How to calculate core binding energy shifts between material

[ehermes]

Hello,

I wish to calculate the shift of the core 3d binding energies of Pd in different materials. For example, XPS experiments indicate an approximately 3.5 eV stronger 3d binding energy in PdO2 than in metallic Pd, and I wish to reproduce this value. I understand that the Slater-Janak transition state approach (which can be selected with ICORELEVEL=2 and CLZ=0.5) gives values that are most directly comparable to experiment (Lizzit et al, PRB 63 205419). However, I am unsure how to compare the core level energies for different materials, due to the different zeros of energy. Should I use a slab model and correct by the work function? Or is there some way of putting these two calculations on the same energy reference for bulk system calculations?

Thank you,
Eric Hermes

[ehermes]

Hello,

I've found that if I do a slab calculation in the initial state approximation (ICORELEVEL=1), and calculate the core level energies as Efermi - Ecore - Evac where Ecore is the reported energy of the core state, Efermi is the Fermi level energy, and Evac is the value of the local potential in the middle of the vacuum gap (calculated with vtotav), I get core level shifts that are in decent agreement with experiment. Specifically, I get a shift for the 3d state of Pd of 1.8 eV for PdO and 3.8 for PdO2 relative to metallic Pd (as compared to the approximately 1.8 eV for PdO and 3.5 eV for PdO2). This method of calculating the core level energy on an absolute scale makes sense if the reported core energy Ecore is taken as relative to the Fermi level. If it is taken as relative to the zero of energy, then to my understanding the correct way of calculating the shift would be Evac - Ecore. However, this does not give quantitative shifts; I obtain a shift of 0.8 eV for PdO and 2.1 eV for PdO2.

I suspect that the latter approach is the correct one. I have inspected the source code, and while I do not understand what is happening in cl_shift.F, it does not appear that the core state eigenenergies are taken as relative to the Fermi level. In addition, if I compare the core level energy of the Pd 3d state for a Pd(111) slab vs a Pd(100) slab, I find that the first approach (Efermi - Ecore - Evac) gives a shift of 0.7 eV, whereas the second approach (Evac - Ecore) gives a shift of about 0.02 eV. This worries me, as the second approach gives very poor quantitative agreement with experiment -- thought I admit that it is entirely possible that the first approach only gets the right answer out of sheer coincidence.

Please let me know whether what I am doing is correct. In the mean time, I will attempt to do calculations in the final state approximation and using the Slater-Janak transition state approach, but these calculations will be much more computationally intensive due to the need to use larger slab supercells and the need to run a separate calculation for each Pd atom that I wish to measure the binding energy of (as some Pd-Te intermetallic phases have many chemically distinct Pd atoms).

Thanks,
Eric Hermes