  We present here a formulation of the electronic ground-state energy in terms
of the second order reduced density matrix, using a duality argument. It is
shown that the computation of the ground-state energy reduces to the search of
the 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$_2$.
