A time-dependent discrete variable representation method

We have developed a novel discrete variable representation (DVR) method whe re not only the amplitudes of the wave function at the DVR grid points can change but also the positions of these grid points can move as a function o f time. Since the Gauss-Hermite basis set is used as the primitive basis fu nctions (PBF) to construct the DVR basis set, the method appears as a semic lassical one with a small number of PBF but converges very fast to the quan tum with an increasing PBF. We have investigated the dynamics of a reaction coordinate with or without coupling to a heat bath of harmonic oscillators to demonstrate the validity of the proposed method. The excellent agreemen t of the calculated tunneling probabilities with numbers obtained by tradit ional quantum grid method (FFT) and the fast computability of the present m ethod compared to the latter are remarkable. (C) 2000 American Institute of Physics. [S0021-9606(00)30113-1].