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

[Melissa A. Hines]

Dear Fabian,

Mark Hybertsen (Brookhaven) gave a tutorial on the analysis of core level spectra at a VASP workshop in 2014. His slides are posted at https://wiki.bnl.gov/CFN-Computation/index.php/Workshop2014 (see Wednesday). I found them quite useful in understanding many of these questions.

He also discusses the reference energy question, which is dependent on the type of XPS (gas phase vs solid/surface). This is essentially a question of whether the reference is the vacuum energy (gas phase) or the Fermi energy (conducting solid/surface).

His tutorial (same web page) goes through the calculation of a number of P-containing molecules and compares the accuracy of the  three approximations. (There is a small bug in one of his calculations. As I recall there was a typo in some of his ENCUTs.) I have a more extensive comparison that I will send you by e-mail.

Melissa

On Jan 18, 2018, at 12:02 PM, fabian via ase-users <ase-users at listserv.fysik.dtu.dk<mailto:ase-users at listserv.fysik.dtu.dk>> wrote:


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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