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

Abstract

The low-lying eigenstates ψ_n 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 ψ_n 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=N_e=10), S=1/2 states of nonatetraenyl (N=N_e=9), S=0 states of its anion and cation, and spin densities through undecapentaenyl (N=N_e=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 ¹A_g and 1 ¹B_u excitations of alternating even polyenes, their reduced oscillator strengths, the 1 ¹A↔1¹B transition of regular odd anions, and the nearly uniform negative and positive spin densities of regular polyene radicals.