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We report the first global study of dynamic correlation energies (DCEs)associated with rotational motion and quadrupole shape vibrational motion in acovariant energy density functional (CEDF) for 575 even-even nuclei with protonnumbers ranging from $Z=8$ to $Z=108$ by solving a five-dimensional collectiveHamiltonian, the collective parameters of which are determined from triaxialrelativistic mean-field plus BCS calculation using the PC-PK1 force. Aftertaking into account these beyond mean-field DCEs, the root-mean-square (rms)deviation with respect to nuclear masses is reduced significantly down to 1.14MeV, which is smaller than those of other successful CEDFs: NL3* (2.96 MeV),DD-ME2 (2.39 MeV), DD-ME$\delta$ (2.29 MeV) and DD-PC1 (2.01 MeV). Moreover,the rms deviation for two-nucleon separation energies is reduced by $\sim34\%$in comparison with cranking prescription.

Global study of beyond-mean-field correlation energies in covariant energy density functional theory using a collective Hamiltonian method