We present in detail the construction procedure of two high quality global potential energy surfaces that have recently been used in quasiclassical and quantum dynamics studies for the reaction N(D-2)+H-2--> NH+H. The procedure is based on the reproducing kernel Hilbert space method to interpolate high-level multireference configuration interaction ab initio calculations using augmented polarized triple zeta basis sets. A particular molecular coordinate system has been adopted to treat the nonadditive three body interaction as well as to guarantee the triangle inequalities of three molecular bond lengths and permutation symmetry of the two hydrogen atoms. A new radial reproducing kernel that remains finite at short distances while decaying to zero at large distances has been introduced, especially, for treating the molecule in the linear H-N-H configurations. Moreover, a robust procedure has been devised to handle the cusp in the two-body H-2 interaction associated with the 1 A" potential energy surface. The resulting surfaces are smooth, accurate, efficient to evaluate, exactly reproducing the input data upon which they are based and represent a significant improvement over previous surfaces for this reaction. (C) 2001 American Institute of Physics.