Nuclear energy density-functional theory (DFT) provides a microscopic framework for predicting nuclear masses with sub-MeV accuracy by incorporating pairing correlations and deformation effects. A key ingredient for reaching this precision is the inclusion of dynamical correlation energies (DCEs), comprising rotational correction energy (RCE) and vibrational correction energy (VCE). These quantities are typically estimated at the mean-field level using phenomenological formulas based on the cranking approximation. In this work, we benchmark these phenomenological approximations of the DCEs against quantum-number projected-generator coordinate method (PGCM) calculations based on covariant DFT for odd-mass chromium isotopes, including even-even counterparts for comparison. We find that the phenomenological RCEs generally agree with exact angular-momentum projection (AMP) results, except in cases where symmetry restoration significantly shifts the energy minimum, leading to large deviations. The phenomenological VCEs typically range from 0.7 to 1.1 MeV and are consistent with PGCM results, but tend to be overestimated by up to 0.6 MeV for some odd-mass isotopes. These findings highlight the limitations of phenomenological formulas, particularly for odd-mass systems, and underscore the need for more accurate treatments to improve the predictive power of DFT for nuclear masses beyond the sub-MeV level.

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• Binding energy & masses
• Nuclear many-body theory
• Nuclear structure & decays
• 39 ≤ A ≤ 58
• Nuclear density functional theory