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The indirect nuclear spin-spin coupling tensor, $\mathbf J$, between mercurynuclei in Hg-containing systems can be of the order of few kHz and one of thelargest measured. We conduct an analysis of the physics behind the electronicmechanisms that contribute to the one- and two-bond couplings $^n {\mathbfJ}_{\mathrm{Hg}-\mathrm{Hg}}$ ($n=1, 2$). We performed calculations for$J$-couplings in X$_2^{2+}$ and $X_3^{2+}$ ions ($X$ = Zn, Cd, Hg), withinpolarization propagator theory, using the random phase approximation (RPA) andthe pure zeroth order approximation (PZOA), with Dirac-Hartree-Fock (DHF) andDirac-Kohn-Sham (DKS) orbitals, both at four-component and ZORA levels. We showthat the "paramagnetic-like" mechanism contribute with more than 99.98\% to thetotal isotropic component of the coupling tensor. By means of an analysis ofthe molecular and atomic orbitals involved in the total value of the responsefunction, we find that the $s$-type valence atomic orbitals have a predominantrole in the description of the coupling. This fact allows us to develop aneffective model from which quantum electrodynamics (QED) effects on$J$-coupling in the aforementioned ions can be estimated. The estimated QEDcorrections were found in the interval $(0.7; ~ 1.7)$\% of the totalrelativistic effect on isotropic one-bond $^1 {\mathbf J}$ coupling and fromthe interval $(-0.2; ~ -0.4)$\%, in Zn-containing ions, to $(-0.8; ~ -1.2)$\%,in Hg-containing ions, of the total isotropic coupling constant in the studiedsystems. We also show that estimated QED corrections cast a visible dependenceon the nuclear charge $Z$ of each atom $X$ in the form of a power-law $\proptoZ^5$.

Relativistic and QED corrections to one-bond indirect nulcear spin-spin couplings in X$_2^{2+}$ and X$_3^{2+}$ ions (X = Zn, Cd, Hg)