An approach for the construction of accurate potential energy surfaces for reaction rate calculations is presented. It employs Shepard interpolation with reference points randomly selected from range of geometries relevant for the reaction rate. Quantum dynamics calculations, which use the multiconfigurational time-dependent Hartree approach and flux correlation functions to obtain thermal rate constants, monitor the convergence of the potential energy surface with increasing number of reference points. As a test of the approach, the H + CH4 --> H-2 + CH3 reaction is studied and the analytic Jordan-Gilbert potential energy surface is reproduced by the interpolation scheme. About 40 reference points are required in the interpolation to obtain a converged interpolated surface which reproduces the thermal rate constants with errors smaller than 20%. (C) 2003 American Institute of Physics.