Solving the Dirac equation, using the large component only, in a Dirac-type Slater orbital basis set

We solve the Dirac equation by solving the two-component energy-dependent equation for the large component that results from the elimination of the small component. This requires for every occupied orbital the diagonalization of a Hamiltonian. Advantages are, however, that these Hamiltonians are all bounded from below, unlike the Dirac Hamiltonian, and that only a basis set for the large component is needed. We use Dirac-type Slater orbitals, adapted from solutions to the hydrogen-like atom. This offers the perspective of performing relativistic calculations to the same accuracy as non-relativistic ones, with a comparable number of basis functions.