Relativistic equation-of-motion coupled-cluster method for the double-ionization potentials of closed-shell atoms

We report the implementation of the relativistic equation-of-motion coupled-cluster method to calculate the double-ionization spectra (DI-EOMCC) of the closed-shell atomic systems. This method is employed to calculate the principal valence double-ionization potential values of He and alkaline-earth-metal (Be, Mg, Ca, Sr, and Ba) atoms. Our results are compared with the results available from the NIST database and other $\mathit{ab}\mathit{initio}$ calculations. We have achieved an accuracy of $\sim 0.1\%$, which is an improvement over the first-principles $T$-matrix calculations [Y. Noguchi et al., J. Chem. Phys. 123, 144112 (2005)]. We also present results using the second-order many-body perturbation theory and the random-phase approximation in the equation-of-motion framework, and these results are compared with the DI-EOMCC results.

Figure 1

Diagrammatic form of the $R_2$ and $R_3$ operators. Lines with down and up arrows denote the occupied and unoccupied orbitals, respectively. An arrow with a circle means a detached occupied orbital.

Figure 2

Diagrams contributing to the $2h$ block.

Figure 3

Diagrams contributing to the $3h$-$1p$ block.

Figure 4

Relative deviations in percent from the NIST values.