We investigate the microscopic structure of strongly coupled ions in warm dense matter using ab initio simulations (DFT-MD) and hypernetted chain equations (HNC). We demonstrate that an approximate treatment of quantum effects by weak pseudo-potentials fails to describe the highly degenerate electrons in warm dense matter correctly. However, one component HNC calculations for the ions agree well with first principle simulations if a linearly screened Coulomb potential is used. These HNC results can be further improved by adding a short range repulsion that accounts for bound electrons. Examples are given for recently studied light elements, Lithium and Beryllium, and for Aluminum where the extra short-range repulsion is essential.