Molecular Heterogeneous Catalysis, Wiley (2006), 352729662X

116 Chapter 3

For the one-dimensional chain, n = 1 and n = 2. When the adatom orbitals have n surface atom neighbors the interaction appears to depend linearly on n . It decreases with the number of surface atom neighbors ns.

When all of the bonding orbitals are occupied, the attractive contribution to the interaction energy is proportional to Γ. The inverse dependence on β stems from the need to localize an electron at a surface atom in order to bind with an adatom electron. The larger the bandwidth, the larger is the delocalization energy with a weakening of the interaction energy. The binding energy to a surface atom of increasing coordinative saturation increases with decreasing number of surface-atom neighbors as (√ns)−1.

In the weak adsorption limit, the interaction energy is proportional to the metal local electronic density of states at the Fermi level [ρ(E)F ]:

An example of the local density of states at a Rh surface is given in Fig. 3.3b. The local DOS initially increases with the electron energy, then shows large fluctuations and finally decreases when the electron-valence band is fully occupied. Expression (3.30), however, is only valid for very weak interactions. For this reason, experimental studies have never obtained evidence that the adsorption energies relate strongly to the details of the local density of states at the Fermi level. For stronger interactions, the local density if states is sampled over an energy interval around the Fermi level that is proportional to the interaction energy. The general result is an increase in the interaction energy with electron occupation of the valence band as long as the bonding surface fragment orbitals are occupied and a decreasing interaction energy when the antibonding surface fragment orbitals also become occupied.

The limiting case of µ > 1 corresponds to the surface molecule limit. This is usually close to the surface chemical bonding situation found in practice. The corresponding local electron density of states distribution is shown schematically in Fig. 3.29b. This electron distribution corresponds now to a bonding and antibonding orbital of the adatom–surface atom molecular complex with orbital energies + and −, respectively, and a small contribution to the local density of states from electrons of the same energy of the metal valence electrons. In the one-dimensional system the orbital energies + and − are α + β and α − β , respectively. This implies nearly complete localization of an electron at atom 1 and a very small bond order between surface metal atoms 1 and 2.

Bonding in the surface molecule limit is illustrated in a di erent way by the surface bond formation scheme presented in Fig. 3.30. Step 1 represents the localization of an electron on a surface atom, with complete rupture of the chemical bonds with neighboring atoms. Step 2 represents the formation of the molecule complex between the adatom and the surface atoms. Step 3 involves the formation of the adsorption complex by embedding of the surface molecule complex into the vacancy of the surface atom.

In the surface molecule limit, |EMA| |Eloc| and |Eemb| Eloc. This implies that the dominant correction to the surface–molecule complex energy EMA is Eloc, which is proportional to the sublimation energy of a surface atom, which increases with increasing coordinative saturation as √ns. The embedding energy is equal to the weakened metal

The Reactivity of Transition-Metal Surfaces 117

Figure 3.30. Chemisorption can be considered as the sum of three terms: E = EMA + Eloc + Eemb[3].

surface atom interaction energy:

The stronger the interaction with the surface (increasing µ), the smaller is the embedding energy. The surface metal–metal bonds weaken owing to the interactions of the metal atoms with the adsorbate. The general result of the above analysis is that electronic e ects that influence the adsorption bond are largest when the interaction energy is weakest. Therefore, changes in interaction energy due to coordinative unsaturation of surface atoms will be largest when the interaction energy is small compared with the metal–metal bond strength.

The analysis presented implies that in order to model appropriately the dynamics of surface processes the force field potentials used for MD simulations will require potentials that incorporate bond weakening (with the neighboring atoms) not directly involved in the adatom–surface metal atom complex. Changes in next-neighbor bonds also occur but decrease exponentially with distance. Interestingly, when the chemical bonds with neighboring metal atoms weaken, the bonds between atoms two and three then slightly increase (Fig. 3.27). This is a consequence of Bond Order Conservation. The decrease in bond order of one of the neighboring bonds increases the bond order of the other.

An important quantitative approach to determine force field parameters that satisfy the above criteria is the Embedded-Atom Method and modifications[17] such as the Modified Embedded Atom Method. According to the Embedded Atom Method, the energy per metal atom at the position r = r0 equals

where n denotes the number of nearest-neighbor atoms and n0 the number of nearest neighbors in the bulk of the metal, E0 is the sublimation energy and the function F is

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Figure 3.31. Bond-order function F and bond-order correction energy per bond F /n for Rh. Values indicated by the circles are obtained from the atomic energies for fcc, bcc, simple cubic (sc), and diamond

cubic (dc) systems. In all systems the atoms are equally spaced at r0 , the equilibrium nearest-neighbor distance of Rh in an fcc lattice. AE0 = 5.48 eV, adapted from P. van Beurden[18].

The functional form of F gives a similar logarithmic relationship between the bond length and the number of bonds as earlier used in the Bond Order Conservation formulation. nie in its most elementary definition equals to

j=i

where ρ(rij ) is the spherically averaged atomic electron density of atom j. In the Modified Embedded Atom Method ne can be seen as an e ective coordination number. Hence F can be considered a Bond Order correction term to the total energy.

An example of the bond-order function F is shown in Fig. 3.31. In Fig. 3.31 one notes the decreasing value of the bond order per bond Fn with increasing coordination number, as predicted according to the Bond Order Conservation theory.

3.5.1 Molecular Orbital View of Chemisorption. A Summary

A schematic illustration that summarizes the essential electronic structure features that determine chemisorption was proposed by Ho mann[1]and is reproduced here in Fig. 3.35. In the weak adsorption limit interactions (1) and (2) represent the attractive HOMO– LUMO interactions described in Section 3.3. Interaction (3) between the doubly occupied

The Reactivity of Transition-Metal Surfaces 119

Figure 3.32. a) The electronic interactions of the surface chemical bond. b) Bondweakening and bond strengthening[1].

adsorbate orbitals and occupied surface orbitals is repulsive. The interaction between the adsorbate and the metal can lead to electron excitation within the adsorbate and the metal surface. In this process, surface–metal bonding orbitals become depleted and antibonding surface orbitals above the Fermi level become partially filled (process 5). This weakens the surface–metal bond energies. The relative position of the Fermi level of the metal with respect to the bonding and antibonding adsorbate–surface orbitals determines their electron occupation. Depletion of newly formed antibonding orbitals with energies higher than the Fermi level increases the adsorbate–surface energy (process 4). Figure 3.32b highlights the balance of bond weakening and strengthening interactions upon formation of the chemisorptive bond.

3.6 Elementary Reaction Steps on Transition-Metal Surfaces. Trends with Position of a Metal in the Periodic Table

3.6.1 General Considerations

In this section, we move from the elucidation of molecular and atomic adsorption to the fundamental features that control surface reactivity. We start by initially describing dissociative adsorption processes. We focus on elucidating surface chemistry as well as the understanding of how the metal substrate influences the intrinsic surface reactivity. We will also pay attention to geometric ensemble-size related requirements. The Brønsted– Evans–Polanyi relationship between transition-state energy and reaction energy discussed in Chapter 2 is particularly useful in understanding di erences in reactivity between di erent metal surfaces.

120 Chapter 3

where ET ST is the transition-state energy and δER is the change in reaction energy compared to a reference state with transition-state energy ET◦ S . When the reaction paths for elementary steps are similar, the change in activation energy can be predicted from the overall change in the reaction energy. For bond breaking reactions, this involves the energy di erence between the adsorbed molecule state and the dissociated surface product fragments. We will use the Brønsted–Evans–Polanyi relationship quite extensively to predict trends in the activation energies with changes in the metal substrate.

We will continue to base our exposition to a significant extent on theoretically obtained results. We use mainly the results from periodic DFT slab calculations which represent the transition-metal surface. Ground-state properties and especially the transition-state energies may depend sensitively on many detailed aspects of the calculations. Important factors, for instance, are:

–the density functional used to compute the exchange correlation contribution to the energy

–accounting for spin polarization of the surface electrons

–the determination of local energy minima and maxima

–the size of the unit cell, which may contribute spurious or desired lateral interaction terms

–the number of metal atom layers used in the slab model and the distance between the slabs

–the particular optimization scheme used and the details of which metal atoms are optimized

–the inclusion of zero-point vibrational frequency corrections

The errors in computed energies may vary for each item by more than 10 kJ/mol. For this reason one has to be extremely careful when comparing energies obtained by di erent authors directly. Fortunately, the situation is much better when one compares spectroscopic data such as vibrational energies. The primary goal of theoretical analysis has to be a qualitative understanding supported by “semi”-quantative numerical correlations. The best approach is to compare systematically results obtained by the same method or similar model systems. Notwithstanding the great insights obtained by the use of current computational approaches, there remains a need for more accurate methods applicable to large systems.

As an illustration we will conclude this section with a short discussion on studies to establish theoretically the transition-state energy for CH4 dissociation on an Ni(111) surface. Using a slab of Ni atoms of three layers, a 2 x 2 unit cell with the top layer and adsorbate fully relaxed, Watwe et al.[19] predicted an activation energy of CH4 on Ni(111) of 127 kJ/mol. Increasing the size of the unit cell to 3 x 3, including spin polarization and increasing the number of layers to five decreases the transition state energy to 101 kJ/mol[20]. The zero-point vibrational correction decreases the barrier energy by at least further a 10 kJ/mol[21]. This reduces the transition-state energy computed with the most frequently used approach by approximately 30 kJ/mol, which amounts to 25%. Yang and Whitten[22], using a very di erent ab initio configuration interaction approach with embedded clusters obtained a value for the transition state energy of 71 kJ/mol. Whereas the latter values are close to experimental data, here one has to be careful also. As we have seen in Chapter 2, and we will note in the following section also, step edges or kinks may be present experimentally and act to reduce the measured activation energies significantly. Therefore, even when present in minute amounts they may dominate the outcome

The Reactivity of Transition-Metal Surfaces 121

of experiments. Notwithstanding the di culties mentioned, remarkable new insights have been obtained recently owing to the close comparison of theoretical results and experimental data. Keeping the above comments in mind we will now proceed with an analysis of computed results, not always mentioning the details of the models used as these can be found in the papers referred to.

3.6.2 Activation of CO and Other Diatomics

We start this subsection with reaction paths for the activation of CO and subsequently extend this to other diatomic molecules. In a subsequent subsection we then advance ideas learned from diatomic molecules to slightly more complex molecules such as methane and ethane to examine C–H and C–C activation.

In Fig. 3.20 we show that the change in metal a ects the adsorption energy of adatoms much more so than that of adsorbed molecules. The thermodynamics for dissociative adsorption therefore become more unfavorable with increasing d-electron valence-bond occupation of the metal atoms in a row of the periodic table. This trend is a general result that is likely observed for all dissociation reactions.

Figure 3.33. Reaction energy diagram of CO dissociation on the terrace or on the stepped surface of Ru(0001)[23]. The barrier energy E = –195 kJ/mol corresponds to the energy of adsorption of molecule atop; E = –186 kJ/mol, CO three-fold adsorbed; E = –180 kJ/mol, CO adsorbed in the hollow of the step.

The electronic energy and geometric changes for CO dissociation on a terrace and on a step of Ru(0001) are given in Fig. 3.33. On a terrace of the Ru(0001) surface, CO shifts from an atop to three-fold position at a cost of 12 kJ/mol. The CO bond, which is initially oriented perpendicular to the surface, bends towards the bridging position between two metal atoms as it stretches. The C–O bond in the transition state was found to be nearly parallel to the surface with a nearly zero bond order between the carbon and oxygen atom. The C atom is close to its final state above an hcp site. The oxygen atom is asymmetrically situated over a neighboring bridge site. Two of the three final O bonds are close to their final state. The activation barrier was calculated to be quite high at 224

122 Chapter 3

kJ/mol. Additional energy is released when the neighboring C and O atoms di use away from each other.

The reaction proceeds by stretching the CO bond as well as tilting the CO axis toward the surface. This helps to lower the 2π state and enhances the transfer of electrons from the metal into this state. This charge transfer of electrons into the 2π state (backdonation) weakens the CO bond and thus aids CO activation.

The preferred reaction path for CO dissociation occurs over the bridge site, thus avoiding the closer atop site (see Fig. 3.34a). Activation over the atop site is actually higher in energy and in addition would form C and O atoms at hcp adsorption sites. The resulting hcp adsorption site for O would be 50 kJ/mol less favorable than the adsorption of oxygen at an fcc site. In Fig. 3.34b the stretched CO intermediate is shown for the dissociation of CO along a step edge.

Table 3.4. CO transition-state energies according to the Brønsted–Evans–Polanyi relation (kJ/mol).

δET ST = 0.85 δ∆ER

Hammer and Nørskov[4] isolated the transition states for various diatomic molecules such as CO, N2, and O2 and nicely demonstrated that they all show very similar structures whereby the adsorbate–adsobate bond is significantly stretched and the product framents can form fairly strong bonds with the surface. The transition states are all considered late (for a definition of a late transition state, see Chapter 2) and have comparable values of α of approximately 0.9.

The Brønsted–Evans–Polanyi relation applied to the CO dissociation reaction results in Table 3.4. The quantum-chemical result upon which this is based is the dissociation of CO over Ru(0001) with 2 x 2 coverage.

The results show that there is an increase in the activation barrier for the transition state moving across a row from left to right in the periodic table. This increase corresponds with the increase in the d-valence electron occupation.

The high reactivity of the metals such as Fe, Co or Ru, as reflected in the relatively low activation energies, is essentially due to the increased stabilization of the adatom products such as C or O compared with CO on the metal surface. As we learned in previous sections, the heat of adsorption of a molecule varies much less with the adsorption site or the metal than do adsorbed atoms. Therefore, the relative interaction energies of the latter dominate the trends in reactivity.

Inspection of the changes in the local density of states of CO in the transition state and ground state show that there is a reduced interaction between C and O in the transition state. Essentially the C and O can be considered already separated in the transition state.

The Reactivity of Transition-Metal Surfaces 123

Figure 3.34a. The transition state for CO decomposition on a flat Ru(0001) surface[23].

Figure 3.34b. The transition state for CO decomposition on a stepped Ru(0001) surface, side and top views[23].

The local density of states on C and O are now more similar to those of the separated atoms than to those from an adsorbed molecule. A similar conclusion can be found for dissociation of many diatomic molecules.

Dissociation at stepped surfaces leads to significantly reduced activation barriers for many reaction systems. The activation energy and the corresponding transition state for CO dissociation on a stepped Ru(0001) surface are shown in Figs. 3.32 and 3.33b. The computed activation energy for CO has now become 104 kJ/mol and an intermediate state along the step can be identified.

The reduced activation energies for diatomic molecules at step edges appears to be quite general. Two factors tend to contribute. First, as Fig. 3.35 indicates, dissociation of the molecule over a step provides enhanced 2π back-donation into the bond weakening antibonding CO orbital.

124 Chapter 3

Figure 3.35. Orbital interaction between CO 2π* and edge atom d-atomic orbitals (schematic).

Figure 3.36. Reaction path for CO dissociation on the Ru(0001) surface (hcp→hcp) schematic).

Another important contribution that can result in a significant lowering of the activation energy is the specific configuration that the resulting product fragments adopt with respect to one another and the metal surface. For the dissociation of CO on a terrace, the C and O atoms that form tend to share a bond with a metal atom on the surface, as seen in Fig. 3.36. This ultimately destabilizes this state by 25 kJ/mol compared with the state where C and O are further removed from one another and do not share metal atoms. This raises the barrier for CO activation. When CO dissociates at a step, C and O atoms that form preferentially bind to the bottom and the edge of the step, respectively. The destabilization that results from a shared bonding with a metal surface atom is absent.

Figure 3.37. Structure of the “side–on”NO at the bridge sites on Pt(100)[24a].

The latter concept is basic to the specific dependence of the activation energies of elementary reaction steps on di erent surfaces. There is not always an immediate relation with the coordinative unsaturation of the metal surface atoms. Ge and Neurock[24a] noted an exeptionally low barrier for the dissociation of NO adsorbed on the non-reconstructed Pt(100) surface. The corresponding transition state is shown in Fig. 3.37. The calculated activation energies for NO dissociation over the (111) and (110) surfaces are 160 and 105

The Reactivity of Transition-Metal Surfaces 125

kJ/mol, respectively. The calculated barrier on the (100) surface is only 93 kJ/mol. These results are in very good agreement with those presented by Eichler and Hafner[24b]. In addition, since the dissociative reaction energy is 86 kJ/mol, it implies a barrier of only 7 kJ/mol for the recombinative association of Nads and Oads on this surface. We will return to this point in later sections. The low barrier for NO dissociation on the (100) surface relates to two factors. First, since NO dissociation proceeds over the valley created by the four neighboring Pt atoms, it allows for substantial electron back-donation. Second, the Nads and Oads product atoms that form do not share bonds with the same surface metal atom which significantly reduces the repulsive interaactions.

Nørskov et al.[25] elegantly demonstrated that the similarity in the transition state structures for N2, O2, CO, and NO could be used to establish a universal relationship between the activation energy and the heat of reaction for the dissociation of all of these molecules over di erent metal surfaces. They derived the following relationships for reactions that occur over the close-packed surfaces and step edges all energies in eV.

Ea = (2.07 ± 0.07) + ER(0.9 ± 0.4) close-packed surfaces

Ea = (1.34 ± 0.09) + ER(0.87 ± 0.05)steps:

The large value of α in these Brønsted–Evans–Polanyi relations is consistent with a late transition state for the dissociation reactions as discussed in Chapter 2. The only parameter in the universal relations is the reaction energy ER, which can be easily calculated.

Figure 3.38. Transition-state energies for the Boudouard reaction 2CO −→ CO2 + Cads at a step on the Ru(0001) surface[23].

The dissociation of CO can also occur via the Boudouard disproportionation reaction where two CO molecules react together to form CO2 and surface carbon: 2CO→ CO2 + C. The transition state for this reaction on a step of the Ru(0001) surface is given in Fig. 3.38. This reaction proceeds via an associative reaction in which a CO molecule at the bottom of a step recombines with a CO molecule adsorbed at the edge of the step. A C atom is then generated at the bottom of the step to form CO2. The bent form of the CO2-type transition state is indicative of its negative charge. The computed activation energy of 206 kJ/mol is higher than that for CO dissociation at a step edge.