Knot-isomers of Moebius Cyclacene: How Does the Number of Knots Influence the Structure and First Hyperpolarizability?

Four large ring molecules composed by 15 nitrogen-substituted benzene rings, named as "knot-isomers of Moebius cyclacene", i.e. non-Moebius cyclacenes without a knot (0), Moebius cyclacenes with a knot (1), non-Moebius cyclacenes with two knots (2), and Moebius cyclacenes with three knots (3), are systematically studied for their structures and nonlinear optical properties. The first hyperpolarizability (beta_0) values of these four knot-isomers structures are 4693 (0) < 10484 (2) < 25419 (3) < 60846 au (1). The beta_0 values (60846 for 1, 10484 for 2 and 25419 au for 3) of the knot-isomers with knot(s) are larger than that (4693 au for 0) of the knot-isomer without a knot. It shows that the beta_0 value can be dramatically increases (13 times) by introducing the knot(s) to the cyclacenes structures. It is found that introducing knots to cyclacenes is a new means to enhance the first hyperpolarizability.