| Recently, considerable attentions have been paid to synthesize excellent nonlinear optical(NLO) materials, due to their potential applications in the field of optoelectronics technology. The theoretical calculation plays an important role in designing and synthesizing efficient nonlinear optical materials. It is well-known that the second-order nonlinear optical response is a measure is a standard to measure the merit of nonlinear optical materials. Results indicate that the organic systems with excellent second-order nonlinear optical response mainly include: the use of molecules with extended π-electron systems, the donor-π-conjugated bridge-acceptor(D-π-A) model, twisted π-electron systems, helical conjugated molecule and so on.Interestingly, the M?bius Cyclacenes with a knot is a special π conjugated system. For example, the Hückel rule(4n+2) is not suitable for the M?bius Cyclacenes. Significantly, the effect of interesting and twisted π conjugated systems on the charge distribution and nonlinear optical properties has been investigated. Our group has explored the effect of knot number and the effect of shapes on the structure and(hyper)polarizability.The helical complexes have been of great interest to chemists and researchers because of wide applications in materials science, nanotechnology and optical and electronics devices. Since Abe’s group investigated the second NLO response of the spirolinked push-pull polyenes, and the helical conjugated structure may have the excellent transparency and NLO properties. Recently, a series of alternating pyridine-pyrimidine oligomers with helical cavities have been synthesized. Champange’s group has explored their NLO properties and found that the nonlinear optical responses remain small with the increasing chain length in the absence of substituents, while the first hyperpolarizability can be enhanced by adding substituents. On the other hand, investigations have revealed that the alkali doping effect can significantly enhance the NLO response of planer or tubular π-conjugated systems.Thus, in present work, we have investigated the relationship between the structure and nonlinear optical properties of M?bius and helical π conjugated systems. Firstly, we mainly design six M?bius Cyclacenes containing 13 to 18 benenzne rings, and calculate the relationship between the NLO properties and structure. Secondly, we select alternating pyridine-pyrimidine(Py-pym) oligomers with twelve heterocycles as parent molecule, and design three new complexes by doping two alkali metals M(M=Li, Na and K) into the helical cavities of the Py-pym oligomers(Scheme), focusing on the relationship between the structure and NLO properties of the pyridine-pyrimidine-2M(Py-pym-2M).1. In present work, six [n]MC(n=13-18, n is the number of benzenoid rings) were systematically investigated to explore the size-dependent effects on structures, electro-optical properties and frontier molecule orbits(FMO). According to the dihedral angles(C-C-C-C), the un-twisted area and twisted area are defined, respectively. The twisted area mainly distributes on seven or eight benzenoid rings for [n]MC(n=13-18). Further, the polarizability(α0) and first hyperpolarizability(β0) of [n]MC(n=13-18) were calculated with three density functional methods(BHand HLYP, Cam-B3 LYP and M06-2X). Results show that the α0 values increase linearly with increasing the number(n) of benzenoid rings. Significantly, the β0 values are increased to zigzag with increasing the number(n) of benzenoid rings. Interestingly, when n is even(14, 16 and 18), the electron transfer is from the twisted area to the un-twisted area, but the electron transfer is from the un-twisted area to the twisted area when n is odd(13, 15 and 17).2. Three helical complexes pyridine-pyrimidine-2M(Py-pym-2M) were designed by doping two alkali metals M(Li, Na and K) into the helical cavities. Results show the structures of Py-pym-2Na and Py-pym are very similar, and the interaction energy of Py-pym-2Na is smaller than those of Py-pym-2Li and Py-pym-2K. It indicates the Na atom possesses an appropriate size to fit in the helical cavities of Py-pym. Significantly, due to the alkali-metal-doped effect, the first hyperpolarizability(β0) values of Py-pym-2M(M=Li, Na and K) enhance almost 264-620 times larger than that of Py-pym. Specially, the Py-pym-2Na has the largest β0 value. |