Atomic and Ionic Radii -- Lanthanoid Contraction

As one moves progressively across the 4f series from cerium to lutetium, both the atomic radius and, more particularly, the ionic radius of the Ln³⁺ ions show a gradual, cumulative decrease with increasing atomic number. This steady, cumulative decrease in ionic size across the lanthanoid series is given the specific name lanthanoid contraction.

The underlying cause of lanthanoid contraction traces directly to the shielding behaviour of the 4f electrons themselves. As one moves from one lanthanoid element to the next across the 4f series (from Ce toward Lu), the nuclear charge increases by exactly one unit at each step (one additional proton), and the one additional electron gained at each step is added into the SAME inner 4f sub-shell that was already being filled. Crucially, the 4f sub-shell has a diffuse, poorly-shielding shape -- 4f orbitals are radially more spread out and less effective at screening outer electrons from the nuclear charge than, say, d or p orbitals in a comparable position would be. Consequently, the shielding effect that each additional 4f electron provides to the OTHER, outer (valence-shell) electrons is relatively poor. With this weak shielding, as the nuclear charge steadily increases across the series, the valence shell (and, correspondingly, the ionic radius of the Ln³⁺ ion) is pulled progressively closer in toward the nucleus at each step. As a direct result, the EFFECTIVE nuclear charge actually experienced by the 4f electrons themselves (and by the outer valence electrons) increases somewhat faster than it otherwise would with good shielding, and the size of the Ln³⁺ ion correspondingly decreases steadily across the series, as plotted in Figure 4.11.

Lanthanoid contraction has two headline, well-documented consequences, each developed in turn. The first consequence concerns basic character: moving from Ce³⁺ toward Lu³⁺, the basic character of the Ln³⁺ ions systematically DECREASES across the series. This follows directly from the shrinking ionic radius: as the Ln³⁺ ion becomes progressively smaller, the ionic character of the Ln-OH bond in the corresponding hydroxide, Ln(OH)₃, correspondingly decreases (equivalently, the covalent character of that bond increases), and this shift toward more covalent Ln-OH bonding results, in turn, in a systematic decrease in the basic character of the hydroxide -- so La(OH)₃, at the very start of the series with the largest La³⁺ ion, is the most strongly basic lanthanoid hydroxide, while Lu(OH)₃, at the very end of the series with the smallest Lu³⁺ ion, is the least basic (most nearly amphoteric) of the lanthanoid hydroxides.

The second consequence concerns the close chemical similarity observed among the lanthanoids as a family. Across the ENTIRE fourteen-element f-series, only about a 10 pm total decrease in atomic radius, and about a 20 pm total decrease in ionic radius, is observed from one end of the series to the other -- a genuinely small absolute change in size, spread out gradually over fourteen consecutive elements. Precisely because this element-to-element change in size is so small at each individual step, the chemical properties of neighbouring (and even fairly widely separated) lanthanoids remain quite closely similar to one another throughout the series -- directly explaining why the lanthanoids, as a family, are notoriously difficult to separate from one another by ordinary chemical means, and why their chemistry, as studied throughout this chapter, can largely be discussed as one broadly unified family rather than fourteen sharply distinct elements. …