18.2 Explicit input for ECPs

For each of the pseudopotentials the following information has to be provided:

• a card of the form
  ECP,atom, $n_{core},l_{max},l'_{max}$;
  where $n_{core}$ is the number of core electrons replaced by the pseudopotential $V_{ps}$, $l_{max}$ is the number of semi-local terms in the scalar-relativistic part of $V_{ps}$, while $l'_{max}$ is the corresponding number of terms in the SO part:
  
  $$V_{ps}= -\frac{Z-n_{core}}{r} + V_{l_{max}} +\sum_{l=0}^{l_{... ...ax}} \Delta V_l {\cal P}_{l} \vec{l}\cdot\vec{s} {\cal P}_{l} ;$$
  
  
  the semi-local terms (with angular-momentum projectors ${\cal P}_{l}$) are supplemented by a local term for $l=l_{max}$.

• a number of cards specifying $V_{l_{max}}$, the first giving the expansion length $n_{l_{max}}$ in
  
  $$V_{l_{max}} = \sum_{j=1}^{n_{l_{max}}} c_j r^{m_j-2} e^{-\gamma _j r^2}%,$$
  
  
  and the following $n_{l_{max}}$ ones giving the parameters in the form
  
  $$m_1, \gamma _1, c_1; m_2, \gamma _2, c_2; \ldots$$
  
  

• a number of cards specifying the scalar-relativistic semi-local terms in the order $l=0,1,\ldots , l_{max}-1.$ For each of these terms a card with the expansion length $n_l$ in
  
  $$V_l -V_{l_{max}}=\sum_{j=1}^{n_l} c_j^l r^{m_j^l-2} e^{-\gamma _j^l r^2}$$
  
  
  has to be given, and immediately following $n_l$ cards with the corresponding parameters in the form $m_1^l, \gamma_1^l, c_1^l; m_2^l, \gamma_2^l, c_2^l; \ldots$
• analogously, a number of cards specifying the coefficients of the radial potentials $\Delta V_l$ of the SO part of $V_{ps}$.