Difference in XAS spectra calculated using Quanty and Crispy

asked by Saki IMADA (2025/03/15 12:30)

Dear Developers,

I've calculated Ti4+ in Oh using the parameters for SrTiO3 in your paper (PRB 85,165113 (2012)). When I use Crispy, I can get a spectrum similar to that in the paper. However, I get a slightly different spectrum when I use an input file based on the one downloaded from the Tutorials page for the “NiO ligand field.” I can find the famous 7 peaks in both XAS spectra, but the energy difference between “eg” and “t2g” peaks differs. When I use an input file created by Crispy (.lua file) to run Quanty directly, I can get the same spectra as one using Crispy. So, my question is: Is there any difference in settings between Hamiltonians or other parts, such as an approximation, to shorten the calculation time?

Many thanks, Saki

Answers

, 2025/03/16 13:38

Dear Saki,

“Is there any difference in settings between Hamiltonians or other parts”,

most probably yes, but without having the input files it is hard to judge. Ligand field theory calculations are based on parameters. For SrTiO3 you have the following set of parameters:

  1. 10Dq, the onsite splitting between the t2g and eg orbitals of the Ti, without Hybridisation
  2. 10DqL, the onsite splitting between the t2g and eg orbitals on the ligand
  3. pdsigma or Veg, the hopping between the ligand (O-2p) orbitals and the Ti-d orbitals of eg type making sigma bonds
  4. pdpi or Vt2g, the hopping between the ligand (O-2p) orbitals and the Ti-d orbitals of t2g type making pi bonds
  5. Delta, the energy difference between the $d^0$ and $d^1$ configuration
  6. U, the spherical part of the Coulomb interaction
  7. F2, F4, the non-spherical part of the Coulomb interaction

and for the XAS final state with a core hole:

  1. Q the spherical part of the Coulomb interaction between the Ti 2p and Ti 3d
  2. Fpd2, Gpd1, Gpd4, the non-spherical part of the Coulomb interaction between the 2p and 3d orbitals
  3. zeta_2p The core hole spin-orbit coupling.

You are free to choose these parameters arbitrary. They are, based on the material experimentally known and can also be calculated within some accuracy.

The parameters 10Dq, pdsigma, dppi, can be obtained from DFT with reasonable accuracy (not perfect though error about 20% +- 100meV). The parameters F2, F4, Fpd2, Gpd1, Gpd3 and zeta_2p can be obtained from atomic Hartree-fock or also for the solids. (differences are not so big between codes, errors about 20%)

The parameters U, Delta and Q are harder to calculate. These depend on “screened” Coulomb interactions. One can either look at experimental Trents, or do constraint RPA calculations. Neither is perfect and errors can be of the order of several eV.

Last but not least, there is one parameter related to convergence. This is the number of configurations included in the calculation and set in the restrictions. For Ti 4+ you will need to include the configurations upto d^4 (5 configurations) to get full convergence. You can however reproduce the results with only 4 or 3 configurations and slightly different parameters.

The theory is relatively old (goes back to one of the first attempts to understand solids in the 1930s). In our review paper https://doi.org/10.1103/PhysRevB.85.165113 we used the Slater integrals (F2, F4, etc) obtained from the Wannier functions, i.e. from NMTO. In Crispy you standardly use the Hartree-Fock values. The difference is about 10%.

Hope this helped a bit, best wishes, Maurits

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