Quantum chemical investigation on the structure and first hyperpolarizability for N‐substituted [ n ]cyclacene

Six N‐substituted [ n ]cyclacene ( n  = 5, 6, 7,…,10) molecules were designed to study the relationship between the structure and first hyperpolarizability. Their static first hyperpolarizabilities ( β 0 ) were obtained by MP2/6‐31 + g(d) level. Two interesting relationships between the β 0 value and the structure have been found: (1) The β 0 value increases with the increase of the number n when n is odd: 3155 ([5]cyclacene) < 48,905 ([7]cyclacene) < < 393,444 ([9]cyclacene), and when n is even: 357,620 ([6]cyclacene) < 618,608 ([8]cyclacene) < 3,513,644 a.u. ([10]cyclacene). (2) The β 0 values (in the range of 357,620 ~ 3,513,644 a.u.) of the N‐substituted [ n ]cyclacene (when n is odd) are much larger (in the range of 3155~393,444 a.u.) than that of the N‐substituted [ n ]cyclacene (when n is even). Furthermore, their frequency‐dependent β (−2ω; ω, ω) and β (−ω; ω, 0) (ω = 0.005, 0.01, and 0.0239 a.u.) were also estimated by Møller–Plesset perturbation/6‐31 + g(d) level. Among the frequency‐dependent β (ω), [10]cyclacene has the largest β (−ω; ω, 0) and β (−2ω; ω, ω) to be 1.2 × 10 8 (ω = 0.01) and 2.9 × 10 7 a.u. (ω = 0.005 a.u.), which are much larger than the static β 0  = 3.5 × 10 6  a.u. by 34 and 8 times. Our present work may offer a new idea in the design of high‐performance tubiform nonlinear optical materials . Copyright © 2011 John Wiley & Sons, Ltd.