Analytical evaluation of pseudopotential matrix elements with Gaussian-type solid harmonics of arbitrary angular momentum

An efficient formalism for evaluating pseudopotential matrix elements with Gaussian-type solid harmonics of arbitrary angular momentum is presented. It is based on the tensor coupling technique, which is especially well suited for treating Gaussian-type solid harmonics of arbitrary angular momentum. Closed analytical expressions are derived for the matrix elements as well as for their nuclear displacement derivatives. The efficiency of the implementation into our new parallel density functional program PARAGAUSS and the quality of the pseudopotential approach is tested for a set of representative molecules and cluster models. To this end the results of pseudopotential calculations are compared to those of nonrelativistic and scalar-relativistic all-electron calculations.