TRANSFER-MATRICES, BAND STRUCTURES, AND LOCALIZED ORBITALS IN QUASI-ONE-DIMENSIONAL SYSTEMS

We present a scheme that-within certain approximations-connects the si ngle-particle energies of defect-induced localized orbitals in quasi-o ne-dimensional systems to the band structures of related periodic stru ctures. The mathematical foundations for the scheme are based on a tra nsfer-matrix formulation of the Schrodinger equation. In contrast to m ost earlier approaches based on transfer matrices, the present formula tion is directly related to parameter-free methods for electronic-stru cture calculations with more or less well-converged basis sets. Thereb y, the transfer matrices get a dimension that in the general case is l arger than two and it is, in addition, shown that a complete descripti on of the system requires the introduction of a complementary set of m atrices. However, in the ultimate formulation of the scheme, neither s et of matrices needs to be defined. The scheme is illustrated through three examples, for which the band structures of the periodic structur es have been obtained using a first-principles, density-functional, fu ll-potential LMTO method for helical polymers. The three examples incl ude transpolyacetylene 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 dist ortions of the dihedral angle. We finally discuss the approximations a nd limitations of the approach and will give some simple estimates of their implications. (C) 1996 John Wiley & Sons, Inc.