Normalization of the Gaussian binning trajectory method for indirect reactions

The method of Gaussian weighted trajectories combines the classical description of gas-phase chemical reactions and Bohr quantization of final fragment vibrations. In practice, trajectories are assigned Gaussian statistical weights such that the closer the final vibrational actions to integer values, the larger the weights. This approach, called classical trajectory method with Gaussian binning (CT-GB) in the following, is a practical implementation of classical S matrix theory (CSMT) in the random phase approximation. However, CSMT is non unitary and consequently, the most utilized version of CT-GB is not strictly normalized to unity. In other words, the sum of product and re-formed reagent state populations is not exactly equal to one. The purpose of this work is to show that normalizing these populations to unity should significantly improve the quality of the predictions for indirect reactions. This finding is illustrated from calculations on the D+ + H2 reaction.