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

The ground-state fermion second-order reduced density matrix (2-RDM) is det ermined variationally using itself as a basic variable. As necessary condit ions of the N-representability, we used the positive semidefiniteness condi tions, P, Q, and G conditions that are described in terms of the 2-RDM. The variational calculations are performed by using recently developed semidef inite programming algorithm (SDPA). The calculated energies of various clos ed- and open-shell atoms and molecules are excellent, overshooting only sli ghtly the full-CI energies. There was no case where convergence was not ach ieved. The calculated properties also reproduce well the full-CI results. ( C) 2001 American Institute of Physics.