CTM4XAS: Discussion of tutorial exercises
Exercise 3: manipulating the atomic multiplet spectrum of Ti3+
a) What is the configuration and ground state symmetry of Ti3+?
Ti3+ has a 3d1 configuration. The ground state can be determined with Hunds rules. The maximum spin for
one electron is S=1/2; the maximum orbital moment is L=2. The third Hunds rule tells that the ground state
has a minimum value of J, i.e. J=L-S=3/2. The term symbol is 2D3/2.
b) Calculate the atomic multiplet spectrum of Ti3+ (ti3b).
The atomic multiplet spectrum of Ti3+ has many peaks due to the transition from 3d1 [2D3/2] to 2p53d2.
All final states with J=1/2, J=3/2 and J=5/2 are allowed.
CTM4XAS: Discussion of tutorial exercises
c) Set Fpd and Gpd to zero and repeat the calculation (ti3c).
Because the 2p3d coupling is switched off, the L3 edge and the L2 edge do not mix. This yields a ratio of
2:1 for the L3 and L2 edge (cf. exercise 2e). The other splittings in the spectrum are due to the 3d3d
interactions in the 2p53d2 final state.
d) Set Fpd, Gpd and the 2p spin-orbit coupling to zero (ti3d).
This yields a similar spectrum as figure 3c, but now with the L3 and the L2 edge merged into one L edge. Note
that the small peak at 462 eV is still present. This peak, and all other fine structure, is due to the 3d3d
multiplet effects.
CTM4XAS: Discussion of tutorial exercises
e) Set Fdd to zero and repeat the calculation (ti3e).
f) Set the 2p spin-orbit parameters to zero(ti3e).
CTM4XAS: Discussion of tutorial exercises
g) Set the 3d spin-orbit coupling to zero(ti3g).
The 3d spin-orbit splitting is small and the final state effect will not visibly modify the spectral shape. The
ground state 3d spin-orbit splitting however will split the 2D state into its J=3/2 and J=5/2 components.
Setting the 3d spin-orbit coupling to zero sets both J states equal in energy and hence significantly
modifies the spectral shape. Note that this effect of the 3d spin-orbit splitting is potentially important in all
open shell systems.