At the moment, the algorithm uses a canonical generalized Hartree-Fock reference, which results in much larger and far more sparse determinant spaces. As an example, an H 10 /STO-6G ring with canonical RHF orbitals has a full Hilbert space dimension of 63504, whereas with GHF the full Hilbert space is three times larger with dimension 184756. In any case, the RLCI algorithm is agnostic to the type of reference: if the method can handle a more challenging GHF reference, it can also handle a RHF reference. In Tab. 1, we compare the performance of the RLCI algorithm for a series of hydrogen rings with an interatomic separation of 1.5 Å and an STO-6G basis. This interatomic distance was previously found to exhibit strong correlation in hydrogen rings. Using the GHF reference, fully correlating all electrons, and utilizing rings ranging from 10 to 16 atoms, the full Hilbert space spans from 10 5 to nearly 10 9 determinants. All parameters for the calculations were the same as those used previously, with the exception that the greedy initialization for each trial was done in batches corresponding to 1/10 of the subspace k. As observed in the prototypical cases, only a small percent of the full Hilbert space is necessary to capture a significant portion of the FCI correlation energy. For the H 10 ring, 2% of the Hilbert space is sufficient to capture 98% of the correlation energy. For the H 14 ring, even 0.05% of the Hilbert space is sufficient to capture over 91% of the correlation energy. The results in Tab. 1 are consistent with the observations found for the smaller, prototypical systems.