A comparison of time‐dependent and time‐independent quantum reactive scattering—Li+HF→LiF+H model calculations

Reactive scattering probabilities are computed over a wide range of collision energies for a model system based on the Li+HF→LiF+H reaction using both grid based time‐dependent and time‐independent quantum mechanical methods. The computations are carried out using a fixed Li–F–H angle which is chosen to be that at which the barrier to the chemical reaction is lowest. The calculated reaction probabilities for this system display many sharp features as a function of energy which are ascribed to scattering resonances. The time‐independent calculations have been carried out on a very dense energy grid, thus permitting detailed comparison between time‐independent and time‐dependent methods (in the latter case, a single computation of the wave packet dynamics provides information on the energy dependence over a given energy range). The results show that the time‐dependent calculations are capable of reproducing even the sharpest resonance features computed using the time‐independent method. The time‐dependent techniques are conceptually very simple and therefore easily implemented. The results presented also demonstrate that the grid based time‐dependent quantum mechanical methods used here are able to describe threshold energy dependence of reaction probabilities where the exit channel kinetic energy is effectively zero. The nature of some of the resonance structures are investigated by computing the time‐independent continuum wave functions at the ‘‘resonance’’ energies thus mapping out the nodal structure of the wave functions. The good agreement between time‐independent and time‐dependent methods is shown to be maintained when a centrifugal barrier is added to the potential to simulate the effect of nonzero orbital angular momentum.

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