Codifying systematic trends in d- and f-electron materials

As one moves around the periodic table the extent of delocalisation of valence electrons varies significantly and in a systematic way, particularly in transition metals and rare earths. This leads to a subtle competition between metallic and magnetic behaviour and is nicely codified in a reorganised periodic table presented by Smith and Kmetko in 1983.

The version below is presented by Piers Coleman in his long-awaited textbook Introduction to Many-Body Physics.

The bottom part illustrates how as one moves from 3d to 5f to 4f the electrons become more localised due to the tail of the atomic wave function becoming smaller. As the principle quantum number (n=3,4,5) increases the electrons become more delocalised to the larger number of nodes in the radial wave function.

Materials near the localisation-delocalisation boundary are both the most interesting and the most challenging to describe theoretically.

Note that plutonium is at the boundary, which is arguably why it has such a rich phase diagram and properties characteristic of a strongly correlated metal.