We explain the earlier observation that Taylor series expansions of atomic energies essentially terminate after the second-order term if the atoms' ionization energies obey I-n = n(I-1). Our analysis provides some support for the validity of the widely-used electronegativity and hardness formulas 0.5(I + A) and 0.5(I - A), for the atoms in Groups IIA and IVA - VIIIA, oxygen being an exception. (c) 2006 Elsevier B.V. All rights reserved.