We present exact results for a diatomic molecule described by the Ande
rson model which includes both on-site and intersite hybridization, as
well as the on-site Coulomb repulsion between f- and conduction elect
rons (the Falicov-Kimball term). The mixed valence behaviour is demons
trated in the subspace with N = 2 electrons, while the competition bet
ween Kondo screening and RKKY interaction is investigated for N = 4 el
ectrons. The Falicov-Kimball term restricts the range of stability of
the mixed valence state, and increases the values of the Kondo tempera
ture and of the crossover temperature to disordered f-moments in the K
ondo and RKKY regime, respectively, while it increases the temperature
above which the ferromagnetic correlations between f-moments are dest
abilized for N = 3 electrons.