FIGURE 6 Molecular orbitals corresponding to the dominant
electron transitions of the OM3@GYs complexes. H and L
represent the highest occupied molecular orbital (HOMO) and the lowest
unoccupied molecular orbital (LUMO), respectively
It is well-known that for the Li@calix[4]pyrrole electride with
large β 0value,58 the electron
involved in the critical excited state is in the HOMO, which is derived
from the diffuse excess electron cloud of the alkali atom. This means
that the excess electron makes a significant contribution to the large
hyperpolarizability of electride. It can be found from Figure 6 that the
electron clouds of HOMO and crucial excited states of
OM3@(GDY/GTY) are mainly distributed over the
(GDY/GTY)– moiety. Therefore, we speculate that
(GDY/GTY)– unit is the main source of the large first
hyperpolarizability value of the system. Obviously, electronic
transition characteristics of the topic systems are different from those
of electride molecules with excess electrons.
To show the contribution of (GDY/GTY)– to the first
hyperpolarizability of
OM3+@(GDY/GTY)–, we
take
OLi3+@(GDY/GTY)– as
an example and calculate the first hyperpolarizabilities of
(e @GDY)– and
(e @GTY)–. The structures of
(e @GDY)– and
(e @GTY)– were obtained by removing
OLi3+ from the optimized structures of
OLi3+@GDY– and
OLi3+@GTY–,
respectively. Subsequently, the β 0 values of the
(e @GDY)– and
(e @GTY)– anions were calculated to be 483232
and 711447 au at the CAM-B3LYP/6-31+G(d) level. Clearly, the large first
hyperpolarizabilities of
OLi3+@GDY– (265248
au) and OLi3+@GTY–(653420 au) are almost from the contributions of the graphyne anion
units.
The spatial contribution of the electrons to the NLO response of
OLi3@(GDY/GTY) is explored in terms of first
hyperpolarizability
density.61 Electron
density ρ (r , F ) can be written as Taylor expansion
with respect to the externally applied electric field F :
\(\rho\left(r,F\right)=\rho^{(0)}\left(r\right)+\sum_{j}\rho_{j}^{(1)}\left(r\right)F_{j}+\frac{1}{2!}\sum_{j}{\sum_{k}\rho_{\text{jk}}^{(2)}}\left(r\right)F_{j}F_{k}+\cdots\)(5)
From above equation and expansion formula of dipole moment in power of
the field, a component of first hyperpolarizability can be expressed by:
\(\beta_{\text{ijk}}=-\frac{1}{2!}\int{r_{i}\rho_{\text{jk}}^{(2)}(r)dr^{3}}\)(6)
where
\({\rho_{\text{jk}}^{\left(2\right)}\left(r\right)=\left.\ \frac{\partial^{2}\rho(r)}{\partial F_{j}\partial F_{k}}\right|}_{F=0}\)(7)
The electron density was calculated at the CAM-B3LYP/6-31+G(d) level
using F = 0.003 au. We focus on the βxxxand βyyy components which are the important
components of β 0 value of
OLi3@(GDY/GTY). The local contribution
function\({-\text{xρ}}_{\text{xx}}^{(2)}\left(r\right)\)and\({-\text{yρ}}_{\text{yy}}^{(2)}\left(r\right)\)of the
OLi3@(GDY/GTY) are displayed in Figure 7. Red and white
regions denote positive and negative contributions, respectively, to theβxxx and βyyy values. It
can be seen that the main contribution to the first hyperpolarizability
comes from GDY and GTY moieties. The graphs of\(-x\rho_{\text{xx}}^{(2)}\left(r\right)\) and\(-y\rho_{\text{yy}}^{(2)}\left(r\right)\) for
OLi3@GDY show the fact that the positive local
contribution region is larger than the negative part. This is the reason
why the OLi3@GDY has considerable positiveβxxx (266941 au) and βyyy (280948 au) values. For OLi3@GTY, the\(-x\rho_{\text{xx}}^{(2)}\left(r\right)\ \) function diagram shows
that the positive contribution area is much larger than the negative
part, while the opposite result is observed for the\(-y\rho_{\text{yy}}^{(2)}\left(r\right)\) function. Compared with
the\(-y\rho_{\text{yy}}^{(2)}\left(r\right)\), the\(-x\rho_{\text{xx}}^{(2)}\left(r\right)\) shows a relatively larger
regional scope for both positive and negative contributions. Thus, the
OLi3@GTY possesses large positiveβxxx (521577 au) and relatively small negativeβyyy (–195843 au) values.