next up previous
Next: Method of Computing Cross Up: Theory and Computational details Previous: Parallel Method


Initial Conditions

In all calculations we take $j_i=1$ and $\nu_i=0$, where $j_i$ is the initial rotational angular momentum quantum number of O$_2$ and $\nu_i$ 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 $\Omega$ is not determinable experimentally, we do a calculation for each $\Omega_i$ initially possible and average over all these calculations.[82] For more details regarding parameters for the calculations, basis set sizes, etc. we refer to Ref. th:anth1998. Note that for $J=35$, the maximum $j$ 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, ${\bf q_0}$ and ${\bf q_1}$ are required. We take ${\bf q_0}$ to simply be the real part of the complex initial wave packet. Since the initial condition is complex, ${\bf q_1}$ must be evaluated according to ${\bf q_1} =
{\bf H_s} \cdot {\bf q_0}- (1- {\bf H_s}^2)^{1/2}\cdot {\bf p_0}$ where ${\bf p_0}$ is the imaginary part of the initial condition. [61] The square root operator is also expanded in terms of Chebychev polynomials. Usually, 200 polynomials are sufficient to converge this expansion.


next up previous
Next: Method of Computing Cross Up: Theory and Computational details Previous: Parallel Method
Anthony J. H. M. Meijer 2000-10-05