Jacobi coordinates formulation

The nonadiabatic real wave paeket state-to-state approach introduced here started by numerically solving the mapped Sehrodinger equation for nuclei motion, formulated in terms of the produet Jacobi coordinates... 

The starting point of this approach is solving the time-dependent Schrodinger equation formulated in terms of reactant Jacobi coordinates R, r, rj, 0i, 02, 9)... 

The coordinate problem referred to above for reactive scattering is that the Jacobi coordinates (ra,Ra) that are natural for describing the reactants A-hBC are not appropriate for describing the products, AB-hC. There are several ways to deal with this situation, but most of the recent progress in reactive scattering has been based on the formulation [75] in which the Jacobi coordinates for the various arrangements (i.e. A-hBC, AB-hC, AC+B) are all used simultaneously. For the collinear case of Fig. 1.2, for example, the expansion for the wavefunction in this approach is... 

It should be clear from Fig. 2b (Part I) that either set of mass-scaled Jacobi coordinates alone provides a complete description of the available collinear coordinate space. However, it should be equally clear that while Ra and Va are better suited to describing translational and vibrational motions in the reactant channel, Rc and Tc are more appropriate for a corresponding description of the products. It therefore seems natural to retain both sets of coordinates at once, using each set for convenience as required. Moreover, formulations of quantum reactive scattering based on this idea are quite easy to construct. Indeed a comprehensive account of such a formulation, for the... 

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