The Faddeev Random Phase Approximation is a Green's function technique that
makes use of Faddeev-equations to couple the motion of a single electron to the
two-particle--one-hole and two-hole--one-particle excitations. This method goes
beyond the frequently used third-order Algebraic Diagrammatic Construction
method: all diagrams involving the exchange of phonons in the particle-hole and
particle-particle channel are retained, but the phonons are described at the
level of the Random Phase Approximation. This paper presents the first results
for diatomic molecules at equilibrium geometry. The behavior of the method in
the dissociation limit is also investigated
