Molecular dissociation energies characterized by number of electrons and equilibrium bond length

Abstract

For a homonuclear diatomic molecule with a fixed nuclei, the input information in solving the Schrödinger equation for the ground-state energy at equilibrium is the atomic number Z of the constituent atoms plus the equilibrium bond length R e. As the atomic energy is determined by Z and R e → ∞, the dissociation energy D, conveniently divided by N 2, where N = 2 Z is the total number of electrons, can be expressed as D N 2 = d( Z 2, e), where e is chosen from scaling arguments as e = R e Z 1/3. Plots are presented for a variety of homonuclear diatomic molecules, plus some heteronuclear molecules, to show that over a significant range of d the dependence on the variable e is weak. This dependence appears to be reduced further, for the lightest molecules considered, if Z is replaced by the von Weizsäcker inhomogeneity kinetic energy. Some account is also taken of the fact that homonuclear diatomic molecules may not bind beyond some critical atomic number Z c⩾ 100.