A generalization of the rotating bond order model potential is discussed. The new functional representation is used for fitting the ab initio potential energy values of the H+H-2 system and the main features of a LEPS potential energy surface for the N+N, system, For H+H-2 we analyze the accuracy obtained when fitting the ab initio potential energy values using different functional representations. For N+N-2 we examine the deviation of some dynamic and kinetic properties calculated on the new model potential from those obtained from the original LEPS.