Some guidelines to create transition metal PP

There are some important points that have to be considered when PPs for d-elements are constructed:

• For a very accurate calculations it is important to reproduce the $f$-logarithmic derivatives exactly. There is a simple reason for this: The tails of neighboring d-electrons penetrate the core of the atoms easily (LCAO picture) and these tails also experience the $f$-potential (i.e. the $d$-tails contain $f$-components if they are developed into spherical components centered around neighboring atoms). The correct description of the $f$-part is especially important for the $4d$ elements and less important for the $3d$ elements: for the $4d$ elements the total error might be up to $2~\%$ in the lattice constant and 500 meV in the cohesive energy, for $3d$-elements the error is generally less than $1~\%$ in the lattice constant and less than 100 meV in the cohesive energy. You should be aware of these problems, if you compare with other less accurate PP calculations.[90] We note that some late $3d$, $4d$ and $5d$ potentials have been updated to improve the $f$-scattering properties. These potentials are available around April/May 2009.
• There are two possibilities to create a such accurate PPs:
  • The AE-potential might be truncated at a relative small cutoff i.e. use the line

    
     RCLOC = 1.2-2.0 (atomic units)
    

    RCLOC must be smaller than half the nearest neighbor distance. This is generally sufficient. Matter of fact, the smaller RCLOC the better, but too small RCLOC often result in ghoststates.
  • The second choice is sometimes preferable: It is possible to use a (normconserving) $f$-PP as local potential. This requires less fiddling, because $f$ logarithmic derivatives are automatically correct. In this case the line

    
     ICORE = 3
    

    has to be added to PSCTR and the line

    
     3  0.5        7   2.2     7   2.2
    

    or

    
     3  0.5       23   2.2    23   2.2
    

    has to be added to the description section of the PSCTR file (V_RHFIN has to be changed as well). In the second case the $f$-PP will be non-norm conserving. Often this is sufficient for a good description of the $f$-part. The only disatvantage of this procedure is that it results in $s$ and $p$ like ghoststates very often.
• If the $f$-electrons are described accurately, than the $s$ and especially the $p$ non locality will very strong. This results in serious problems in the Kleinman-Bylander factorization, and generally two $s$ and $p$ reference energies must be included to get an accurate description of $s$ and $p$ states.
• A second not unusual problem is the description of the semi core $p$ states in $4d$ and to a lesser extend $3d$ and $5d$ elements. If the semi core $p$-states are treated as core states (frozen core), some compromise have to made in the description of the $p$ logarithmic derivatives. Generally the $p$ reference energies must be positive, for instance for Mo the following reference energies were used:

  
   1  0.3       15   2.4    23   2.7
   1  2.0       15   2.4    23   2.7
  

  This results in small deviations in the logarithmic derivatives at negative energies, but a better description of the $p$ logarithmic derivatives will result in ghost states near the semi core $p$-states.

  The only straight forward solution to this problem is to treat the $4p$-states as valence states. Frequently it is not possible to construct an accurate PP for the $5p$ states without doing so. For spin polarized calculations it is always necessary to treat the $4p$ states as valence states.