Correlated π-electronic states: Pyrene, 16-site polyene, and D2h symmetry adaptation

Abstract

Diagrammatic valence bond (DVB) theory is a general approach to electron correlations in quantum cell models that conserve total spin. VB diagrams are a convenient many-electron basis for combining spin, point-group, and other symmetries in oligomers with a large but finite basis. Half-filled Hubbard or Pariser–Parr–Pople (PPP) models with 16 sites have ∼34.7×106 singlet diagrams. Improved DVB methods yield exact low-lying states of the 16-site polyene in C2h symmetry and of pyrene in D2h symmetry. Several generalizations of symmetry adaptation are necessary for large bases, including new rules for linearly independent basis vectors and an iterative method for Hamiltonian matrix elements that avoids overlap and inversion. The number and dimensions of the disjoint invariant subspaces Sm encountered in symmetry adaptation depend on the connectivity. D2h symmetry adaptation is much simpler for acenes than for pyrene, linear stilbene, or polyphenyls. Standard PPP parameters account well for the 11 pyrene states identified in linear and two-photon spectra. Polyenes to N=16 show systematic deviations, with the 2 1Ag threshold decreasing less rapidly with N than experiment. We discuss perturbations that break electron-hole, parity, or point-group symmetry on the low-energy states, test the second π-electron approximation for pyrene, and comment on the feasibility of DVB for N=18 or 20 sites.