Numerical solution of the radial Dirac equation in pseudopotential construction

Details Numerical solution of the radial Dirac equation in pseudopotential construction Numerical solution of the radial Dirac equation in pseudopotential construction

2007-10-17

arxiv.org/abs/0710.3408v2

Physics

Atomic Physics

Bachelor thesis, 35 pages, typos corrected

Scientific paper

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.

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