Electrides are a class of materials consisting of non-nuclear excess electrons as quasi-F centers or Farbe centers within a positively charged lattice framework, and have significant applications in the fields of electrochemistry, spintronics, and electrode materials. Using first-principles quantum mechanical calculations, we have demonstrated exotic electronic structures of zirconium-rich electrides, Zr2X (X = O, Se, and Te), and obtained the quantitative values of charge transfer (oxidation states), and projected density of states associated with the localized quasi F-centers. The localized interstitial anionic electrons exhibit significant charge transfer values of approximately -1.88, -2.01, and -1.79 per atom in Zr2O, Zr2Se, and Zr2Te, respectively, and contribute actively in the electronic band structures and density of states at the Fermi level. From the 2D contour plot of the electron localization function (ELF), it has been predicted that the spatial distribution of the quasi-F centers stabilizes in the form of a one-dimensional pattern, with localized ELF sites interconnected with delocalized electron channels. Further, low work-function values of Zr2X, ranging from 2.7-3.4 eV, confirm the electride properties of these binary compounds, promising applications in electro-catalytic oxidations and anode materials in batteries. These unique electronic properties of anionic electrons free from nuclear binding in Zr2X have not been reported yet in the literature.