Critical phenomena in isoelectronic diatomic sequences—the 14-electron sequence

A theory of isoelectronic molecules which describes stable and metastable members of a sequence has been developed. To achieve this synthesis, it has been necessary to require that the total electronic energy surface E(R,Z,Z') for the sequence contain critical points—that is, values of the nuclear charges Z and Z' at which energy minimum, maximum [at R_e(min) and R_e(max)], and horizontal inflection points occur. For ground state sequences a primary physical source of these extreme points is the screened, coulombic repulsion of like-charged atomic centers in the diatomics. With this realization, we can write analytical forms that have the correct scaling behavior and which properly model the screened, coulombic repulsion for E along certain straight-line trajectories in the (Z,Z') plane. This leads to the observation that R_e(max) values diverge logarithmically in λ-like transitions wherever the screened coulombic repulsion becomes small as the nuclear charges vary along those trajectories. At the horizontal inflection points the E surface contains A₂ folds, as required by Thom's theorem for analytical surfaces containing one control parameter. Within the isoelectronic sequence molecular subgroups have been noted and explained in terms of the underlying atomic shell structures of the molecules' constituent atoms. Using input data for seven stable molecules together with the analytical surface selected for study, we have estimated the equilibrium bond distances R_e(min), dissociation energies D_e(min), and harmonic force constants E⁽²⁾(min) for 18 other neutral and charged species.