[Wien] Which fermi energy for XPS?

[Peter Blaha]

No, I don't think so.

Every calculation uses its own Energy-zero (the average of the Coulomb-potential
in the interstitial region is set to zero), so clearly one must use
EF and E-2p from the same (half-core hole) calculation.

Eventually, you can check the k-mesh, as with a small k-mesh, EF could vary a bit.
(I hope you have used "comparable k-meshes". This means the mesh for the
2x2x1 supercell should be by by a factor of two smaller in x,y than for the primitive cell
(eg. 2x2x2   vs 4x4x2)

Am 10.04.2015 um 19:33 schrieb 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
>
>
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-- 
-----------------------------------------
Peter Blaha
Inst. Materials Chemistry, TU Vienna
Getreidemarkt 9, A-1060 Vienna, Austria
Tel: +43-1-5880115671
Fax: +43-1-5880115698
email: pblaha at theochem.tuwien.ac.at
-----------------------------------------