Although a two-center three-electron (2c-3e) bond between homonuclear atoms is well characterized, this is not the case for the SthereforeO bond, especially in neutral radicals resulting from the addition of a hydroxyl group on various sulfur substrates. A structural, energetical, and topological study is presented for prototypical radicals, ionic and neutral, RSOH-, RR'SOH2+, and RR'SOH, with R, R'= H, CH3. Three calculation methods have been applied, BH&HLYP, MP2, and CCSD(T), with different basis sets to determine the domains of accuracy of the more approximate ones to use them for larger systems. Qualitative and quantitative criteria, defined from the topological analysis of the electron localization function, are proposed to characterize such a 2c-3e bond. They specify the number and type of basins and their hierarchy of bifurcation, the global charge transfer between the fragments, the localization of the integrated spin density, and the electron delocalization between the lone pairs of the interacting atoms. Surprisingly, the neutral radicals show an intermediate behavior between the pure 2c-3e SthereforeO bond in anions and the electrostatic interaction in cations, despite the low energy of bond formation. As in the radical anions, the substitution favors the formation of a 2c-3c bond.