The stability of S-states of unit-charge Coulomb three-body systems: From H− to H2+

High accuracy non-relativistic quantum chemical calculations of the ground state energies and wavefunctions of symmetric three-particle Coulomb systems of the form {m1(±)m2(±)m3(∓)}, m1 = m2, are calculated using an efficient and effective series solution method in a triple orthogonal Laguerre basis set. These energies are used to determine an accurate lower bound to the stability zone of unit-charge three-particle Coulomb systems using an expression for the width of the stability band in terms of g, the fractional additional binding due to a third particle. The results are presented in the form of a reciprocal mass fraction ternary diagram and the energies used to derive a parameterised function g(a3), where a3=m3 (-1)/(m1(-1)+m2(-1)+m3(-1)) is the reciprocal mass of the uniquely charged particle. It is found that the function is not minimal at a3 = 0 which corresponds to ∞H(-) nor is it minimal at the positronium negative ion (Ps(-)) the system with the least absolute energetic gain by association with a third particle; the function g(a3) is minimal at m1∕m3 = 0.49, and a possible physical interpretation in terms of the transition from atomic-like to molecular-like is provided.