Accounting for electron–electron and electron–lattice effects in conjugated chains and rings

Abstract

Minimum total energy calculations are reported for π-conjugated hydrocarbons including neutral (ground, 1 1Bu, 2 1Ag) and doped (1+ and 2+) chains and rings with up to eight carbon atoms. Two models are considered; first, a semiempirical π-electron Hamiltonian that includes both electron–electron (Hubbard) and electron–lattice (Longuet-Higgins–Salem) interactions, and second, an accurate ab initio complete-active-space self-consistent-field (CASSCF) treatment that includes the π-electron correlation effects most important in determining the bond geometries. The results of the ab initio calculations can be used to estimate the phenomenological parameters entering the semiempirical Hamiltonian and thus to obtain quantitative predictions of bond geometries from the semiempirical treatment. The two models yield qualitatively the same results for the bond geometries in all states considered, and the changes in bond geometry following excitation from ground to doped or excited states find natural interpretation in terms of short-chain limiting behaviors of soliton and polaron distortions familiar for longer chains. Further, the absolute values and sensitivities of the phenomenological parameters of the semiempirical model to various fitting schemes provide an indication of the different roles played by electron–lattice and electron–electron interactions in determining the properties of these systems. While electron–lattice interactions are found to be the most important factor in determining bond geometries, particularly in the ground and doped states, electron–electron interactions play an important and subtle role in determining the bond geometries and relative energetic orderings of the excited states.