Insights into the Staggered Nature of Hydrogenation Reactivity over

Mar 9, 2009 - Paul Crawford, Bronagh McAllister and P. Hu*. School of Chemistry ... What Makes a Good Catalyst for the Deacon Process? Herbert Over an...
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J. Phys. Chem. C 2009, 113, 5222–5227

Insights into the Staggered Nature of Hydrogenation Reactivity over the 4d Transition Metals Paul Crawford, Bronagh McAllister, and P. Hu* School of Chemistry, The Queen’s UniVersity of Belfast, Belfast, BT9 5AG, United Kingdom ReceiVed: June 14, 2008; ReVised Manuscript ReceiVed: January 18, 2009

Hydrogenation reactions at transition metal surfaces comprise a key set of reactions in heterogeneous catalysis. In this paper, density functional theory methods are employed to take an in-depth look at this fundamental reaction type. The energetics of hydrogenation of atomic C, N, and O have been studied in some detail over low index Zr, Nb, Mo, Tc, Ru, Rh, and Pd surfaces. Detailed bonding analysis has also been employed to track carefully the chemical changes taking place during reaction. A number of interesting horizontal and vertical trends have been uncovered relating to reactant valency and metal d-band filling. A general correlation has also been found between the reaction barriers and the reaction potential energies. Moreover, when each reaction is considered independently, correlation has been found to improve with decreasing reactant valency. Bonding analysis has pointed to this being related to the relative position of the transition state along the reaction coordinate and has shown that as reactant valency decreases, the transition states become progressively later. 1. Introduction Hydrogenation reactions at solid surfaces are the cornerstone of heterogeneous catalysis and are responsible for the formation and interconversion of the most fundamental of molecules. For example, the reaction of adsorbed hydrogen with atomic oxygen at certain transition metal surfaces produces water,1 and that with atomic nitrogen, ammonia.2 Moreover, the surface hydrogenation of the simple CO molecule or atomic carbon can produce a broad spectrum of hydrocarbons.3,4 Transition metal hydrogenations have long been employed industrially to produce both bulk and fine chemicals.5-7 More recently, however, these heterogeneous processes have attracted attention in fuel cell technology research: first, in the hydrogenation/dehydrogenation of organic molecules in terms of hydrogen fuel production,8 and second as a means of cleansing poisoned fuel cell catalysts.9 As a consequence, the fundamental study of transition metal catalyzed hydrogenation reactions remains an important and fascinating area, with the potential to provide breakthroughs, both purely scientific and technological. Two quantities of particular importance in the physical chemistry of surface hydrogenations are the reaction barrier and the potential energy change of reaction. The former provides a measure of the likelihood of the event to occur, and the latter gives the potential of a species to react with atomic hydrogen once adsorbed. In bond cleavage reactions at surfaces, the reaction barrier and potential energy of reaction are known to be linked by the so-called Bronsted-Evans-Polanyi (BEP) relationship.10 A number of key ideas have been developed over the past decade or so to explain how the electronic structure of the metal catalyst influences the potential energy of reaction and the reaction barrier of bond cleaving reactions at surfaces. These models include reactivity being linked to the filling of the d-band,11 the density of states at the Fermi level,12 and the d-band center picture of Hammer and Norskov.13 The origin of the BEP relation has also been well scrutinized by Liu and Hu.14 * Corresponding author. E-mail: [email protected].

Periodic trends in heterogeneous bond formation reactions, including hydrogenations, are much less understood. A number of excellent theoretical works have addressed this class of reactions.15-17 These studies, however, have tended to be restricted to particular metal surfaces, and general reactivity trends were not the primary focus of the work. In a number of recent papers, we have begun to shed some light on the difficult issue of bond formation trends at transition metal surfaces. For example, we have systematically analyzed the barrier trends in the hydrogenation of NH and N over the 4d metals.18 Here it was found that the key parameter in determining the barrier trends was the perturbation of the (NHx)-metal bonding at the transition state by the approaching H atom. The degree of perturbation was greater if H approached the reactant over a bridge site. Interestingly, the magnitude of perturbation was also found to be proportional to the forming reactant H bonding. Importantly, it was found that on surfaces where the potential energy surface (PES) of adsorbed H was relatively flatter H could approach the reactant over a top site and escape producing the large perturbation in (NHx)-metal bonding, and thus react with a lower barrier. This work suggested that reactivity was a balance between the corrugation of adsorbed hydrogen’s PES and the strength of the forming reactant H bond. Subsequent work examined charge transfer during the course of N hydrogenation over transition metals.19 Here it was found that as the reaction proceeds, charge is lost from the adsorbed hydrogen to the surface metal atoms. Interestingly, a strong correlation was found between the reaction barriers and the Parr electrophilicity index20,21 of the transition metals, which contains both electronegativity and chemical hardness terms. This study suggests that at a fundamental level, the energetics of the overall process are influenced by the propensity of the surface metal atoms to accept electronic charge in going from the initial adsorbate state to the transition state. We have also examined trends in C-O and C-N bond formations over transition metal surfaces.22 In this work it was found that the reaction energies and reaction barriers of CO

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Hydrogen Reactivity over 4d Transition Metals formation span a much greater range over the 4d transition metals than do those of CN formation. Moreover, a good BEP relationship was observed in the case of CO formation but not for CN formation. Analysis suggested that the disparity in reaction energy trends related to the valency difference in O and N. Namely, in the final state, N generally interacts with the surface, whereas in the case of CO there is generally no interaction between O and the surface. This in turn results in the reaction potential energies for CO formation following the trend in O chemisorption energy, which is quite varied, and the trend in those for CN formation becoming somewhat more dampened. In addition, Mulliken population analysis revealed that N also interacts more extensively than O with the surface at the transition state, thus resulting in the formation of earlier transition states than those for CO formation. This result explained the absence of a BEP relation in the case of CN formation. In the present study we extend our previous work on hydrogenation reactivity at transition metal surfaces. Herein we address how the valency of the reactant affects its trend in reaction potential energy and reaction barriers on moving across the 4d series. We have chosen to study the reaction of C + H, N + H, and O + H in a comparative manner, over Zr(001), Nb(110), Mo(110), Tc(001), Ru(001), Rh(111), and Pd(111). These atomic hydrogenations allow us to discuss without ambiguity the concept valency, and the systems are simple enough to provide a clear picture of the bond breaking/making events taking place during the course of the reactions. Each reaction has been studied on the surface of the 4d transition metals from Zr to Pd. This provides a data set large enough from which to draw meaningful conclusions, and it also allows us to follow reactivity trends stepwise as the d-band gradually fills moving from left to right across the period from Zr to Pd. The hydrogenation of C, N, and O are the first elementary steps in the formation of methane, ammonia, and water, respectively. 2. Calculation Details The calculations were performed within the DFT framework23 using the generalized gradient approximation exchange-correlation functional (GGA) of Perdew, Burke, and Ernzerhof.24 Ultrasoft pseudopotentials in which relativistic effects were not included replaced the true atomic core potentials, and the valence states were expanded in a plane wave basis set where the cutoff energy was set to 360 eV. The surfaces were represented by metal slabs which were comprised of four atomic layers; the vacuum region between adjacent slabs was set in excess of 10 Å. A p(2 × 2) unit cell was large enough to model the reactions, and a Monkhorst-Pack mesh with 3 × 3 ×1 k-point sampling was found to provide adequate accuracy. In all of the calculations, the adsorbates and the top layer of metal atoms were fully optimized, while the three lower layers were fixed at their bulk truncated positions. The most stable chemisorption structures were taken as the initial states of the reactions; all possible transition states were located using the constrained minimization method.1 The convergence criterion in all of the geometric optimizations was set to 0.05 eV/Å. Zero point energy corrections were not included. 3. Results and Discussion 3.1. Reaction Potential Energies. The calculated reaction potential energies of each of the three reactions over the 4d metals will be addressed first. In each of the calculations the atomic reactants are taken to react from their respective

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Figure 1. Reaction potential energies for the three hydrogenation reactions considered in this paper calculated over the 4d transition metals: C + H f CH (bottom curve), N + H f NH (middle curve), and O + H f OH (top curve).

TABLE 1: Calculated Reaction Potential Energies (∆E) Corresponding to the Hydrogenation of Atomic C, N and O over the Perfect Surfaces of the 4d Transition Metals Considered in This Work reaction potential energies (∆E), eV surface

C+H

N+H

O+H

Zr(001) Nb(110) Mo(110) Tc(001) Ru(001) Rh(111) Pd(111)

0.26 -0.08 -0.19 0.12 -0.24 -0.38 -0.10

0.97 0.37 0.36 0.40 -0.06 -0.13 -0.12

2.12 1.14 1.33 1.08 0.75 0.37 0.45

equilibrium adsorption sites on the perfect surfaces of the metals. Our calculated values are given in Table 1 and plotted in Figure 1. Inspection of Figure 1 reveals a number of intriguing features; clear horizontal and vertical valency related trends can be observed. It is informative to consider how the reaction energies vary on early, middle, and late transition metals. Looking at Zr, we can see that the reaction energies become progressively more endothermic in the order C + H > N + H > O + H. Thus, the greater the atomic valency of the reactant, the more exothermic the hydrogenation tends to be. On Zr the jumps in endothermicity are 0.71 eV in moving from C + H to N + H and 1.15 eV in moving from N + H to O + H. If we now consider Tc, where the d-band is around half-full, we can see that the same pattern is followed. Here, however, the jumps in endothermicity with decreasing reactant valency are seen to be smaller: 0.28 and 0.68 eV, respectively. On Pd, where the d-band is almost full, the pattern which has held from Zr is broken. Here, both C + H and N + H have roughly the same reaction energy. In this case, the reaction energy of O + H is ∼0.57 eV greater than that for C + H and N + H. If the horizontal trends are now considered, it can be seen that here also reactant valency has a marked effect. In the case of C, which has the highest valency, the reaction energies are relatively constant across the period. There are seen to be slight peaks at Zr, Tc, and Pd and dips at Mo and Rh. The reaction energies range from -0.38 eV on Rh to 0.26 eV on Zr, a spread of only 0.64 eV. The reaction energies for the hydrogenation of N show moderate variation over the 4d metals. They drop to a flat region after Zr and then drop further to a second flat region after Tc. The reaction energies range from 0.97 eV on Zr to -0.13 on Rh, a spread of 1.1 eV. In the case of O hydrogenation, the most significant variation in reaction energies is seen to occur. Here a peak is seen at Mo with a rise in energy at Zr and Pd, and dips are seen at Nb and Rh. The reaction energies

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Figure 2. Reaction barriers for the three hydrogenation reactions considered in this paper calculated over the 4d transition metals: C + H f CH (bottom curve), N + H f NH (middle curve), and O + H f OH (top curve).

TABLE 2: Calculated Reaction Barriers (Ea) Corresponding to the Hydrogenation of Atomic C, N, and O over the Perfect Surfaces of the 4d Transition Metals Considered in This Work reaction barriers (Ea), eV surface

C+H

N+H

O+H

Zr(001) Nb(110) Mo(110) Tc(001) Ru(001) Rh(111) Pd(111)

1.08 0.78 0.88 1.04 0.72 0.63 1.16

1.83 1.60 1.54 1.55 1.12 0.96 1.33

2.67 1.98 2.19 1.76 1.50 1.31 1.33

range from 2.12 eV on Zr to 0.37 eV on Rh, a relatively large spread of 1.75 eV. 3.2. Reaction Barriers. Reaction barriers have been calculated for each of the three reactions over the seven transition metals. Only the lowest energy reaction pathways are considered in this paper (geometric structures can be found in our previous work18). Generally speaking, the relative stabilities of bridge and top site transition states have been found to be in line with our previous work on N hydrogenation,18 the one exception being that a bridge site transition state is the more stable for O hydrogenation over Ru(001). Our calculated reaction barriers are given in Table 2 and plotted in Figure 2. Examination of Figure 2 quickly reveals that the reaction barriers are, on the whole, a reflection of the reaction energies. The same vertical and horizontal trends are seen to be largely followed. On each surface, barriers are seen to increase with decreasing valency. Again this effect is more exaggerated on the early metals and is seen to diminish with the gradual filling of the d-band. It is interesting to note that the ordering is again anomalous on Pd. Here, however, it is the barriers of N + H and O + H that are roughly equal. The barriers for C + H show the least variation. Peaks are again seen at Zr, Tc, and Pd. The differences from the reaction energy trend are the following: there is no dip at Mo, and the peak at Pd is exaggerated relative to that in Figure 1. The barriers range from 1.16 eV on Pd to 0.63 eV on Rh, a spread of 0.53 eV. In the case of N + H, moderate variation is again observed. Here the pattern is quite close to the respective trend in Figure 1. The notable differences is that the drop from Zr to the first flat region is somewhat softened, and the second flat region is replaced by a stepwise decrease from Tc to Rh and then an exaggerated increase at Pd, similar to that seen for C + H. The reaction barriers range from 1.83 eV on Zr to 0.96 eV on Rh, a spread of 0.87 eV. The reaction barriers for O + H are seen to have the greatest variation across the period. The trend is more or less identical to that of the reaction energies. Here the

barriers range from 2.67 eV on Zr to 1.31 eV on Rh, a spread of 1.36 eV. At this point it is worth pointing out an important principle which can be derived from the above results: it appears that, for surface hydrogenation reactions, as the valency of the reactant decreases, the kinetic sensitivity to the relative fullness of the d-band increases on moving through a particular period. The vertical and horizontal energy-valency relationships observed in the reaction potential energies and reaction barriers are summarized succinctly in Table 3. 3.3. Analysis. In Figure 3a the reaction barriers of all three hydrogenation reactions are plotted against their respective potential energies. Inspection of Figure 3a reveals a general correlation which quantifies the relationship between the trends in Figures 1 and 2. All of the points are seen to fall roughly along the line Ea ) 0.8∆E +1.1. There is, however, moderate scatter, and the correlation coefficient R2 is seen to be around 0.9. This result shows that the reaction potential energies are perhaps the most important factor in the kinetics of surface hydrogenation reactions and importantly that there appears to be a universal relationship between the reaction barriers and the reaction energies. As noted, there is moderate scatter, and the correlation between Ea and ∆E is somewhat less than expected, judging by what has been found in similar plots for bond dissociation reactions at surfaces. In previous work on the oxidation and nitrogenations of carbon, reactant valency was found to have an effect on such correlations.22 That is to say, with increased reactant valency, the correlation between the reaction barriers and reaction potential energies decreased. Thus, to investigate whether this effect is present in surface hydrogenation reactions, an individual plot of Ea against ∆E has been made for each atomic reactant. The plot for C + H is shown in Figure 3b, that for N + H in Figure 3c, and that for O + H in Figure 3d. Examination of Figure 3b-d reveals a striking increase in correlation between Ea and ∆E with decreasing reactant valency. The greatest scatter is indeed seen for the highest valency reactant, namely, carbon. Here, the correlation is quite poor with the correlation coefficient R2 only around 0.57. In the case of nitrogen, the medium valency reactant, there is moderate scatter and the correlation coefficient R2 is seen to be higher at 0.83. Interestingly, for oxygen, the lowest valency reactant, all of the points fall neatly along a straight line, and the correlation coefficient R2 is almost 1. It can therefore be seen that it is indeed this valency effect which is responsible for the overall correlation not being as tight as may be expected. That is, the poor correlation observed in the case of C + H is distorting the general picture. But what is the origin of the observed link between reactant valency and the correlation between Ea and ∆E ? It is wellknown that such correlations are particularly tight in the case of bond cleavage reactions at surfaces due to the geometric relationship between the transition state and the final reaction products.10 That is, the transition state occurs very late along the reaction coordinate and thus resembles closely the reaction products in geometry. Could the converse explain the poor correlation between Ea and ∆E in the case of C + H? In order to answer this question, we have measured the relative distance at which the transition state of C + H, N + H, and O + H lies along the reaction coordinate on Zr(001). To judge the relative position of each transition state along the reaction coordinate, we must first consider the bonding changes taking place during the course of the reaction. In the case of surface hydrogenation reactions, there are three bond making/breaking events; namely: (i) a loss of bonding between

Hydrogen Reactivity over 4d Transition Metals

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Figure 3. Plots showing the correlations between the calculated reaction barriers and the respective reaction potential energies. (a) Overall correlation for the 21 reactions is shown. In the remaining three plots individual correlations for C + H, N + H, and O + H are given. That for C + H is shown in (b), that for N + H in (c), and that for O + H in (d).

TABLE 3: Summary of Both the Vertical and Horizontal Energy-Valency Relationships Observed in the Reaction Potential Energies and Reaction Barriers in the Hydrogenation of C, N, and O over the Perfect 4d Transition Metal Surfaces Considered in This Study vertical trends increase in endothermicity with atomic valence decrease, eV

decrease in reactivity with atomic valence decrease, eV

surface

CfN

NfO

CfN

NfO

Zr(001) Nb(110) Mo(110) Tc(001) Ru(001) Rh(111) Pd(111)

0.71 0.45 0.55 0.28 0.18 0.25 -0.02

1.15 0.77 0.97 0.68 0.81 0.50 0.57

0.75 0.82 0.66 0.51 0.40 0.33 0.17

0.84 0.38 0.65 0.21 0.38 0.35 0

horizontal trends reaction potential energies, eV reactant C N O

reaction barriers, eV

low, high

spread

low, high

spread

-0.38, 0.26 -0.13, 0.97 0.37, 2.12

0.64 1.10 1.75

0.63, 1.16 0.96, 1.83 1.31, 2.67

0.53 0.87 1.36

the surface and H, (ii) formation of bonding between the reactant and H, and (iii) subsequent loss of bonding between the surface and the reactant. Thus, a pertinent measure of the relative position of the transition state along the reaction coordinate is therefore the relative percentage loss in bonding between both reactants and the surface during transition state formation. The difficulty, however, lies in how such intangible quantities can be measured. Herein, we have employed Mulliken population analysis25,26 to quantify the bonding changes taking place during transition state formation. Within this scheme a high overlap population between two atoms indicates a high degree of covalency between the atoms. This approach has proven to be extremely useful in the analysis of bonding in solid materials.27 As model systems thereactionsoverZr(001)havebeenaddressed.Thesurface-reactant overlap populations for C, N, and O have been determined at an fcc site on Zr(001). In the case of H, the overlap population was calculated at an hcp site. As the reactions proceed, however, H is observed to migrate to a bridge site in order to react with the other species. On the other hand, C, N, and O are seen to move very little from their original position, although some bonding to the surface is lost as interactions with H are

established. The reactant-surface overlap populations have also been calculated for each of the transition states. The values from this bonding analysis are given in Table 4. Table 4 reveals a number of interesting bonding trends. In the first instance, the overlap populations at the initial states show a clear valency related feature: The covalency of the interactions between Zr and the reactants decreases stepwise from C with an overlap population of 1.59 |e| to H with an overlap population of 0.60 |e|. Consideration of the transition state data shows a clear covalent interaction between H and the reactants at the transition state. In the case of C + H, this interaction is somewhat less compared to those of N + H and O + H. It is also worth noting that in response to this interaction, there is a concurrent loss of bonding between the surface and C, N, and O. Moreover, it can also be seen that during the formation of each transition state, H is seen to lose a greater percentage of its initial bonding to the surface. This is in line with the fact that H moves from a hollow site to a bridge site, and the other reactants remain almost fixed to the surface during transition state formation. The most important phenomenon revealed by this data is, however, the relationship between the valency of the reactant

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Figure 4. Bar chart showing the total percentage of initial reactant-surface bonding lost during transition state formation for C + H, N + H, and O + H as indicated by Mulliken population analysis.

TABLE 4: Mulliken Analysis Values for C + H, N + H, and O + H over Zr(001)a bonding

IS OP, |e|

TS OP, |e|

Zr-H Zr-C C-H

0.60 1.59 0

0.22 1.31 0.22

Zr-H Zr-N N-H

0.6 1.29 0

0.09 0.92 0.36

Zr-H Zr-O O-H

0.6 0.9 0

0.18 0.52 0.34

% IS

total % decrease

C+H 37 82

30.1

N+H 15 71

46.6

O+H 30 58

53.3

a

IS OP denotes the total overlap population between the particular reactant and the surface at its equilibrium adsorption site on Zr(001); it is summed over a number of bonds. TS OP denotes the total overlap population between the particular reactant and the surface at its respective transition state site on Zr(001); again, it is summed over a number of bonds. % IS indicates the percentage of initial state bonding remaining at the transition for a particular reactant. Total % decrease indicates the total percentage of initial reactant-surface bonding lost during transition state formation in the case of a particular system.

and the relative position of the respective transition state along the reaction coordinate. Take C + H, for instance; here there is only ∼30% decrease in total surface-reactant bonding during transition state formation. This is indicative of an early transition state and would certainly account for the poor correlation observed between Ea and ∆E. In the case of N + H, a moderate loss of ∼47% in total reactant-surface bonding is seen. This implies that for N + H, the transition state is occurring further along the reaction coordinate. Indeed, this is in line with the greater correlation observed between Ea and ∆E for this system. For O + H, however, the total loss in surface-reactant bonding during transition state formation is observed to greater than 50% (∼53%), thus indicating that the transition state for O + H lies furthest of the three along its respective reaction coordinate. This well explains the significant correlation between the reaction barrier and the reaction potential energies in the case of O + H. The total percentage of initial reactant-surface bonding lost during transition state formation for C, N, and O is summarized in the form of a bar chart in Figure 4. 4. Conclusions In summary, this study represents an extensive and systematic investigation into the fundamental nature of hydrogenation reactions at transition metal surfaces. The energetics of atomic

C, N, and O hydrogenation over low index surfaces of Zr, Nb, Mo, Tc, Ru, Rh, and Pd have been studied in great detail. Bonding analysis has also been employed to scrutinize the chemical changes taking place during the course of the reactions. With regard to the overall energy trends, a somewhat staggered reactivity pattern is observed on moving across the period, and a number of interesting valency related features are uncovered. The vertical and horizontal reaction energy trends may be summarized as follows: i. On each of the surfaces considered, with the exception of Pd(111), the reaction energies are seen to increase with decreasing reactant valency; e.g., on Zr(001) there is a 0.71 eV jump in endothermicity in going from C to N and a 1.15 eV jump in going from N to O. This effect is seen to diminish as the d-band gradually fills on moving from Zr to Rh and is completely lost on Pd. ii. On moving from left to right across the period, the reaction energies are seen to become less endothermic. The spread in reaction energies is seen to increase stepwise with decreasing valency of the reactant. On the whole, the reaction barrier trends largely reflect those of the reaction potential energies, that is, i. On each surface except Pd(111), there is a concurrent decrease in reactivity with a decrease in reactant valency; e.g., on Zr(001) there is a 0.75 eV increase in the reaction barrier in going from C to N and a 0.84 eV in going from N to O. Once again this valency effect decreases as the d-band gradually fills on moving across the period from Zr to Rh and disappears at Pd. ii. On moving across the period from left to right, the reaction barriers are seen to decrease, although the decrease is somewhat staggered. Also, the spread in reaction barriers is seen to increase stepwise with decreasing reactant valency. Analysis has revealed that a universal relationship exists between the reaction barriers and the reaction potential energies. Moreover, a striking relationship between the reactant valency and the degree of correlation between Ea and ∆E has been found. Mulliken population analysis has been employed to understand the physical origin of this valency effect. Our analysis can be summarized as follows: i. The overall correlation between Ea and ∆E for the 21 reactions is reasonably good with R2 at 0.9. ii. Considered independently, the correlation increases stepwise as the valency of the reactant decreases; e.g., for C + H, N + H, and O + H, the R2 values are 0.57, 0.83, and 0.97, respectively. iii. Bonding analysis has shown that the relative position of the transition state in surface hydrogenation reactions moves further along the reaction coordinate with decreasing reactant valency. iv.The valency-correlation phenomenon is therefore nicely explained in terms of the transition state becoming increasingly later with decreasing reactant valency, as it is well-known that there is good correlation between Ea and ∆E in reactions where the transition state is considered late. References and Notes (1) Michaelides, A.; Hu, P. J. Am. Chem. Soc. 2000, 122, 9866. (2) Ertl, G. Catal. ReV.sSci. Eng. 1980, 21, 201. (3) Vannice, M. A. Catal. ReV.sSci. Eng. 1979, 14, 153. (4) Schulz, H. Appl. Catal., A 1999, 186, 3. (5) Somorjai, G. A. Introduction to Surface Chemistry and Catalysis; Wiley: New York, 1994. (6) Masel, R. I. Principle of Adsorption and Reaction on Solid Surfaces; Wiley: New York, 1996.

Hydrogen Reactivity over 4d Transition Metals (7) Smith, M. B. Organic Synthesis, Chemistry Series; McGraw-Hill: New York, 1994. (8) Hodoshima, S.; Takaiwa, S.; Shono, A.; Satoh, K.; Saito, Y. Appl. Catal., A 2005, 283, 235. (9) Takenaka, S.; Shimizu, T.; Otsuka, K. Int. J. Hydrogen Energy 2004, 29, 1065. (10) (a) Evans, M. G.; Polanyi, N. P. Trans. Faraday Soc. 1936, 32, 1333. (b) Pallassana, V.; Neurock, M. J. Catal. 2000, 191, 301. (c) Liu, Z.-P.; Hu, P. J. Chem. Phys. 2001, 114, 8244. (d) Logadottir, A.; Rod, T. H.; Nørskov, J. K.; Hammer, B.; Dahl, S.; Jacobsen, C. J. H. J. Catal. 2001, 197, 229. (e) Michaelides, A.; Liu, Z.-P.; Zhang, C. J.; Alavi, A.; King, D. A.; Hu, P. J. Am. Chem. Soc. 2003, 125, 3704. (11) Feibelman, P. J.; Hamann, D. Phys. ReV. Lett. 1984, 52, 61. (12) Parr, R. G.; Yang, W. Proc. Natl. Acad. Sci. U.S.A. 1985, 82, 6723. (13) Hammer, B.; Norskov, J. K. Surf. Sci. 1995, 343, 211. (14) Liu, Z. -P.; Hu, P. J. Chem. Phys. 2001, 114, 8244. (15) Honkala, K.; Hellman, A.; Remediakis, I. N.; Logadottir, A.; Carlsson, A.; Dahl, S.; Christensen, C. H.; Norskov, J. K. Science 2005, 307, 555. (16) Reuter, K.; Frenkel, D.; Scheffler, M. Phys. ReV. Lett. 2004, 93, 116105.

J. Phys. Chem. C, Vol. 113, No. 13, 2009 5227 (17) Popa, C.; Offermans, W. K.; van Santen, R. A.; Jansen, A. P. J. Phys. ReV. B. 2006, 74, 155428. (18) Crawford, P.; Hu, P. J. Chem. Phys. 2006, 124, 44705. (19) Crawford, P.; Hu, P. J. Phys. Chem. B. 2006, 110, 4157. (20) Maynard, A. T.; Huang, M.; Rice, W. G.; Covell, D. G. Proc. Natl. Acad. Sci. U.S.A. 1998, 95, 11578. (21) Parr, G.; Szentpaly, L. V.; Liu, S. J. Am. Chem. Soc. 1999, 121, 1922. (22) Crawford, P.; Hu, P. J. Chem. Phys. 2007, 126, 194706. (23) Payne, M. C.; Teter, M. P.; Allen, D. C.; Arias, T. A.; Joannopolous, J. D. ReV. Mod. Phys. 1992, 64, 1045. (24) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. ReV. Lett. 1996, 77, 3865. (25) Mulliken, R. S. J. Chem. Phys. 1955, 23, 1833. (26) Sanchez-Portal, D.; Artacho, E.; Soler, J. M. J. Phys.: Condens. Matter 1996, 8, 3859. (27) Segall, M. D.; Shah, R.; Pickard, C. J.; Payne, M. C. Phys. ReV. B. 1996, 54, 16317.

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