[Wien] N1s binding energy in TiN

Thu Jan 17 12:04:28 CET 2019

On Thu, 2019-01-17 at 02:46 -0600, Laurence Marks wrote:
> My three cents. I think an agreement of 0.1eV should be considered as
> fortuitous. There are many issues which are glossed over even with
> the miraculous exact functional:
> 
> 1) The Slater method is a very clever use of the mean value theorem
> for an integral. However, it is only 1 value. You can check the
> literature, I remember seeing papers where people use a range of
> holes to more accurately do the integral.

Thanks for the pointer, I'll do some reading. This should not be a
problem for the delta-scf method, right?

I've always stuck with the Slater's method up to now since if I
understand the delta-scf method properly then for insulators you need
to place the electron in background and the E_b is than calculated
as E^tot_finalstate(N-1) - E^tot_initialstate(N) + μ. However I'm not
sure how to include the lat part. And if you do just
E^tot_finalstate(N-1) - E^tot_initialstate(N) you get a really bad
results. Metals are better since you can place the electron to valence
band and do  E^tot_initialstate(N) - E^tot_finalstate(N), which gives
in practice almost identical results as the Slater's approach.

BTW I did found it interesting that for metals and the Slater's
transition state calculations it actually doesn't matter if you place
the extra half electron in the valence band or in background (0.02eV
difference for TiN).

> 
> 2) The simple dft-based calculations assume that the final states are
> plane waves. Rigorously the exiting photoelectron in XPS is an
> evanescent Bloch wave (for a crystal). There is literature on this,
> but I doubt that it has been combined with DFT.

This is probably beyond my knowledge/interest I could check how large
differences this could cause.

I've actually seen some articles where authors claim to calculate good
absolute binding energies (Ozaki, T., & Lee, C.-C. (2017). Absolute
Binding Energies of Core Levels in Solids from First Principles.
Physical Review Letters, 118(2), 026401. 
https://doi.org/10.1103/PhysRevLett.118.026401) and their way to good
absolute results was the exact coulomb cutoff method and some penalty
functional, but I'm not sure how much this would be applicable to lapw
method.

> 3) In experiments you have to worry about photoelectron diffraction,
> and there will be some shifts to higher apparent binding energy due
> to phonon inelastic scattering. And you have to worry about charging
> and band bending for insulators, chemisorption induced work function
> changes (how clean is your XPS?)....

The photoelectron diffraction and phonons is probably something I can't
do anything about, except for hoping that it does not affect the
relative shifts however I've always thought that the work function,
charging, etc. could be neglected considering you do proper change
compensation and align the measured spectra properly (either with the
adventitious carbon or preferably with respect to Au), than you should
have just the proper value with respect to the Fermi energy?

What I have found more problematic for semiconductors is that from
normal calculations you don't get the correct position of Fermi level,
since its somewhere in the band gap. In those cases I've tried to align
the experimental spectra to the valence band maximum for comparison
with calculations which sort of works but introduces extra
uncertainties.

Anyway thank you for the thoughts.
Best regards
Pavel Ondračka
> 
> _____
> Professor Laurence Marks
> "Research is to see what everybody else has seen, and to think what
> nobody else has thought", Albert Szent-Gyorgi
> www.numis.northwestern.edu
> 
> On Thu, Jan 17, 2019, 02:29 Peter Blaha <pblaha at theochem.tuwien.ac.at
>  wrote:
> > Sorry for the confusion. The quoted values in the pdf are probably
> > from 
> > a lousy calculation and are ment only to demonstrate the effect (if
> > I 
> > remember correctly, only a 4x bigger P supercell, but for sure not 
> > converged, I also don't remember which functional, ....) and only 
> > accidentally match experiment.
> > 
> > My general experience is that core-eigenvalues (taken with respect
> > to EF 
> > !!) are 10-15% off, while slater TS gives 1-2 %, i.e. an order of 
> > magnitude better.
> > 
> > 
> > On 1/17/19 9:15 AM, Pavel Ondračka wrote:
> > > Dear Wien2k mailing list,
> > > 
> > > I'm looking for some advice regarding the calculation of core
> > level
> > > binding energies (to compare with XPS experiments). First of all
> > there
> > > is this nice lecture where prof. Blaha actually shows some
> > calculations
> > > 
> > https://urldefense.proofpoint.com/v2/url?u=http-3A__susi.theochem.tuwien.ac.at_reg-5Fuser_textbooks_WIEN2k-5Flecture-2D&d=DwIGaQ&c=yHlS04HhBraes5BQ9ueu5zKhE7rtNXt_d012z2PA6ws&r=U_T4PL6jwANfAy4rnxTj8IUxm818jnvqKFdqWLwmqg0&m=tkgGA6DHWOQZpcOauDl3Lx8BZ_vGdV0W35tV5es6rQw&s=RWPHx3CucXJZx8K7anGE8WYmvRBxkjijDa1up4sQ7Rg&e=
> > > notes_2011/Blaha_xas_eels.pdf of core levels with perfect
> > results. For
> > > example with TiN the deltaSCF method gets 397.1eV for the N1s
> > level as
> > > compared to 397.0eV experiment. The trouble is that I'm not able
> > to
> > > reproduce this.
> > > 
> > > I've done some calculations before and I was never really happy
> > with
> > > the absolute values which were always few eV off but I've always
> > > thought this is just the limitation of xc functional or
> > methodology.
> > > Hence seeing the nice results in the lecture surprised me.
> > However, I'm
> > > not able to reproduce the values even for metals from the
> > example. For
> > > the TiN I'm getting values of 404.8eV with the slaters transition
> > state
> > > approach and 404.6eV with delta-scf (here I'm using the formula
> > for
> > > metals E_b = E^tot_initialstate(N) - E^tot_finalstate(N), i.e.
> > placing
> > > the core-electron in the valence band and with PBE). I have
> > thought
> > > that this is maybe functional difference, since while taking LDA
> > > instead of PBE shifts the results differ almost by 4eV (to
> > 400.9eV).
> > > However with the PBE I get the core energy ε_i as 377.4eV
> > (consistent
> > > with the mentioned pdf where it is 377.5eV) so maybe this is not
> > just
> > > about functional?. I've already checked convergence with
> > supercell size
> > > as well as numerical parameters and I'm actually out of ideas.
> > > 
> > > To be honest, I'm not much concerned personally about the
> > discrepancy
> > > since the chemical shifts seem to be reasonable even if the
> > absolute
> > > values are not. I just think that if it is possible to get the
> > absolute
> > > values right (or at least closer to experiment) as in the lecture
> > pdf,
> > > the results would of course look way better, therefore I'll be
> > grateful
> > > for any comments and help.
> > > 
> > > Best regards
> > > Pavel
> > > 
> > > 
> > > 
> > > 
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