[^2]. Results for the energy of H$_{16}$ divided by 2 are shown as squares in Fig. \[fig1\]. OP-NOFT-0 works equally well for this longer chain. The total energy at dissociation is twice that of H$_{8}$, and the slightly increased binding energy per atom at equilibrium arises from an increase in the correlation energy, as expected from more effective screening in the larger system.

The N$_2$ molecule is a severe test for correlated electronic structure methods because of its triple-bond. Our results are compared to other methods in Fig. \[fig3\]. The OP-NOFT-0 curve is above the CASSCF reference at all interatomic separations and deviates little from it until $~2$Å, beyond which the deviation increases with separation until it stabilizes at $~5$Å. OP-NOFT-0 correctly dissociates the molecule into two non-interacting fragments, but cannot capture correlations among the 3 electrons with unpaired spin in each isolated atom. It captures only intra-shell correlations among electrons of opposite spin, consistent with seniority restricted CI calculations in Ref. [@Bytautas2011].

![Dissociation curve of the N$_2$ molecule. \[fig3\]](N2_twographs.pdf){width="\columnwidth"}

It is interesting to note that in all the systems studied, the positivity condition $(2,2)$ was found to be sufficient at near equilibrium up to intermediate separations dominated by dynamic 