We report the first global study of dynamic correlation energies (DCEs) associated with rotational motion and quadrupole shape vibrational motion in a covariant energy density functional (CEDF) for 575 even-even nuclei with proton numbers ranging from Z = 8 to Z = 108 by solving a fivedimensional collective Hamiltonian, the collective parameters of which are determined from triaxial relativistic mean-field plus BCS calculation using the PC-PK1 force. After taking into account these beyond mean-field DCEs, the root-mean-square (rms) deviation with respect to nuclear masses is reduced significantly down to 1.14 MeV, which is smaller than those of other successful CEDFs: NL3* (2.96 MeV), DD-ME2 (2.39 MeV), DD-MEδ (2.29 MeV) and DD-PC1 (2.01 MeV). Moreover, the rms deviation for two-nucleon separation energies is reduced by ∼ 34% in comparison with cranking prescription. Nuclear energy density functional theory is nowadays one of the most important microscopic approaches for large-scale nuclear structure calculations in medium and heavy nuclei based on a universal energy density functional (EDF) with a few parameters constrained by the properties of finite nuclei and nuclear matter or neutron stars. It stands out as a unique microscopic model that can describe not only the masses of all existing nuclei, but also other key quantities for simulating nucleonthesis process, including beta decay rate and fission rate in a unified way [1]. However, it is still a challenge for the current implementation of EDF to achieve satisfied accuracy. Therefore, great efforts have been devoted in many aspects to improving the accuracy of the EDF for atomic nuclei and subsequently deepening our understanding on the origin of elements in universe. Nuclear binding energy or mass is one of the most fundamental properties of atomic nuclei. The root-meansquare (rms) deviation with respect to the measured nuclear masses in the EDF is typically around several MeV. Only after taking into account the beyond mean-field dynamic correlation energies (DCEs) in global fitting of the EDF to nuclear masses can one achieve the rms deviation of a few hundred keV [2,3] by keeping a good description of nuclear matter properties. In these studies [2,3], the DCEs related to rotational and vibrational motions have been included phenomenologically with the cranking prescription. A better treatment of these DCEs is to carry out calculation with exact quantum number projec- * zpliphy@swu.edu.cn † mengj@pku.edu.cn tion and generator coordinate method (GCM), which has been done based on a Skyrme SLy4 force [4,5] with the assumption of topological Gaussian overlap approximation (GOA) or based on Gogny D1M and D1S forces [6] without using the GOA. In both the beyond mean-field (BMF) calculations, only axially deformed configurations are included and the obtained quadrupole DCEs are on average 3 − 4 MeV. Although the BMF approaches with exact projections and GCM for triaxially deformed nuclei have already been developed in recent years [7][8][9], they cannot be ado...

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