Band structure of one-dimensional polymers via an SCF-Xα scattered-wave method. I. General formalism

A model of the multiple-scattering type is presented to study the band structure of periodic one-dimensional conductors. The potential is of a modified muffin-tin form: spherically averaged inside the atomic spheres, cylindrically averaged outside a cylinder enclosing the polymer and spatially averaged in between. Taking advantage of the periodicity of the system and using the Born-Kármán periodic boundary conditions the occurring infinite hypermatrix of the problem can be brought into a block-diagonal form. Thus the formalism includes only matrices of the order of the unit cell. The necessary steps for carrying out self-consistent calculations are discussed. In this connection a theorem is proved which allows the normalization of a scattered wave orbital function for an arbitrary outer surface.