Chemical potential, Teller's theorem, and the scaling of atomic and molecular energies

Abstract For atoms and homonuclear diatomic molecules, it is argued that the electronic energies have the forms [Formula: see text] and [Formula: see text] [Formula: see text], respectively,where Z is the atomic number, N is the number of electrons, and R is the internuclear distance. By using the Lieb-Simon theorem that the Thomas-Fermi theory is exact in the limit of large atomic number and the Teller theorem that molecules are not bound in the Thomas-Fermi theory, it is then shown, among other results, that the electron-electron repulsion energy for neutral systems has no term in Z2 and that the nucleus-nucleus repulsion energy for neutral molecules is probably [unk](Z5/3). For neutral atoms, it is predicted and verified that the chemical potential (electronegativity) is [unk](Z-1/3) for large Z. Tetrahedral and octahedral molecules are briefly discussed.