Simple Model of a Transition Metal

Here we try to gain insight into the trends in reactivity of the metals without getting lost in too much detail. We therefore invoke rather crude approximations. The electronic structure of many metals shows numerous similarities with respect to the sp band, with the metals behaving essentially as free-electron metals. Variations in properties are due to the extent of filling of the d band. We completely neglect the lanthanides and actinides where a localized f orbital is filled, as these metals hardly play a role in catalysis. 

Our representation of a metal is shown in Fig. 6.18. It possesses a block-shaped, partly filled sp band behaving as a free electron gas and a d band that is filled to a certain degree. The sp band is broad as it consists of highly delocalized electrons smeared out over the entire lattice. In contrast, the d band is much narrower because the overlap between d states, which are more localized on the atoms, is much smaller. 

If we consider the energy gained by forming the metal from the individual atoms, the sp band gives a contribution of approximately 5 eV for all metals. The variation in bonding energy across the transition metals is due to the d band. We will look at its properties and contribution to bonding in more detail. 

We approximate the d band by a narrow rectangular box, as shown in Fig. 6.18, where 

Remembering that there is always a repulsive term that is proportional to the overlap of the orbitals and the number of participating neighbors, we obtain 

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