D-band center

Prominent in both first-order Raman spectra Fig. 10a is the broad D-band centered at 1341 cm. Two second-order features, one at 2681 cm = 2(1341... 

Figure 6.30. Position of the center of the d band for the three series of transition metals. Note that the d band center shifts down towards the right of the periodic table. When the d band is completely filled, it shifts further down and becomes, effectively, a core level with little influence on the chemical behavior of...

This expression indicates that the change in hybridization energy is opposite and proportional to the shift of the d band center. Thus, if the d band shifts upwards the hybridization energy increases and vice versa. Strain and the associated shift of the d band can be brought about by growing the desired metal pseudomorfically on another material with a different lattice constant. The term pseudomorfic means that the overlayer grows with the same lattice constant as the substrate. The overlayer may thereby be strained or compressed depending on the lattice constants of the two materials. 

Figure 2.19 The energy of activation of the reduction reaction for various interactions with the d-band (a) as a function of the position of the d-band center (b) as a function of the coupling strength. The parameters are = 0.1 eV, Wd = 1 eV, A = 0.5eV, and A = 4eV in (a), = 2.0eV in (b), = —0.5 eV. The horizontal line indicates the value in the absence of...

Figure 9.12 Binding energies of O versus d-band center (relative to the Fermi level, - sp) of the Pt and Pt3Co alloy surfaces. Labels identify the adsorption sites. The line is the best hnear fit. (Reproduced with permission from Xu et al. [2004].)...

Figure 9.14 Kinetic current density (squares) at 0.8 V for O2 reduction on the Pt monolayer deposited on various metal single-crystal surfaces in a 0.1 M HCIO4 solution, and calculated binding energies (circles) of atomic oxygen (BEq), as a function of calculated d-band center (relative to the Fermi level, ej — sp) of the respective surfaces. The data for Pt(lll) were obtained from [Markovic et al., 1999] and are included for comparison. Key 1, PIml/ Ru(OOOl) 2, PtML/Ir(lll) 3, PtML/Rh(lH) 4, PtML/Au(lll) 5, Pt(lll) 6, PIml/ Pd(lll). (Reproduced with permission from Zhang et al. [2005a].)...

Models of CO adsorption show that top site binding is governed by the CO HOMO (5cr orbital) donating electrons into the metal unoccupied states, with simultaneous back-donation of electrons from the metal s occupied dxz and dyz states into the CO LUMO 2tt orbital). Therefore, it follows that the standard chemisorption model, which considers shifts in the total d-band center, can be inaccurate for systems in which individual molecular orbitals, involved in bonding with the adsorbate, shift differently due to external interactions. In particular, we have shown that the formation of hybrid orbitals with the support material can lead both to downward shifts in the metal d-band center, which do not affect the adsorption of molecules to the metal surface, and to upward shifts that are vitally important. 

Figure 2.30. Computed CO chemisorption energies as a function of the d-band center (ed) of the metal surface. From Ref. [69].

Figure 4.5 shows solutions to the Newns-Anderson model using a semi-elliptical model for the chemisorption function. The solution is shown for different surface projected density of states, nd(e), with increasing d band centers sd. For a given metal the band width and center are coupled because the number of d electrons must be conserved. 

Figure 4.5. Calculated change in the sum of the one-electron energies using the Newns-Anderson model. The parameters are chosen to illustrate an oxygen 2p level interacting with the d states of palladium with a varying d band center, ed. In all cases, the number of d electrons is kept fixed. The corresponding variations in the metal and adsorbate projected densities of states are shown above. Notice that the adsorbate-projected density of states has only a small weight on the antibonding states since it has mostly metal character. Adapted from Ref. [4].

Figure 4.6. Variations in the adsorption energy along the 4d transition metal series. The results of full DFT calculations are compared to those from the simple d band model and to experiments. Below the same data are plotted as a function of the d band center. Adapted from Ref. [4].

Ligand effects in adsorption - changing the d band center... 

For one kind of transition metal atoms, the d band center can be varied by changing the structure. As mentioned above, the band width depends on the coordination number of the metal and this leads to substantial variations in the d band centers [19]. Atoms in the most close-packed (111) surface of Pt have a coordination number of 9. For the more open (100) surface it is 8 and for a step or for the (110)... 

Figure 4.8. Schematic illustration of the coupling between bandwidth and d band center for a band with a fixed number of d electrons. When the bandwidth is decreasing the only way of maintaining the number of d electrons is to shift up the center of the band.

Pt surfaces tend to restructure into overlayers with an even higher density of Pt atoms than the close-packed (111) surface [21]. The Pt atoms are closer to each other on the reconstructed surfaces than in the (111) surface. The overlap matrix elements and hence the bandwidth are therefore larger, the d bands are lower and consequently these reconstructed surfaces bind CO even weaker than the (111) surface. The reconstructed Pt surfaces are examples of strained overlayers. The effect of strain can be studied theoretically by simply straining a slab. Examples of continuous changes in the d band center and in the stability of adsorbed CO due to strain are included in Figure 4.10. The effect due to variations in the number of layers of a thin film of one metal on another can also be described in the d band model [22,23]. 

For atomic chemisorption, similar structural effects are found (see the middle panel of Figure 4.10). As for molecular chemisorption, low-coordinated atoms at steps bind adsorbates stronger and have lower barriers for dissociation than surfaces with high coordination numbers and lower d band centers. The d band model thus explains the many observations that steps form stronger chemisorption bonds than flat surfaces [1,20,24-28]. The finding that the correlation with the d band center is independent of the adsorbate illustrates the generality of the d band model. 

Again the d band centers are found to describe changes in adsorption energies quite well [34-37]. This is illustrated in Figure 4.12, through the electrochemically determined variations in the hydrogen adsorption energy, for different Pd overlayers as a function of the calculated d band shifts [38]. 

As described in Chapter 2, a number of spectroscopic surface methods give information relating to d band shifts [45]. Ross, Markovic and coworkers have developed synchrotron-based high resolution photoemission spectroscopy to directly measure d band centers giving results in good agreement with the DFT calculations [46]. Another possibility is to exploit the fact that in some cases a shift in the d states can be measured as a core-level shift, as the d states and the core levels shift... 

Figure 4.13. Calculated shifts in the d band centers for a number of overlayer structures. The shifts are calculated relative to the d band center for the pure overlayer metal surface. The shifts therefore reflect the change in reactivity of the overlayer relative to the pure metal. Adapted from ref. [44].

Under the assumption that AE0 in Eq. (5) is independent of the metal considered, all effects due to having several metal components, are to be found in the AEd term. We have seen above that Ed is a function of the d band center, and for small variations in ed, the relationship must be linear ... 

The d band center is given by the first moment of the chemisorption function, Eq. (10). We therefore need to understand qualitatively how ( ) behaves for a multi-component system. To see this it is useful to expand the metal wave functions... 

The arguments behind the d band model are quite general and should apply to the interactions in the transition state as well as in the initial and final (adsorbed) states of the process. We therefore expect correlations between the d band center and transition state energies to be the same as for chemisorption energies. This is illustrated in the bottom panel of Figure 4.10. Figure 4.16 shows in detail how the activation energy for methane on different Ni surfaces scales with the center of the d bands projected onto the appropriate metal states to which the transition state couples. 

Figure 6.16. Illustration of the d-band model governing surface chemical bonding on transition metal surfaces. As the d-band center of a catalytic surface shifts downward more antibonding orbitals become occupied and the surface bond energy of an adsorbate (here an oxygen atom) decreases. An upward shift in the d-band center predicts strengthening of the surface bond.

Ruban et al. established an atomic d-band center model.91 Based on this model, they examined the impact of surroundings to the activity and how the activity can be altered. They revealed that the shift of the d-band depended on the difference in the size... 

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