Self-consistent full-potential total-energy Korringa-Kohn-Rostoker band-structure method: Application to silicon

The self-consistent full-potential total-energy Korringa-Kohn-Rostoker (KKR) coupled channel equation method for full-potential electronic band-structure determinations is applied to the case of silicon. For efficiency, the coupled channel equations are partially decoupled by using the point group symmetry of each basis atom, and solved on a linear radial mesh by using the Coulomb functions close to the singularity of the potential at the origin. In the KKR energy search, Chebyshev approximations for the scattering matrices as functions of energy save solving the coupled channel equations at many different energies. The results include the self-consistent anisotropic potential, the charge density, the energy band structure, the equilibrium lattice constant, and the bulk modulus. As expected, the energy bands agree well with results from other band-structure methods. We find that the cutoff of the spherical multipole expansion of potential and charge density must be chosen independently of the cutoff for the scattering matrices that determines the dimension of the secular matrix. In the case of silicon, we find that an ${\mathit{l}}_{\max }$ of 8 is sufficient for the potential and charge density, while the scattering matrices need at least ${\mathit{l}}_{\max }$=6. The equilibrium lattice constant converges to the experimental value with increasing ${\mathit{l}}_{\max }$ and the bulk modulus converges to 96 GPa at ${\mathit{l}}_{\max }$=6.