The ground-state energy of atomic and molecular ions and its variation with the number of electrons

Abstract

The ground-state energy E of atomic and molecular ions is formally a unique functional of the ground-state electron density ρ(r), but the functional is not known. However, for atomic ions, the Hamiltonian is uniquely specified once the atomic number Z and the number of electrons N are given. Thus E = E(N,Z) for such atomic ions. In this work, attention is therefore focussed first on modelling this quantity, which, for given N, can certainly be calculated from the Schrödinger equation for Z ≥ N. Of particular interest are the possibilities of usefully specifying (∂E/∂N)_z and (∂²E/∂N²)_z for integral values of N, these derivatives then being related to the chemical concepts of electronegativity and hardness respectively. The generalization to diatomic molecular ions is also briefly discussed.