Relativistic equation-of-motion coupled-cluster method: Application to closed-shell atomic systems

We report our successful implementation of the relativistic equation-of-motion coupled-cluster (EOMCC) method. This method is employed to compute the principal ionization potentials (IPs) of closed-shell rare-gas atoms, He-like ions, Be-like ions, along with Na${}^{+}$, Al${}^{+}$, K${}^{+}$, Be, and Mg. Four-component Dirac spinors are used in the calculations, and the one- and two-electron integrals are evaluated using the Dirac-Coulomb Hamiltonian. Our results are in excellent agreement with available measurements, which are taken from the National Institute of Science and Technology database. The accuracies of the calculations are estimated to be within one half of a percent for He-like and Be-like ions and 1% for the heavier systems. We also present results using the second-order many-body perturbation theory and random-phase approximation in the EOMCC framework. These results are compared with those of EOMCC at the level of single and double excitations in order to assess the role of the electron correlation effects in the intermediate schemes considered in our calculations.