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Large scale ab initio calculations of the electric contribution (i.e. theelectric field gradient) to the electric quadrupole hyperfine interactionconstants $B$ for the $5p~^2P_{3/2}$ state in $^{109}$Cd$^+$ ion and the$5s5p~^3P_{1,2}$ states in neutral $^{109}$Cd atom were performed. To probe thesensitivity of $B$ to different electron correlation effects, six sets ofvariational multi-configuration Dirac-Hartree-Fock and relativisticconfiguration interaction calculations employing different strategies werecarried out. The calculated electric field gradients, together withexperimental values of $B$, allow us to extract a new value of the nuclearelectric quadrupole moment $Q$($^{109}$Cd) = 0.634(22) b which is about 5\%larger than the recommended value [Stone, At. Data Nucl. Data Tables 111-112, 1(2016); Pyykk\"{o}, Mol. Phys. 116, 1328 (2018)]. Efforts were made to providea realistic theoretical uncertainty for the final $Q$ value based onstatistical principles and correlation with the magnetic dipole hyperfineinteraction constant $A$.

Ab initio calculations of the hyperfine structure of 109Cd, 109Cd+ and reevaluation of the nuclear quadrupole moment Q(109Cd)