[Wien] Which fermi energy for XPS?

[David Olmsted]

I am modeling XPS binding energy using a half core-hole, offset by
background charge.  As I understand the method that has been explained here
recently, one computes the binding energy as the energy of the state from
case.scfc minus the Fermi energy from ':FER' in case.scf.  Should the Fermi
energy be for the configuration with the half core-hole, or a configuration
without the core-hole?  As explained below, from my results it looks as if
it should be the same configuration, but without the core hole.

Some details:
Version 14.2
I am computing the differences in the XPS binding energy for Al-2p for
cyrstals in the Al-P-O-H system to see how the binding energy changes
between hydrated and non-hydrated configurations.  This is for comparison
with experimental results.  (The actual material is amorphous, but I am
hoping the effects of on the spectra will be at least qualitatively
similar.)

The simplest structure is AlPO4, berlinite.  I have run two configurations,
the primitive cell with 18 atoms, including 3 Al atoms, and a 2x2x1
supercell.  In each case I have made one Al unique, then added one-half
core-hole in case.inc and offset it with -0.5 background charge in case.inm.
For simplicity I will show the results just for the triplet state.  Lines
are from case.scf and case.scfc.

-------- 2x2x1 supercell, no core-hole
:LABEL4: using the command: run_lapw -ec 0.00001 -p
<skip>
:FER  : F E R M I - ENERGY(TETRAH.M.)=   0.0547409802
:NEC01: NUCLEAR AND ELECTRONIC CHARGE    720.00000   720.00112
:NEC02: NUCLEAR AND ELECTRONIC CHARGE    720.00000   720.00000
:NEC03: NUCLEAR AND ELECTRONIC CHARGE    720.00000   720.00000

-------- primitive cell, no core-hole
:LABEL4: using the command: run_lapw -ec 0.00001 -p -NI
<skip>
:FER  : F E R M I - ENERGY(TETRAH.M.)=   0.0564539224
:NEC01: NUCLEAR AND ELECTRONIC CHARGE    180.00000   180.00073
:NEC02: NUCLEAR AND ELECTRONIC CHARGE    180.00000   180.00000
:NEC03: NUCLEAR AND ELECTRONIC CHARGE    180.00000   180.00000

-------- 2x2x1 supercell, half core-hole
:LABEL4: using the command: run_lapw -ec 0.00001 -p
<skip>
:WARN  :        CHARGED CELL with  -0.500
:FER  : F E R M I - ENERGY(TETRAH.M.)=   0.0609755546
:NEC01: NUCLEAR AND ELECTRONIC CHARGE    719.50000   719.50115
:NEC02: NUCLEAR AND ELECTRONIC CHARGE    719.50000   719.50000
:NEC03: NUCLEAR AND ELECTRONIC CHARGE    719.50000   719.50000
<case.scfc>
:2P 001: 2P                  -5.274530454 Ry

------- primitive cell, half core-hole
:LABEL4: using the command: run_lapw -ec 0.00001 -p -NI
:WARN  :        CHARGED CELL with  -0.500
:FER  : F E R M I - ENERGY(TETRAH.M.)=   0.0944258517
:NEC01: NUCLEAR AND ELECTRONIC CHARGE    179.50000   179.50067
:NEC02: NUCLEAR AND ELECTRONIC CHARGE    179.50000   179.50000
:NEC03: NUCLEAR AND ELECTRONIC CHARGE    179.50000   179.50000
<case.scfc>
:2P 001: 2P                  -5.268297265 Ry

--------------

The energy of the state differs by 6 mRy (85 meV) between the supercell and
the primitive cell, making me hopeful that the supercell is reasonably
converged as to size.  The Fermi energy, though differs by 40 mRy (540 meV),
so probably the supercell is not converged with respect to size for the
Fermi energy.  In the limit of a large supercell, it would seem that the
Fermi energy should converge to the Fermi energy for the configuration
without the core hole.  So it seems to me that I should use the Fermi energy
from the configuration without the core-hole and compute the binding energy
as -5.2745 - 0.0547 = -5.329 Ry.  Is this correct?

Thanks,
  David

David Olmsted
Assistant Research Engineer
Materials Science and Engineering
210 Hearst Memorial Mining Building
University of California
Berkeley, CA 94720-1760