Calculation of an atom–surface scattering model using the S-matrix KVP

For the first time, we solve the model elastic atom–surface scattering problem with the S-matrix Kohn variational principle (KVP). The KVP consists of Hamiltonian matrix equations over a basis that includes both scattering and L² functions. For ease of evaluation, we choose the L² basis to be a pointwise representation (e.g. a discrete variable representation). Also for efficient solution, we use the reduced dimensional eigenbasis found by diagonalizing the Hamiltonian in the pointwise representation using the procedure of successive diagonalization and truncation. It is found that even upon further optimization, the KVP method appears to be too slow for solving large-scale single energy problems.The method is demonstrated to be efficient however, if the S-matrix elements for many different energies is desired.