We demonstrate behaviors of correlation effects in the calculations of atomic properties through two commonly employed many-body methods, namely the multiconfiguration Dirac-Hartree-Fock (MCDHF) and the relativistic coupled-cluster (RCC) methods. Particularly, we have benchmarked excitation energies, electric dipole (E1) matrix elements, magnetic dipole hyperfine structure constants ($A_{\text{hf}}$), and isotope shift (IS) constants in the singly ionized magnesium (${\mathrm{Mg}}^{+}$) systematically at different levels of approximation of both methods. We have also estimated the E1 polarizability of the ground state and lifetimes of the excited states using the E1 matrix elements from both methods. All these results are compared with the experimental values wherever available. We find that the computed results agree well with each other with a few exceptions; in particular, the $A_{\text{hf}}$ and IS constants from the RCC method are found to agree with the measurements better. This comparison analysis would be useful in evaluating the above-discussed properties in other atomic systems using the MCDHF and RCC methods more reliably.

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• Atomic & molecular structure
• Electron correlation calculations for atoms & ions
• Fine & hyperfine structure
• Configuration interaction
• Coupled cluster
• Electronic structure
• First-principles calculations
• Quantum chemistry methods