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 configurations at the large-dime nsion limit and mean-held theory of phase transitions. We show that the fin ite size scaling method can be used for the calculations of the critical pa rameters of the few-body Schrodinger equation. In this approach, the finite size corresponds to the number of elements in a complete basis set used to expand the exact eigenfunction of a given Hamiltonian. The critical parame ters such as the critical nuclear charges will be used to explain and predi ct the stability of atomic and molecular negative ions. For N-electron atom s with 2 less than or equal to N less than or equal to 86, results show tha t, 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 magne tic held.