Numerical solution of the radial Dirac equation in pseudopotential construction

In the present work we study numerical solution of the radial Dirac equation in a specific case - ab-initio pseudopotential generating process - which is needed within the electronic structure calculations using a Density Functional Theory (DFT) combined with a pseudopotential method. We give a brief introduction to DFT, derive the radial Dirac and Schrodinger equations, show how to solve them both for a given energy and as an eigenvalue problem using a known asymptotic behavior of the solution. Next we compare the nonrelativistic and relativistic eigenvalues for one electron atom. Finally we state a few words about the computer implementation.