  The second-order reduced density matrix method (the RDM method) has performed
well in determining energies and properties of atomic and molecular systems,
achieving coupled-cluster singles and doubles with perturbative triples (CC
SD(T)) accuracy without using the wave-function. One question that arises is
how well does the RDM method perform with the same conditions that result in
CCSD(T) accuracy in the strong correlation limit. The simplest and a
theoretically important model for strongly correlated electronic systems is the
Hubbard model. In this paper, we establish the utility of the RDM method when
employing the $P$, $Q$, $G$, $T1$ and $T2^\prime$ conditions in the
two-dimension al Hubbard model case and we conduct a thorough study applying
the $4\times 4$ Hubbard model employing a coefficients. Within the Hubbard
Hamilt onian we found that even in the intermediate setting, where $U/t$ is
between 4 and 10, the $P$, $Q$, $G$, $T1$ and $T2^\prime$ conditions re
produced good ground state energies.
