Interatomic potentials at short range using Madelung's equations

Interatomic potentials at short range are investigated starting from the united atom electron density. Prior work has utilised time independent Rayleigh-Schrodinger perturbation theory, adapted to overcome difficulties with convergence of the power series in internuclear distance, and has been confined to diatomic species. This work presents a time dependent approach, based on Madelung's equations, in which the electron density evolves continuously from that of the united atom to the density of the polyatomic system; no power series is involved, there are no convergence difficulties and the approach is applicable to polyatomic systems. Electronic separation and interaction energies are calculated and compared to previous calculations. Some triatomic and tetratomic arrays of hydrogen atoms are examined and three and four body interaction terms estimated.