The above analysis shows the fact that intramolecular charge transfer in the C18 derivatives is unidirectional along the principal axis, and their first hyperpolarizability is anisotropic as a result. The unit sphere representation of the hyperpolarizability tensor proposed by Tuer et al. is a popular technique for intuitively visualizing the anisotropy of molecular hyperpolarizability . As can be seen from the upper panel of Figure , the four molecules exhibit completely different first hyperpolarizability tensors corresponding to their respective non-zero Cartesian component of the hyperpolarizability. The hyperpolarizability tensor of H-C18-H is less evident, which is consistent with its relatively small first hyperpolarizability. The hyperpolarizability tensor of H-C18-NO2 is slightly more pronounced than that of H-C18-H, and its direction is in the negative x-axis direction. The NH2-C18-H and NH2-C18-NO2 exhibit significant Further comparative analysis revealed that the diagonal tensors βyyy(-2ω;ω,ω) of H-C18-H and βxxx(-2ω;ω,ω) of NH2-C18-H, H-C18-NO2, and NH2-C18-NO2 are the components that contribute the most to non-zero Cartesian components due to charge transfer along the principal axis, as shown in Table . Therefore, we plotted the density isosurface of the βyyy(0;0,0) tensor ( (0;0, 0) We decompose the diagonal tensor component of the first hyperpolarizability in the principal axis of each molecule into the contributions from its constituent units to investigate the structural origin of their response characteristics. The decomposed first hyperpolarizability values of each structural unit are plotted in Figure . Due to the calculation errors, there are slight differences that can be ignored between the first hyperpolarization of each molecule calculated by the FF method (in Table ) and the sum of the values of each unit of the molecule (in Figure ). The mall negative value of Since the molecular hyperpolarizability of direct experimental observations are usually the dynamic value measured in an external field at a certain frequency, we also calculated the frequency-dependent first hyperpolarizability under the incident light. At the three external frequencies we are focusing on, the β0(-2ω;ω,ω) is enlarged by perturbation of the external field, and higher frequency can induce larger value. The NH2-C18-NO2 is more sensitive to the external fields and exhibits extremely significant β0(-2ω;ω,ω) than other molecules under the action of high-frequency case. For example, under an external electric field with a wavelength of 1460 nm, the β0(-2ω;ω,ω) of NH2-C18-NO2 relative to that of H-C18-H increases sharply from 8.6 times in zerofrequency limit to 16.2 times.