  Low-energy structure of even-even $^{108-116}$Cd isotopes is analyzed using a
collective model that is based on the nuclear density functional theory.
Spectroscopic properties are computed by solving the triaxial quadrupole
collective Hamiltonian, with parameters determined by the constrained
self-consistent mean-field calculations within the relativistic
Hartree-Bogoliubov method employing a universal energy density functional and a
pairing force. The collective Hamiltonian reproduces the observed quadrupole
phonon states of vibrational character, which are based on the moderately
deformed equilibrium minimum in the mean-field potential energy surface. In
addition, the calculation yields a low-lying excited $0^+$ band and a
$\gamma$-vibrational band that are associated with a deformed local minimum
close in energy to the ground state, consistently with the empirical
interpretation of these bands as intruder bands. Observed energy spectra,
$B(E2)$, and $\rho^2(E0)$ values are, in general, reproduced reasonably well.
