The electronic structures of polyparaphenylene (PPP), polyacetylene (PA), and their derivatives with small energy gaps have been studied by the Hückel and MNDO crystal orbital methods. The effect of nuclear relaxation and heteroatomic substitution on the energy gaps (Eg) have been taken into account by compelete geometry optimization using periodic boundary conditions as opposed to earlier cluster based calculations. Calculations were done on the following polyacetylene derivatives: polypyrrole (PPy), polythiophene (PT), polyisothianaphthene (PITN), poly (5,5’-bithiophene methenyl) (PBTM, 11, X=S, R=H, m1=m2=1), and poly (5,5’-bipyrrole methenyl) (PBPM, 11, X=NH, R=H, m1=m2=1). Energetics and band gaps for the two isomeric forms, the quinoid and aromatic structures of PPy and PT, are discussed and critically compared with previous calculations. Perturbational molecular orbital theory is invoked to explain the narrower Eg for PITN, PBTM, and PBPM, relative to that of PA. Calculations for PPP derivatives {m-polybenzo[b]thiophene (PBT,5b), polybenzo[b,f]thieno[3,4-c]thiophene (PBTT, 5a, X=S), and polybenzo[b,f]pyrrolo[3,4-c]pyrrole (PBPP, 5a, X=NH)} show that the Eg of some of these polymers is substantially smaller than that of PPP. Comments on ways to stabilize structures with desired small energy gaps are made. A correlation of the Eg with heteroatom perturbation and geometrical relaxation is given. It is found that Eg is controlled not by aromatic vs quinoid contributions, but by the geometrical and heteroatomic effects on the frontier orbitals of the polymer.

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System size dependence of the free energy surface in cluster simulation of nucleation Electron energy state dependence on the shape and size of semiconductor quantum dots J. Appl. Phys. 90, 6416 (2001); 10.1063/1.1412578Theoretical study of the size dependence of ionization potential and electron affinity of metallic clustersThe total electronic energy of a special class of finite clusters is calculated using the backfolding theorem and the properties of the trapezoidal quadrature. The resulting formula consists of a linear term, proportional to the size of the molecule and the remainder. It is found that the remainder is an irregular (or periodic) function of the cluster's size. As a consequence the validity of the extrapolation of properties from smallsize clusters to infinite solid state is questioned.

Torsional potential curves for simple infinite polysilane derivatives are calculated by various ab initio and semiempirical crystal orbital methods. The comparison includes polysilane, poly(difluorosilane), poly(methylsilane), poly(dimethylsilane), and poly(diethylsilane) and the two simplest carbon analogues polyethylene and poly(tetrafluoroethylene) as well as polygermane. Generally, the potential curves are more flat going from the carbon compounds to the silicon compounds. For polysilane the all-trans conformation is comparable or less stable in energy than the gauche conformation. The addition of bulkier side groups locks in the all-trans conformation relative to the gauche conformation. Connection of energetic with the thermochromic properties of polysilanes is discussed. A vibrational analysis and the corresponding phonon dispersion curves of polysilane with both all-trans and helical conformations are given for the first time.

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