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The ground-state fermion second-order reduced density matrix (2-RDM) is determined variationally using itself as a basic variable. As necessary conditions of the N-representability, we used the positive semidefiniteness conditions, P, Q, and G conditions that are described in terms of the 2-RDM. The variational calculations are performed by using recently developed semidefinite programming algorithm (SDPA). The calculated energies of various closed- and open-shell atoms and molecules are excellent, overshooting only slightly the full-CI energies. There was no case where convergence was not achieved. The calculated properties also reproduce well the full-CI results.

Variational calculations of fermion second-order reduced density matrices by semidefinite programming algorithm