Quantum dynamics on adaptive grids : the moving boundary truncation method

A novel method for integrating the time-dependent Schrödinger equation is presented. The moving boundary truncation (MBT) method is a time-dependent adaptive method that can significantly reduce the number of grid points needed to perform accurate wave packet propagation while maintaining stability. Hydrodynamic quantum trajectories are used to adaptively define the boundaries and boundary conditions of a fixed grid. The result is a significant reduction in the number of grid points needed to perform accurate calculations. A variety of model potential energy surfaces are used to evaluate the method. Excellent agreement with fixed boundary grids was obtained for each example. By moving only the boundary points, stability was increased to the level of the full fixed grid. Variations of the MBT method are developed which allow it to be applied to any potential energy surface and used with any propagation method. A variation of MBT is applied to the collinear H+H₂ reaction (using a LEPS potential) to demonstrate the stability and accuracy. Reaction probabilities are calculated for the three dimensional non-rotating O(³P)+H₂ and O(³P)+HD reactions to demonstrate that the MBT can be used with a variety of numerical propagation techniques.