  Phonon spectra of cubic rubidium niobate and rubidium tantalate with the
perovskite structure are calculated from first principles within the density
functional theory. Based on the analysis of unstable modes in the phonon
spectra, the structures of possible distorted phases are determined, their
energies are calculated, and it is shown that $R3m$ is the ground-state
structure of RbNbO3. In RbTaO3, the ferroelectric instability is suppressed by
zero-point lattice vibrations. For ferroelectric phases of RbNbO3, spontaneous
polarization, piezoelectric, nonlinear optical, electro-optical, and other
properties as well as the energy band gap in the LDA and GW approximations are
calculated. The properties of the rhombohedral RbNbO3 are compared with those
of rhombohedral KNbO3, LiNbO3, and BaTiO3.
