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We present here a formulation of the electronic ground-state energy in termsof the second order reduced density matrix, using a duality argument. It isshown that the computation of the ground-state energy reduces to the search ofthe projection of some two-electron reduced Hamiltonian on the dual cone of$N$-representability conditions. Some numerical results validate the approach,both for equilibrium geometries and for the dissociation curve of N$_2$

The electronic ground-state energy problem: A new reduced density matrix approach