Recently, a method based on relativistic nuclear energy density functional (EDF) has been employed to study relations between collective excitations in finite nuclei with the nuclear matter symmetry energy, and the phase transition density nt and pressure Pt at the inner edge separating the liquid core and the solid crust of a neutron star. By using the thermodynamic method, relativistic EDF and experimental data on the properties of charge-exchange dipole transitions, isovector giant dipole and quadrupole resonances and pygmy dipole transitions, the neutron star liquid-to-solid phase transition density and pressure are constrained. The analysis shows that accurate measurements are necessary to further constrain the symmetry energy parameters and the structure of neutron star crust.