Lanthanoids and Actinoids

• f orbitals:

  • Consist of the cubic set and the general set
  • l = 3
  • ml = 3, 2, 1, 0, -1, -2, -3
  • All orbitals are ungerade
  • Have three nodal planes
• The general set of f orbitals is used for non-cubic symmetry. Three of these orbitals are common with the cubic set.

  
• The cubic set of orbitals is used in a cubic environment e.g., octahedral or tetrahedral.

  
• Although being 'valence' electrons, the 4f electrons are essentially buried and screened from the chemical environment. The orbitals have high angular nodality - diffuse orbitals with a large number of angular nodes.

  
• Most of bonding is ionic in character. The lanthanoids have a large metallic/cationic radius.

  • Coordination are typically large, being 7, 8 and 9
  • 6 is possible but requires bulky ligands
  • 10 is possible but requires chelating ligands with a small bite angle
• The lanthanoid contraction:

  • 4f orbitals are not the outermost orbitals
  • 3+ configuration has 5s and 5p electrons as size determining
  • Overlap between the probability function of 4f with 5s and 5p = poor at shielding
  • This gives a contraction of size

  
• The average radial velocity of an electron is proportional to atomic number, i.e. for heavier atoms there are relativistic effects on the mass of the electron. These effects account for ~ 10% of the lanthanoid contraction.

  
• As a consequence of the large value of the 4th ionisation energy, 3+ predominates.

  • Ce, Pr and Tb are found in 4+ OS due to electron configurations
  • 4f orbitals are at higher energy at the start of the series, therefore less energy required to remove 4th electron
  • Nd, Sm, Eu, Tm, Dy and Yb are found in 2+ OS with relatively increased 3rd ionisation energies

  
• UV-Vis spectroscopy probes the transitions of valence electrons, including f-f transitions (forbidden).

  • d orbitals are influences by ligand field splitting
  • f orbitals have no ligand field effects
  • f orbitals are buried and sufficiently large to take into account the interaction between S and L (spin-orbit coupling)
• The electronic spectra of Ln have many transitions, a large number of excited state terms.

  • Weak transitions, reduced vibronic coupling due to poor interaction with ligands
  • Sharp transitions, d-d transitions are broad as a consequence of different vibrational energy levels
• Ln3+ does not interact with the ligand environment - colours are often indicative of the lanthanide.

  • 4f - 5d transitions are allowed
  • Intense transitions at high energy
  • For Eu2+ energy of 4f is raised and transitions are in the visible region

  
• For a general configuration of fn:

  • Microstates = 14!/n!(14-n)!
• For each distinct combination of n electrons, there are n! permutations. For 2 different electrons:

  • Remove equivalent arrangements e.g., ab = ba
  • 14!/2!(14-2)! = 2*(2l + 1)!/n!(2*(2l + 1)-n)! = 91
• When including J into the calculated number of microstates it creates a significant number of energy levels. The increased number of excited state terms means we can expect to see more f-f transitions.

  
• Electronic excitation: an electron is promoted to an excited state (absorption spectroscopy).
• Non-radiative decay: energy is lost as the excited state cascades to lower vibrational and rotation energy levels, a fast process.
• Radiative decay: f electrons are not involved in bonding (vibration/rotation) and therefore f-f transitions are more likely to result in radiative decay (emission spectroscopy).
• Direct excitation of the Ln series gives a small separation between the energy of the incoming photon and emitted photon - this is a Stokes shift.

  
• The antenna effect is seen when Ln is excited indirectly using a ligand antenna, seen with aromatic ligands.

  
• Fluorescence:

  • Short-lived
  • On the ps to ns timescale
  • Decay from an excited state of the same multiplicity to the ground state

  
• Phosphorescence:

  • Long-lived
  • On the ns to μs scale
  • Decay from an excited state of a different multiplicity compared to the ground state

  
• During the antenna effect, the ligand captures light and is promoted to an excited singlet - radiative decay occurs. There is then intersystems crossing (ISC) to an excited triplet, then excited states of Ln, then luminescence.

  
• Intersystem crossing: at a certain point the potential energy of singlet and triplet states intersect and transfer between the two states is possible.
• Internal transfer: similar to intersystems crossing, but there is no change in spin multiplicity.
• Lifetimes of excited states:

  • Triplet state has a longer lifetime
  • Return to the ground state requires a spin-forbidden electronic transition
  • Energy between a triplet and singlet state cannot be lost through non-radiative decay
• During quenching, energy is lost to the vibrational modes of solvated groups e.g., water. This encapsulates Ln with a multidentate ligand to avoid water coordination.

  
• The magnitude of the magnetic dipole moment, μz, generated by an electron, with spin angular momentum, S is given by:

  • μeff = -gμBS
  • g = proportionality factor, a dimensionless constant dependent on environment (2.0023 for a free electron)
  • μB = the Bohr magneton, a constant for expressing the magnetic moment of an electron (9.274 X 10-24 J T-1)

  For a multi-electron system:

  • μeff = -g[S(S + 1)]1/2μB
  • S = total spin quantum number

  
• Where orbitals are degenerate and can be transformed into each other via rotation, electrons are able to move between orbitals.

  • This creates an associated magnetic moment
  • This can only occur for d block compounds when there is an open shell t2g configuration
  • Where this is not the case the magnetism from orbital angular momentum is said to be quenched

  
• All orbitals are degenerate in a free ion d block element. For a d1 system with an electron in the dxy orbital, the d(x^2-y^2) is equivalent in energy. The transformation is a single rotation and creates a magnetic moment, providing the orbital angular moment component of paramagnetism. The same principle can be applied to f orbitals.

  
• The magnetic moment will be linked with total electron spin (S), electron orbit angular momentum (L) and the total angular momentum (J), which arises due to spin-orbit coupling.

  • gS = proportionality factor of an electron  ~ 2
  • gL= electron orbital proportionality factor = 1
  • gJ = Lande proportionality factor, which is linked to J

  
•  

  There are different values of J and these create multiple f-f transitions.

  • The value of J is linked to the observed magnetic moment
  • In most cases, the energy difference between the ground state and excited state is thermally inaccessible
  • i.e. only the ground state J value is observed in magnetism
  • Where this is not the case we have exception from the J moment determined values

  
• For Sm3+ and Eu3+ the energy difference between the ground and lowest energy excited state terms are thermally accessible. This causes a Boltzmann population distribution. This gives a mixture of J states which all contribute to the magnetic moment and causes deviations based on their relative population.

  
• Pitchblende: ore of uranium with an abundance of 2.3 ppm (higher than tin).
• Thorite: treatment with potassium gives thorium with an abundance of 8.1 ppm (more than boron).
• Thorium and uranium are the only naturally occurring actinoids - the rest are formed using particle colliders and during nuclear explosions.
• Naturally occurring actinoids:

  • Protactinium has two naturally occurring isotopes which arise due to radioactive decay of uranium
  • Alpha decay is the loss of a helium nucleus
  • Beta decay is a neutron into a proton, electron and antineutrino

  
• Every known isotope of An's are radioactive.

  • Only 232Th, 235U and 238U have long enough half-lives to have survived since the formation of the solar system
  • Stability depends on atomic mass and numbers of protons/neutrons
  • Even number of proton and neutrons > odd numbers of protons, even of neutrons . Odd numbers of protons and neutrons

  
• For s and p orbitals, direct scalar relativistic effects cause them to contract. This manifests by adding shielding for valence electrons. For d and f orbitals, they are expanded by a process known as indirect relativistic orbital expansion.

  • Contracted s and p orbitals provide better shielding and the orbitals are expanded
  • Binding energy of 5f electron is ~50% of expected
  • Destabilisation of f orbitals allows electrons to be removed more easily
• Oxidation states of actinoids:

  • The lower the potential, the lower the Gibbs energy, the more stable the state is
  • The gradient between points is the potential of the redox couple
  • Early actinoids behave like transition metals (5f up to Np are involved in bonding)
  • Late actinoids are typically 3+ with 5f contracting along the series

  
• Actinoids require a new model of spin-orbit coupling: j-j coupling.

  • Looks at the individual coupling for l and s for each electron to give j
  • Previous model works well for lanthanoids
  • For actinoids the spin-orbit coupling is not large enough to completely ignore interelectronic repulsions