We begin our analysis with the well-studied dihydrogen molecule. At equilibrium, a single large-weighted configuration corresponds to the HF solution, with electron fluctuations into the doubly-excited space accounting for the bulk of the correlation energy. Upon stretching, this molecular orbital picture becomes inadequate as two equally-weighted configurations come to dominate the ground-state wavefunction. Despite the correlation energy tending towards zero at dissociation (in fact, the singlet and triplet states are isoenergetic, and the UHF energy is exact), the entanglement characteristic of the singlet state does not follow such a trend as mentioned above. As shown in Fig. , this is well-reflected by many of the metrics presently under consideration: 2 γ αβ only has its connected portions survive, 2 δ αβ , captured in both the trace and squared Frobenius norm of 2 ∆. As must follow from the exactness of UCCSD, ⟨S 2 ⟩ UCCSD here does not reflect any spin entanglement. 2 Γ αα takes on no values while the elements of 1 Γ αα contribute to the increasing squared Frobenius norm of 2 ∆ as it approaches 8 at dissociation, the previously derived limit for this system. There is a notable non-monotonicity in the ratio α, which declines as the bond length is stretched beyond 1Å. This ratio does not appear to be applicable beyond models like the Hubbard model, possibly due to the delicate balance between phenomena such as nodeinduced confinement, orbital contractions, and polarization effects that can modulate the kinetic energy in molecular systems. H 4 is a challenging molecule that has been the subject of many studies in a variety of geometric configurations. A previous report has shown that the NOONs are identical for square and rhombic geometric configurations, yet notable differences occur in the underlying electronic structures. Indeed, that report motivated us to look beyond quantities related to 1 Γ. We investigate two reaction coordinates -the P4 rectangular D 2h dissociation into hydrogen dimers and the S4 square D 4h dissociation into hydrogen atoms. In the former, the HF determinant and the lowest energy doubly-excited configuration contribute significantly as the system crosses into the square geometry. There is a region of both spin and spatial frustration as we approach a crossing of the S 0 and S 1 surfaces, alongside a near-degenerate T 1 . 70 Fig. (left) shows that in the singlet ground-state, the 2 ∆ quantities correctly flag the electronically challenging region surrounding the square geometry with lattice parameter approaching 1.06Å (2 Bohr). Spin-symmetry breaking in UCCSD shows similar behavior (though with a slightly wider peak), and we note that at 1.05Å the UCCSD wavefunction is in equal parts of singlet and triplet character (averaging out to ⟨S 2 ⟩ = 1). This is consistent with the open-shell singlet (two electrons in two degenerate orbitals) picture implied by Huckel/MO theory. We again find that the largest eigenvalue of 2 Γ decreases in the square regime. In contrast, these metrics corresponding to the quintet state (shown in the right panel of Fig. ) are all flat. As was the case for H 2 , the energy ratio α does not seem to contain interpretable information here. In the case of the S4 dissociation to separate hydrogen atoms (Fig. ), the 2 ∆ quantities reveal that, in contrast to the P4 coordinate, S4 does not involve a closed-shell region aptly described by mean-field theory (invoking the statistical sense with which we interpret correlation strength, indeed we can describe such a state as weakly correlated). As was the case in P4, the S4 quintet state (Fig. right panel) is always weakly correlated, with all of our investigated metrics -except α -flat-lining. Interestingly, in the singlet case the squared Frobenius norm and the magnitude of the trace of 2 ∆ are the only metrics that increase with lattice parameter; ⟨S 2 ⟩ UCCSD decreases (and appears to plateau at a value less than the maximum value of unity from the P4 coordinate), as do the maximum eigenvalues of the cumulant, albeit ever so slightly. As a brief aside, it has been noted that the S4 model of equivalent side lengths, R S4 , has an identical spectrum of NOONs as some trapezoidal configurations in the C 2v geometry with one side length t 2 and the other parallel side consisting of infinitely separated hydrogen atoms. In the cases of R S4 = 2.0Å and t 2 = 1.793Å, although neither can be considered weakly correlated, the S4 example is known to exhibit additional correlation effects. Metrics based on the NOON spectrum of 1 Γ are unable to detect any difference (in other words, the derived from the 2 ∆ in these examples: the trace of the 2 ∆ evaluates to -0.844 and -0.344 in the S4 and trapezoidal geometries, respectively, while the squared Frobenius norms are 1.37 and 0.52, respectively. Thus, in contrast to the NOONs these 2 ∆-based quantities are able to distinguish between two very different regimes of electron correlation.