Design of natural collision coordinates to describe dissociation of polyatomic molecules

We introduce a set of conditions to be satisfied by natural collision coordinates in order to enable the nonseparable multidimensional bound-continuum Franck-Condon integrals, arising in the quantum theory of collinear polyatomic dissociation processes, to be reduced to one-dimensional integrals. Because these conditions are not satisfied by available natural collision coordinate schemes, we investigate, in detail, the nature of one set of coordinates which satisfies these conditions. It is demonstrated that these coordinates can be chosen to faithfully represent the asymptotic motions of the fragments as well as the motion of the fragments in the Franck-Condon region on the repulsive electronic surface. The kinetic energy operator is displayed as an explicit function of the repulsive surface coordinates. The half-collision boundary conditions are described in a fashion to enable numerical computations of the continuum functions along the reaction coordinate.