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Information on the format 6 for pseudopotentials

The format 6 for ABINIT pseudopotentials allows to use pseudopotentials generated from the FHI98PP code (Fritz-Haber-Institute, Berlin). This code is available at this URL.

A few lines must be added to the file generated by the FHI98PP code, and are described in the present file. ABINITv1.9 is able to read format 6 pseudopotential files without core correction. ABINITv2.2 is able to read them with core correction (thanks to AF).

The original cpi file

We will suppose that the user has been able to generate a cpi file from the FHI98PP code. There is one such file in the ~abinit/tests/Pspdir directory, with the name al_h.cpi (the FHI98PP code generated a file named al:h.cpi, but the name was changed, to allow portability under DOS/Windows) . It begins by:

0.30000000000000E+01   3

0.0000 0.0000 0.0000 0.0000 0.0000 .00e+00 .00e+00 0.0000 .00e+00 .00e+00 0.0000 .00e+00 .00e+00 0.0000 .00e+00 .00e+00 0.0000 .00e+00 .00e+00 0.0000 .00e+00 .00e+00 0.0000 .00e+00 .00e+00 0.0000 .00e+00 .00e+00 0.0000 .00e+00 .00e+00 493 0.10247000000000E+01 1 0.48076923076923E-03 0.91926957204792E-04 0.72762392428392E+00 2 0.49264423076923E-03 0.94197553047751E-04 0.72762434262851E+00 3 0.50481254326923E-03 0.96524232608030E-04 0.72762477651319E+00 … …

From these numbers, we will make direct use of:

  • those on the first line, i.e. the number of valence electrons ( 0.30000000000000E+01 ) and the number of pseudopotential components ( 3 )
  • the first on the 12th line, i.e. the number of mesh points ( 493 )

The new file

For the purpose of generating the corresponding file readable by ABINIT (also found in the ~abinit/tests/Pspdir directory, with the name 13al.981214.fhi), the following seven lines have been added at the beginning of the al_h.cpi file:

Aluminum, fhi98PP : Hamann-type, LDA CA PerdewWang, l=2 local

13.000 3.000 981214 zatom,zion,pspdat 6 7 2 2 493 0 pspcod,pspxc,lmax,lloc,mmax,r2well 0.0 0.0 0.0 rchrg, fchrg, qchrg 5— These two lines are available for giving more information, later 6 7-Here follows the cpi file from the fhi98pp code-

Similar lines must be added at the beginning of other cpi files, in order to make them readable by ABINIT.

Line 1 is simply a header, that might include any information, and that will be printed without modification in the output of ABINIT.

Line 2 describes:

  • the atomic number (zatom);
  • the ionic charge (zion, number of valence electrons);
  • the date of pseudopotential generation.

The two first information are crucial, the third one is not really important. The atomic number is 1 for Hydrogen, 8 for Oxygen, and so on. The ionic charge should be the same number as the first number mentioned in the cpi file (called ‘number of valence electrons’).

Line 3 describes:

  • the format of the pseudopotential (pspcod; must be 6 for this format);
  • the XC functional used to generate the pseudopotential (pspxc ; the same numbers as for the input variable ixc should be used, see ~abinit/doc/users/abinit_help.html)
  • the maximal angular momentum of the wavefunctions described in the pseudopotential file (lmax=0 if only s-wavefunctions are present, lmax=1 for s and p wfs, lmax=2 for s, p and d wfs … ; lmax+1 must be equal to the ‘number of pseudopotential components’ mentioned in the cpi file, as the second number of the first line)
  • the angular momentum of the potential to be used as local pseudopotential (lloc=0 if s-potential is local; lloc=1 if p-potential is local ; … )
  • the number of radial mesh points (mmax, same meaning as in the cpi file; first number on the 12th line)
  • the last number can be set to 0 .

Line 4 describes 3 parameters needed to read the model core-charge if core correction is needed. - rchrg: radius at which the core charge vanish (i.e. cut-off in a.u.) - fchrg: amplitude of core charge (if =0 non core-correction performed, if >0 core-correction is applied). The specific value of fchrg has no physical meaning in fhi98pp scheme of core correction. - qchrg: integrated model core charge (it’s not actually used by abinit, and can be set to any value)

rchrg can be inferred by the pp file. Indeed, if the pp has been generated with the core-correction option, at the end of ‘cpi’ file there will be:

 do i=1,mmax
    rad(i), f(i), f1(i), f2(i)
 end do

that is, the radial grid, the core charge (f), and their first(f1) and second (f2) derivative on the radial mesh; rchrg can be equal to any value of rad(i) to which f,f1 and f2 are reasonably vanished.

Line 5-7 have no interest up to now.

A pseudopotential with format 6 will be treated by the routine psp6in.f, that calls psp5lo.f (local part) and psp5nl.f (non-local part). There is no psp6lo.f or psp6nl.f.

The integral of (V(r)+Zion/r) r^2 in psp5lo.f is performed from 0 to the highest allowed radius (usually about 100 a.u.), except that beyond 20 a.u. no value of abs(V(r)) larger than 2.0d-8 is tolerated. This will allow to cut off spurious behaviour of pseudopotential whose data file is written in single precision.