A completely general three-dimensional (3D) method of generating energies and gradients from a prior list of ab initio energies is developed. The method assumes the minimum amount of input data given a priori, i.e., only the potential energy surface (PES). The method introduced may be cast into either a local or global regime. In the local regime, the domain of the PES is sorted, broken into small regions, and interpolation of the energy and gradients takes place in these regions. In the global regime, the energies of the PES are used to formulate a single global interpolant. (C) 2002 Elsevier Science B.V All rights reserved.