It shows clearly that the new effective interaction PC-PK1 can provide a good description not only for the ground state properties in spherical and deformed nuclei but also for the nuclear spectroscopic properties of low-lying excitation states. In summary, a new parametrization PC-PK1 for the nuclear covariant energy density functional with nonlinear point-coupling interaction has been proposed by fitting to ob- servables of 60 selected spherical nuclei, including the binding energies, charge radii and empirical pairing gaps. By scaling the coupling constants in PC-PK1 in accordance with the QCD-based Lagrangian, it is found that all the nine parameters are natural. The success of PC-PK1 has been illustrated through the description for infinite nuclear matter and finite nuclei including the ground-state and low-lying excited states. VIII. SUMMARY For the spherical nuclei, PC-PK1 can provide better descriptions for the binding energies in comparison with DD-PC1, PC-F1, PC-LA, and NL3* sets. For neutron skin thicknesses, the DD-PC1 provides better description as compared with the other effective interactions due to its smaller symmetry energy at saturation density. Taking Yb and U isotopes as examples, it is found that the PC-PK1 reproduces the deformations and their corresponding evolutions with neutron number quite well. After taking into account the rotational correction energy in the cranking approximation, the binding energies given by PC-PK1 are in very good agreement with data within 1 MeV, which indicates that PC-PK1 achieves the same quality as DD-PC1 in the description for deformed nuclei. Moreover, PC-PK1 provides good description for isospin dependence of binding energy along either the isotopic or the isotonic chains, which makes it reliable for application in exotic nuclei. It is noted that the rotational correction energy evaluated using the cranking approximation may differ from that using angular momentum projection. Constrained calculations have also been performed for $^{240}$Pu in order to investigate the fission barrier. It is found that the PC-PK1 provides not only a good description for the deformation of the ground state [56] but also the energy difference between the ground-state and the shape isomeric state [57]. Furthermore, after including the triaxiality, the fission barrier given by PC-PK1 is in agreement with the empirical value [58]. The predictive power of the PC-PK1 is also illustrated in the description for the collective 17