3.3 Nonlinear optical (NLO) properties and absorption spectrums
The NLO properties of the studied complexes have been explored by calculating their static first hyperpolarizabilities (β 0), which are given in Table 2. As listed in Table 2, it is noticed that the β 0 values of GYs are less than 0.50 au, whereas the OM3+@GYs complexes show much larger β 0 values in the range of 227–653420 au. Among the OM3+@GYs series, OLi3+@GTY has the largest β 0 value. Note that it has a unique structure where the OLi3 is coplanar (d = 0.000) with GTY.
To investigate whether the first hyperpolarizabilities of these doped systems depend upon the atomic number of M in superalkali unit and the pore size of graphyne subunit, the relationships betweenβ 0 values and different superalkali unit as well as different sized graphyne are illustrated in Figure 5. For the OM3+@GY complexes, the β 0 varies in the order 227 (M = Li) < 4334 (M = K) < 7952 au (M = Na). Undoubtedly, the maximum β 0 value belongs to ONa3+@GY. Upon the combination with OM3, the β 0value of GDY dramatically increases to 224425–278540 au. Different from the case of OM3+@GY, theβ 0 value of OM3+@GDY has no clear dependence on the atomic number of M. Remarkably, OLi3+@GTY has the largest β 0 value up to 653420 au among all the studied complexes (see Figure 5a), which is about 40 and 15 times as large as those of ONa3+@GTY (16246 au) and OK3+@GTY(43713 au), respectively. It indicates the important effect of the atomic number of M on β 0 value of OM3+@GTY (M = Li, Na, and K).
Data in Table 2 and Figure 5b display that the β 0value increases quite rapidly in the order OLi3+@GY< OLi3+@GDY< OLi3+@GTY, demonstrating that the effect of pore size of graphyne on theβ 0 value of OM3+@GYs is significant. Notably, the β 0 value is enhanced by approximate 2880-fold from 227 au (OLi3+@GY) to 653420 au (OLi3+@GTY). Therefore, the selection of GTY with large pore is an effective strategy for enhancing the β 0 of the OLi3-doped graphyne molecules. When ONa3and OK3 are doped into GYs, theβ 0 values of the resulting complexes vary in the sequence of OM3+@GY< OM3+@GTY< OM3+@GDY (M = Na and K). The results suggest that the medium-sized GDY should be a better match for OM3 (M = Na and K) in forming complexes with higher NLO response.
TABLE 2 The first hyperpolarizabilitiesβ 0 (au), transition energies ΔE (eV), oscillator strengths f 0, and difference of dipole moment Δμ (Debye) between ground state and crucial excited state of the GY/GDY/GTY and OM3@(GY/GDY/GTY) (M = Li, Na, and K)