On the accuracy of the discretization Techniques in approximate relativistic methods

Several non-singular 2-component methods for relativistic calculations of t he electronic structure of atoms and molecules lead to cumbersome operators which are partly defined in the coordinate representation and partly in th e momentum representation. The replacement of the Fourier transform techniq ue by the approximate resolution of identity in the basis set of approximat e eigenvectors of the p(2) operator is investigated in terms of the possibl e inaccuracies involved in this method. The dependence of the accuracy of t he evaluated matrix elements on the composition of the subspace of these ei genvectors is studied. Although the method by itself appears to be quite de manding with respect to the faithfulness of the representation of the p(2) operator, its performance in the context of the standard Gaussian basis set s is found to be encouragingly accurate. This feature is interpreted in ter ms of approximately even-tempered structure of the majority of Gaussian bas is sets used in atomic and molecular calculations.