Symmetry-breaking structural and charge oscillations are calculated for (C${}_{\mathit{p}}$H${}_{\mathit{p}}$)${}^{\mathrm{-}}$ lattices (p=5 to 9) and used to predict Coulombic expansion coefficients, x-ray photoelectron spectra, and crystallographic features that can be compared with experimental results. Extension of these predictions to other dopant concentrations is provided by derived analytical expressions. The parameters for the infinite lattices are derived from oligomer-ion results obtained from modified neglect of differential overlap calculations. Such calculations on oligomer ions with different parametrizations provide essentially identical changes in charge and structural parameters upon doping and these changes are in excellent agreement with the results of infinite-chain calculations. The degree to which oligomer-ion segments retain the structural parameters of charged arrays for the infinite lattice is remarkable. Derived geometries and charge distributions indicate two different types of charged defects, solitons (or antisolitons) and split solitons (or split antisolitons), and the geometry and charge distribution of the latter defects is shown to correspond to the average of those for two soliton lattices that have a relative shift of two CH units. At least in the absence of an external Coulomb field, soliton and split-soliton lattices for p odd are quasidegenerate, and the lattices for p even consist of alternating sequences of solitons and split antisolitons.

Large oscillations in local chain-axis direction are predicted, which is a consequence of both oscillations in bond angles and the nonequivalence of even (and odd) bond lengths. Including these effects provides predicted Coulombic expansion coefficients that are in good agreement with observations for Na-doped polyacetylene. Much smaller bond-angle oscillations are predicted for anion lattices than for cation lattices, which can be at least partially explained by Coulomb effects. Observed ${}^1$${}^3$C NMR chemical shifts are consistent with predictions for oligomers, and good agreement is obtained between calculated and observed x-ray photoelectron spectra for sodium-doped polyacetylene. Emphasis is placed on the results of crystallographic studies of alkali-metal-doped polyacetylene and on the relationship between the experimentally derived symmetry breaking in interchain packing and the molecular symmetry breaking predicted by theory. Since presently available experimental data are insufficient for complete determination of structure, the present theoretical results can be useful for refinements in the interpretation of these data, as well as for refined crystal-packing calculations.

• Received 2 January 1992

DOI:https://doi.org/10.1103/PhysRevB.46.10515