We present here a systematic study by quantum mechanical methods of a series of molecules (HOOF, HOOCl, HOONO, HOOCN, FOOF, ClOOF, ClOOCI, and FOONO), corresponding to substitutions of one or both hydrogens in hydrogen peroxide. The emphasis is on the structural and energetic properties and on the features of the internal modes, in particular, the torsion around the O-O bond, which leads to the chirality changing isomerization. The cis and trans barriers appear to vary remarkably upon substitution by halogen groups. They are compared with experimental and theoretical information, when available, and analyzed by reference to a previous systematic analysis of the effects of alkyl substitutions. Torsional levels were calculated, and their distribution as a function of temperature was determined. This information is of interest for statistical approaches to equilibrium properties and to rates of processes where torsional anharmonicity is relevant, as required for recent atmospheric modeling studies and also for prototypical chiral separation experiments, in view of a possible dynamic mechanism for chirality exchange by molecular collisions. Dipole moments are also presented.