Transfer matrices, band structures, and localized orbitals in quasi-one-dimensional systems

Abstract

We present a scheme that—within certain approximations—connects the single-particle energies of defect-induced localized orbitals in quasi-one-dimensional systems to the band structures of related periodic structures. The mathematical foundations for the scheme are based on a transfer-matrix formulation of the Schrödinger equation. In contrast to most earlier approaches based on transfer matrices, the present formulation is directly related to parameter-free methods for electronic-structure calculations with more or less well-converged basis sets. Thereby, the transfer matrices get a dimension that in the general case is larger than two and it is, in addition, shown that a complete description of the system requires the introduction of a complementary set of matrices. However, in the ultimate formulation of the scheme, neither set of matrices needs to be defined. The scheme is illustrated through three examples, for which the band structures of the periodic structures have been obtained using a first-principles, density-functional, full-potential LMTO method for helical polymers. The three examples include trans-polyacetylene and polycarbonitrile as examples of conjugated polymers as well as the hydrogen-bonded polymer hydrogen fluoride. In both cases, we study solitonic defects. As the last example, we study selenium helices with special emphasis on defects involving local distortions of the dihedral angle. We finally discuss the approximations and limitations of the approach and will give some simple estimates of their implications. © 1996 John Wiley & Sons, Inc.