Further Spectroscopy

• l: orbital angular momentum quantum number

  • The magnitude of total orbital angular momentum
  • Describes the interaction of electron orbits
• ml: magnetic quantum number

  • Expresses the orientation of the orbital angular momentum relative to an axis
  • There are 2l + 1 values
• s: spin angular momentum quantum number

  • The magnitude of spin angular momentum (1/2)
• ms: magnetic spin quantum number

  • Describes the orientation of the spin angular momentum
  • 2s + 1
• L: total orbital angular momentum quantum number

  • Describes interaction of electron orbits
  • The magnitude of total angular momentum
• ML: total orbital magnetic quantum number

  • Expresses the orientation of the orbital angular momentum relative to an axis
  • 2L + 1 values
• S: total spin angular momentum quantum number

  • Describes interaction of electron spin
  • The magnitude of total spin angular momentum
• MS: total spin magnetic quantum number

  • Describes the orientation of the total spin angular momentum
  • 2S + 1 values
• Term symbols: used to express the collective electronic properties of a system. This ignores closed shells as they have net zero electron spin and orbital angular momentum.
• J: total angular momentum

  • Represents the coupling that occurs between electron spin and electron orbit
  • Significant for heavier atoms with 5d, 4f and 5f orbitals
• The lowest energy term symbol:

  • The ground state term symbol
  • The term with the greatest spin multiplicity lies lowest in energy for a given conformation
  • For a term with given multiplicity, the greater the value of L, the lower the energy
• Values of J are always positive or 0:

  • < 7 f electrons, L-S is the lowest energy value of J
  • > 7 f electrons, L+S is the lowest energy value of J
  • = 7 f electrons, L = 0, S = J
• Microstate: each specific arrangement of energy for each molecule in a system. There needs to be a representation of all possible electronic arrangements.
• Microstate tables can be used to determine spectroscopic terms. Each microstate is one value of ML and the number of microstates will correlate to the value of 2L + 1.
• Crystal field theory orbital splits:

  A - non-degenerate

  T - triply-degenerate

  E - doubly-degenerate
• T1g - electron density in two cartesian axes

  T2g - electron density in three cartesian axes
• Non-crossing rule: the same terms of symmetry should not cross in an Orgel diagram.
• High spin d1 configuration:

  • T -> E transition
  • Triply degenerate in the ground state
• High spin d9 configuration:

  • E -> T transition
  • Doubly degenerate in the ground state
• d5 configuration:

  • 6S ground term
  • Only 1 molecular term, 6A1g
• d2, d8, d3 and d7 all have free ion F term symbols.
• Tanabe-Suagno diagrams

  x-axis: E/B

  y-axis: delta Oh/B
• Tanabe-Sugano diagram: correlation diagram that includes low spin and high spin states. Scaled by the Racah parameter, B, providing quantitative descriptions of electron-electron repulsion.

  
• Orgel diagrams: show the relative energies of orbitals and terms as a function of delta Oh.

  
• UV-vis transition lines in Tanabe-Sugano diagrams:

  1. Sharp - line is parallel but weak (spin forbidden)
  2. Broad - line is not parallel
  3. Broadest - line is even less parallel

  
• Calculating delta Oh in Tanabe-Sugano:

  • Each peak represents a transition from the ground state to the excited state
  • Each transition is E/B

  
• UV-Vis:

  • Molecular vibrations last longer than electronic transitions
  • Transitions to different vibrational states results in a broad peak
  • During molecular vibration symmetry is lost and mixing between orbitals can occur
• Characteristic UV-Vis triplet peaks can be used to determine oxidation states of metals within frameworks/arrays of linked tetrahedra.
• X-Ray Absorption:

  • X-rays are used to excite core electrons
  • Energy of incoming photon > core electron binding energy = ejection of electron
  • Core-hole is quickly refilled
  • Transitions to higher unfilled orbitals occur before ejection
• The energy difference between the core-hole and the electron is released in the form of a fluorescent X-ray photon. This is characteristic for elements and can be applied to elemental composition analysis.

  
• XAS and XANES Regions:

  1. Pre-edge region: shows vibration of absorption through matter as photon energy is increased - the energy of an incoming photon is not enough to excite a core electron
  2. X-ray Absorption Near Edge Structure (XANES): the region just before and after (up to 50 eV past the edge), the energy of the photon is enough to excite a core electron
  3. Extended X-ray absorption fine structure (EXAFS): the oscillatory structure after (can be > 1000 eV pas the edge) the electron has been ejected

  
• XANES:

  • Oxidation state: kinetic energy required to excite core electron depends on pull of the nucleus
  • Coordination geometry: s -> d transitions are Laporte forbidden for Oh systems, however for Td there is p-d hybridisation and more intense transitions
• K and L1 edges excite s electrons, L3 and L3 edges excite p electrons.

  
• EXAFS:

  • The outgoing electron can be seen as a spherical wave that is scattered back by neighbouring atoms
  • The interference between the outgoing and back-scattered wave give rise to EXAFS oscillations

  
• EXAFS depends on:

  • The type of neighbour
  • The distance of neighbours
  • The number of neighbours
  • The thermal disorder of the neighbours
• Early XAS experiments used photographic plates (decay process after excitation released a fluorescent photon).

  • L3 edges with intense allowed p -> d transition caused burning of the plates and left intense white lines
  • L3 edges of d block metals can use the white line height to measure the extent of available d orbitals (also measure of OS)
  • Pt NPs have an intense white line as the surface is oxidised to Pt2+
  • White line can also indicate particle size i.e. changes in surface to volume ratio

  
• CeO2:

  • Applications in catalysis due to oxygen storage capacity
  • Facile changing between Ce (III) and Ce (IV) allows it to provide or store oxygen depending on reaction conditions
  • Both Au/CeO2 and Pt/CeO2 are active WGS catalysts

  
• Scattering paths can be single or multiple scattering effects.

  • Large number of paths available within a repeating unit
  • EXAFS can be modelled by considering the limited number of paths that have the most contribution
  • Effect on the spectrum is more pronounced for short scattering paths and those with neighbours of high MW

  
• EXAFS function:

  • Can be represented as a summation of the sine waves produced from the outgoing photoelectron wavefunction, together with the backscattered wavefunction from each coordination shell of atom type j
  • Many parameters that contribute to the amplitude and phase components of data (simplified to limited set of variables)

  
• Amplitude: the mean squared disorder parameter (sigma squared), the coordination number (N), and the interatomic distance between absorber and scatterer (R)