Lanthanides and actinides: f-block chemistry

The family name does not specify every electron state

Lanthanoids denotes the La–Lu family and actinoids Ac–Lr in the IUPAC collective names; lanthanides and actinides are common corresponding terms. Membership is not a requirement for the same occupied f subshell in every neutral atom or ion. State the particular ion and its formal electron assignment.

The +3 state is widespread among lanthanoid ions, with important element- and environment-dependent alternatives such as Ce(IV), Eu(II) and Yb(II). For selected ionic bookkeeping, Ce(III) is 4f¹ and Ce(IV) 4f⁰; Gd(III) 4f⁷. Their formal isolated-ion total electron counts are 55, 54 and 61 from atomic numbers 58 and 64.

Selected U(IV) and U(VI), atomic number 92, have formal total counts 88 and 86 and common formal 5f² and 5f⁰ assignments. These are ionic bookkeeping configurations, not exact measured U populations in every covalent complex. Early actinoids can support several oxidation states, and patterns change across the series and with the ligand environment.

Compare the role of f orbitals without an absolute ban

The relatively shielded 4f orbitals of many lanthanoid ions make electrostatic interactions and ionic-size trends useful starting descriptions. High and variable coordination numbers are common; there is no universal octahedral-only rule. The gradual size change across comparable trivalent ions helps organize trends, while speciation, hydration, ligands and phase still affect actual behavior.

More spatially available 5f and 6d orbitals in selected early-actinoid environments can participate in bonding and influence structure. A primary 2019 experimentally grounded computational study of specific metal–ligand systems shows a structure-directing role for f-orbital overlap-driven covalency. That result challenges an absolute assertion that f orbitals are always nonbonding; it does not assign the same covalency or geometry to every f-block compound.

The balance of orbital energies, overlap and electrostatic effects needs a named comparison and evidence. Shielded does not mean forbidden from every interaction, and formal f⁰ does not mean no metal–ligand covalency. The ordinary d-block splitting patterns earlier in the chapter cannot simply be copied onto every f-ion spectrum.

The free-ion angular-momentum estimate is a deeper model

On a first reading, retain that an orbital contribution can make a spin-only estimate inadequate. The following free-ion calculation is an optional deeper comparison. For a selected Russell–Saunders coupled ion, g_J=1+[J(J+1)+S(S+1)−L(L+1)]/[2J(J+1)] and μ_eff=g_J√[J(J+1)] μ_B. L,S,J label orbital, spin and total angular momentum in this restricted model, with J nonzero here.

For selected Ce(III) 4f¹ use L=3,S=1/2,J=5/2. The Landé factor is 6/7 and moment approximately 2.53546 μ_B, compared with the one-unpaired-electron spin-only value√3≈ 1.73205 μ_B. For selected Gd(III) 4f⁷ use L=0,S=7/2,J=7/2; g_J=2 gives√63≈ 7.93725 μ_B, matching the corresponding seven-unpaired spin-only result.

These are free-ion estimates, not measured magnetic values for every complex at every temperature. Crystal-field states, magnetic coupling, excited-state populations and other conditions can change an actual response. The comparison explains an omitted term; it is not a general method to identify an unknown material from one magnetic number.

A binding-constant ratio is not a recovered separation factor

In an invented ideal 1:1 comparison at 298.15 K, let fictional ions LnA and LnB have formation constants β_A=10⁶ and β_B=2× 10⁶ with the same dimensionless free-ligand activity. Treat each metal pool independently and the free ligand as externally maintained. Bound fraction is βa_L/(1+βa_L). These constants are teaching inputs, not measurements for named lanthanoids.

At a_L=10⁻⁶, the bound fractions are 0.500 and 2/3≈ 0.666667, giving ratio 4/3. At a_L=10⁻³, they are 1000/1001≈ 0.999001 and 2000/2001≈ 0.999500, giving ratio≈ 1.000500. The constant ratio remains 2, but both metals approach complete binding and their bound-fraction ratio approaches 1.

Actual separation additionally depends on competing balances, phases, ligand capacity, selectivity definitions, recovery and process conditions. A larger formation constant can help a comparison without providing a universal measured separation factor. This toy supplies no extraction, isotope separation or material-handling procedure.

Uranyl retains its own axial and equatorial distinction

In the selected idealized entity [UO₂(H₂O)₅]²⁺, assign the two oxo ligands −2 each and water neutral. The entity charge then gives U+6 and a formal 5f⁰ metal assignment. The two axial O donors plus five equatorial water O donors give seven directly bound donor atoms, while the water-molecule count is five. A multiple metal–O bond still contributes one bound atom to this direct-donor count.

The donor topology can be idealized as pentagonal bipyramidal with a linear axial O–U–O unit and five equatorial O directions. Normalizing every donor radius to one would only illustrate topology; actual axial and equatorial distances differ. Uranyl compounds have varied equatorial arrangements, and a mineral structure cannot by itself establish one universal solution hydration number.

A primary molecular-dynamics study reported a five-water equatorial arrangement for its finite 300 K hydrated-ion simulation. Its conditions and sampling do not establish the same number for every solvent, concentration or phase. Secondary-shell waters are not direct donors in this specified entity.

The formal metal electron count is 92−6=86. The whole written ion has 156 electrons:92+7× 8+10× 1−2. These are different counts; total electrons in the entire entity must not be called its f occupancy. Structural evidence, electron-assignment conventions and actual electronic populations continue to answer different questions.

Worked examples

Try it yourself

1. Using Ce atomic number 58, find the formal total electron count of Ce(IV).

   Show the answer and reasoning

   54.

   58−4=54; the selected 4f⁰ assignment is a subshell count rather than the total 54.

2. For fictional LnA with β=10⁶ and maintained a_L=10⁻⁵, find the bound fraction in the same 1:1 ideal model.

   Show the answer and reasoning

   10/11≈ 0.90909.

   βa_L=10 and f=10/(1+10), under the stated fixed-free-ligand assumptions.

3. Does changing a direct-donor count from seven to a count of five mean the same thing as counting the five water molecules?

   Show the answer and reasoning

   No.

   The two axial oxo donors also belong to the seven-donor entity; ligand entities and bound atoms are different counts.

4. Does a formal f⁰ assignment prove that no metal–ligand covalency can exist?

   Show the answer and reasoning

   No.

   Formal occupancy and the whole bonded electronic structure are different descriptions; other orbitals and mixing can contribute.

What to carry forward

• Specify the ion rather than only its family.
• Keep total electrons, f occupancy and actual population distinct.
• Treat f-orbital bonding as a contextual question.
• Use free-ion magnetism within its limited model.
• A binding contrast does not by itself establish recovered separation.
• Retain uranyl’s axial/equatorial and direct/secondary-shell distinctions.