Chapter 23: The f-block Elements

The f-block Elements

The two series of elements in the f block derive from the filling of the seven 4f and 5f orbitals, respectively. This occupation of f orbitals from f¹ to f¹⁴ corresponds to:

4f Elements (Lanthanoids)

Cerium (Ce) to Lutetium (Lu) in Period 6

Symbol: Ln

Core-like 4f orbitals • Predominantly ionic bonding • Uniform +3 oxidation state

5f Elements (Actinoids)

Thorium (Th) to Lawrencium (Lr) in Period 7

Symbol: An

More diffuse 5f orbitals • Covalent bonding possible • Variable oxidation states

Key Point: The lanthanoids are sometimes called the "rare earth elements"; however, this name is inappropriate because they are not particularly rare, except for promethium (Pm) which has no stable isotope. Even thulium, the "rarest" lanthanoid, has a crustal abundance greater than silver!

The f-block in the Periodic Table

57La

58Ce

59Pr

60Nd

61Pm

62Sm

63Eu

64Gd

65Tb

66Dy

67Ho

68Er

69Tm

70Yb

71Lu

89Ac

90Th

91Pa

92U

93Np

94Pu

95Am

96Cm

97Bk

98Cf

99Es

100Fm

101Md

102No

103Lr

23.1 The Valence Orbitals

Key Points: The 4f orbitals make very little contribution to bonding: their radial distribution functions lie within the 6s and 5d orbitals from which electrons are easily removed to form the 3+ ion. Lanthanoids thus display predominantly ionic bonding. The 5f orbitals are slightly more diffuse and the actinoids have a richer chemistry that includes covalent bonding.

To understand the chemistry of f-block elements, we must consider how the 4f and 5f orbitals project out from the core. The f and d orbitals have been compared to flower petals:

4f Orbitals (Daisy Petals)

Lack inner radial maximum
Poorly shielded from nuclear charge
Buried below 5d and 6s orbitals
Contract sharply → become core-like
Minimal overlap with ligand orbitals

5f Orbitals (More Extended)

Have an inner radial maximum
More penetrating, better shielding
More diffuse than 4f
Can overlap with ligand orbitals
6d orbitals extend even further

Radial Distribution Functions: Sm³⁺ vs Pu³⁺

The consequence of these orbital characteristics is fundamental:

Lanthanoids behave like Group 2 metals with nondirectional electrostatic bonding
Early actinoids (Th–Pu) resemble d metals with rich complexes and oxidation states
Later actinoids become more lanthanoid-like as 5f contracts into core

Lanthanoid Chemistry

The lanthanoids are all electropositive metals with remarkable uniformity of chemical properties. The significant difference between two lanthanoids is often only their size, which allows "tuning" of compound properties.

23.4 General Trends

Key Points: The lanthanoids are highly electropositive metals that most commonly occur in their compounds as Ln(III); other oxidation states are stable only when an empty, half-filled, or full f subshell is produced.

(a) Electronic Structures

Z	Name	Symbol	M config	M³⁺ config
57	Lanthanum	La	[Xe]5d¹6s²	[Xe]
58	Cerium	Ce	[Xe]4f¹5d¹6s²	[Xe]4f¹
59	Praseodymium	Pr	[Xe]4f³6s²	[Xe]4f²
60	Neodymium	Nd	[Xe]4f⁴6s²	[Xe]4f³
61	Promethium	Pm	[Xe]4f⁵6s²	[Xe]4f⁴
62	Samarium	Sm	[Xe]4f⁶6s²	[Xe]4f⁵
63	Europium	Eu	[Xe]4f⁷6s²	[Xe]4f⁶
64	Gadolinium	Gd	[Xe]4f⁷5d¹6s²	[Xe]4f⁷
65	Terbium	Tb	[Xe]4f⁹6s²	[Xe]4f⁸
66	Dysprosium	Dy	[Xe]4f¹⁰6s²	[Xe]4f⁹
67	Holmium	Ho	[Xe]4f¹¹6s²	[Xe]4f¹⁰
68	Erbium	Er	[Xe]4f¹²6s²	[Xe]4f¹¹
69	Thulium	Tm	[Xe]4f¹³6s²	[Xe]4f¹²
70	Ytterbium	Yb	[Xe]4f¹⁴6s²	[Xe]4f¹³
71	Lutetium	Lu	[Xe]4f¹⁴5d¹6s²	[Xe]4f¹⁴

(c) The Lanthanoid Contraction

Lanthanoid Contraction:

All Ln³⁺ ions have the electron configuration [Xe]4fⁿ, and their radii contract steadily from 116 pm for La³⁺ to 98 pm for Lu³⁺ (an 18% decrease). This is attributed to the increase in effective nuclear charge as electrons are added to the poorly shielding 4f subshell.

Ionic Radii of Ln³⁺ (pm)

La³⁺
116

Ce³⁺
114

Nd³⁺
111

Sm³⁺
108

Eu³⁺
107

Gd³⁺
105

Dy³⁺
103

Er³⁺
100

Yb³⁺
99

Lu³⁺
98

(e) Standard Potentials and Oxidation States

The oxidation state Ln(III) prevails through the 4f row. However, some elements show atypical oxidation states (+2 or +4) when they can attain relatively stable electron configurations:

🔹

Ce⁴⁺ (f⁰)

Empty subshell

Strong oxidizing agent

⚡

Eu²⁺ (f⁷)

Half-filled

Stable reducing agent

🔷

Tb⁴⁺ (f⁷)

Half-filled

Tb₄O₇ in air

✨

Yb²⁺ (f¹⁴)

Filled subshell

Strong reductant

Element	E°(Ln³⁺/Ln) / V	r(Ln³⁺) / pm	Oxidation Numbers
La	−2.38	116	3
Ce	−2.34	114	3, 4
Eu	−1.99	107	2, 3
Gd	−2.28	105	3
Tb	−2.31	104	3, 4
Yb	−2.22	99	2, 3
Lu	−2.30	98	3

23.5 Electronic, Optical, and Magnetic Properties

(a) Electronic Absorption Spectra

Key Points: Lanthanoid ions typically display weak but sharp absorption spectra because the f orbitals are shielded from the ligands. The spectra are largely independent of the coordination environment.

Lanthanoid(III) ions are weakly coloured, with absorptions from f–f transitions. Key characteristics:

Much narrower bands than d-metal complexes
Insensitive to coordinated ligands (4f buried beneath 5s, 5p)
Molar absorption coefficients: 1–10 dm³ mol⁻¹ cm⁻¹ (vs ~100 for d-metals)
Laporte forbidden transitions with little vibronic enhancement

Ion	Colour	Ground State	μ/μ_B (theory)	μ/μ_B (observed)
La³⁺	Colourless	¹S₀	0	0
Ce³⁺	Colourless	²F_5/2	2.54	2.46
Pr³⁺	Green	³H₄	3.58	3.47–3.61
Nd³⁺	Violet	⁴I_9/2	3.62	3.44–3.65
Sm³⁺	Yellow	⁶H_5/2	0.84	1.54–1.65
Eu³⁺	Pink	⁷F₀	0	3.32–3.54
Gd³⁺	Colourless	⁸S_7/2	7.94	7.9–8.0
Tb³⁺	Pink	⁷F₆	9.72	9.69–9.81
Dy³⁺	Yellow-green	⁶H_15/2	10.65	10.0–10.6
Ho³⁺	Yellow	⁵I₈	10.60	10.4–10.7
Er³⁺	Lilac	⁴I_15/2	9.58	9.4–9.5
Lu³⁺	Colourless	¹S₀	0	0

Example 23.1: Deriving Ground-State Term Symbol

Problem: What is the ground-state term symbol of Pr³⁺ (f²)?

Answer: Following Hund's rules:

Two electrons in different f orbitals: M_L = (+3) + (+2) = +5 → L = 5 (H term)
Lower-spin arrangement is triplet: S = 1 → ³H
Less than half-full shell: lowest J = |L−S| = 4

Ground state: ³H₄

(b) Luminescence

Key Points: Lanthanoid ions show useful emission spectra with applications in phosphors, lasers, and imaging. The strongest emissions are from Eu³⁺ (red) and Tb³⁺ (green).

Visible Spectrum & Lanthanoid Emission

Tb³⁺

Eu³⁺

■ Tb³⁺: ⁷F₆₋₀ ← ⁵D₄ (green, 480–580 nm) ■ Eu³⁺: ⁷F₀₋₆ ← ⁵D₀ (red, 580–700 nm)

Antenna Effect: Luminescence is greatly enhanced by placing a light-absorbing group on the ligand. Energy transfers from the antenna to excited states of the lanthanoid (Jablonski diagram).

Applications of Lanthanoid Luminescence

💡

Phosphors

Eu³⁺ in YVO₄

Red phosphors in displays

🔬

Nd:YAG Laser

Nd³⁺ in Y₃Al₅O₁₂

1.064 μm emission

🏥

MRI Agents

Gd³⁺ complexes

Magnetic resonance imaging

🧲

Strong Magnets

Nd₂Fe₁₄B, SmCo₅

10× iron strength

(c) Magnetic Properties

The magnetic moment μ is expressed in terms of total angular momentum J:

μ = g_J{J(J+1)}^1/2μ_B

where the Landé g-factor is:

g_J = 1 + [S(S+1) − L(L+1) + J(J+1)] / 2J(J+1)

Theory agrees well with experiment because the unpaired 4f electrons are core-like and couple strongly with orbital angular momentum but interact little with ligands.

23.6–23.8 Compounds of the Lanthanoids

Binary Ionic Compounds

Key Points: The structures of ionic lanthanoid compounds are determined by the size of the lanthanoid ion; binary oxides, halides, hydrides, and nitrides are all known.

Oxides

All lanthanoids react with O₂ at high temperatures to give sesquioxides Ln₂O₃, but some form higher oxides:

CeO₂ – Cerium dioxide (fluorite structure), widely used as catalyst
Pr₆O₁₁, Tb₄O₇ – Mixed Ln(III)/Ln(IV) oxides formed in air
EuO, YbO – Monoxides (rock-salt structure), white insulators

La₂O₃ structure: La³⁺ coordination number = 7
Lu₂O₃ structure: Lu³⁺ coordination number = 6

Halides

Lanthanoids react directly with halogens to form trihalides LnX₃:

LaF₃: La³⁺ in irregular 11-coordinate environment
LaCl₃: La³⁺ in 9-coordinate tricapped trigonal prism
CeF₄: Only Ln(IV) fluoride stable at room temperature
SmI₂: Important reducing agent (blue THF solutions)

Sm(s) + ICH₂CH₂I(l) → SmI₂(s) + C₂H₄(g)

Hydrides

All lanthanoid metals react with H₂ to give binary hydrides (LnH₂ to LnH₃):

Dihydrides adopt fluorite structure
Most are black, metallic conductors: Ln³⁺(H⁻)₂(e⁻)
EuH₂, YbH₂: White insulating solids (4f⁷, 4f¹⁴)
LaNi₅H₆: Studied for hydrogen storage

23.7 Ternary and Complex Oxides

Lanthanoid ions frequently occupy cation positions in perovskites and garnets:

Perovskites (ABO₃)

LaFeO₃, GdFeO₃ structure type

High-T_c superconductors: LnBa₂Cu₃O₇

Garnets (A₃B₂O₁₂)

8-coordinate Ln sites

YAG (Y₃Al₅O₁₂), YIG (Y₃Fe₅O₁₂)

23.8 Coordination Compounds

Key Points: An abundance of lanthanoid(III) complexes are formed with anionic polydentate ligands containing oxygen-atom donors suited for electrostatic bonding. Coordination numbers usually exceed 6 and ligands adopt geometries that minimize interligand repulsions.

Without strong orbital overlap, Ln³⁺–ligand bonds are electrostatic. Stable complexes require:

Polydentate chelating ligands
Hard donors (O, F preferred)
Macrocyclic ligands for nonlabile complexes

CN = 9
Tricapped trigonal prism
[Ln(OH₂)₉]³⁺

CN = 8
Square antiprism
[La(acac)₃(OH₂)₂]

Ion-exchange separation: Smaller Ln³⁺ ions (heavier lanthanoids) are more strongly complexed by eluents and elute first. This enabled the separation of all lanthanoid ions.

23.9 Organometallic Compounds

Key Points: The organometallic chemistry of lanthanoids is dominated by Ln(III) compounds with bonding that is predominantly ionic. The 18-electron rule does not hold. Steric effects are far more important than electronic effects.

Key differences from d-block organometallics:

No π backbonding (5d empty, 4f buried) → No stable CO, alkene complexes
Need good donor ligands (Cp, N-heterocyclic carbenes)
18-electron rule NOT applicable
Very air/moisture sensitive
Large Ln³⁺ accommodates three Cp ligands easily

Important Complex Types

[Ln(Cp)₃]

Tris-cyclopentadienyl

Tend to oligomerize

[Ln(Cp*)₃]

Pentamethyl-Cp

η⁵ ⇌ η¹ equilibrium

[Ce(C₈H₈)₂]

Cerocene

η⁸-cyclooctatetraene

[Sm(Cp*)₂]

Samarocene (Sm²⁺)

Reacts with N₂

Catalytic Applications

Ln(III) organometallics (especially [Ln(Cp*)X]) are highly active catalysts for:

Ziegler–Natta polymerization of alkenes
σ-bond metathesis (C–H activation in methane!)
Not poisoned by CO or sulfides

Lu–CH₃ + ¹³CH₄ → Lu–¹³CH₃ + CH₄ (methane C–H activation)

Actinoid Chemistry

The chemical properties of actinoids show much less uniformity than lanthanoids. The early members (Ac–Am) resemble the early d metals with a rich variety of oxidation states.

⚠️ Radioactivity: Most actinoids are radioactive, with many having short half-lives. Only Th and U have long-lived isotopes sufficient for large-scale chemistry. Transuranium element chemistry is often performed on microgram or even single-atom scales!

23.10 General Trends

Key Points: The early actinoids (Th–Pu) do not exhibit the chemical uniformity of the lanthanoids, but behave more like d-block elements. A prevailing motif is the collinear O═An═O unit. As the 5f block is traversed, the 3+ oxidation state becomes increasingly dominant.

Z	Name	Symbol	Config	Oxidation States	t_1/2 (most stable)
89	Actinium	Ac	[Rn]6d¹7s²	3	21.8 y
90	Thorium	Th	[Rn]6d²7s²	4	1.41×10¹⁰ y
91	Protactinium	Pa	[Rn]5f²6d¹7s²	3, 4, 5	3.28×10⁴ y
92	Uranium	U	[Rn]5f³6d¹7s²	3, 4, 5, 6	4.47×10⁹ y
93	Neptunium	Np	[Rn]5f⁴6d¹7s²	3, 4, 5, 6, 7	2.14×10⁶ y
94	Plutonium	Pu	[Rn]5f⁶7s²	3, 4, 5, 6, 7	8.1×10⁷ y
95	Americium	Am	[Rn]5f⁷7s²	2, 3, 4, 5, 6	7.38×10³ y
96	Curium	Cm	[Rn]5f⁷6d¹7s²	3, 4	1.6×10⁷ y
97	Berkelium	Bk	[Rn]5f⁹7s²	3, 4	1.38×10³ y
98	Californium	Cf	[Rn]5f¹⁰7s²	2, 3, 4	900 y

The Uranyl Unit: AnO₂²⁺

Linear or nearly linear dioxido units dominate the chemistry for oxidation numbers +5 and +6 of U, Np, Pu, and Am:

Molecular Orbital Diagram for AnO₂²⁺

Linear O═An═O (D_∞h symmetry)

σ bonding: O 2p with An 6d_z² (g) and 5f_z³/6p_z hybrid (u)
π bonding: O 2p with An 6d_π and 5f_π orbitals
Very strong An–O bonds: dissociation energy 618 kJ/mol for UO₂²⁺
Extremely slow O atom exchange (t_1/2 ~ 10⁹ s)

Frost Diagrams: Oxidation State Stability

Principal Oxidation States of Selected Actinoids

Th

+4

U

+3 +4 +5 +6

Np

+3 +4 +5 +6 +7

Pu

+3 +4 +5 +6 +7

Am

+2 +3 +4 +5 +6

Cm–Lr

+2 +3

Example 23.3: Assessing Redox Stability

Problem: Use the Frost diagram for Th to describe the relative stability of Th(II) and Th(III).

Answer: Th²⁺ lies above lines connecting Th(0) with higher oxidation states → susceptible to disproportionation. Th(III) has steep negative slope → readily oxidized by water. Th(IV) is the exclusive stable oxidation state in aqueous solution.

Th³⁺(aq) + H⁺(aq) → Th⁴⁺(aq) + ½H₂(g) E° = +3.8 V

23.12–23.13 Thorium, Uranium, Plutonium

Because of their ready availability and low radioactivity, Th and U chemistry can be performed with ordinary laboratory techniques.

Thorium

Key Point: Thorium occurs almost exclusively as Th(IV). Eight-coordination is common: ThO₂ (fluorite), ThCl₄/ThF₄ (8-coordinate). The coordination number can reach 10–11 in some complexes!

Uranium

Uranium has more varied chemistry with access to U(III) through U(VI):

U³⁺ (f³)

Powerfully reducing

Deep orange-red solutions

U⁴⁺ (f²)

Common, stable

UCl₄ starting material

UO₂⁺ (U⁵⁺)

Disproportionates

Unstable

UO₂²⁺ (U⁶⁺)

Very stable uranyl

Yellow, fluorescent

Uranium Hexafluoride

UF₆ is synthesized on large scale for isotope separation (gaseous diffusion/centrifugation):

UO₂ + 4 HF → UF₄ + 2 H₂O

3 UF₄ + 2 ClF₃ → 3 UF₆ + Cl₂

UF₆ sublimes at 57°C and F exists as single isotope → ideal for mass-based separation.

Uranocene: [U(C₈H₈)₂]

Uranium forms remarkable sandwich compounds with cyclooctatetraene dianion (C₈H₈²⁻):

D_8h symmetry with eclipsed rings
20 electrons from two C₈H₈²⁻ fill bonding orbitals
Two 5f electrons in weakly bonding e_3u (fφ) orbital
Triplet ground state (two unpaired electrons)
Only known compounds with possible φ bonding contribution!

Plutonium

⚠️ Environmental Hazard: Plutonium is potentially dangerous near nuclear processing plants. It may leach into groundwater and contaminate soils. Understanding Pu complexation with natural ligands (carbonate, phosphate) is crucial for environmental safety.

Plutonium shows remarkable redox complexity—four oxidation states can coexist in solution:

Pu³⁺, Pu⁴⁺, PuO₂⁺, PuO₂²⁺ separated by less than 1 V
PuO₂⁺ tends to disproportionate → Pu⁴⁺ + PuO₂²⁺
Carbonate stabilizes Pu(VI) as [PuO₂(CO₃)₃]⁴⁻
At least 6 allotropic forms of Pu metal!

Nuclear Applications

⚛️

Nuclear Fission

²³⁵U

Chain reaction power generation

🔋

RTG Power

²³⁸Pu

Space probe power sources

🚨

Smoke Detectors

²⁴¹Am

α-particle ionization

🔬

Neutron Source

²⁵²Cf

Spontaneous fission

Key Comparisons: Lanthanoids vs Actinoids

Property	Lanthanoids (4f)	Actinoids (5f)
f orbitals	Core-like, no radial node	More diffuse, inner maximum
Bonding	Predominantly ionic	Covalent character (early An)
Dominant oxidation state	+3 throughout series	Variable (+3 to +7 for early An)
Ligand-field effects	Negligible	Small but observable
Spectra	Sharp, narrow bands	Broader, more intense bands
Coordination numbers	High (6–12)	High (up to 12)
Characteristic unit	Ln³⁺	AnO₂ⁿ⁺ (n = 1, 2)
Radioactivity	Only Pm unstable	All radioactive

Exercises:
1. Give a balanced equation for the reaction of any lanthanoid with aqueous acid.
2. Explain the variation in ionic radii between La³⁺ and Lu³⁺.
3. Derive the ground-state term symbol for Tb³⁺, Nd³⁺, Ho³⁺, Er³⁺, Lu³⁺.
4. Predict what species form when Pu metal is dissolved in dilute HCl.