  The lowest positive- and negative-parity bands of $^{20}$Ne and neutron-rich
even-even Ne isotopes are investigated using a theoretical framework based on
energy density functionals. Starting from a self-consistent relativistic
Hartree-Bogoliubov calculation of axially-symmetric and reflection-asymmetric
deformation energy surfaces, the collective symmetry-conserving states are
built using projection techniques and the generator coordinate method. Overall
a good agreement with the experimental excitation energies and transition rates
is obtained. In particular, the model provides an accurate description of the
excitation spectra and transition probabilities in $^{20}$Ne. The contribution
of cluster configurations to the low-energy states is discussed, as well as the
transitional character of the ground state. The analysis is extended to
$^{22}$Ne and the shape-coexisting isotope $^{24}$Ne, and to the drip-line
nuclei $^{32}$Ne and $^{34}$Ne. The role of valence neutrons in the formation
of molecular-type bonds between clusters is discussed.
