Polarizability and second hyperpolarizability of open-shell π-conjugated compounds from spin projection method calculations

The Löwdin spin projection technique has been applied to the calculation of the polarizability (α) and second hyperpolarizability (γ) of polyacetylene (PA) chains bearing neutral soliton or charged polaron defects. For both types of systems, α and γ smoothly evolve when successive spin contaminations are removed and converge towards a non-spin-contaminated value. Comparisons between the α and γ of these open-shell systems and their corresponding closed-shell analogs, i.e. regular PA chains and PA chains bearing a positively charged soliton, demonstrate the dual role of spin pairing and charge on the linear and non-linear responses of π-conjugated systems.