This is the first of a series of papers in which we investigate the unimolecular dissociation of hydroperoxyl. Using the DMBE IV potential energy surface [Pastrana et al., J. Phys. Chem. 94, 8073 (1990)], in the present study 726 bound states of HO2((X) over tilde) up to-the H+O-2 dissociation threshold are calculated in an attempt to access the extent of the coupling between the modes of the system. The first approach involves an analysis of the nodal structure of the wave functions. While the wave functions for the lowest states are regular and; assignable, the degree of mixing and complexity rapidly increases with energy. The wave functions close to the dissociation threshold are mostly irregular without any clear cut nodal structure and fill the entire coordinate space available. Nevertheless, a small number of regular states, that are associated with large excitation in the O-2 stretching coordinate and no or only little excitation in the other modes, are found even at high energies. The second approach used to study the degree of intramolecular coupling is an analysis of the energy spectrum. The nearest neighbor level spacing distribution, which probes the short-range correlation, as well as the Sigma(2) and Delta(3) statistics, which are sensitive to the long-range correlations in the spectrum, are investigated and compared to the distributions predicted for regular and irregular spectra. Both of these approaches indicate that the system is almost totally irregular with a Brody parameter of about 92%. In addition, the sum of states at a particular energy, which is extremely important in all statistical models for unimolecular dissociation, is approximately calculated from the volume of classical phase space and found to be in excellent agreement with the exact quantum mechanical result.