Molecular Heterogeneous Catalysis, Wiley (2006), 352729662X

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from left to right in the periodic table, and therefore also the corresponding overlap with adatom orbitals. As a consequence, the di erences in energy between bonding and antibonding 2px transition-metal surface-orbital fragments also decrease. The antibonding orbital fragments progressively become more occupied, which is apparent from the local density of states plot in Fig. 3.18. The adatom bond energies then decrease with increasing d-valence electron occupation, as seen in Fig. 3.19. Figure 3.20 illustrates the general observation that along a row of the periodic table the adatom-metal surface interaction energy tends to decrease with increasing d-valence electron occupation.

Figure 3.18. The local density of states of the oxygen 2px for oxygen adsorbed on di erent metal surfaces, adapted from Hammer and Nørskov[4].

Table 3.1 DFT-calculated binding energy for atomic C on the most dense surface for selected noble netals. Values are reported in kJ/mol.

The Reactivity of Transition-Metal Surfaces 107

Table 3.2 DFT-calculated binding energy for atomic O on the most dense surface for selected noble netals. Values are reported in kJ/mol.

Figure 3.19. The adsorption energies and adatom surface distances for atomic O and S adsorbed on di erent transition metals, adapted from Hammer and Nørskov[4].

DFT-computed binding energies of C and O are summarized in Tables 3.1 and 3.2. One notes in both tables the large di erences in the adsorption energies of the adatom. C is bound more strongly than O since fewer antibonding surface fragment orbitals are occupied. The adatom bond energies are seen to decrease across individual rows in the periodic table. Ru and Rh are exceptions, which may be the result of fact that Ru has

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the hcp structure whereas Rh has the fcc structure. As one proceeds down a column in the periodic table the interaction with the O atom decreases. The binding energy of the C adatom increases on moving down a column of the periodic table. This is mainly due to the increasing overlap with the more spatially extended d-valence orbitals. The trends for oxygen are di erent for two reasons. The first is that the occupation of antibonding surface orbitals is larger for oxygen than carbon because of the larger number of electrons on oxygen. This results in a larger Pauli repulsion when the overlap with the d-orbital electrons increases. The second factor relates to the fact that the work function increases down a column, which results in a decreased back-donation from the metal to the adatom. This will influence oxygen more than carbon due to the relatively lower position of the oxygen atomic orbitals over carbon with respect to the Fermi level of the metal. For the Group VIII metals, the bond energies of adatoms such as H varies much less when di erent metals are compared, since there is only interaction through a single σ-type bond. A characteristic value is 120 kJ/mol, which is just enough for the H2 molecule to dissociate.

Figure 3.20. (Left) Calculated and model estimates of the variation in the adsorpion energy of molecular CO compared with atomically adsorbed C and O for the most close-packed surface of the 4d transition metals. (Right) Calculated molecular and dissociative chemisorption of NO. Solid symbols are DFT calculations; open symbols are Newns–Anderson model e ective medium[3] calculations. For CO, dissociative chemisorption appears to the left of rhodium. For NO, dissociative chemisorption appears further to the right, i.e., also on rhodium, adapted from Hammer and Nørskov[4].

Figure 3.20 illustrates that there are much larger changes in bond energies for atoms as we span over di erent metals across the periodic table than for changes in the bond energy for molecules such as CO. The changes in the bond energies for CO across the periodic table are much less. This is due to the conflicting tendencies for the donative and back-donative interactions.

The other important parameter for the surface chemical bond is surface topology, i.e. the dependence of the surface bond energy of a surface adatom on the coordinative unsaturation of surface metal atoms. The changes in the adsorption properties of C on di erent Ru surfaces with di erent local coordination numbers have been studied in detail. A summary of the results is given in Table 3.3. Note that on the dense Ru(0001) surface atomic carbon prefers to bind to the three-fold coordination sites.

surfaces

Figure 3.21. Adatom chemisorption. Surfaces bind more strongly when surface atoms have fewer neighbors.

However, for topological reasons, C prefers the two-fold bridge sites on the more open Ru surfaces. The bond energies are listed along with the site code, x(y), which describes the adsorption site, where x refers the number of Ru neighbors coordinated to C, and y refers to the nearest number of metal Ru neighbors. One notes that at constant x, the interaction energy uniformly increases with decreasing y, in line with predictions according to the Bond Order Principle[11] (see also Section 3.5). The result is illustrated in a schematic fashion (Fig. 3.21). The chemical bonding between an adsorbate and the metal surface controls the adsorbate’s potential reactivity. The metal surface provides

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binding sites that can stabilize active fragments critical to the overall catalysis, thus dramatically lowering the activation barrier from that found in the analogous vapor-phase chemistry. Strong chemical bonds between the adsorbate and the surface generally help to activate internal adsorbate bonds. Weaker adsorbate-surface bonds on the other hand generally help to enhance bond-making processes or association reactions. The nature of the metal–adsorbate bonding therefore is critical to the overall catalytic cycle since the cycle is nothing more than a complex array of bond breaking and making processes.

Bond breaking within the adsorbing molecule occurs when the metal can lower the energetics associated activating specific bonds in the adsorbate. For CO, this involves populating the antibonding CO 2π orbital which weakens the CO bond energy. The vibrational bond frequency typically decreases and the CO bond length tends to increase by a few tenths of an angstrom . Similarely bond weakening occurs between the metal atoms within the transition–metal surface upon adsorption. The stronger the metal–adsorbate bond, the greater is the degree of metal–metal bond weakening. This again is consistent with bond order conservation principles. An adlayer of atomic intermediates such as C, O or N can significantly weaken the metal–metal surface bonds. As a consequence, the metal–metal distances in the surface layer as well as the interlayer spacing of the outermost surface layer can lengthen[12]. The results of periodic DFT calculations for a 2 x 2 adlayer of nitrogen bound to Pt(111), for example, show that the Pt atoms directly bound to N expand outward whereas the neighboring Pt atoms (not bound to N) contract inwards (as seen in Fig. 3.22), thus roughening the surface.

Figure 3.22. The computed DFT changes in bond distances between Pt atoms at the Pt(111) surface upon adsorption of nitrogen atoms.

Bond weakening within a metal cluster may be much more significant than that within a metal surface since the coordination numbers of the metal atoms involved in adsorbate bonding are typically lower in the cluster than those in the closed packed surface. For example, the metal–metal atom distances for O adsorbed to a Pd6 cluster and a Pd18 cluster shown in Fig. 3.23 are significantly longer for the Pd atoms bonded to O in the small cluster as compared with that in the large cluster. The Pd coordination numbers on the bare Pd6 cluster are all 4 whereas those in the center of the Pd18 cluster are 9, which matches that of the close-packed Pd(111) surface. The smaller Pd6 cluster can accommodate the forces due to bond weakening more completely. Small clusters can even rearrange upon the adsorption of a single molecule. Pd clusters, for example, show a significant expansion in the Pd bond lengths upon the adsorption of ethylene, thus opening up these bonds and changing the geometry of the metal cluster.

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Figure 3.23. Adsorption-induced changes in bond length on a small and a large cluster[13].

Figure 3.24. The calculated bond energy of ethylene as a function of cluster size[14].

Figure 3.24 shows the changes in adsorption energy for ethylene on Pd as a function of Pdx cluster size. Ethylene prefers to adsorb in the π-bound state on the very small Pd clusters. Di-σ-adsorption in which two of the C atoms of ethylene interact with the two Pd atoms can result in a much stronger interaction which would weaken the Pd–Pd bonds and induce large deformations in the cluster shape (see Fig. 3.25a and b). The large change in the cluster structure weakens ethylene adsorbed in the di-σ mode, thus resulting in a preference for ethylene to adsorb in the π-adsorption mode on the cluster. Because of the high coordinative unsaturation of the Pd atoms in small clusters, ethylene binds strongly and the bond energy is substantially higher than that of Pd adsorbed

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Figure 3.25. The adsorption of π (a) and di-σ (b) bonded ethylene to a Pd4 cluster[14].

Figure 3.26. Adsorption of ethylene on Pd18 cluster[15].

on the Pd(111) surface. The clusters must typically approach around 20 atoms and in addition, the atoms to which the adsorbate binds must maintain the same number of nearest neighbor metal atoms as on a closed packed surface. The calculated interaction energies between the cluster and the bulk then become comparable. This is illustrated in Fig. 3.26.

The reactivity of the cluster edge atoms is, of course, higher than that for the higher coordinated sites for atoms found in the center. Therefore, comparison of di erent adsorption modes should be restricted to calculations performed on the same cluster, otherwise di erences in cluster response may determine di erence in adsorption energies, rather than di erences in adsorption topology.

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3.5 Elementary Quantum Chemistry of the Surface Chemical Bond

The interaction of an adatom with transition-metal surface atoms results in the broadening and shifting of the atomic orbital energies. There is not only a change in the electron distribution on the adatom, but also in the metal atoms involved in the surface chemical bond. Upon formation of the adsorbate surface chemical bond, the interaction between the surface atoms weakens.

In a very elementary fashion, this can be described with Bond Order Conservation theory[11] . This approximate theory assumes spherical electron densities around each of the atoms, and hence ignores hybridization. It is based on Pauling’s observation that bond lengths between atoms in complexes depend logaritmically on the bond order x of each bond:

If the two center interaction that comprises the chemical bond is described by a Morse potential then a simple relation follows between the potential Q(x) and the bond order:

where Q0 is the bond strength for the bond at equilibrium. Bond Order Conservation implies:

1)If an atom has n neighbors rather than one, the total bond strength can be written as a sum of two-body interactions:

2)The total bond order xtn of an atom is independent of number and type of neighboring atoms. The total bond order is then conserved:

This enables one to relate the bond orders of chemical bonds with di erent numbers of neighbors. For instance, let us calculate the bond order for a chemical bond between two atoms a complex in which the central atom has n neighbors:

The bond order per bond is found to decrease with increasing number of bonds n. Since xi depends exponentially on bond distances, the bond length is found to increase logarithmically with n. Proposition 1 then provides an expression for the bond strength as a function of coordination number:

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The total bond strength increases with decreasing coordination number, but less than proportionally. This analysis assumes that all of the atoms are equivalent. When the adatom is di erent from the metal atom, the changes in chemical bonding are more complex.

Within a molecular orbital scheme, the relevant parameters are the overlap energies β of the atomic orbitals with surface atom orbitals and the overlap energies between the metal atomic orbitals on the di erent atoms β. The other important parameters are the relative energies of adatom orbitals and metal-atom orbital energies.

If one assumes a one-dimensional open-chain model for the adatom–metal system, with one atomic orbital per atom and all orbital energies equivalent, within tight binding theory, analytical solutions for the molecular orbital energies can be found[3].

Figure 3.27. Open-chain model with the end atom being di erent from the other atoms (α0 = α).

Without the adatom, the electrons in the chain are distributed over molecular orbitals between the metal orbital energies αm +2β and αm −2β, αm. In the chain each metal atom has two neighbors. When this number is eight or twelve as in a bulk metal, the electron distribution of the electrons within the metal would be found to vary approximately between αm + 2 n2 β and αm − 2 n2 β. When the metal electron valence bond is half occupied and all bonding orbitals make an attractive contribution to the chemical bond, this interaction is proportional to √n. This is a very general result.

In Fig. 3.28 the molecular orbital scheme for a two-atom system is compared with that for a multi-atom cluster, with the central atom having n neighbors. In the latter case only the two molecular orbitals are shown that arise when the central atom interacts with its neighbors. The atomic orbital on the atom at the center is assumed to be spherical as an s-atomic orbital, and hence it interacts only with a symmetric combination of atomic orbitals on the neighboring atoms ψn:

where ϕi are the atomic orbitals on the neighboring atoms. As a consequence, the band gap between the bonding and antibonding orbitals formed by the interaction of ϕ0 on the central atom and ψn is found to be proportional to √n.

The repulsive part to the interaction energy, which one finds when all the orbitals are doubly occupied, is proportional to n as follows from the expression

The solution that one finds for the electron density distribution of the adatom in the

open chain (Fig. 3.27) depends sensitively on the ratio µ = β , i.e. the relative interaction

β

between adatom and surface and between the surface atoms[3]. Two di erent scenarios

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Figure 3.28. Interaction scheme between two atoms and one atom in a cluster[16], Eattr √n β ;

Erep = −nβ S.

Figure 3.29. (a) Weak adsorption limit µ 1; (b) surface molecule limit µ 1. Local density of state( ) on adatom O (see Fig. 3.27). α + 2β and α − 2β are the boundaries of the metal electron density of states assumed to be a linear chain.

can result. The first when µ 1, which is known as the weak adsorption limit. In the second, µ 1, which is known as the surface molecule limit. These two situations are shown schematically in Fig. 3.29.

In the weak adsorption limit µ 1 (Fig. 3.29a), there is a small broadening of the electron density at the atoms. The broadening 2Γe equals