The geometrical parameters, vibrational frequencies, and binding energies for $(H_2O_3)_n$ (n = 1-5) have been investigated using various quantum mechanical techniques. The possible structures of the clusters (n = 2-5) are fully optimized and the binding energies are predicted using energy differences at each optimized geometry. The harmonic vibrational frequencies are also determined and zero-point vibrational energies (ZPVEs) are considered for the better prediction of the binding energy. The best estimation of the binding energy for the dimer is 8.65 kcal/mol. For n = 2 and 3, linear structures with all trans forms of the HOOOH monomers are predicted to be the lowest conformations in energy, while the cyclic structures with all cis-HOOOH monomers are preferable structures for n = 4 and 5.