We introduce new generalized (reverting to) and extended (not reverting to the original) 4-parameter forms of the (8-2) Potential Energy Functional (PEF) of Wang et al. [13], which itself is a modification of the Buckingham exponential-6. The new forms have a tunable, singularity-free short-range repulsion and an adjustable long-range attraction and are capable of describing even the strong ion-dipole interactions present in the halide- and alkali metal-water dimers. They are slightly better than the 4-parameter generalized Buckingham exponential-6 (gBe-6) and of comparable quality with the 4-parameter extended Morse (eM) PEFs introduced recently by us. (C) 2014 Published by Elsevier B.V.