Linearized atomic-cell orbital method for energy-band calculations.

Abstract

A variational principle for the scrR operator appropriate to a polyhedral atomic cell is applied to the case of periodic boundary conditions. The scrR operator extends the radial logarithmic derivative concept to atomic cells of arbitrary shape. The muffin-tin-orbital (MTO) methods of Andersen, valid for local atomic spheres, generalize to a formalism based on polyhedral atomic-cell orbitals (ACO). Each ACO is a solution of the Schr\"odinger equation or modified Dirac equation, in local-density-functional theory, within an atomic polyhedron. The local potential function may be nonspherical. Imposition of periodic boundary conditions leads to a direct generalization of the Korringa-Kohn-Rostoker method, replacing the muffin-tin geometry by the space-filling lattice of Wigner-Seitz polyhedra. A linear cellular method is derived in close analogy to the linear MTO method of Andersen. Energy bands of fcc Cu are computed as a demonstration of the feasibility of the method.