  We report our successful implementation of the full fledged 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 those available measurements, which are
taken from the National Institute of Science and Technology database (NIST). We
also present results using the second order many-body perturbation theory
(MBPT(2)) and random phase approximation (RPA) 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 .
