  We report an implementation of the core-valence separation approach to the
4-component relativistic Hamiltonian based equation-of-motion coupled-cluster
with singles and doubles theory (CVS-EOM-CCSD), for the calculation of
relativistic core-ionization potentials and core-excitation energies. With this
implementation, which is capable of exploiting double group symmetry, we
investigate the effects of the different CVS-EOM-CCSD variants, and the use of
different Hamiltonians based on the exact 2-component (X2C) framework, on the
energies of different core ionized and excited states in halogen (CH$_3$I, HX
and X$^-$, X = Cl-At) and xenon containing (Xe, XeF$_2$) species. Our results
show that the X2C molecular mean-field approach [Sikkema et al., J. Chem. Phys.
2009, 131, 124116], based on 4-component Dirac-Coulomb mean-field calculations
($^2$DC$^M$) is capable of providing core excitations and ionization energies
that are nearly indistinguishable from the reference 4-component energies for
up to and including fifth-row elements. We observe that two-electron integrals
over the small-component basis sets yield non-negligible contributions to core
binding energies for the K and L edges for atoms such as iodine or astatine,
and that the approach based on Dirac-Coulomb-Gaunt mean-field calculations
($^2$DCG$^M$) are significantly more accurate than X2C calculations for which
screened two-electron spin-orbit interactions are included via atomic
mean-field integrals.
