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I’m reading Assa Auerbach’s Interacting electrons and quantum magnetism.

In 1.3, it says

In contrast, transition metals and mixed valence rare earth compounds contribute $d$ and $f$ electrons to the conduction band. There, the electrons are mostly localized within a small radius $\langle r_{ij}\rangle \ll a$ around the ions, where $a$ is the lattice spacing.

I wonder why are $d$ and $f$ electrons near to the ions?

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Promoted from a comment:

The filling sequence order of orbitas: $1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s$. The energy of orbital $4d$ is greater than that of $5s$, and $4f$ is greater than $6s$. The principle quantum number $n$ mainly determine the size of the orbital. Therefore, the size of $4f$ is much smaller than $6s$.

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  • $\begingroup$ Although these $d$ and $f$ electrons have a smaller energy based on radius alone (a more negative potential energy), they have a significant amount of rotational kinetic energy (based on angular momentum). This makes the $4f$ electron easier to free from its state within the atom. The rotational kinetic energy can contribute to overcoming the negative potential energy of the closer orbital distance. $\endgroup$ Commented Apr 13, 2023 at 21:38

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