Spin orbit coupling operator
asked by Miguel Carvalho (2024/08/15 13:45)
Dear All
I am analyzing some XAS data using Quanty by doing a ligand calculation of a CoO6 cluster.
In my output file I get a <l.s> value of -1.014 (<psi|l.s opperator|psi>), if I do branching ratio analysis in the corresponding spectra generated I get <l.s>~-1.17. at first I thought this is because I am doing a calculation at a temperature above 0 K, lowering the temperature in the simulated spectra leads to slightly larger <l.s> from branching ratio but still very similar to -1.17. The number of holes I am using is the one obtained from the ligand calculation for both BR determination.
Is this difference because the BR analysis is flawed and 20% difference is expected?
Answers
Dear Miguel,
The spin-orbit coupling sum rule assumes that the $L_3$ edge corresponds to states with a core hole in the $j=3/2$ states and the $L_2$ edge to states with a core hole in the $j=1/2$ states. This is an approximation and not completely valid. For this reason the sum-rules give slightly different numbers than the ground-state expectation value.
You can check if this is indeed the reason.
Check 1) You can turn of the 2p-3d electron interaction in the calculation. At this point there is no mixing between the states and the sum-rule should become exact.
Check 2) You can plot the partial exceptions into the j=1/2 and j=3/2 states. This shows you how much the edges mix due to the Coulomb interaction. An example you can find in one of the tutorials we discuss at our workshop. You can find these here |https://www.quanty.org/_media/workshop/heidelberg/october_2022/tutorial_tuesday_and_wednesday.zip
Best wishes, Maurits
Dear Maurits
Thank you. I will take a look.
Best regards Miguel