Based on a three-parameter molecular orbital-type pair-potential function, we have proposed a generalized interatomic pair-potential function. This new function has been demonstrated to be able to describe accurately and adequately the potentials of the metastable diatomic dications (e.g., He-2(++), BeH++, AlH++), and the ground states of covalent bonding systems (e.g., H-2, Si-2, HCl, NO, LiH, HeH+, and He-2(+)), ionic bonding systems (e.g., NaCl), and van der Waals weakly binding systems (e.g., rare-gas, alkaline-earth, group 12, rare-gas metal dimers, and rare-gas halides). (C) 2014 Elsevier B.V. All rights reserved.