Estimation of $J$ and $F^4/F^2$ from input parameter $U$

One can estimate $J$ and $F^4/F^2$ from input $U$ value via Yukawa-type screened Coulomb potential by the following keyword:

  scf.Yukawa                       on      # default=off

By setting scf.Yukawa=on, only $U$ values in <Hubbard.U.values ... Hubbard.U.values> are read and $J$ values in <Hund.J.values ... Hund.J.values> and scf.Slater.Ratio are ignored. Instead, $J$ values and $F^4/F^2$ will be automatically generated by estimating the Thomas-Fermi screening length corresponding to the input $U$ values [21,22]. As an example, for the following orbitals defined by:

  <Definition.of.Atomic.Species
    Ni Ni6.0S-s2p2d2f1  Ni_CA13S
    O  O5.0-s2p2d1      O_CA13
  Definition.of.Atomic.Species>

when scf.Yukawa=on and $U$ values are set to:

  <Hubbard.U.values   # eV  
    Ni 1s 0.0 2s 0.0 1p 0.0 2p 0.0 1d 6.4 2d 3.0 1f 0.0
    O  1s 0.0 2s 0.0 1p 0.0 2p 0.0 1d 0.0
  Hubbard.U.values>

one can see the following message in the standard output before SCF loop begins:

  *******************************************************
        Calculating Thomas-Fermi screening length 
  *******************************************************

  <species: Ni, angular momentum= 2, multiplicity number= 0>
   TF-screening-length lambda= 1.340787 1/au
   Hubbard U= 6.400000 eV
   Hund J= 1.154943 eV
   Slater F0= 6.399932 eV
   Slater F2= 9.321381 eV
   Slater F4= 6.847820 eV
   F4/F2= 0.734636

  <species: Ni, angular momentum= 2, multiplicity number= 1>
   TF-screening-length lambda= 0.271461 1/au
   Hubbard U= 3.000000 eV
   Hund J= 0.380184 eV
   Slater F0= 3.000017 eV
   Slater F2= 2.970544 eV
   Slater F4= 2.352036 eV
   F4/F2= 0.791786

These $U$, $J$, and $F^4/F^2$ values will be used for a subsequent DFT+$U$ SCF loop. The input file, 'NiO-Yukawa.dat' can be found in the directory 'work'.