
Information on the format 1 for pseudopotentials.

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The format 1 for ABINIT pseudopotentials allows to use pseudopotentials
from the set of LDA pseudotentials for the whole periodic table,
build by DC Allan and A.Khein. They have been generated according
to the Troullier-Martins technique.
See ~abinit/doc/users/bibliography.html for the corresponding references.

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     The pspcod=1 psp files are formatted data files
     which give potentials and projector functions on a real space
     radial grid.

     Firstly, the radial grid runs from index 0 to 2000 (2001 points),
     with grid points given by the following equation (given as fortran):
      nmax=2000
      do j=0,nmax
       x=dble(j)/dble(nmax)
       r(j)=100.d0*(x+.01d0)**5-1.d-8
      enddo

     The psp file consists of a number of header lines followed by the
     data on the radial grid.  The header section is as follows:

     title  (single 80 character line)
     zatom, zion, pspdat
     pspcod, pspxc, lmax, lloc, mmax, r2well
     ...then, for l=0 to lmax, the following 2 lines:
      l,e99.0,e99.9,nproj,rcpsp
      rms,ekb1,ekb2,epsatm
     ...finally one more line:
      rchrg,fchrg,qchrg

     The data may be located anywhere on the line as long as it is provided
     in the order indicated (it is read with free format).
     In the case of Si with lmax=2, the header may look like the following
     10 lines:


  Si  Fri Oct 08 11:18:59 1993
  14.00000   4.00000    930920                zatom, zion, pspdat
    1    1    2    2      2001    .00050      pspcod,pspxc,lmax,lloc,mmax,r2well
    0  19.464  25.000    2   1.8971118        l,e99.0,e99.9,nproj,rcpsp
    .00112760   6.1457108933   4.4765165955  29.74712295   rms,ekb1,ekb2,epsatm
    1  21.459  28.812    2   1.8971118        l,e99.0,e99.9,nproj,rcpsp
    .00119946   3.2090654032   2.0935248528  19.11150542   rms,ekb1,ekb2,epsatm
    2   8.223  21.459    0   1.8971118        l,e99.0,e99.9,nproj,rcpsp
    .00098688    .0000000000    .0000000000  -3.97301006   rms,ekb1,ekb2,epsatm
    1.70000000000000     .22513330685109     .96523597101781   rchrg,fchrg,qchrg

     zatom is the atomic number of the atom (14 for Si)
     zion is the number of valence electrons (4 for Si)
     pspdat is a code revision date (930920 for this case)
     pspcod is another index describing the code (1 for this case)
     pspxc is an index showing the choice of exchange-correlation (1)
     lmax is the highest angular momentum for which a pseudopotential
      is defined, which is also used for the local potential (2)
     lloc is the angular momentum used for the local potential (2)
     mmax is the number of grid points (2001)
     r2well is the prefactor of a harmonic well sometimes used to bind
      electrons which would otherwise be unbound in lda (.00050)
     l is the angular momentum (0, 1, or 2 for Si for this case)
     e99.0 is the planewave cutoff needed to converge to within 99.0% of the
      kinetic energy of the atom (various numbers for various l)
     e99.9 is the planewave cutoff needed to converge to within 99.9% of the
      kinetic energy of the atom (various numbers for various l)
     nproj is the number of projection functions used for each l (2)
     rcpsp is the pseudopotential core radius
     rms is a measure of pseudopotential quality reflecting the value of the
      penalty function in designing the potential
     ekb1, ekb2 are the Kleinman-Bylander energies for each projection
      function for each l
     epsatm is the integral Int[0 to Inf] (4*Pi*r*(r*V(r)+Zion))
     rchrg is the core charge radius for additional core charge used to
      match the xc contribution to the hardness matrix
     fchrg is the prefactor of the core charge expression
     qchrg is the total (integrated) core charge

     Following the header are, for l=0 to lmax, the pseudopotentials
     in the form of a title line followed by 667 lines of data, each line
     containing three numbers so that the radial grid values from 0 to 2000
     are given.  The title line gives the value of l first followed by some
     text.  For the case of Si, e.g., for l=0, this line is

      0 =l for Teter pseudopotential


     ...followed by the 667 lines, 3 numbers each, giving the l=0
     potential on the radial grid described above.

     Following the pseudopotentials are the first projection functions,
     again given for each l with a title line followed by 667 data lines.

     Following the first projection functions for each l are the second
     projection functions, if any (determined by nproj).

     Following the second projection functions, if any, are several lines
     of additional data which is not read by plane_wave but is provided
     to describe more about the details of the construction of the
     pseudopotential.  Omission of these lines does not affect the running
     of plane_wave (at this time).

     If you do not wish to use core charges, simply set fchrg to 0 and
     use rchrg=1, qchrg=0.

     If you wish to make a local potential, use lmax=lloc=0, nproj=0, and
     you need not provide any projection function(s) (at this time).
     The values of rms, ekb1, ekb2, epsatm, e99.0, e99.9 are used only
     for information (at this time) so may be set to 0 when creating
     a pseudopotential file.  rcpsp is still used as the definition of the
     pseudopotential core radius so it must be provided.


     To best understand this data structure, it is recommended to study
     several pseudopotential files and compare their contents with the
     description given here.


     Inside ABINIT, a pseudopotential with format 1 will be treated by
     the routine psp1in.f, that calls psp1lo.f (local part),
     psp1nl.f (non-local part), and psp1cc.f (XC core correction).

     As a matter of numerical accuracy, note that the integral
     of (V(r)+Zion/r) r^2 in psp1lo.f is performed from 0 to the highest
     allowed radius (usually about 100 a.u.), without cut-off.
     V(r)+Zion/r should tend rapidly to zero
     for large radii (beyond 5 a.u.), but this correct behaviour will
     not be enforced by the routine. If the tail of V(r) is inaccurate
     (i.e. if the pseudopotential is in single precision), there
     will be large inaccuracies in the integral, because of the r^2
     factor.




