Transition energies of mercury and ekamercury (element 112) by the relativistic coupled-cluster method

The relativistic coupled-cluster method is used to calculate ionization potentials and excitation energies of Hg and element 112, as well as their mono- and dications. Large basis sets are used, with l up to 5, the Dirac-Fock or Dirac-Fock-Breit orbitals found, and the external 34 electrons of each atom are correlated by the coupled-cluster method with single and double excitations. Very good agreement with experiment is obtained for the Hg transition energies, with the exception of the high (≳12 eV) excitation energies of the dication. As in the case of element 111 [Eliav et al., Phys. Rev. Lett. 73, 3203 (1994)], relativistic stabilization of the 7s orbital leads to the ground state of ${112}^{+}$ being 6${\mathit{d}}^9$7${\mathit{s}}^2$, rather than the ${\mathit{d}}^{10}$s ground states of the lighter group 12 elements. The ${112}^{2+}$ ion shows very strong mixing of the ${\mathit{d}}^8$ ${\mathit{s}}^2$, ${\mathit{d}}^9$s, and ${\mathit{d}}^{10}$ configurations. The lowest state of the dication is 6${\mathit{d}}^8$7${\mathit{s}}^2$ J=4, with a very close (0.05 eV) J=2 state with strong ${\mathit{d}}^8$ ${\mathit{s}}^2$ and ${\mathit{d}}^9$s mixing. No bound states were found for the anions of the two atoms.