parison with those with DD-PC1, PC-F1, PC-LA ,and NL3*. In general, PC-PK1 improves the overall agreement with data in comparison with the other interactions, especially for N = 82 and N = 126 isotones. The deviations are within 1 MeV for N = 82 isotones and 2 MeV for both N = 20 and N = 50 isotones. A remarkable improvement in the binding energies as well as proper isospin dependence for N = 126 is found in the calculations with PC-PK1. In short, PC-PK1 provides better prediction for not only the binding energies but also its isospin dependence. From the binding energies, one can extract the two-neutron separation energies, S$_{2}$$_{n}$ = E$_{B}$ ( N,Z ) − E$_{B}$ ( N − 2 ,Z ). In Fig. 4, the two-neutron separation energies for even-even O, Ca, Ni, and Sn isotopes predicted by PC-PK1 are shown in comparison with data [23] and those by DD-PC1, PC-F1, PC-LA, and NL3*. Generally speaking, similar as the other interactions, the calculation with PC-PK1 reproduces the experimental two-neutron separation energies quite well. For the oxygen isotopic chain, all the effective interactions predict the last bound neutron-rich nucleus as $^{28}$O contrary to experiment in which $^{24}$O is so far the last bound neutron-rich nucleus. One can also find that the deviations are large for the even-even 58 − $^{68}$Ni which can be attributed to the underestimation of binding energies as shown in Fig. 2. Moreover, visible deviations between different predictions can be seen in the neutron-rich Sn isotopes, which requires future experimental confirmation. B. Two-neutron separation energy C. Single-particle level In Figs. 5, 6, the calculated single-particle energies for $^{16}$O, $^{40}$Ca, $^{132}$Sn, and $^{208}$Pb by PC-PK1 are shown in comparison with data [43] and those by DD-PC1, PC-F1, PC-LA, and NL3*. The experimental values are extracted from the single-nucleon separation energies or excitation energies [43]. The theoretical single-particle energies are the eigenvalues of the Dirac equation for nucleon. It should be kept in mind that the calculations are performed by neglecting particle-vibration coupling [44]. In Figs. 5, 6, it is clearly shown that the single-particle levels near the magic numbers and the corresponding shell gaps given by PC-PK1 are in good agreement with the experimental 13