Scalar-relativistic spline augmented plane-wave method using a Douglas Kroll transformation in coordinate representation

Abstract

A scalar-relativistic Hamiltonian, which contains all relativistic corrections up to second order in the fine structure constant, is derived with coordinate representation of the first order Douglas Kroll transformation. In addition to the correction of second order in the fine structure constant, this Hamiltonian contains the exact relativistic kinetic energy as well as the exact relativistic potential correction up to terms linear in the external potential. Based on this Hamiltonian, we develop a scalar-relativistic extension of the Spline Augmented Plane-Wave method, and show that the matrix elements with the new operator can be evaluated elegantly when using an alternative basis of Spline functions. As a first test we investigate solid silver and gold. By comparing the energies of the core states with the solutions of the radial Dirac equation we find that the stabilization of the s levels are slightly overestimated. Even smaller deviations from the Dirac energies are found for higher angular momentum. By comparing the valence band structure with the results for other scalar-relativistic operators, which can be used in a variational context, we find the new operator superior in all aspects: s-type bands are reproduced quite well, and again bands which are dominated by higher angular momenta behave even better. On the contrary, the results obtained with simpler scalar-relativistic Hamiltonians are unsatisfactory.