Ordinary LCAO-MO theory allows for the ab-initio definition of alpha and beta parameters occurring in the Huckel theory including overlap of simple sigma homonuclear systems. One- and two-electron terms not included in Huckel theory are explicitly considered. When such correction terms are neglected in the very spirit of Huckel theory, simple calculation in the hydrogenic approximation for the ground states of H-2(+), H-2, He-2(+), He-2 at the corresponding bond lengths shows serniquantitative agreement with experimental or accurate theoretical results for the bond energies, providing a simple and clear physical picture of the nature of the chemical bond. (C) 2002 Elsevier Science B.V. All rights reserved.