In all calculations we take and , where is the initial rotational angular momentum quantum number of O and its initial vibrational angular momentum. An incoming Gaussian wave packet is used to describe the initial state in the entrance channel. Because the quantum number is not determinable experimentally, we do a calculation for each initially possible and average over all these calculations. For more details regarding parameters for the calculations, basis set sizes, etc. we refer to Ref. th:anth1998. Note that for , the maximum was increased to 99.
In order to initiate the Chebychev expansion we use the method described in Ref. th:gray1999. To begin the iteration in Eq. (5) above, and are required. We take to simply be the real part of the complex initial wave packet. Since the initial condition is complex, must be evaluated according to where is the imaginary part of the initial condition.  The square root operator is also expanded in terms of Chebychev polynomials. Usually, 200 polynomials are sufficient to converge this expansion.