Here, |Φ a i ⟩ = T 1 |Φ 0 ⟩ and |Φ ab ij ⟩ = T 2 |Φ 0 ⟩ are singly and doubly excited determinants, respectively. H N in the Eq.( ) is the normal-ordered four-component Dirac-Coulomb (DC) Hamiltonian unless otherwise mentioned and the subscript c implies that only the connected terms survive in the contraction between H N and T , which ensures the size-extensivity of the method. Once the cluster amplitudes are solved, the coupled-cluster correlation energy of a many-electron system can be computed using the following equation: