Quantum critical phenomena and stability of atomic and molecular ions

In this review we discuss quantum phase transitions and the mapping between symmetry breaking of electronic structure con® gurations at the large-dimension limit and mean-® eld theory of phase transitions. We show that the ® nite size scaling method can be used for the calculations of the critical parameters of the few-body Schr È odinger equation. In this approach, the ® nite size corresponds to the number of elements in a complete basis set used to expand the exact eigenfunction of a given Hamiltonian. The critical parameters such as the critical nuclear charges will be used to explain and predict the stability of atomic and molecular negative ions. For N-electron atoms with 2 ø N ø 86, results show that, at most, only one electron can be added to a free atom in the gas phase. However, doubly charged atomic negative ions might exist in a strong magnetic ® eld.