We report the implementation of the four-component spinor relativistic equation-of-motion (EOM) coupledcluster method within the single- and double-excitation approximation to calculate the ionization potential of molecules. We have applied this method to calculate vertical ionization potentials of the molecules XH (X = F, Cl, Br, I) along with Cl₂ and Br₂ in their closed-shell configuration. We have also presented intermediate results using the second-order many-body perturbation-theory level in the EOM framework to understand the role of electron correlation. All the calculated values are compared with the available experimental results. Our results are found to be in good agreement with sophisticated experiments, and relative deviation of less than 1% is achieved for all the considered systems.