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We analyze the size and alternation dependence of the second static hyperpolarizability γ(0;δ,N) of N-site Hückel rings with transfer integrals t(1±δ). Regular (δ=0) rings lead to a simple γ(0;0,N)̃ N5 dependence, while alternating (δ≳0) chains show a δ−6 divergence in the band limit. Analytical results for noninteracting electrons clarify the evolution from molecules to polymers, show strong enhancement of γ(0;δ,N) in the region Nδ≊1, and connect previous oligomer and polymer calculations.
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Spano et al. (1993) studied this question.
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