The Theoretical Approach

When a H2 molecule approaches a metal surface, as indicated in Figure 4.14 it will first feel the van der Waals interaction. This is a weak interaction due to polarization effects, which typically amounts to only 10 kJ mol-1 for H2 and thus only leads to adsorption at very low temperatures or high pressures.

When approaching even closer there may be an exchange between the hydrogen electrons and the electrons in the metal leading to associative chemisorption, that is the H2 molecule remians intact. The typical situation for hydrogen is, however, that this associative chemisorption is also very weak and the hydrogen only interacts strongly with the metal if it is allowed to dissociate. Whether this happens is naturally dependent on the height of the barrier Ea indicated in Figure 4.14. If no barrier is found the molecule will dissociate straightforwardly, as is the case for most transition metals where the probability for dissociative sticking of hydrogen is always close to one. If the barrier is large, as indicated by the full line there will be an activation energy for dissociation and the sticking coefficient will drop accordingly. This barrier is typical for the late transition metals and especially for the noble metals and the so-called free electron metals where there is no d-electron to facilitate the reaction. If the H2 molecule dissociates, the proton may, dependent on the type of metal and its potential energy diagram, enter into the metal, where

Potential Energy Diagram Hydrogen
Fig. 4.14 Schematic potential energy diagram for a hydrogen molecule approaching a metal surface. In this case the metal hydride formation is endothermic. See the text for details.

it can either occupy interstitial sites or form a regular metal hydride, but that is beyond the scope of this chapter and will be discussed in chapter 6. Thus the potential energy diagram shown in Figure 4.14 basically sets the scene for the hydrogen dissociation and recombination since that is given by the height of the activation energy barrier Eaand the depth of the chemisorption well of the adsorbed hydrogen atoms AHads. The adsorption energy will then be Eads = AHads + Ea.

The individual elements of this potential energy diagram are readily explained: When an atom or molecule approaches a metal surface with free electrons, image charges will be introduced through polarization. This leads to an attractive interaction, the so-called Van der Waals interaction, which is proportional to d-3, where d is the distance between the atom/molecule and the surface. However, if the electrons in the surface and the molecule do not adjust there will be a strong repulsion proportional to e-d since this is the manner in which the electronic wave-functions decay far from the surface and the atom/molecule. The dotted line going very steeply upwards indicates this repulsive behavior.

The chemisorption is due to an interaction between the states of the H2 molecule and the electrons in the metal. The simple picture is given by the Newns-Anderson model where an adsorbate state is lowered and broadened when interacting with a sea of valence electrons in a metal, as indicated in Figure 4.15. Basically, all metals have a broad band of sp-electrons that are populated up to the Fermi level. Since these metals can be considered more or less as free electrons their density of states (DOS) is usually assumed to be proportional to vE, as indicated in Figure 4.15. In the case of associative H2 chemisorption the interaction is rather weak

Distance from surface

Chemisorption

Metal

Fig. 4.15 The hydrogen molecule far away from a metal surface is formed by overlap between the two 1s electrons of the individual atoms forming a bonding and antibonding orbital. When the molecule approaches a surface these orbitals become broadened and lowered due to the interaction with the metal sp-band.

Metal

Fig. 4.15 The hydrogen molecule far away from a metal surface is formed by overlap between the two 1s electrons of the individual atoms forming a bonding and antibonding orbital. When the molecule approaches a surface these orbitals become broadened and lowered due to the interaction with the metal sp-band.

and further approach to the surface results again in strong Pauli repulsion, as indicated by the dotted line, unless dissociation takes place. If we took a hydrogen atom and approached it to the surface its energy would be much higher since it requires 4.55 eV to dissociate a H2 molecule. This is indicated by the slashed curve. The atom also feels a van der Waals attraction but that is negligible on this scale where the hydrogen atoms are simply falling into a chemisorbed state. Where the crossover occurs determines the size of the barrier for dissociation. Since all metals basically have this feature how do the differences arise? The d-electrons have not yet been considered and they are the key to the difference. The d-electrons form a considerably narrower d-band since these orbitals are more localized than the sp-orbitals. Remember the width of the band is proportional to the overlap of the orbitals. The effect of the d-band is illustrated schematically in Figure 4.16 where we now let our hydrogen molecule approach a transition metal with a partially filled d-band, which naturally also has a broad sp-band.

Just as in Figure 4.15 the interaction with the sp-band will lead to a lowering and broadening of the molecular levels, that is the molecular chemisorption. But in addition to this interaction there will also be a coupling to the narrow d-band. Just as we considered a simple interaction between the two 1s orbitals in the atomic hydrogen leading to the bonding and antibonding orbitals in the hydrogen molecule in Figure 4.15 we may now consider the interaction between each of the lowered (and broadened) a orbitals of the hydrogen molecule interacting with the narrow d-band in a similar manner. This will lead to a splitting of each of the a orbitals into a bonding and antibonding orbital, as indicated in Figure 4.16. The effect of this interaction is basically the holy grail of catalysis. Notice how the antibonding orbital of molecular hydrogen a * is being pulled below the Fermi level and thus

Band Theory Norskov
Fig. 4.16 The hydrogen molecule is as in Figure 4.15 interacting with the metal sp-band becoming lowered and broadened but now the molecular levels also interacts with a narrow d-band, resulting in a splitting of

the two molecular orbitals into bonding and antibonding orbitals. Notice how the internal bonding of the hydrogen molecule becomes weakened due to the filling of the otherwise empty a * state.

Hammer Norskov Nature 1995

Projected DOS (arb. units)

Fig. 4.17 Projection of the H2 states onto the metals states. The dark shaded states are the projection of the down-split a * while the light shaded is the down-split a state. See text for details. Adapted from (Hammer and Norskov (1995), Ref. [185]).

Projected DOS (arb. units)

Fig. 4.17 Projection of the H2 states onto the metals states. The dark shaded states are the projection of the down-split a * while the light shaded is the down-split a state. See text for details. Adapted from (Hammer and Norskov (1995), Ref. [185]).

filled with electrons. This increases the bonding to the surface by weakening the internal bonding of the molecule since it is an antibonding orbital that is being filled. Thus the internal bonding is weakened and hence its dissociation becomes much easier - that is the activation energy for dissociation Ea shown in Figure 4.14 is reduced and dissociation of the molecule becomes much easier, forming adsorbed atomic hydrogen on the surface. This hydrogen may now diffuse into the metal forming interstitials or metal hydrides, dependent on the energy potential, as indicated to the far left in Figure 4.14, or it may interact with other surface intermediates forming useful compounds, as is the case in catalysis.

The above strongly idealized picture captures the main effects of molecules approaching a surface and is also applicable to other molecules like CO, N2 and O2. Nevertheless, when turning to the real density functional theory (DFT) calculations [185], which describe the approach much more accurately, the picture becomes considerably more complex, as is seen from Figure 4.17. In the left panel are the bonding a and the antibonding a * orbitals of the Al(111) surface. Notice that the levels are broadened. In the next panel is shown the result of the interaction with a d-band metal Cu(111). We still have the two bands, but it is now clear that an additional splitting due to the interaction with the d-band is occurring. The last panel shows the interaction with pure Pt(111) and here the additional splitting due to the d-band becomes even clearer. The downshifted antibonding orbital is shifted way below the Fermi level and is being filled, weakening the internal bond of the hydrogen molecule. This picture corresponds well with the experimental observation that the free electron metals are not good at dissociating hydrogen. When entering the transition metal series dissociation happens readily while it becomes difficult again when going to the far right, that is the noble metals, due to the filling and lowering ofthe d-band.

To understand the trends in reactivity we must consider the reaction pathway for dissociating hydrogen and, in particular, the detail ofthe transition state where the

Potential Energy Diagram For

Fig. 4.18 Potential energy diagram for hydrogen approaching various metal surfaces as indicated. For further details please consult the text and the literature. Adapted from (Hammer and N0rskov (1995), Ref. [185]).

Fig. 4.18 Potential energy diagram for hydrogen approaching various metal surfaces as indicated. For further details please consult the text and the literature. Adapted from (Hammer and N0rskov (1995), Ref. [185]).

hydrogen is dissociating. The DOS shown in Figure 4.17 is for the situation where the hydrogen molecule is in the transition state and the potential energy diagram is shown in Figure 4.18. Notice the very high barrier for dissociating hydrogen on Al(111) where there is no interaction with a d-band. The barrier simply disappears over the d-band metal, but start to reappears when going to the noble metals such as Cu(111) where the d-band is filled and basically only results in a repulsive interaction with the molecular orbitals.

This effect is even more pronounced if going to the even more noble metals like Ag and Au and has been treated in great detail by Norskov et al. [186].

Was this article helpful?

+4 0
Guide to Alternative Fuels

Guide to Alternative Fuels

Your Alternative Fuel Solution for Saving Money, Reducing Oil Dependency, and Helping the Planet. Ethanol is an alternative to gasoline. The use of ethanol has been demonstrated to reduce greenhouse emissions slightly as compared to gasoline. Through this ebook, you are going to learn what you will need to know why choosing an alternative fuel may benefit you and your future.

Get My Free Ebook


Post a comment