Valence-bond theory of linear Hubbard and Pariser-Parr-Pople models

Abstract

The ground and low-lying states of finite quantum-cell models with one state per site are obtained exactly through a real-space basis of valence-bond (VB) diagrams that explicitly conserve the total spin. Regular and alternating Hubbard and Pariser-Parr-Pople (PPP) chains and rings with $N_e$ electrons on $N\left(\le 12\right)$ sites are extrapolated to infinite arrays. The ground-state energy and optical gap of regular $U=4\mathrm{}\left|t\right|\mathrm{}$ Hubbard chains agree with exact results, suggesting comparable accuracy for alternating Hubbard and PPP models, but differ from mean-field results. Molecular PPP parameters describe well the excitations of finite polyenes, odd polyene ions, linear cyanine dyes, and slightly overestimate the absorption peaks in polyacetylene ${\left(\mathrm{CH}\right)}_x$. Molecular correlations contrast sharply with uncorrelated descriptions of topological solitons, which are modeled by regular polyene radicals and their ions for both wide and narrow alternation crossovers. Neutral solitons have no midgap absorption and negative spin densities, while the intensity of the in-gap excitation of charged solitons is not enhanced. The properties of correlated states in quantum-cell models with one valence state per site are discussed in the adiabatic limit for excited-state geometries and instabilities to dimerization.