A general self-consistent-field tight-binding linear-combination-of-atomic-orbitals (LCAO) formalism is given for three-dimensional polymers containing many atoms in the elementary cell with all neighbors interacting, taking overlap explicitly into account. This formalism, which corresponds essentially to the formulation given by Roothaan for closed-shell molecules, has been developed with the aid of Hermitian complex matrices. The special cases of nearest-neighbor approximation and of a linear chain are then derived from the general expression obtained. Finally, formulas are given, again in complex-matrix formulation, for the dependence of the energy levels and wave functions of the polymer on the wave number k.

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Two different local-density approximations, the Gáspár-Kohn-Sham and the Perdew-Zunger approximations, of the density-functional method have been used to calculate structural and electronic properties of polyethylene systems with several different dihedral angles. For each system, the CC bond lengths and the CCC and HCH bond angles are optimized simultaneously. All the parameters appear to be strongly coupled with torsional freedom and vary with the change in dihedral angle in a pattern similar to that of the total energy. The total energy has an absolute minimum for the planar zigzag conformation but a distinct local minimum for the quasistable helical conformation. Another minimum occurs in the energy curve close to this gauche minimum. The calculated valence and conduction bands are discussed and compared with other theoretical calculations and experiment. ͓S0163-1829͑96͒02239-4͔

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Articles you may be interested inCrystal orbital calculation of coupled Hartree-Fock dynamic (hyper)polarizabilities for prototype π -conjugated polymers Erratum: "Assessment of conventional density functional schemes for computing the polarizabilities and hyperpolarizabilities of conjugated oligomers: An ab initio investigation of polyacetylene chains" [J.Assessment of conventional density functional schemes for computing the polarizabilities and hyperpolarizabilities of conjugated oligomers: An ab initio investigation of polyacetylene chains

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