Time-dependent scattering calculations usually involve propagating a complex wave packet. Chemical reaction probabilities are obtained by appropriate analysis of the evolving wave packet. One analysis technique involves accumulation and Fourier analysis of time-dependent final state amplitudes in the asymptotic product region[2,3,4]. For simplicity we refer to this as the ``asymptotic analysis method.'' Analysis techniques can also be based on calculating the flux through a more general surface dividing reactants and products[5,6,7].
Recently, wave packet approaches that use only real algebra have been suggested[8,9,10,11,12]. The approach we use  may be viewed as a time-dependent variation on ``time-independent wave packet'' approaches[8,9,10], or an extension to reactive scattering of ideas in Ref. . A Chebyshev iteration[9,11,13] is used to propagate the real part, and reaction probabilities are obtained with a variation on the asymptotic analysis method[2,3,4].
Our main aim is to show that flux-based methods may also be used with real wave packets, which makes the real wave packet approach much more flexible. We also provide motivation for this result by showing the relationship between asymptotic analysis and flux-based methods.
Sec. 2 shows that the asymptotic analysis method is identical to a flux-based T-matrix method of Ref.  for obtaining state-resolved reaction probabilities in one particular limit. It further shows that a flux based method to calculate total reaction probabilities[5,6] is a special case of both. Sec. 3.1 outlines the main ideas behind the real wave packet propagation, and Sec. 3.2 shows how to calculate both total and state-resolved reaction probabilities using flux analysis with real wave packets. Sec. 4 applies the flux formalism with real wave packets to the D + H2 DH + H (J=0) reaction and compares with results obtained with asymptotic product analysis. Sec. 5 summarizes, notes the relative merits of asymptotic analysis and flux-based analysis methods, and points to an interesting new application of our approach.