The ABINIT Users Mailing List ( CLOSED )

[paul.boulanger@umontreal.ca]

Hi all (kon'nichiha Mikami-san),

        I have found a peculiar problem with the PAW calculations, concerning 
certain elements.  Let’s focus on the more simple case, Germanium. I wanted 
to generate an atomic data file using uspp->abinit, and I started to play 
around with the partial-core cutoff radius for the non-linear core-exchange 
*. I have found that the band gap varies greatly with the chosen radius, 

rcore (a.u)    relaxed cell parameter (Angstrom)    indirect band gap  (eV)   
        direct gap
1.00                     5.802                                               
-0.17                                         0
1.45                     5.758                                                
0.34                                         0.285

        This seems peculiar to me, because if we take a look to the 
densities**, we see that the valence densities have only a small overlap with 
the d electrons, which would imply that non-linear core corrections should be 
small. I have also observed that if we don’t specify any value for the 
partial-core cutoff radius, uspp->abinit seems to impose a cutoff radius of 
1,47 a.u. How this radius is chosen, is unknown to me. But, we can see in the 
preceding table that this cutoff radius gives an erroneous band gap, because 
Ge as an indirect band gap between the Gamma point and point X. In fact, PBE 
should result in a metal system with band overlap but there should be a 
direct gap at Gamma. 

        I have tested other model systems with the same crystal structure, to 
verify the universality of this band gap variation. I have found that it does 
not modify the gap for C and Si, which seems to indicate that it arises from 
the d electrons. In the case of Ga and As, there is also this kind of 
variation. In the specific case of GaAs, we find:
 
        With PAW:

        Rcore of As (a.u)                band gap (eV) 
              1.0                                          0
              1.2                                          0.713
              1.47                                        1.315
 
        With FHI:        
      
               Rcore of As (a.u)                 band gap (eV)
                             1.0                            0.568
                              nocore                    0.547

        In this case, we compare the results with the same calculation, but 
with a Troullier-Martins scheme pseudopotential generated with the FHI 
package. We can see that the discrepancies between the two are quite large 
and that the default value of 1.47 a.u chosen by uspp->abinit is quite wrong. 
We seem to have a correct behavior in the FHI calculation, the variation is 
small, which reflects the overlap in the densities.
        It therefore seems that the partial-core cutoff radius determines the 
band gap in the PAW case. This raises the question of how should we define 
the partial-core cutoff radius, or minimally that we should take precautions 
when choosing this parameter. Maybe someone with more experience with atomic 
data file generation as a comment on this?? 
I have not identified the source of the problem, which can be in the 
generation of the atomic data (maybe compilation problems) or the 
implementation in Abinit. 

paul

* The source files for the generation of the atomic data and the input files 
for abinit are available on request.

**  In the Ge_ps.out file, which is also available on request.