he accuracy of a full core treatment of $\rm I^-$ anion based on a zero-electron pseudo-potential ($ZEP$) including core polarization pseudo-potential ($CPP$) is examined on reference compounds $\rm LiI^-$ and $\rm CsI^-$ considered as one-electron systems. The results are compared to {\itshape ab initio} $CASPT2$ calculations involving 8 active electrons on iodine and 3 (respectively 9) on lithium (respectively cesium). An original scheme is proposed to build a pseudo-potential describing the short-range electron-$\rm I^-$ interaction beyond the point charge approximation. The importance of the $ZEP$ in one-electron calculations is estimated for the mentioned anions.