The equilibrium geometry of Ag0 centers formed at cation sites in KCl has been investigated by means of total-energy calculations carried out on clusters of different sizes. Two distinct methods have been employed: First, an ab initio wave-function based method on embedded clusters and second, density-functional theory ~DFT! methods on clusters in vacuo involving up to 117 atoms. In the ab initio calculations the obtained equilibrium Ag0 -Cl2 distance Re is 3.70 Å, implying a large outward relaxation of 18%, along with 7% relaxation for the distance between Ag0 and the first K1 ions in ^100& directions. A very similar result is reached through DFT with a 39-atom cluster. Both approaches lead to a rather shallow minimum of the total-energy surface, the associated force constant of the A1g mode is several times smaller than that found for other impurities in halides. These conclusions are shown to be compatible with available experimental results. The shallow minimum is not clearly seen in DFT calculations with larger clusters. The unpaired electron density on silver and Cl ligands has been calculated as function of the metal-ligand distance and has been compared with values derived from electron-paramagnetic resonance data. The DFT calculations for all cluster sizes indicate that the experimental hyperfine and superhyperfine constants are compatible when Re is close to 3.70 Å. The important relation between the electronic stability of a neutral atom inside an ionic lattice and the local relaxation is established through a simple electrostatic model. As most remarkable features it is shown that ~i! the cationic Ag0 center is not likely to be formed inside AgCl, ~ii! in the Ag0 center encountered in SrCl2, the silver atom is probably located at an anion site, and ~iii! the properties of a center-like KCl:Ag0 would experience significant changes under hydrostatic pressures of the order of 6 GPa.