Mixed valence compounds - XAS spectra
asked by Manuel Knauft (2024/08/16 15:21)
Dear all,
I am a PhD student trying to simulate XAS spectra of a mixed valence compound. The nominal electron count according to the stochiometry is 7.5, while DFT calculations show that the number of electrons on (one of) the ions is closer to 8.3. However, the StartRestrictions field in the Eigensystem function allows only for an integer number of electrons. I could not find any literature specifying how to tackle this problem.
Thus I am unsure about what the correct method for obtaining the spectra is:
i) Performing two calculations with 7 and 8 electrons as an initial filling and summing the spectra in such a way that the groundstate occupation agrees with the DFT results. In this case, do I take the Delta to be the same in both calculations?
ii) Performing a calculation with 8 electrons (or 7?) initial filling and tune the charge transfer energy such that the occupation is close to the DFT result
iii) Something else entirely
Any hint in the right direction is much appreciated!
Thanks and best regards
Manuel Knauft
Answers
Dear Manuel,
In order to make the answer more specific, let's assume you have a transition metal oxide Ni4O5 such that each Ni is 2.5+. Furthermore assume that the crystal structure of our non-existent crystal Ni4O5 is such that all Ni atoms are equivalent.
The total number of electrons in a Quanty calculation always needs to be an integer number. You can't split electrons. The electron occupation of a shell will, for the Eigen-states however not be integer. Even in NiO this is not an integer number. For a ligand field calculation for NiO you can start the calculation with 8 electrons on the Ni d-shell and 10 electrons on the Ligand shell (O-2p derived). This is the configuration d^8 L^10 (there are 45 states in this configuration). Then there is the excited state configuration d^9 L^9 (with 100 states). States in these two configurations interact with each other (configuration interaction) and eigenstates are superpositions of states in these configurations. Such that for NiO the final d shell occupation of the ground-state is around 8.2. (80% d8 and 20% d9).
For the hypothetical compound Ni4O5 we have a problem. The oxidation state of Ni is 2.5+. There are a few approximations you can make.
1) You can do a ligand field calculation starting from d^7L^10 and one starting from d^8L^10 and (incoherently) add the spectra of these two calculations. This is computationally the cheapest approximation, but not the most accurate. Note that for the calculation you start with d^8 you will get a final d-shell occupation of 8.2. For the calculation that started from d^7 you will probably get a final d-shell occupation of 7.8 or so. Note that neither sites should have the DFT occupation. You can tune delta to get the average occupation to be the same as the DFT results, but I'm not sure this is needed / correct.
You should define Delta for the d8 configuration and use the onsite energies you obtain (ed and eL) to be the same for the two calculations. Delta_eff_d7 is then U smaller than Delta_eff_d8. (This again is an approximation).
2) Do a two site cluster including 2 Ni atoms and 2 Ligand shells. You can find an example here |https://journals.aps.org/prb/abstract/10.1103/PhysRevB.94.195127 Note that one has to be a bit careful as one should not just do a two site Ni dimer calculation. The compromise for the hopping between the Ni atoms and the ligand atoms used in the linked paper however works reasonably well.
Hope this helped a bit, Maurits