excitation spectra and transition probabilities in $^{150}$Nd as well as the characteristic collec- tive observables for Nd isotopes in a five-dimensional collective Hamiltonian in which the parameters are determined by constrained calculations for triaxial shapes. There are also many extensions of nuclear covariant energy density functional theory beyond mean-field using projection techniques [65] and generator coordinate methods [66, 67]. More micro- scopic analysis of nuclear low-lying states in context of these frameworks with PC-PK1 is in progress. The density-dependent parametrization DD-PC1 is determined mainly from the masses of deformed nuclei and the EOS of nuclear matter. However, the calculations of the rear- rangement terms for the density-dependent parametrization can be nontrivial in some cases, in particular for RPA calculations. Here the nonlinear parametrization PC-PK1 has been optimized to the masses, charge radii and empirical pairing gaps for selected 60 spherical nuclei. It has been illustrated that the PC-PK1 can provide very good descriptions for both spherical and deformed nuclei. Therefore, the non-linear parametrization is very useful as it combines the simplicity with very good predictions for many nuclear properties. We thank P. Ring and T. Nikˇsi´ c for stimulating discussions and kind help in the com- parison with density-dependent point-coupling results. This work was partly supported by the Major State 973 Program 2007CB815000 and the NSFC under Grant Nos. 10775004, 10947013 and 10975008 and the Southwest University Initial Research Foundation Grant to Doctor (No. SWU109011). Acknowledgments 18