Self-Consistent Full-Potential Relativistic Korringa Kohn-Rostoker Coupled Channel Equation Method for the Determination of the Electronic Structure of Solids

A new implementation of local density functional theory for periodic solids, which is based on the full -potential extension of the Korringa-Kohn-Rostoker (KKR) method, is presented and applied. The Schrodinger equation for a periodic anisotropic potential is solved using multiple scattering theory, which leads to a secular equation with nonlinear energy dependence. The energy search thus requires multiple evaluations of the scattering matrices at many different energies. The use of Chebyshev function approximations for the scattering matrices as a function of energy is found to significantly reduce the computing time for the energy search without any loss of precision in contrast to the usual linearization approximation. The method is efficient and precise as shown for the case of silicon. It is found that the cutoff of the spherical multipole expansion of potential and charge density can be chosen independently of the cutoff for the wave functions. Very good convergence of the multipole expansions is obtained with an l_{rm max } of 8 for the potential and electron charge density and an l_{rm max} of 6 for the wave functions. With these values the energy bands of the self-consistent charge density are stable up to 0.01 eV and total energy calculations lead to values for the equilibrium lattice constant and the bulk modulus that agree very well with experiment and other local density calculations. Further, the method is generalized to include all relativistic effects. The Dirac equation for a general anisotropic 4 by 4 potential is solved inside Voronoi polyhedra surrounding each basis atom. As illustration, the relativistic method is used to calculate the self-consistent electronic band structure, the Fermi surface, the equilibrium lattice constant and the bulk modulus of the fcc transition metals Pd, Ir, Pt, and Au, as well as the self-consistent electronic band structure of the semiconductors GaAs, InSb, and InN and the equilibrium lattice constant and the bulk modulus of InSb. If the cutoff of the multipole expansions of the wave functions is at least l_{ rm max} = 4, the agreement of the calculated equilibrium lattice constants and bulk moduli with experiment is comparable to that obtained with other local density approaches.