Ab initio calculations at the UMP2/6-311++G(2d,2p) and CCSD(T) levels are used to analyze the interactions in complexes pairing the hydroperoxyl radical (HOO) with dihydrogen trioxide (HOOOH). The structures obtained are analyzed by the Atoms in Molecules (AIM) and Natural Bond Orbital (NBO) methodologies. Six minima were located on the potential energy surface, with stabilization energies in the range between 12 and 26 kJ mol−1. Red shifts of OH bonds in HOO and HOOOH moieties upon complex formation lie in the ranges between 90–330 cm−1 and 90–270 cm−1, respectively.