[QE-users] Ionization energy with HSE

[Giuseppe Mattioli]

Dear Shivesh Sivakumar
There is no difference in the calculations you mention, you can use  
pp.x and average.x after HSE calculations in the case of 2D to 0D  
systems (otherwise, in the case of fully periodic 3D systems it is  
nonsense to use average.x to find the vacuum level as potential  
asymptote...). However, the "physical relevance" of such calculations  
is another matter: if you calculate the HOMO-vacuum level energy  
difference, you are totally neglecting the rearrangement of electrons  
in the N-1 (i.e., ionized) final state. Your crude estimate from  
ground-state eigenvalues might be quite inaccurate. There are tons of  
literature on this subject, and if you want to know more, you might  
start from here: Dabo et al., Phys. Rev. B 2010, 82, 115121. In the  
case of isolated systems (e.g., molecules or clusters), you can use  
some different program, implementing localized orbital basis sets, and  
calculate total energy differences such as E(N-1)-E(N), where N is the  
number of electrons of the neutral species. In periodic/plane-wave  
calculations this is not possible due to the fact that in charged  
system a diffuse countercharge, necessary to the convergence of the  
Ewald's sum, is added to the system, shifting the total energy. AFAIK,  
you can simulate real ionization processes and calculate the  
corresponding energies by using excited-state codes such as YAMBO,  
that use the QE ground state to calculate several spectroscopic  
observables.
HTH
Giuseppe


Quoting Shivesh Sivakumar <shiveshsivakumar at gmail.com>:

> Hello users,
>
> I was wondering whether the ionization energy calculated from a HSE
> calculation has any physical relevance. I understand the mixing of exact
> exchange gives us a more reliable estimate of the band gap, but is it
> possible to comment on the ionization energy? I intend to do this the same
> way as PBE, LDA etc - Calculate the vacuum level and then compute I.E. as
> Vacuum - HOMO. I also want to know if pp.x and average.x are compatible
> with hybrid functional calculations on QE. I've already calculated the IE
> using PBE for my material but don't know what to expect for HSE.
>
> Any comments or insights would be very appreciated.
>
> Best,
> Shivesh Sivakumar
> University of Washington-Seattle
> WA-98105



GIUSEPPE MATTIOLI
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