Correlated states in finite polyenes: Exact PPP results

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Abstract
Valence bond (VB) diagrams provide a convenient basis for correlated states in systems with one valence state per site. The exact Pariser–Parr–Pople (PPP) solution, including all configuration interactions, is presented for octatetraene (OT), a cyanine dye, and various cyclic systems. We demonstrate rapid computer generation of symmetry adapted VB basis functions, of transformation coefficients due to electron transfer, and of iterative solutions of sparse matrices for any choice of spin-independent intersite interactions. The 2 1Ag state of OT is correctly placed for standard Ohno parameters. The π-electron bond orders and charges of correlated states are contrasted to Hückel and approximate PPP solutions. The length dependence of the strong 1 1Ag→1 1Bu transition is found for even chains and rings of up to N = 8 sites. Extrapolations as N−1 yield a limiting PPP gap around 3 eV, or about 1 eV above the absorption maximum in polyacetylene, the nominally infinite polyene. The role of correlations in narrow-band organic solids and the extension of VB methods to larger systems are discussed.