BKLT equations for reactive scattering. I. Theory and application to three finite mass atom systems

The BKLT equations for reactive scattering are considered in detail, both from a formal and computational point of view. The equations are very attractive because they do not require any matching of wave functions. It is shown how these equations may be solved for a general collinear three-finite mass atom system. Special care is taken to treat subleties in the theory arising from restrictions on the ranges of the vibrational coordinate of the various diatoms due to the skewing angle being less than 90°. In addition, the structure of the equations is explored in detail since this has significance for their optimum solution. It is found that the structure of the equations for asymmetric systems leads to important redutions in the size of the matrix which must be inverted within the present, nonpropagative method. Other solution methods are also discussed to some extent. Finally, the method is illustrated by an application to the H+H2 exchange reaction with the Porter–Karplus potential surface. The results obtained agree well with those obtained earlier by Diestler using a close coupling, propagation procedure.