The full nine-dimensional vibrational problem of the (\mathbf{H}{s}^{+})complex is investigated: (i) using a model Hamiltonian which is based on the approximation that apart from the energy barrier for the internal propeller-like rotation motion all the other barriers on the potential energy hypersurface of the complex are assumed to be infinitely high, and (ii) applying an adiabatic approximation by which the nine-dimensional vibrational model Hamiltonian SchrΓΆdinger equation can be separated into three smaller subsystems. The relevant sections of the potential energy surface which are needed to describe all the vibrational modes and the major couplings between them are determined by ab initio calculations at the configuration interaction level of theory, and an analytic potential energy function is obtained by fitting to the ab initio data. The calculated energies of the low-lying bound and quasi-bound vibrational levels of the (\mathrm{H}{5}^{+})and (\mathrm{D}{5}^{+})ions allow a complete assignment of all the vibrational bands which have been observed in the photodissociation spectra of (\mathrm{H}{5}^{+})and provide dissociation energies (D_{0}) for the (\mathrm{H}{5}^{+})and (\mathrm{D}{\xi}^{+})ions which are in good agreement with the most recent experimental data. (c) 1994 Academic Press, Inc.