A scalar relativistic full-potential LCAO method

We present a new scalar relativistic formulation for the full-potential linear-combination-of-atomic-orbitals method based on the density-functional theory. Three approximations are introduced to overcome computational difficulty. The first is to consider only the large component of the four-component spinor, neglecting the small component. The second is to neglect the energy dependence in the Hamiltonian reduced for the large component. The third is to replace the material-dependent potential with the atomic potential in relativistic corrections. After the three approximations, we identify the mass-velocity and Darwin terms and also the spin-orbit coupling, where the latter is to be omitted according to the definition of the scalar relativistic formulation. The computational effort of the present method is reduced considerably in comparison with that of the fully relativistic method, being almost the same as that of the nonrelativistic method. We apply the present method within the local-density approximation to several diatomic molecules with heavy elements, crystalline Au, and crystalline InSb. The results are improved considerably in comparison with the nonrelativistic results. The calculated structural properties are in good agreement with the fully relativistic results and also with the experimental results. The calculated electronic properties are also improved considerably in comparison with the nonrelativistic results and are also in good agreement with the fully relativistic results except for the effect due to the spin-orbit coupling.