Molecular Heterogeneous Catalysis, Wiley (2006), 352729662X

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Figure 3.7. The Local Density of States on surface and adsorbate atoms corresponding to Fig. 3.6a.

Figure 3.8a. (a) Schematic diagram of the σ-interaction. The model is based on adsorption of CO on a single Ni atom[7]. (b) Schematic orbital diagram of the π-orbital structure. An allylic configuration is formed in the model of a single CO molecule intracting with a Ni atom[7].

for the π and 2π orbitals are –11 eV and –9 eV and –6 eV. For CO adsorbed at the three-fold site, the strong rehybridization of the 2π and 1π states create a weak bonding π-type contribution near the Fermi level. The repulsive interactions appear to dominate. A comparison of the total BOOP’s of atop and three-fold coordinated CO with the metal d orbitals gives as a result

One-fold: BOOP(σ) = –0.07; BOOP(π) = 0.02

Three-fold: BOOP(σ) = –0.11; BOOP(π) = –0.03

The CO molecule also interacts with the transition-metal s, p valence electron band, which is partially occupied with one electron per atom. The main contribution to the attractive interaction with CO is due to the interaction with the s, p valence electrons. Figure 3.7 shows the LDOS of the Ru valence s-electrons, with peaks that correspond to the interaction with CO orbitals. In the three-fold coordination site the Pauli-repulsive

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The orbital interactions of CO adsorbed atop two di erent Rh atoms in an Rh10 cluster are shown in Fig. 3.9 a and b. In these calculations, only the C and O positions of CO have been optimized. The apex atom of Rh in this cluster has only three neighbors, whereas atoms at the edge of this cluster have six neighbors. CO is expected to bind more weakly to an atom in the latter. Indeed the bond energy is computed to be –86 kJ/mol at the apex atom and only –65 kJ/mol at the edge atom. Interestingly the bond energy for CO adsorbed atop the Rh(111) surface atom is nearly twice that of these computed cluster values. The lower adsorption energy calculated on the cluster relates to the relatively high ionization potential of the Rh cluster (6 eV). In Fig. 3.9b the LDOS and OPDOS interactions are shown for the initially doubly occupied 5σ and empty 2π orbitals of CO and the Rh 4d orbitals. We again note the bonding nature of the 5σ lone-pair orbital interaction at low energy (the double peak at low energy in OPDOS is the result of mixing between the dz2 transition-metal orbital and the CO(4σ) and CO(5σ) states). There is a strong antibonding interaction which appears in the energy regime of the metal d- electrons. On the other hand, the interaction with the CO-2π orbital and atomic dxz and dyz orbitals is attractive.

We find, as a general result, that the attractive interaction between CO and metal d-electrons is due to the bonding interaction with the 2π orbitals. Repulsive interactions are due to the interactions between doubly occupied metal orbitals and those in the molecule. The molecular orbitals involved are the 4σ, 5σ and 1π orbitals.

Again we note that the average energy for the local density of states on the d-electrons on the atom with lowest metal-atom coordination number N has increased, compared with the average position of the d-electron LDOS on the atom with the larger number of neighbors. This is expressed in the following relation:

where Nm and N are the number of nearest neighbours of a metal atom, respectively. The electronic interactions between the molecular orbitals of adsorbate and d states

of the metal that result upon adsorption are shown schematically in Figs. 3.10 and 3.11 within the context of tight-binding theory. We first analyze the NH3 nσ lone-pair interaction and the CO 5σ-type interaction with the d-valence electrons. It is important to focus on the interaction with the d-valence electrons since their interaction with the adsorbate is mainly responsible for di erences in reactivity between di erent metals.

If the d–valence electron band and the 5σ–orbital are both completely filled with electrons, the interaction energy will be repulsive since Pauli repulsion is proportional to the overlap of S and |β|. When the d-electron valence bond is partially empty, this repulsive interaction is decreased because the antibonding orbital fragments become less occupied. The decrease in repulsive energy with a decrease in number of metal-atom neighbors of the surface atom involved in the adsorbate bond relates to an increase in the number of empty antibonding orbitals, determined by the electron density between max and EF (see Fig. 3.10).

In the chemisorbed state the adsorbate surface-orbital fragments are made up of a mix of adsorbate σ and metal valence-electron molecular orbitals. The σ-electron occupation of the adsorbate, which was originally 2 electrons, decreases upon adsorption. This type of interaction is therefore referred to as an electron-donative interaction.

DFT cluster results on the interaction between metal d states and the unoccupied CO-2π orbitals indicate significant 2π electron density in the d–valence electron regime

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Figure 3.10. Orbital interaction of doubly occupied nσ lone pair orbital with d-valence energies ∆ σ

surface overlap energy intergral). The d-valence band is partially occupied.

Figure 3.11. Scheme of back-donating interaction with the unoccupied adsorbate orbital π . The expression for ∆Eπ is similar to ∆Eσ in Fig. 3.10.

and that the interaction in that regime is bonding. The back-donative orbital interaction scheme is shown in Fig. 3.11

The di erences in symmetry between π and σ orbitals lead them to interact with di erent metal orbitals. The antisymmetric 2π orbital on CO prefers to interact with dxz or dyz atomic orbitals, whereas the 5σ orbital prefers to interact with the metal dz2 orbital. The orbital interactions between the metal d–valence electrons and adsorbate orbital is now bonding. This bonding interaction stabilizes the energy by a downward

the interaction energy increases with a decrease in the number of metal surface–atom neighbors for the metal atoms involved in the chemisorptive bond.

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Figure 3.12. Group orbital Density of States as computed using Extended H¨uckel theory for the s atomic orbitals of the Ag(111) surface[10]. The metal electron energy increases from right to left.

The orbital interaction scheme in which the attractive contribution of the adsorbate surface bond is estimated from the donative and respective back-donative interactions is called the Blyholder model. It is the analogous to the Chatt–Dewar model which is used to describe chemical bonds in organometallic complexes.

Figure 3.12 illustrates the importance of the concept of surface group orbitals. A surface group orbital is defined as a symmetry combination of atomic orbitals on the metal atoms to which an adsorbed molecule or atom is attached. For example, the adsorption of a probe molecule such as CO at a three-fold coordination site results in an interaction between the 5σ lone-pair orbital on CO, which is σ symmetric, and, hence when we limit the example to the interaction with s-atomic metal orbitals with the symmetric combination of the s-atomic orbitals on the coordinating metal atom.

The CO π-symmetric orbitals does not interact with the metal ψgs state but instead with the two antisymmetric s-atomic orbital combinations:

Analogous surface group orbitals can be constructed from the d, or p-atomic orbitals. Figure 3.12 shows the local density of states of such group orbitals as a function of electron

The Reactivity of Transition-Metal Surfaces 101

energy. The results are shown for extended Huckel calculations on Ag(111) indicate that the symmetric group orbitals have a maximum density at the lower energies. At somewhat higher energies, the single atomic orbital densities (relevant for atop adsorption) become the maximum. At the highest energies, the antisymmetric atomic orbital energies have the maximum in density. Hence, a low electron occupation of the metal-valence band provides a high electron density at the Fermi level for the high coordination s-symmetric interaction. A higher electron occupation of the valence band favors s-symmetric interactions in the atop configuration. It pushes adsorbates to atop positions. π-Type interactions are optimum at higher electron occupations and always tend to prefer high coordination.

The preference for CO to be adsorbed atop is typical for Co, Rh, Ru, Ir and Pt. On Ni and Pd, however, CO prefers to adsorb at the higher coordination sites. We have already discussed that the preference for atop adsorption is the result of the minimization of the repulsive interaction between doubly occupied π and σ states on CO and the occupied d-valence electron orbitals on the metal atom. Back-donation into unoccupied 2π molecular orbitals is maximum in high coordination sites. The back-donative interaction is enhanced by the additional interactions with antisymmetric combinations of surface s-atomic orbitals. The shift to higher coordination of CO on Ni and Pd indicates less involvement of the d-valence electrons in the surface chemical bond, consistent with the decrease in spatial extension of the d-atomic orbitals, when a metal changes position moving upward in a column or from left to right in a row of the periodic table.

For NH3 adsorption to Cu in two-fold coordination (Fig. 3.4) an analysis of the surface chemical bonds has been made with the surface orbital densities decomposed according the corresponding group orbitals. One notes the density of states at lower energies as well as the lower energy position of bonding and antibonding interactions for two-fold coordination compared to one-fold coordination.

3.3.1 Bonding in Transition-Metal Complexes

The importance of hybridization (see Addendum 3.11), between d-, s- and p-metal orbitals in chemical bonding is easily understood for the molecular organometallic transitionmetal complexes. The bonding in the tetrahedral Ni(CO)4 complex, for instance, can best be understood by initially considering the 5d–atomic orbitals doubly occupied with 10 electrons.

Figure 3.13. Interaction of four 5σ orbitals of CO with the four empty Ni sp3 orbitals (schematic).

The 4s and three 2p orbitals of Ni are empty and can hybridize into four empty equivalent sp3 orbitals. Combination with the four doubly occupied CO5σ orbitals leads to the formation of four bonding and four antibonding σ-type orbitals. The corresponding molecular orbital scheme is shown schematically in Fig. 3.14. The bonding σ as well as the non-bonding d-orbitals are occupied. The Ni(CO)4 complex is further stabilized by

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the additional back-donating interacting between the Ni-d orbitals and CO 2π orbitals. The bonding scheme nicely follows the 18-electron stability rule, which can be used to rationalize the stability of carbonyl complexes. In the Ni(CO)4 complex, the Ni atom contributes ten valence electrons whereas the four CO molecules contribute eight valence electrons.

It explains, for instance the stability of isoelectronic Co(CO)−4 and the consequential acidity of HCo(CO)4. It also predicts that the Co2(CO)8 complex is a stable dimer. There is a change in the ratio of number of CO ligands with metal-atom electron count. For Fe, which has 8 d-electrons, this becomes Fe(CO)5. For chromium this is Cr(CO)6, since Cr has 6 d-atomic electrons. In this way these complexes again satisfy the 18 electron rule. For CrL6 the resulting molecular orbital scheme is given in Fig. 3.15. The change in ligand number implies a change in shape of the molecule and of the hybridization.

The Ni(CO)4 sp3 hybridization scheme is based on the formation of the four bonding sp3 orbitals directed towards the corners of a tetrahedron. The prototype example for such bonding is CH4. The two other hybridization schemes of importance are d2sp3, giving 6 directed orbitals for octahedral coordination, and dsp2, given four directed orbitals for a square planar coordination. The latter is characteristic for complexes which contain 16 valence electrons, e.g. PtCl4 2−. In PtCl4 2− two σ electrons are counted for each Cl− ion.

The recombination of Co(CO)4 to Co2(CO)8 can also be understood within the octahedral d2sp3 hybridization scheme. Let us put six of the nine Co d-electrons into the three nonbonding Co d-orbitals. Four of the six d2sp3 orbitals form bonding orbitals with the four 5σ CO orbitals, that each donate two electrons. Two lone–pair type d2sp3 orbitals are left. One orbital can be doubly occupied whereas the other contains the final electron that is left. The latter orbital can combine with an equivalent orbital of another Co(CO)4 radical. A Co(CO)3 fragment contains three dangling d2sp3 orbitals each of which is occupied with one electron. Hence it can combine with three other such fragments to form Co4(CO)12 (see also Chapter 5,pages 226, 227).

For Pt, the Pt4(CO)10 carbonyl complex is formed. In the Pt4 framework, the Pt atoms have fully occupied d-atomic orbitals. Each Pt atom has one dangling free sp3 orbital and three sp3 orbitals that interact with the three neighboring Pt atoms. These form six σ bonds between the Pt atoms. Within this bonding scheme, all of these orbitals are initially empty. A total of 20 electrons have to be donated by the σ-lone pair orbitals of CO in order to fill the ten bonding σ-type orbitals. This is accomplished by the adsorption of four CO molecules at the apices and six CO molecules at the edges. In contrast to Ni4(CO)10 such multi–metal carbonyl Pt complexes are stable. Because the Pt-Pt distances are relatively long, Pauli repulsion between the doubly occupied d-atomic orbitals is reduced and thus easier to overcome than for the shorter metal–metal bonds that would appear in complexes formed from Ni. As we will see, the stabilizing interaction between Pt and the CO 2π orbitals is also more e cient because of the larger spatial extension of Pt d-atomic orbitals.

Interestingly, the negatively charged Chini complexes can be analyzed using these same principles. They are based on the triangular Pt3 bonding motif. In line with our earlier discussion one predicts the neutral Pt trimer to be Pt3(CO)9, with a CO molecule coordinated between two Pt atoms and a CO molecules coordinated end-on the layered Chini complexes. The Pt s,p-atomic orbitals are sp2 hybridized. The Pt pz atomic orbital remains unoccupied. The layered Chini complexes are then constructed by stacking of negatively charged Pt3(CO)6 units. Whereas the σ framework has doubly occupied σ-type orbitals, the Pt(pz ) orbitals are empty and hence can combine with a second

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Figure 3.16. The layered Chini complexes are constructed from Pt3(CO)6 units.

Pt3(CO)6 unit, when electrons are available to occupy the bonding orbital combination that is formed between the Pt(pz ) orbitals of the two trimers. Doubly charged layered Chini complexes are stable compounds. The corresponding orbital scheme of a Pt3(CO)6 unit is shown in Fig. 3.17. The partial density of states for the Chini complex is shown in Fig. 3.17 along with a representation of some of the corresponding orbitals. The d-valence region of the Pt atoms lies between –10 and –5 eV. In the energy range –16 to –14.8 eV and –13 to –11 eV the density of states is dominated by the bonding of the lone pair σ-CO interactions with the initially empty Ptσ-atomic orbitals. The lone pair interaction results in a rehybridization of 4σ and 5σ orbitals which is very similar to that for CO adsorbed on a metal surface. In the energy regime of -13 to -11 eV there is the interaction with the Pt d–atomic orbital and CO 1π orbitals.

The electron density range –9 to –6.6 eV is dominated by bonding, nonbonding and antibonding interactions between the d electrons and also the interactions with rehybridized 1π, 2π , 4σ and 5σ orbitals. This leads to localization of charge on oxygen atoms as well as antibonding d-electron interactions with the hybridized 4σ and 5σ CO orbitals. The HOMO consists mainly of occupied nonbonding dxz and dyz orbitals. The LUMO is comprised of the bonding combination of 3Pt 5pz orbitals and the unoccupied CO 2π -orbital fragments. The electron density regime representing the non-occupied orbitals between –4 and –1 eV consists mainly of the antibonding interaction between the CO 2π orbital and the Pt atomic orbitals.

We note that in clusters as on the surfaces the contribution of metal d as well as s and p electrons to the formation of ligand or adsorbate bonds plays a very important role. Electron donation of the 5σ–ligand orbitals can “glue” together cluster-atom fragments that otherwise would not be stable. Comparison of Fig. 3.17 and 3.6 indicates that there are many similarities between the interaction of CO on a transition-metal surface and a carbonyl complex. A main di erence is the low CO/metal atom ratio at the surface as compared to that in the carbonyl complex. Hence binding of CO to a transition-metal surface tends to weaken metal atom bonds, whereas in carbonyl complexes the binding to CO is essential to the stability of the complex.

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Figure 3.17. DFT calculated molecular orbitals of Pt3(CO)6 as well as their local density of state contributions on Pt and C.

3.4 Chemisorption of Atoms: Periodic Trends

The dissociation of diatomic molecules such as CO, NO, and N2 leads to the formation of the strongly bound adatoms at the surface. We focus here initially on the binding of carbon and oxygen adatoms. The results, however, generally apply to other adatom bonding to transition-metal surfaces. The preferred adsorption site for atomic carbon and oxygen depends on the surface topology. They generally prefer binding to the higher coordination sites. On the dense (111) surfaces of face-centered cubic structures, this is typically the three-fold coordination site. The strong bond energy stems from the fact that both O and C atoms have empty, or partially occupied, low-energy 2p atomic orbitals, that can form strong bonding orbitals with available surface sites. The corresponding antibonding orbital fragments are only partially occupied. Second, the repulsive Pauli interaction between electrons in the doubly-occupied adatom atomic orbitals and doubly-occupied surface valence-electron orbitals is reduced, as result of the weak interaction with the doubly-occupied low-energy atomic 2s orbitals. Figure 3.18 compares the interaction energies for O bound to di erent Group VIII and IB metals. Figure 3.18(a) shows the O 2px local density of states for each of the di erent metals. The d-electron occupation increases from the left to right. The d-electron density of the transition-metal surface before adsorption is also shown. The spatial extension of the d-valence electron density decreases