Third-Order Nonlinear Optical Responses of Bis(15-crown-5)-stilbenes Binding to One- or Two-Alkali Metal Cation (Li⁺, Na⁺and K⁺)

College of Resources and Environmental Science, Jilin Agricultural University, Changchun 130118, China

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Corresponding author: Yuhl@jlau.edu.cn; chengzhiqiang@jlau.edu.cn

摘要

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Abstract: Bis(15-crown-5)-stilbenes containing crown ether parts have been widely used in a variety of chemical applications, such as cation detectors, because of their ability to selectively bind to alkali metal cations, Bis(15-crown-5)-stilbenes and its derivatives with complexation of one- or two-alkali metal cation (Li⁺, Na⁺ and K⁺) have been theoretically investigated by quantum chemistry methods. The coordination of alkali cations results in partial shrinkage of crown ethers, which directly affected natural distribution analysis charges and molecular orbital energy levels. The number of alkali metal ions has significant effects on absorption spectra and mean second hyperpolarizability. When one alkali metal ion was added to the anticonformer of bis(15-crown-5)-stilbene, the absorption spectra were obviously redshifted and the mean second hyperpolarizability values were slightly increased; while two alkali metal ions were added to bis(15-crown-5)-stilbene, the absorption spectra were obviously blue shifted and the mean second hyperpolarizability values decreased. On the other hand, as the radius of the alkali ions increaseed, the mean second hyperpolarizability values of the compounds increased gradually. It indicated that the mean second hyperpolarizability value was sensitive to the number and radius of the alkali metal cations, thus the third order nonlinear optical response can be used as a signal to detect the number and type of alkali metal ions.
- Bis(crown)-stilbene /
- Cation detector /
- Metal cation /
- Quantum chemistry /
- Second hyperpolarizability

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1. Conformers of bis(15-crown-5)-stilbenes.

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2. Structures of the metal cation derivatives of bis(15-crown-5)-stilbenes.

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Figure 1. The structures of the compounds with 1 as the parent and their localized orbital locator (LOL) maps obtained by B3LYP/6-31G(d,p) level.

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Figure 2. The fragments (F1 to F5, left panel) of the compounds and their NPA charges (right panel) obtained at the B3LYP/6-31G(d,p) level, $\Delta q= $$ q({\rm {L}}\cdot{({{\rm{M}}^{+/2+}})_2}) - q({f\rm{L}})$(L was the ligand).

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Figure 3. The frontier molecular orbital energy levels of 1 and compounds with 1 as their parent.

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Figure 4. The absorption spectra and electron density difference diagram of the studied compunds obtained at TD-CAM-B3LYP/6-311+G(d,p) (purple and blue indicate electron density accumulation and depletion, respectively).

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Figure 5. Static mean second hyperpolarizabilities ($ \bar \gamma $) of compounds with (a) 1, (b) 2 and (c) 3 as the parent computed by the CAM-B3LYP and BHandHLYP functionals.

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Figure 6. Schematic diagram of the $ - x \times \rho _{xxxx}^{(3)} $ for the compoundscomputed at the CAM-B3LYP/6-311G(d,p) level. Blue and purple colors indicate the positive contribution, while yellow and orange colors indicate the negative contribution.

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Figure 7. The frequency-dependent second hyperpolarizabilities associated with the photoelectric Kerr effect ($\gamma {\rm{EOKE}}(−{\omega};{\omega},0,0)$, left panel ) and frequency-dependent second hyperpolarizabilities associated with the second harmonic generation $\gamma^{{\rm{SHG}}}(-2{\omega};{\omega},{\omega},0)$ right panel.

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Table I. The selected geometrical parameters and interaction energies E_int calculated at the B3LYP/6-31G(d,p) level.

Compound	Bond length/Å						Dihedral/(°)	E_int/(kcal/mol)
	M⁺–O	O···O^a	O···O ^b	C2−C3	C3−C4	C4−C5	C1−C2−C5−C6
1	—	2.806 (2.982)^c	2.806 (2.982)^c	1.463 (1.480)^c	1.350 (1.334)^c	1.463 (1.481)^c	−12.4 (−14.6)^c
1·Li⁺	2.21	2.798	2.600	1.457	1.352	1.461	11.0	−120.0
1·Na⁺	2.31	2.798	2.728	1.457	1.352	1.461	14.4	−93.7
1·K⁺	2.70	2.798	2.769	1.457	1.352	1.461	−0.3	−66.9
1·(Li⁺)₂	2.20	2.597	2.597	1.465	1.348	1.465	0.6	−221.1
1·(Na⁺)₂	2.30	2.724	2.724	1.465	1.348	1.465	0.7	−180.1
1·(K⁺)₂	2.70	2.759	2.760	1.465	1.348	1.465	15.9	−124.3
^a The average O···O bond length of O1···O2, O2···O3, O3···O4, O4···O5 and O5···O1 bonds. ^b The average O···O bond length of O6···O7, O7···O8, O8···O9, O9···O10 and O10···O11 bonds. ^c The values determined by X-ray analysis in Ref.[21].

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Table II. The enthalpy and Gibbs free enthalpy (kcal·mol^-1·K^-1) and entropy (in kcal /mol of the complexation reaction calculated on B3LYP/ 6-31G(d,p) at 298.15 K and 1 atm.

Compound	$\Delta {H }$^⦵	$\Delta {G }$^⦵	$\Delta S$^⦵
1·Li⁺	−120.8	−114.4	21.3
1·Na⁺	−95.2	−87.1	27.1
1·K⁺	−65.8	−57.9	26.7
1·(Li⁺)₂	−235.0	−221.6	44.9
1·(Na⁺)₂	−182.7	−168.1	49.0
1·(K⁺)₂	−122.0	−107.2	49.5

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Table III. The wavelength of the main absorption peak (λ, nm), the transition energies from S0 to S1 state (∆E, eV) and the corresponding oscillator strengths (f_os) , as well as the major contributions obtained at the CAM-B3LYP/6−311 + G(d,p) level.

Compd.	λ	∆E	f_os	MO transition
1	325.2	3.82	1.2904	HOMO→LUMO (94%)
1·Li⁺	343.3	3.61	1.1831	HOMO→LUMO (91%)
1·Na⁺	343.3	3.61	1.1794	HOMO→LUMO (90%)
1·K⁺	345.4	3.60	1.175	HOMO→LUMO+1 (80%)
1·(Li⁺)₂	316.7	3.92	1.2762	HOMO→LUMO (95%)
1·(Na⁺)₂	316.7	3.92	1.2706	HOMO→LUMO (95%)
1·(K⁺)₂	316.7	3.93	1.2547	HOMO→LUMO (95%)

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