S-doped sodalite minerals of the Na8Al6Si6O24(Cl,S)(2) formula, also known as hackmanites, are computationally investigated for the first time, in order to understand their photochromic properties. With combined periodic boundary conditions and embedded duster-type approaches, this paper brings a theoretical overview of the photochromism mechanism, also called tenebrescence in geology. Time-dependent density functional theory (TD-DFT) calculations of sodalite systems containing electrons trapped in Cl vacancies showed an absorption spectrum and a simulated color in agreement with experiment. This modeling highlights the huge effect of the F center's environment such as the direct contribution of the ss cage on the trapped electron and a strong vibronic coupling of the absorption spectrum. TD-DFT and post-Hartree-Fock (SAC-CI) calculations were also operated on S-2(2-)-containing systems in order to determine the exact mechanism of coloration and discoloration, supporting that the key step is a direct through-space charge transfer between the S-2(2-) ion and a Cl vacancy. The geometry modification induced by this charge transfer leads to a large electronic reorganization stabilizing the F center, thus explaining the high stability of the colored state of the mineral.