Negative imaginary potentials in time-dependent quantum molecular scattering

Abstract

Reflection or wrap around of the wavefunction from the grid edges is often avoided in time-dependent quantum mechanical calculations by using a negative imaginary potential (NIP) near the grid edges. The stability of the various (second-order differencing, split operator, Chebyshev polynomial and short iterative Lanczos) schemes used, in conjunction with the NIP, for time evolution is discussed using collinear (He, H ₂ ⁺ ) collisions as a test case. It is shown that the difficulties encountered in obtaining converged reaction probability [P ^R (E)] values at high energies for the system when NIPs are used, are avoided by using a properly chosen damping function externally.