A Dirac all-electron basis and spin-orbit coupled projector implementation of the Projector Augmented Wave Method for atomic systems

The Projector Augmented Wave Method (PAW) [1] provides accurate numerical approximations to the exact eigenfunctions and eigenvalues of the Kohn-Sham equations for large-scale ab-initio electronic structure calculations of molecules and solids, for which exact calculations are impractical.;Relativistic and spin-orbit effects are significant for valence electrons of magnetic and semimetal fourth-row, and of all fifth- and sixth-row elements of the periodic table. Prior to any molecular or solid calculation with the PAW method, one must construct robust sets of projector functions for each of the constituent atomic species. To capture the essential physics of these effects in atoms, we have developed a method to incorporate relativistic and spin-orbit effects into the construction of these PAW projector functions.;The primary description of relativistic electrons is provided by the Dirac equation. It is characterized by 4-component solutions with intrinsic spin. To obtain the benefits of a Dirac formalism without the difficulty of numerically solving the Dirac equation for molecules and solids, we derive a Schrodinger-like PAW Hamiltonian that incorporates relativistic effects by formally investigating the nonrelativistic limit of the Dirac equation.;To demonstrate the accuracy of our results, we compare orbital densities, eigenvalues, and logarithmic derivatives from our method with exact Kohn-Sham results for representative p- and d-block elements.;[1] Peter E. Blochl, Phys. Rev. B vol. 50, num.24: 17953-17979.