Chemistry is principally of Ln³⁺

Why the prevalence of oxidation state III (Ln³⁺)?

Examine Thermodynamic Parameters:

I_1/2/3/4 D_atmH D_hydH(Ln³⁺) D_LH(LnX₃)

these values are available in a Table(import DHatm from larger table for web!)

Ionization

For any given Lanthanide

• As successive electrons are removed from neutral Ln the stabilizing effect on the orbitals is related to their principal quantum number, 4f > 5d > 6s.
• For Ln²⁺ {except for La & Gd} the configuration is [Xe]4fⁿ
• For Ln³⁺ the configuration is always [Xe]4fⁿ

  the 4f binding energy is so great that remaining 4f electrons are regarded as "core-like" (i.e. incapable of modification by chemical means) (except Ce)

• Note that as a rule of thumb: I₄ ~ 2 I₃ ~ 4 I₂ ~ 8 I₁

  Þ I₄ > (I₁ + I₂ + I₃ )

  Therefore in almost all cases Ln³⁺ provides the best energetics

Observing trends across the Lanthanide Series

• The general trend is for increasing ionization energies with increasing Z (i.e. with increase in Z_eff)
• Marked Half-Shell Effects - magnitude ‚ as n in I_n ‚
• Also Quarter/Three-Quarter Shell Effects

  (compare with transition metals - these are not seen clearly with dⁿ configurations)

  Explanation?: interelectronic repulsion is related not just to electron pairing but also to angular momentum of the electrons

  • e.g. in Pr²⁺ (4f³) Æ Pr³⁺ (4f²) ionization removes repulsion between e^- of like rotation, whereas Pm²⁺ (4f⁴) Æ Pm³⁺ (4f³) removes the stronger repulsion between e^- of unlike rotation (Þ latter Ionization Energy is correspondingly lower - hence the local minimum in the I₃ graph at Pm)

  The three-quarter effect is the bigger: interelectronic repulsion is bigger in smaller Lnⁿ⁺

Atomization

D_atmH follows the inverse trend to I₃ {and therefore also to (I₁ + I₂ + I₃ ) }

Þ metallic bonding is correlated with ease of ionization to Ln³⁺ state

this trend is modified slightly due to the different structures of the Ln metals

Some Thermodynamic Observations (Ionic Model style)

The trends in the formation of Ln^III

Formation of Compounds {D_fH(LnX₃(s))} or Ln³⁺(aq) {E°(Ln³⁺(aq)/Ln(s))}

depend on the balance between:

Energy Supplied to effect Ln(s) Æ Ln(g) Æ Ln³⁺(g) + 3e^- [D_atmH + I₁ + I₂ + I₃]

versus

Energy gained from Ln³⁺(g) + 3X^-(g) Æ LnX₃(s) [D_LH(LnX₃(s))] or Ln³⁺(g) Æ Ln³⁺(aq) [D_hydH(Ln³⁺)]

The energies determining trends in E°(Ln³⁺(aq)/Ln(s)) are graphed below:

Production of Ln³⁺(g) shows

• a smooth trend based on size effects (trend based on Z_eff)
• shell structure effects superimposed with clear maxima at half-shell (f⁷) and full-shell (f¹⁴)

  also smaller quarter and three-quarter shell effects

Hydration Energy of Ln³⁺ (also Lattice Energies of LnX₃(s)) shows

• only a smooth ionic-size-based trend (the trend based on Z_eff) and no shell structure effects

Balance of trends in Ionization + Atomization Energies with Hydration (Lattice) Energy

• removes size effects
• leaves only the Shell effects - see values of D_fH(Ln³⁺(aq))

Overall: The most important energy correlations are with I₃

"exceptions to +3 rule" can also be rationalized

Occurrence of +4 oxidation state

predicted from [D_atmH + I₁ + I₂ + I₃ + I₄] which follows trends in I₄

• Ce, Pr Æ Ce⁴⁺ [4f⁰], Pr⁴⁺ [4f¹] ~ early in series 4f orbitals still comparatively high in energy
• Tb Æ Tb⁴⁺ [4f⁷ valence shell] ~ half shell effect

Occurrence of +2 oxidation state

predicted from [D_atmH + I₁ + I₂] which follows trends in D_atmH, which is reverse of trend in I₃

• Eu, Sm, Yb Æ Eu²⁺ [4f⁷], Sm²⁺ [4f⁶], Yb²⁺ [4f¹⁴]

  ~ clear influences of electronic shell structure & from D_atmH

Bibliography