and Ni6Cu would not be recommended as it raised three of four coupling barriers by approximately 50 kJ/mol. Copper yielded unfavorable promotion on cobalt as well, with only three of eight reactions seeing favorable influence. Silver made for interesting case on cobalt as even though it reduced many barriers to methanation, coupling barriers were lowered substantially, upwards of 75 kJ/mol. Co6Au was the only cluster to provide the desired simultaneous effects discussed above, with two exceptions (hydrogenation of methylene, and methylene–methylene coupling). Co6Pd could be considered an ambiguous case with seemingly detrimental coupling barrier increases countered by highly favorable increases in hydrogenation barriers. An experimental study examining the promotive effect of the coinage metals on cobalt revealed the same trends observed here, with copper deemed unfavorable and silver and gold showing promise [16]. However, these findings were reported as a function of catalytic activity, not kinetics, and at far smaller loadings than modeled here. Fe6Cu displayed the best performance of any surface-promoter based on the aforementioned criteria, with favorable results in all but methylidyne hydrogenation. All promoters on iron lowered coupling barriers, though Fe6Ag, Fe6Au, and Fe6Pd lowered hydrogenating barriers as well. The extent of reduction to coupling barriers is greater for silver and palladium than for gold, while silver raised only one hydrogenating barrier, palladium two, and gold three. Based on these results, outside of the superior performance of Fe6Cu, promotion would seem to favor on the order Fe6Ag > Fe6Pd > Fe6Au. The BEP assumption suggests that simple carbon chemisorption can be used as a loose guide to predict barrier trends for the more complicated adsorbates. However, when the promotive effect on barrier heights were compared to the promotive effect on carbon chemisorption, no trends could be assigned. We should not assume that this result undermines BEP validity in general, as the discrepancies in barrier heights could be a result of cluster edgeeffects. A grand assumption in this study was that such effects were similar on all clusters, and should not significantly impact

Table 4 Calculated activation energies for the eight adsorbates under study over pure and promoted FT surface analogs. Reaction

DGz (kJ/mol) Ni

Co +Cu

C þ H ! CH CH þ H ! CH2 CH2 þH ! CH3 CH3 þH ! CH4 C þ CH ! C2 H CH þ CH ! C2 H2 C þ CH3 ! C2 H3 CH2 þ CH2 ! C2 H4 a b c d e f

= Ref. = Ref. = Ref. = Ref. = Ref. = Ref.

[55]. [62]. [21]. [63]. [57]. [64].

40 20 7 74 25 18 52 153

32 28 83 34 88 66 100 6

+Ag 13 20 19 98 18 32 35 176

+Au 6 12 76 128 10 9 25 92

+Pd 2 9 3 134 25 2 20 16

Fe +Cu

34 84 95 67 86 49 0 159

56 45 92 60 32 36 44 170

+Ag 70 61 82 64 10 24 9 64

+Au 46 62 110 84 63 30 71 86

+Pd 15 14 80 130 20 73 147 90

Literature – DFT +Cu

41 118 79 105 91 103 120 170

28 57 101 243 70 70 103 157

+Ag 62 49 74 126 28 44 89 67

+Au 250 19 29 92 58 99 85 75

+Pd 129 36 41 91 29 0 37 35

Ni

Co

Fe f

352b 163b 140b 76b

82 64f 61f 105f 189e 168e 108e 26e

82,a 67c 66,a 62c 147,a 102c 111a 125,c 125d 139d 83d 146d

P.C. Psarras, D.W. Ball / Computational and Theoretical Chemistry 1063 (2015) 1–9

energy trends. Future work will attempt to validate many of the cluster energies in this study with a plane-wave approach. This information can reveal the extent of edge effects in our cluster model. 3.4. Bader analysis (QTAIM) 3.4.1. Bader charge assignments A closer examination of the electronic structure associated with each surface analog was accomplished through Bader analysis. We chose to assign Bader charges for surface atoms (1)–(7) pre- and post-adsorption of carbon. This simple case of chemisorption eliminates possible intra-adsorbate charge transfer, and results may be extrapolated to other adsorbates via the BEP assumption. Extent of charge transfer is indicated by color (Fig. 2), and calculated via:

Dq ¼ qpost-adsorption  qpre-adsorption

ð10Þ

where q represents the Bader charge. For pure nickel, carbon adsorption results in moderate oxidation of the perimeter nickel atoms, and a moderate reduction of the central atom (position 1). This scenario, where a surface atom involved in bonding gained density upon carbon adsorption, was only observed in one other

7

system: Co6Ag. One might presume that the carbon Bader charge would be more positive in these systems, as one-third of the hollow atoms responsible for bonding withdraw, instead of donate, electronic density. This effect is observed on pure nickel, as both the carbon Bader charge and binding energy are the most positive in the nickel cluster group. This trend is not observed on Co6Ag, however, suggesting that the promoter (Ag), and not carbon, is responsible for the reduction of position 1. These trends can be further validated with population analyses. Upon nickel promotion, there is an observable change in charge map appearance, most evidenced by the disappearance of the moderately reduced central atom. Also noticeable is the more anticipated effect of carbon situated in the surface hollow, where each contributing atom is slightly oxidized as they donate density to carbon. This effect can be seen across most systems and is characterized by a slight darkening of the immediate hollow atoms with respect to their neighbors. Clearly, promotion renders nickel less polarizable than the pure cluster. One possible explanation involves a ‘‘pre-conditioning’’ of the nickel surface by promoter substitution, whereby the polarity induced by promoter introduction renders the surface ineligible for much further polarization by an approaching adsorbate. The Bader charge on carbon increases with surface-promotion; however, this trend does not correspond to a linear increase in binding energy, suggesting that

Fig. 2. Schematic representation of charge density differences for cluster atoms measured as qpromoted-surface  qpure-surface (left) and qpost-adsorption  qpre-adsorption (right). Promotion induces large charge redistributions, particularly at the site of promoter substitution and central site. Carbon adsorption is represented by a small silver sphere (right). In most cases, carbon adsorption effectively oxidizes atoms in the hollow-site. Generally, Ni systems were far less susceptible to adsorption-induced charge redistribution than Co and Fe systems.

8

P.C. Psarras, D.W. Ball / Computational and Theoretical Chemistry 1063 (2015) 1–9

the surface-adsorbate bond is less electrostatic in nature. The value of the Laplacian of the charge density at the surface-adsorbate BCP can reveal the nature of this surface-adsorbate interaction. Promotion had the opposite effect on cobalt. There was little charge redistribution upon adsorption over pure Co, though the atoms directly involved in bonding show evidence of mild oxidation. Promotion appears to facilitate surface charge redistribution in Co clusters. Less the case of Cu promotion, carbon BE increased over promoted Co clusters, where in this case carbon Bader charge and BE show a stronger correlation (R2 = 0.8907). Comparison of the effect of promotion on Ni and Co clusters illustrates that the extent of surface redistribution, a measure of surface polarizability, is a poor descriptor of adsorption behavior on clusters, as opposing trends in surface polarizability yield the same effect: an increase in carbon binding strength. Promotion on Fe appears to slightly hinder surface charge redistribution, as the promoted systems show less severe Bader charge differentials. Fe is known to show stronger binding to carbon when compared to Co and Ni, a trend that is supported when comparing the average Bader charge of bonding atoms (qbonding ). This metric produced a reasonable correlation against BE (R2 = 0.7139). Further, the observation that qbonding increases on the order Ni < Co < Fe suggests that surface adsorption phenomena can be described by the change in charge density of atoms immediately involved in bonding. Calculation artifacts of the cluster model may be responsible for the trend discrepancies in these observations.

[4]

[5]

[6]

[7]

[8] [9] [10]

[11]

[12]

[13]

[14] [15]

[16]

4. Conclusion [17]

Reaction energies, activation energies, and Bader charges were calculated for a series of promoted FT surface analogs. Comparison of reaction energies and barrier heights for hydrogenating steps and competitive coupling pathways revealed promising candidates for reducing methane selectivity in FT catalysis. Though Ni is highly methanating and not a commercially viable option, Au and Pd substitution showed promise in reducing barriers to carbon–carbon coupling while simultaneously increasing the barrier to methane formation. Ag and Au showed promise in Co promotion as these metals displayed considerable reduction to carbon–carbon coupling barriers, albeit at a simultaneous reduction to hydrogenating barriers. This implication is less a matter of reducing methane as it is boosting C2 formation and further chain growth. All metals showed favorable promotion on Fe, though this surface had the lowest methane selectivity to start with and further improvement to this catalyst might come at the expense of an unwanted decrease in activity. Bader charge distributions demonstrate that the promoter presence can greatly polarize the vicinity of adsorption, and its influence is largely confined to the pre-conditioning and electronic reconfiguration of the catalyst. Further, the promoter showed minimal participation during the chemisorption process.

[18]

[19] [20]

[21]

[22] [23]

[24] [25]

[26] [27]

[28]

Acknowledgement

[29]

This work was supported by the Ohio Supercomputing Center Project No. PFS0183.

[30] [31]

References [1] M.E. Dry, Fischer-Tropsch reactions and the environment, Appl. Catal., A 189 (1999) 185–190. [2] R. Howarth, R. Santoro, A. Ingraffea, Methane and the greenhouse-gas footprint of natural gas from shale formations, Clim. Change 106 (2011) 679–690. [3] J. Cheng, X. Gong, P. Hu, C.M. Lok, P. Ellis, S. French, A quantitative determination of reaction mechanisms from density functional theory

calculations: Fischer–Tropsch synthesis on flat and stepped cobalt surfaces, J. Catal. 254 (2008) 285–295. H. Li, G. Fu, X. Xu, A new insight into the initial step in the Fischer–Tropsch synthesis: CO dissociation on Ru surfaces, Phys. Chem. Chem. Phys. 14 (2012) 16686–16694. P.M. Maitlis, R. Quyoum, H.C. Long, M.L. Turner, Towards a chemical understanding of the Fischer–Tropsch reaction: alkene formation, Appl. Catal., A 186 (1999) 363–374. J.W. Mirwald, O.R. Inderwildi, Unraveling the Fischer–Tropsch mechanism: a combined DFT and microkinetic investigation of C–C bond formation on Ru, Phys. Chem. Chem. Phys. 14 (2012) 7028–7031. S.B. Ndlovu, N.S. Phala, M. Hearshaw-Timme, P. Beagly, J.R. Moss, M. Claeys, E. van Steen, Some evidence refuting the alkenyl mechanism for chain growth in iron-based Fischer–Tropsch synthesis, Catal. Today 71 (2002) 343–349. P.M. Maitlis, V. Zanotti, The role of electrophilic species in the Fischer–Tropsch reaction, Chem. Commun. (Camb) 13 (2009) 1619–1634. M.E. Dry, The Fischer–Tropsch process: 1950–2000, Catal. Today 71 (2002) 227–241. J. Patzlaff, Y. Liu, C. Graffmann, J. Gaube, Studies on product distributions of iron and cobalt catalyzed Fischer–Tropsch synthesis, Appl. Catal., A 186 (1999) 109–119. M.L. Turner, H.C. Long, A. Shenton, P.K. Byers, P.M. Maitlis, The alkenyl mechanism for Fischer–Tropsch surface methylene polymerisation; the reactions of vinylic probes with CO/H2 over rhodium catalyst, Chem. – Eur. J. 1 (1995) 549–556. N. Balakrishnan, B. Joseph, V.R. Bhethanabotla, Effect of platinum promoters on the removal of O from the surface of cobalt catalysts: A DFT study, Surf. Sci. 606 (2012) 634–643. J. Cheng, P. Hu, P. Ellis, S. French, G. Kelly, C.M. Lok, A DFT study of the transition metal promotion effect on ethylene chemisorption on Co(0001), Surf. Sci. 603 (2009) 2752–2758. E. Iglesia, S.L. Soled, R.A. Fiato, G.H. Via, Bimetallic synergy in cobalt ruthenium Fischer–Tropsch synthesis catalysts, J. Catal. 143 (1993) 345–368. G. Jacobs, T.K. Das, Y. Zhang, J. Li, G. Racoillet, B.H. Davis, Fischer–Tropsch synthesis: support, loading, and promoter effects on the reducibility of cobalt catalysts, Appl. Catal., A 233 (2002) 263–281. G. Jacobs, M.C. Ribeiro, W. Ma, Y. Ji, S. Khalid, P.T.A. Sumodjo, B.H. Davis, Group 11 (Cu, Ag, Au) promotion of 15%Co/Al2O3 Fischer–Tropsch synthesis catalysts, Appl. Catal., A 361 (2009) 137–151. N. Tsubaki, S. Sun, K. Fujimoto, Different functions of the noble metals added to cobalt catalysts for Fischer–Tropsch synthesis, J. Catal. 199 (2001) 236–246. J.A. Kritzinger, The role of sulfur in commercial iron-based Fischer–Tropsch catalysis with focus on C2-product selectivity and yield, Catal. Today 71 (2002) 307–318. I. Leith, The role of promoters in the hydrogenation of carbon monoxide over iron-based catalysts, CSIR-CENG 457 (1983). H.M. Torres Galvis, A.C.J. Koeken, J.H. Bitter, T. Davidian, M. Ruitenbeek, A.I. Dugulan, K.P. De Jong, Effects of sodium and sulfur on catalytic performance of supported iron catalysts for the Fischer–Tropsch synthesis of lower olefins, J. Catal. 303 (2013) 22–30. X. Zhao, Y. Li, J. Wang, C. Huo, CO adsorption, CO dissociation, and C–C coupling on Cu monolayer-covered Fe(100), J. Fuel Chem. Technol. 39 (2011) 956–960. J. Gaube, H. Klein, The promoter effect of alkali in Fischer–Tropsch iron and cobalt catalysts, Appl. Catal., A 350 (2008) 126–132. J. Cheng, P. Hu, P. Ellis, S. French, G. Kelly, C.M. Lok, An energy descriptor to quantify methane selectivity in Fischer–Tropsch synthesis: a density functional theory study, J. Phys. Chem. C 113 (2009) 8858–8863. P. Sabatier, Hydrogénations et dés hydrogénations par catalyse, Ber. Dtsch. Chem. Ges. 44 (1911). J. Cheng, P. Hu, P. Ellis, S. French, G. Kelly, C.M. Lok, Some understanding of Fischer–Tropsch synthesis from density functional theory calculations, Top. Catal. 53 (2010) 326–337. R. Bader, Atoms in Molecules – A Quantum Theory, Oxford University Press, Oxford, 1990. Y. Tal, R.F.W. Bader, T.T. Nguyen-Dang, M. Ojha, S.G. Anderson, Quantum topology. IV. Relation between the topological and energetic stabilities of molecular structures, J. Chem. Phys. 74 (1981) 5162–5167. J. Poater, M. Solà, M. Duran, X. Fradera, The calculation of electron localization and delocalization indices at the Hartree-Fock, density functional and postHartee-Fock levels of theory, Theor. Chem. Acc. 107 (2002) 362. J. Poater, M. Duran, M. Sola, B. Silvi, Theoretical evaluation of electron delocalization in aromatic molecules by means of atoms in molecules (AIM) and electron localization function (ELF) topological approaches, Chem. Rev. 105 (2005) 3947. J. Poater, M. Solà, M. Duran, X. Fradera, New insights in chemical reactivity by means of electron pairing analysis, J. Phys. Chem., A 105 (2001) 2052–2063. M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman, G. Scalmani, V. Barone, B. Mennucci, G.A. Petersson, H. Nakatsuji, M. Caricato, X. Li, H.P. Hratchian, A.F. Izmaylov, J. Bloino, G. Zheng, J.L. Sonnenberg, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, M. A. Jr. J., J.E. Peralta, F. Ogliaro, M. Bearpark, J.J. Heyd, E. Brothers, K.N. Kudin, V.N. Staroverov, R. Kobayashi, J. Normand, K. Raghavachari, A. Rendell, J.C. Burant, S.S. Iyengar, J. Tomasi, M. Cossi, N. Rega, J.M. Millam, M. Klene, J.E. Knox, J.B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R.E. Stratmann, O. Yazyev, A.J. Austin, R. Cammi, C.

P.C. Psarras, D.W. Ball / Computational and Theoretical Chemistry 1063 (2015) 1–9

[32] [33] [34] [35]

[36] [37]

[38] [39] [40]

[41]

[42] [43] [44] [45] [46] [47] [48]

Pomelli, J.W. Ochterski, R.L. Martin, K. Morokuma, V.G. Zakrzewski, G.A. Voth, P. Salvador, J.J. Dannenberg, S. Dapprich, A.D. Daniels, Ö Farkas, J.B. Foresman, J.V. Ortiz, J. Cioslowski, D.J. Fox. A.D. Becke, Density-functional thermochemistry. III. The role of exact exchange, J. Chem. Phys. 98 (1993) 5648–5652. J.P. Perdew, Y. Wang, Accurate and simple analytic representation of the electron-gas correlation energy, Phys. Rev. B 45 (1992) 13244–13249. J.L. Durant, Evaluation of transition state properties by density functional theory, Chem. Phys. Lett. 256 (1996) 595–602. M. Torrent, M. Solà, G. Frenking, Theoretical study of gas-phase reactions of Fe(CO)5 with OH- and their relevance for the water gas shift reaction, Organometallics 18 (1999) 2801–2812. J.B. Foresman, Æ. Frisch, Exploring Chemistry with Electronic Structure Methods, Gaussian Inc., Pittsburgh, PA, 1993. P.J. Hay, W.R. Wadt, Ab initio effective core potentials for molecular calculations. Potentials for K to Au including the outermost core orbitals, J. Chem. Phys. 82 (1985) 299–310. K. Hermann, P.S. Bagus, C.J. Nelin, Size dependence of surface cluster models: CO adsorbed on Cu(100), Phys. Rev. B 35 (1987) 9467–9473. P.A. Derosa, J.M. Seminario, P.B. Balbuena, Properties of small bimetallic Ni–Cu clusters, J. Phys. Chem. A 105 (2001) 7917–7925. H. Burghgraef, A.P.J. Jansen, R.A. van Santen, Methane activation and dehydrogenation on nickel and cobalt: a computational study, Surf. Sci. 324 (1995) 345–356. A. Fielicke, P. Gruene, G. Meijer, D.M. Rayner, The adsorption of CO on transition metal clusters: a case study of cluster surface chemistry, Surf. Sci. 603 (2009) 1427–1433. D.A. Kilimis, D.G. Papageorgiou, Density functional study of small bimetallic Ag–Pd clusters, J. Mol. Struct THEOCHEM 939 (2010) 112–117. G. Rollmann, P. Entel, Electron correlation effects in small iron clusters, Comput. Lett. 1 (2005) 288–296. T.A. Keith, AIMALL (Version 13.11.04), TK Gristmill Software, Overland Park, KS, 2012. W. Tang, E. Sanville, G. Henkelman, A grid-based Bader analysis algorithm without lattice bias, J. Phys.: Condens. Matter 21 (2009) 084204. E. Sanville, S.D. Kenny, R. Smith, G. Henkelman, Improved grid-based algorithm for Bader charge allocation, J. Comput. Chem. 28 (2007) 899–908. G. Henkelman, A. Arnaldsson, H. Jónsson, A fast and robust algorithm for Bader decomposition of charge density, Comput. Mater. Sci. 36 (2006) 354–360. F. Vincent, M. Figlarz, Quelques pr´ecisions sur les param‘etres cristallins et l’intensit´e des raies debye-scherrer du cobalt cubique et du cobalt hexagonal, C. R. Hebd. Seances Acad. Sci. 264C (1967) 1270.

9

[49] A. Taylor, J. Inst. Metals 77 (1950) 585. [50] R. Kohlhaas, P. Donner, N. Schmitz-Pranghe, Z. Angew. Phys. 23 (1967) 245. [51] P.F. Lang, B.C. Smith, Electronegativity effects and single covalent bond lengths of molecules in the gas phase, Dalton Trans. 43 (2014) 8016–8025. [52] B. Hammer, J.K. Nørskov, Theoretical surface science and catalysis— calculations and concepts, Adv. Catal. 45 (2000) 71–129. [53] D.J. Klinke II, S. Wilke, L.J. Broadbelt, A theoretical study of carbon chemisorption on Ni(111) and Co(0001) surfaces, J. Catal. 178 (1998) 540–554. [54] H. Schulz, Short history and present trends of Fischer–Tropsch synthesis, Appl. Catal. A 186 (1999) 3–12. [55] H. Li, C. Chang, J. Ho, Density functional calculations to study the mechanism of the Fischer–Tropsch reaction on Fe(111) and W(111) surfaces, J. Phys. Chem. C 115 (2011) 11045–11055. [56] H. Yang, J.L. Whitten, Chemisorption of atomic H and CHx fragments on Ni(111), Surf. Sci. 255 (1991) 193–207. [57] J.M.H. Lo, T. Ziegler, A first-principle study of chain propagation steps in the Fischer-Tropsch synthesis on Fe(100), J. Phys. Chem. C 112 (2008) 13681– 13691. [58] J.W. Ochterski, Thermochemistry in Gaussian, Gaussian, Inc., Wallingford, CT, 2000. [59] L. Triguero, U. Wahlgren, L.M. Pettersson, P. Siegbahn, DFT and MO calculations of atomic and molecular chemisorption energies on surface cluster models, Theor. Chim. Acta 94 (1996) 297–310. [60] I. Puskas, R.S. Hurlbut, Comments about the causes of deviations from the Anderson–Schulz–Flory distribution of the Fischer–Tropsch reaction products, Catal. Today 84 (2003) 99–109. [61] B.J. Lynch, D.G. Truhlar, How well can hybrid density functional methods predict transition state geometries and barrier heights?, J Phys. Chem. A 105 (2001) 2936–2941. [62] A.V. Zeigarnik, R.E. Valdes-Perez, O.N. Myatkovskaya, CC bond scission in ethane hydrogenolysis, J. Phys. Chem. B 104 (2000) 10578–10587. [63] J.M.H. Lo, T. Ziegler, Theoretical studies of the formation and reactivity of C2 hydrocarbon species on the Fe(100) surface, J. Phys. Chem. C 111 (2007) 13149–13162. [64] X.Q. Gong, R. Raval, P. Hu, CHx hydrogenation on Co(0001): a density functional theory study, J. Chem. Phys. 122 (2005) 024711. [65] R.M. Watwe, H.S. Bengaard, J.R. Rostrup-Nielsen, J.A. Dumesic, J.K. Nørskov, J. Catal. 189 (2000) 16–30. [66] D.E. Jiang, E.A. Carter, Carbon atom adsorption on and diffusion into Fe(110) and Fe(100) from first principles, Phys. Rev. B 71 (2005) 045402.