Correlated states in linear polyenes, radicals, and ions: Exact PPP transition moments and spin densities

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Abstract
The low‐lying eigenstates ψn of the Pariser–Parr–Pople (PPP) model for polyenes with N≤11 carbons are found exactly as linear combinations of nonorthogonal covalent and ionic valence‐bond (VB) diagrams. We extend diagrammatic VB theory to normalize ψn efficiently and to evaluate exactly transition moments, spin densities, and other matrix elements within subspaces of fixed total spin S. Charge orthogonality in the VB basis results in a block‐diagonal overlap matrix whose evaluation is rapid for linear combinations of over 105 diagrams. We obtain S=0 and 1 states of all‐trans decapentaene (N=Ne =10), S=1/2 states of nonatetraenyl (N=Ne =9), S=0 states of its anion and cation, and spin densities through undecapentaenyl (N=Ne =11), all with standard molecular PPP parameters. Correlation effects on excitation energies, on transition moments, and on spin densities are contrasted with one‐electron Hückel results and compared with data on finite polyenes and polyacetylene. Standard PPP parameters successfully describe the 2 1Ag and 1 1Bu excitations of alternating even polyenes, their reduced oscillator strengths, the 1 1A↔1 1B transition of regular odd anions, and the nearly uniform negative and positive spin densities of regular polyene radicals.