Electronic structures, charge distributions, geometries, valence force constants, and vibrational frequencies of the homoatomic clusters F-3(+), Cl-3(+), Br-3(+), and I-3(+) and of the heteroatomic clusters ClF2+, BrF2+, IF2+, BrCl2+, ICl2+, and IBr2+ were determined. The self-consistent field approach extended by MP2-correlation energy or density-functional corrections was applied using various basis sets. It was found that d- and f-type polarization functions play a crucial role as in some other halogen compounds. The MP2 approach yields the most satisfactory results. The effect of the crystalline environment surrounding the Cl-3(+), Br-3(+), and I-3(+) species is successfully simulated by a Madelung potential, Frequencies calculated in the crystal field are in reasonable agreement with the more reliable ones among the experimental results. Coupling force constants were determined. They are not consistent with some empirical ruts. Bonding and charge distributions of the formally mixed-valence systems X(+)Y(2)(0) are discussed. X(+) behaves like a divalent chalcogen with high electronegativity. Each of the X(+)-Y bonds in XY(2)(+) is very similar to the bond in X-Y. We predict the experimentally unknown F-3(+) to be stable in vacuum but not in the solid state. Structures and frequencies of XY(2)(+) species, which are as yet unknown, are also predicted.