Having focused our analysis mostly on the cumulant-based quantities, we briefly circle back to the RDMs themselves to discuss prominent features and their relation to the cumulants. For the sake of clarity, we take minimal basis (STO-6G) H 2 as an illustrative example, since the RDM eigenvalues correspond to the absolute values of the density matrix elements. Being a two-electron system, the block structure is simplified in the singlet such that 1 Γ αα = 1 Γ ββ and only the subblocks related to the 2 Γ αβ portions contribute, while for the triplet state only the 1 Γ αα and 2 Γ αα blocks are non-zero.