What is the shape effect on the (hyper)polarizabilities? A comparison study on the Mِbius, normal cyclacene, and linear nitrogen-substituted strip polyacenes

How does the framework shape influence the static polarizability (α0) and the first hyperpolarizability (β0)? This work, for the first time, presents a comparison study by three models: Möbius strip cyclacene with a knot, normal cyclacene without knot, and linear strip. Opening the knot of the Möbius to form the normal cyclacene, it leads to the increase of α0 from 268 to 323 a.u. and β0 increases about three times from 393 to 1049 a.u. Further, opening the normal cyclacene to form the linear strip, α0 increases from 323 to 476 a.u. While β0 as well increases about three times from 1049 to 2814 a.u.