What is the Shape Effect on the (Hyper)polarizabilities? A Comparison Study on the Moebius, Cyclic, and Linear Nitrogen-Substituted Polyacenes

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How does the framework shape influence the static polarizability (alpha₀) and the first hyperpolarizability (beta₀)? This work, for the first time, presents a comparison study at the MP2/6-31+G(d) level, by using the nitrogen-substituted polyacenes as models: the Moebius strip with a knot, the cyclic strip without knot, and the linear strip. Opening the knot of the Moebius strip to form the cyclic strip, it leads to the increase of the alpha₀ from 268 au to 323 au and the beta₀ value increases about three times from 393 (Moebius) to 1049 au (cyclic). Further, opening the cyclic strip to form the linear strip, the alpha₀ value increases from 323 au to 476 au. While the beta₀ value as well increases about three times from 1049 (cyclic) to 2814 au (linear). The changes in the static (hyper)polarizabilities are well explained by the geometrical differences among the Moebius, cyclic, and linear nitrogen-substituted polyacenes.