A new hybrid method is presented in which modified Shepard interpolation of a potential energy surface is combined with time-dependent quantum dynamics calculations. The propagation of a wave packet composed of fixed-width Gaussian functions allows a one-to-one mapping between the quantum dynamics results and a small number of quantum trajectories, allowing electronic structure theory calculations to be performed preferentially in dynamically-important regions. The method is designed for demonstrable convergence of the quantum dynamics results from ab initio calculations. The photodissociation of NOCl is used as a test case. (C) 2010 Elsevier B. V. All rights reserved.