S-matrix version of the Hulthén–Kohn variational principle for quantum reactive scattering using finite elements

The finite element (FE) method can be applied to solve inelastic and reactive scattering problems for triatomic systems. We use an S-matrix version of the Hulthen–Kohn variational principle for a three-dimensional scattering problem. The asymptotic wavefunction is described by analytical functions and the interaction part by a combination of finite element and discrete variable representation (DVR) functions. Translational and vibrational coordinates are described by FEs and for the angular part a DVR-discretization is used. The FE method is used in order to calculate eigenfunctions for the interior region of the potential at each given DVR-angle and from this set of functions the full three-dimensional eigenfunctions are calculated and are used as a new basis for scattering. The grid is chosen such that it covers all reaction channels and the calculations are done by using only one set of Jacobi coordinates. Results obtained by choosing different FE-discretizations, raising the number of elements and increasing the number of internal three-dimensional eigenfunctions, are compared.