Surface states transition metal surfaces

Our intention is to give a brief survey of advanced theoretical methods used to detennine the electronic and geometric stmcture of solids and surfaces. The electronic stmcture encompasses the energies and wavefunctions (and other properties derived from them) of the electronic states in solids, while the geometric stmcture refers to the equilibrium atomic positions. Quantities that can be derived from the electronic stmcture calculations include the electronic (electron energies, charge densities), vibrational (phonon spectra), stmctiiral (lattice constants, equilibrium stmctiires), mechanical (bulk moduli, elastic constants) and optical (absorption, transmission) properties of crystals. We will also report on teclmiques used to study solid surfaces, with particular examples drawn from chemisorption on transition metal surfaces. 

In the final section, we will survey the different theoretical approaches for the treatment of adsorbed molecules on surfaces, taking the chemisorption on transition metal surfaces, a particularly difficult to treat yet extremely relevant surface problem [1], as an example. Wliile solid state approaches such as DFT are often used, hybrid methods are also advantageous. Of particular importance in this area is the idea of embedding, where a small cluster of surface atoms around the adsorbate is treated with more care than the surroundmg region. The advantages and disadvantages of the approaches are discussed. 

Figure 4.27 presents steady-state potentiostatic r vs 0Na results during NO reduction by H2 on Pt/p"-Al203f2 PInb values well in excess of 4000 are obtained for 0Na values below 0.002. This is due to the tremendous propensity of Na to induce NO dissociation on transition metal surfaces. Since Plj is often found to be strongly dependent on 0, (Figs. 4.26 and 4.27), it is also useful to define a differential promotion index pij from ... 

In the past the theoretical model of the metal was constructed according to the above-mentioned rules, taking into account mainly the experimental results of the study of bulk properties (in the very beginning only electrical and heat conductivity were considered as typical properties of the metallic state). This model (one-, two-, or three-dimensional), represented by the electron gas in a constant or periodic potential, where additionally the influence of exchange and correlation has been taken into account, is still used even in the surface studies. This model was particularly successful in explaining the bulk properties of metals. However, the question still persists whether this model is applicable also for the case where the chemical reactivity of the transition metal surface has to be considered. 

Using perturbation theory. Hammer and Nprskov developed a model for predicting molecular adsorption trends on the surfaces of transition metals (HN model). They used density functional theory (DFT) to show that molecular chemisorption energies could be predicted solely by considering interactions of a molecule s HOMO and LUMO with the center of the total d-band density of states (DOS) of the metal.In particular. 

Figure 2.9. Schematic illustration of the formation of a chemical bond between an adsorbate valence level and the s- and d-states of a transition metal surface. Reproduced from [32].

Very recently, spectroscopic investigations have provided evidence that at least two types of molecular NO can exist simultaneously on transition metal surfaces (12,15.19,20, 21, 22), thus supporting the interesting possibility that the rich diversity of nitrosy1-metal chemistry extends from metal complexes to metal surfaces. Two states of molecular NO have been observed on Ru(001) by electron energy loss spectroscopy (EELS) (13), and also by X-ray photo-... 

We have emphasized the importance of open d-orbitals and a proper atomic state if should dissociate with a low barrier on a transition metal surface. For clusters, however, the same type of dissociation puts up another requirement, which will turn out to be even more significant in the present context There must be at least one open shell valence orbital (of s-character) on the cluster, otherwise the sd-hybridization will not take place (8). For an infinite surface, this requirement can always be satisfied since states with open valence orbitals must at least be reachable by a low energy excitation. For clusters, the same type of excitation may be much more expensive. Since all nickel clusters dissociate it seems clear that a dissociative state is reachable in all cases for nickel. The question that has worried us for the past years is why the same type of states do not always seem reachable for iron and cobalt clusters. The answer to this question is discussed in section VI. 

Two coupling modes are considered for the Pdj CO cluster the first mode (denoted as h) represents vibration of the rigid CO molecule with respect to the transition metal surface. The second mode is either the Pd-Pd vibration wi in the plane of Pd surface atoms (r) or out-of-plane stretch of the surface/sub-surface Pd-Pd bond (z). The total energy surfaces (h,r) and (h,z) are calculated for discrete points and then fitted to a fourth order polynomial. Variational and Quantum Monte Carlo (QMC) methods were subsequently applied to calculate the ground and first excited vibrational states of each two-dimensional potential surfaces. The results of the vibrational frequences (o using both the variational and QMC approach are displayed in Table II. 

Dissociative adsorption of CO has been found on a variety of transition metal surfaces. Broden el al. (17) and Nieuwenhuys (14) correlated the tendency for CO, N2, and NO to dissociate with the position of the transition metal in the periodic table the tendency for dissociation increases the further to the left the metal appears in the table, and it decreases from 3d to 5d metals. Furthermore, the borderline for dissociative or molecular adsorption moves to the right in the sequence CO, N2, NO to O2, being the same order as the bond strength in the free molecules. There is sufficient evidence for the proposed correlation. For example, W and Mo surfaces dissociate CO easily al room temperature dissociative adsorption has not been reported lor Pi, Ir, and Pd(III) surfaces, and CO dissociation has been reported to occur on Ni, Co, and Ru at elevated temperatures. Ben-zinger (IS) suggested that the state of adsorption (molecular or dissociative)... 

It is clear that much work remains to be done to extend our understanding to polax surfaces of transition metal oxides in which the cations have partially filled d orbitals. An especially challenging issue is related to mixed valence metal oxides, such as Fe304, in which the cations exist under two oxidation states. In addition, considering the rapid development of ultra-thin film synthesis and characterization, a simultaneous effort should be performed on the theoretical side to settle the conditions of stability of polar films. More generally, on the experimental side, it seems that one of the present bottlenecks is in a quantitative determination of the surface stoichiometry, an information of prominent interest to interpret the presence or absence of reconstruction. 

A few examples may demonstrate this. The approximation has been used to treat the photodissociation processes of NOHCl [33] and NO2 [34] which include three internal modes. Five dimensional time dependent calculations were performed on the photodissociation of CH3I [35, 36]. The state-to-state chemistry has been investigated for the reactive scattering of H-1-H2 (v=0,l) —> H2 (v=0,l) -1- H collinear system [37]. The MCTDSCF approach has also been applied to surface chemistry, in particular H2 dissociation on a transition metal surface [38] the photodissociation of CH3I on MgO surface [39, 40] and to inelastic molecule-surface scattering [41, 42]. Recently, the MCTDSCF method has been used to investigate multimode effects in the absorption spectrum of pyrazine taking into account 14 vibrational modes [43]. 

Of great importance is the nature of surface bonding of intermediates to the metal this depends very much on the geometry and orientation of the crystal plane on which the chemisorption takes place, and on the orientation and symmetry of emergent orbitals (especially dsp hybrid orbitals at transition metal surfaces) at the metal surface as emphasized and illustrated by Bond (24, 7) (Fig. 5 A). These factors determine the geometry of coordination of the adspecies at the catalyst or electrocatalyst surface. Since that work (41), a great many papers have appeared on molecular-orbital calculations for bonding at surfaces and on surface states and electron-density distributions. 

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