Lower bounds on the ground-state energy and necessary conditions for the existence of bound states: The few-body problem

We consider a positive diatomic molecule consisting of N electrons and two nuclei and obtain some results that exhibit scaling properties of the adiabatic energy Ead---the ground-state energy with the nuclei fixed---under changes in the charges, and we obtain lower bounds on Ead. In particular, with the use of available numerical results for Ead for a single electron in the Coulomb field of two fixed nuclei with charges ZAe and ZBe, we show that composite bound states cannot be formed for N=1 and ZA+ZB{≥}3 nor for N=2 and ZA=ZB{≥}3, results not too far from the true lower limits.