Reactive Quantum Scattering in Two Dimensions

In an effort to develop a more efficient time dependent approach for calculating scattering matrix elements, absorbing boundary conditions are combined together with the channel packet method. The channel packet method relies on calculating two Moller states: one representing reactants and one representing products. The time dependent correlation function between the two Moller states is efficiently computed by individually propagating the Moller states using absorbing boundary conditions as they exit the interaction region of the potential. As a Moller state evolves in time, it will be attenuated by the absorbing boundary conditions without reflecting of the edge of the grid thereby permitting the use of a much smaller grid. The Fourier transform of the correlation function is then used to compute scattering matrix elements. The efficiency of the combination of the channel packet method with absorbing boundary conditions is demonstrated in one dimension through application to the one dimensional square well. The one dimensional square well has an analytic solution which provides a benchmark for testing both the efficiency and accuracy of this approach. Scattering matrix elements obtained using the channel packet method with absorbing boundary conditions are in excellent agreement with the analytic solution. The new approach converges to the correct, analytic solution as well as provides a dramatic reduction in grid size. The reduced grid size results in a faster, more efficient computation.