A flexible new analytical representation for the internuclear potential energy of a diatomic molecule is proposed and tested. The new model may be thought of as a generalization of the prototypical Lennard-Jones (2n,n) function, with the form V(R)=D-e[1-(R-e/R)(n)e(-beta(z)z)](2), where z=(R- R-e)/(R+R-e) is a dimensionless radial distance variable which approaches 1 as R -->infinity. This form explicitly incorporates the theoretically predicted attractive inverse-power asymptotic behavior V(R)=D-C-n/R-n associated with most potential energy curves. This "modified Lennard-Jones" (MLJ) function is tested against other flexible forms for the potential energy by performing nonlinear least-squares fits both to known numerical potential curves and to spectroscopic line positions. (C) 2000 American Institute of Physics. [S0021-9606(00)00909-0].