[ase-users] Calculating core-level shifts in one System and between different systems with VASP

[fabian]

Dear all,

I have a question how to calculate changes in the core level energies in 
the final state approximation (ICORELEVEL = 2) in VASP.
This question is not related to ASE, but i hope it is still allowed to 
post it to this mailing list!

If i am not mistaken in the initial state approach  (ICORELEVEL = 1)  i 
can just take the values which are printed in the list of core state 
eigenenergies
in the OUTCAR file

* "the core state eigenenergies are**
**   1-  1s **....."*

So i get all values with one calculations.
When i perform calculations in the final state approach (ICORELEVEL = 
2),  i have to compare the total energies
of a ground state to a core excited state calculation for evaluating 
core level shifts in DFT.
This is also the explanation in the original Köhler and Kresse paper ( 
Phys. Rev. B 70, 165405) where this process is laid out for VASP:
Here they explain that:

E_B = E(N-1) - E(N)

where E(N-1) is the total energy of the core-ionised system and E(N) is 
the total energy of the neutral system.
E(N) is thus the total energy of my normal DFT calculation?

The VASP "manual" states  that " /absolute energies are not meaning 
full/"and " /Only relative shifts of the core electron binding energy 
are relevant/".
Thus i likely do not get  the total (absolut) energy of the core-ionised 
system E(N-1), by using a core-ionzed PAW potential.
The calculated binding energy must be calculated with respect to some 
reference value depending on our potentials like this?

E_B = E(N-1) - E(N) + E(V_ref)

so only when i compare the E_B of two atoms M and Q of the same element 
this values cancels out?

delta E_B = E_B_M  -  E_B_Q = E_M(N-1)  -   E_M(N) + E(V_ref) - 
[E_Q(N-1) - E_Q(N) + E(V_ref)]
delta E_B = [E_M(N-1) - E_M(N)] - [E_Q(N-1) - E_Q(N)]

Thus i can only use this method to calculate core level shifts, but not 
absolute core level binding energies?
Is this picture correct?

If want to compare the relative shift between atoms in different 
calculations i simply use the total energy's of this system calculate 
the differences between
the "differences " of the two systems and the values should still be 
correct ?
I tried this method already for some simple systems and the relative 
shift is already fitting pretty well to the corresponding experimental data.

This procedure would however only make sense, if the reference  of the 
energies for the two calculations ( E(N-1) -and E(N) ) are the same.
Is this the correct ?
Is it possible to get the relaxation energy in the core-excited state 
calculation, which should be responsible for describing chemical shifts 
in different environments as well

Now i am in the process of calculating core level shifts for a different 
project. And if i use the final state method as above i get relatively 
large errors compared to the
Experimental data. Thus, i also performed the calculations utilising the 
Slater-Janak transition state approximation.
In VASP this is done by setting ICORELEVEL=2 and CLZ=0.5. I could also 
set the electron count clz to a different value between 0 and 1.

The way i understand the Slater-Janak transition state approximation is 
that you exchange the calculations of total energy of the core-ionised 
system and  total energy of the neutral
system with an "evaluation at midpoint". But my values only make any 
sense if i do the same as i did with the complete final state method ( 
clz=1), meaning i still compare the difference
of two total energies.

Is it still justified to compare the total energies of a ground state to 
a  core excited state calculation when i use the Slater-Janak transition 
state approximation? Do i still calculate the
difference between the neutral system E(N) and the "ionized" system 
E(N-0.5) ? What is the physical reasoning behind this?
I was recently told that the Slater transition state is only useful for 
calculating core-level spectra, like EELS or XAS, but cannot be used for 
calculating binding energies, but i found literature where it
was also use for the calculation of XPS core level shifts, however only 
very few?


I would really appreciate if someone could shed some light on this topic 
for me!


All the best


fabian




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