We have investigated the dynamics of a reaction coordinate with or without coupling to a heat bath of harmonic oscillators using a novel time-dependent discrete variable representation (TDDVR) method. The proposed method is semiclassical in nature, theoretically rigorous, and rather straightforward to implement. Excellent agreement of the computed tunneling probabilities and time-averaged tunneling rates with the corresponding exact results demonstrates the efficacy of the proposed approach. Most of the semiclassical calculations reported here have been performed by using classical force, whereas, in a few cases, the quantum force (QF) has been taken into account. It appears that among the TDDVR formulations, it was the first time we have derived a rigorous form of QF from the first principle. (C) 2003 American Institute of Physics.