Critical charges of simple coulomb molecular systems: One‐two electron case

We consider some Coulomb systems with several infinitely massive centers of charge Z and one or two electrons: (Z,e), (2Z,e), (3Z,e), (4Z,e), (2Z,e,e), and (3Z,e,e). It is shown that the physical, integer charges Z = 1,2,… do not play a distinguished role for the total energy and for the equilibrium configuration of a system, giving no indication of a charge quantization. By definition, a critical charge Z_cr for a given Coulomb system (nZ,e) or (nZ,e,e) is a charge which separates the domain of the existence of bound states from the domain of unbound states (the domain of stability), the continuum (the domain of instability). For all the above‐mentioned systems critical charges Z_cr as well as equilibrium geometrical configurations are found. Furthermore, an indication to a branch point singularity at Z = Z_cr with exponent 3/2 was obtained. It is demonstrated that in the domain of the existence the optimal geometrical configuration for both (nZ,e) at n = 2,3,4 and (nZ,e,e) at n = 2,3 corresponds to the Platonic body. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012