Time‐dependent discrete variable representations for quantum wave packet propagation

We present an efficient method for exact wave function propagation with several degrees of freedom based on time‐dependent discrete variable representations (TD‐DVR) of the evolution operator. The key idea is to use basis sets that evolve in time according to appropriate reference Hamiltonians to construct TD‐DVR grids. The initial finite basis representation is chosen to include the initial wavefunction and thus the evolution under the bare zeroth order Hamiltonian is described at each time by a single DVR point. For this reason TD‐DVR grids offer optimal representations in time‐dependent calculations, allowing significant reduction of grid size and large time steps while requiring numerical effort that (for systems with several degrees of freedom) scales almost linearly with the total grid size. The method is readily applicable to systems described by time‐dependent Hamiltonians. TD‐DVR grids based on the time‐dependent self‐consistent field approximation are shown to be very useful in the study of intramolecular or collision dynamics.