N-Methylbenzoaza-18-crown-6-ether derivatives as efficient alkali metal cations sensors: the dipole moment and first hyperpolarizability

Abstract

In this work, the 1-Li⁺, 1-Na⁺ and 1-K⁺ complexes formed by N-methylbenzoaza-18-crown-6-ether derivatives (1) with one alkali metal cation (Li⁺, Na⁺ and K⁺) were investigated. Significantly, the dipole moments of 1-Li⁺, 1-Na⁺ and 1-K⁺ enhance with increasing atomic number. However, their first hyperpolarizabilities (β₀) decrease with increasing the atomic number. Further results show that the interaction energies increase in the order of 1-Li⁺ > 1-Na⁺ > 1-K⁺. Moreover, the transition energies of 1-Li⁺, 1-Na⁺ and 1-K⁺ are inversely proportional to the β₀ values. Therefore, the interaction energy and transition energy are the major factors determining the β₀ values of 1-Li⁺, 1-Na⁺ and 1-K⁺. The combining of large variations of the dipole moment and the first hyperpolarizability can be used as a detection sensor for alkali metal cations. We hope that this work will provide valuable knowledge for designing alkali metal cation sensors by electro-optical properties.

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Introduction

The topical problem of detecting cations has attracted the attention of chemists, clinical biochemists, toxicologists, and environmentalists.¹ In general, the numerous analytical methods for cation recognition not only require samples with large size, but also do not allow continuous monitoring. However, methods based on fluorescent sensors^2,3 possess distinct advantages in terms of sensitivity, selectivity, response time, etc. Therefore, numerous efforts are being devoted to develop selective fluorescent sensors for detecting cations.^1,4–8

Crown ethers possess many remarkable attributes but their most significant property is the capability of selectively binding to metal ions and neutral molecules, which has made them a standard among supra-molecular host molecules.⁹ After extensive studies on searching for the different types of crown compounds for cation binding, the interest has gradually focused on crown ether derivatives with a combination of O and N atoms as part of the macrocycle.¹⁰ Meanwhile, the influence of the crown ethers size and constitution on the binding constant has been studied, showing that the binding constant is mainly dependent on the ratio of the crown ether ring size and the diameter of the cation. Studies have reported that the K⁺, Ca²⁺, Na⁺ and NH₄⁺ are all bound more strongly by 18-crown-6 than by any other macrocycles.¹¹

In terms of the application of azacrown ether fragments in photosensitive ligands, compounds with the nitrogen atom conjugated with the chromophore are intriguing. Especially, the derivatives of N-phenylazacrown ethers and 1-aza-2, 3-benzocrown ethers are important.^2,12–15 However, compared with benzocrown-ether-based analogues, the complexes of N-phenylaza-crown ethers with alkali and alkaline-earth metal cations have lower thermodynamic stability,^9,16 and several efforts have been made to resolve this dilemma.^13,17–22 It was reported that the N-alkyl derivatives of benzoaza-crown ethers, with nitrogen directly connecting to the benzene ring, are favourable for the formation of complexes with the metal and ammonium cations.^22,23 Recently, a series of novel 2-benzothiazole-, 4-pyridine-, and 2- and 4-quinoline-based styryl dyes containing an N-methylbenzoaza-15(18)-crown-5(6)-ether moiety were synthesized, which have high performance as optical molecular sensors for alkali and alkaline-earth metal cations.²⁴ On the other hand, previous studies have demonstrated that cation recognition can be performed by probing the variation of the nonlinear optical (NLO) properties^25–31 such as the theoretical investigation on NLO molecular switches of spiropyran/merocyanine systems as selective cation sensors for alkali, alkaline earth, and transition metals. Different cations produce contrasting β₀ values because of the first hyperpolarizability (β₀), depending strongly on the nature of the binding metal cations, which is the key for detecting cations.³²

In this work, the parent N-methylbenzoaza-18-crown-6-ether derivative (1) shown in Scheme 1, and the electro-optical properties of 1 complexation with alkali metal cations (Li⁺, Na⁺ and K⁺) have been investigated. Significantly, the large contrasts of the dipole moment and the first hyperpolarizability appear when 1 was complexed with alkali metal cations Li⁺, Na⁺ and K⁺, which can therefore be used as a detection sensor for alkali metal cations.

Scheme 1 Structure of N-methylbenzoaza-18-crown-6-ether derivatives.

Computational methods

The geometric structures (1-Li⁺, 1-Na⁺ and 1-K⁺) of the N-methylbenzoaza-18-crown-6-ether derivatives complexed with alkali metal cations were obtained from the experimental data (J. Org. Chem. 2013, 78, 9834–9847). On the basis of optimized geometric structures, the natural bond orbital (NBO) charge was performed with BHandHLYP/6-31+G*. Furthermore, the counterpoise (CP) procedure was used to qualitatively calculate the interaction energy (E_int), which is calculated as the difference between the energies of the fragments and the sum of the energies of monomers, according to eqn (1).

E_int(1−M) = E_1−M(X_AB) − [E₁(X_AB) + E_M(X_AB)] (M = Li⁺, Na⁺ and K⁺) (1)

The same basis set X_AB was used for the monomer and 1-Li⁺, 1-Na⁺ and 1-K⁺ complex calculations. Choosing the appropriate theoretical methods of evaluating the NLO properties is important because the hyperpolarizability depends on the choice of the density functional (DFT) method employed. Because of the lack of experimental data of the first hyperpolarizability for our studied complexes, the theoretical results obtained with different DFT methods may ensure the reliability of the present calculations. Therefore, the dipole moment, polarizability and first hyperpolarizability were performed using four DFT methods (BHandHLYP, CAM-B3LYP, LC-BLYP and M06-2X). Simultaneously, transition properties such as oscillator strength, transition energy and crucial transition were calculated with the BHandHLYP method to explore the original reason of difference of the first hyperpolarizability. Further, based on the geometric structure, the UV-Vis absorption spectra of 1-Li⁺, 1-Na⁺ and 1-K⁺ were investigated by the time dependent (TD) BHandHLYP function, and was processed by SWizard and OriginPro software.

The average dipole moment (μ₀) and polarizability (α₀) are noted as:

The static first hyperpolarizability (β₀) is defined as follows:

where

All the calculations were performed with the Gaussian 09W program package.³³

Results and discussion

1. Geometric structures

The geometric structures of 1-Li⁺, 1-Na⁺ and 1-K⁺ are shown in Fig. 1, and important geometric parameters are listed in Table 1. From Fig. 1, we can see that the alkali metal cations directly interact with the O and N atoms. For each alkali metal cation, the closest neighbors are four O atoms for 1-Li⁺, five O atoms for 1-Na⁺ and six atoms (five O atoms and one N atom) for 1-K⁺, respectively. As demonstrated by the data shown in Table 1, the four O_n–Li⁺ (n = 2–5) distances of 1-Li⁺ range between 1.992 to 2.139 Å, which are smaller than the distances of N₆–Li⁺ (5.126 Å) and O₁–Li⁺ (4.242 Å). For 1-Na⁺, the five O_n–Na⁺ (n = 1–5) distances are about 2.500 Å, which are smaller than the distance of N₆–Na⁺ (3.083 Å). However, the five O_n–K⁺ (n = 1–5) distances and one N₆–K⁺ of 1-K⁺ are in a small range from 2.645 to 2.925 Å. Moreover, the average distance between the metal and the oxygen atom increases in the order of Li⁺ < Na⁺ < K⁺ with enhancing the closest neighbors in combination, resulting in the deformation of geometric structures shown in Fig. 1. Therefore, we could speculate that the interesting geometric structures are induced by the crown ether cavity size and alkali metal cation diameter. The Li⁺ cation has the smallest diameter, which enables the attraction of just four O atoms. The diameter of K⁺ is appropriate for the cavity size of N-methylbenzoaza-18-crown-6-ether, and K⁺ locates in the center of the N-methylbenzoaza-18-crown-6-ether.

Fig. 1 The geometric structures of 1-Li⁺, 1-Na⁺ and 1-K⁺ obtained from the experimental data. Color code: carbon (yellow), hydrogen (green), oxygen (red), nitrogen (blue), and the alkali metal cation (purple).

Table 1 Geometric parameters (Å) of 1-Li⁺, 1-Na⁺ and 1-K⁺, the interaction energy E_int (kcal mol⁻¹) and the NBO charge (au) of alkali metal M, N₆ and N₇ of 1-Li⁺, 1-Na⁺ and 1-K⁺

	1-Li^+	1-Na^+	1-K^+
a See Fig. 1.
O1–M^a	4.242	2.600	2.891
O2–M	2.114	2.505	2.645
O3–M	2.012	2.598	2.827
O4–M	2.139	2.522	2.813
O5–M	1.992	2.409	2.832
N6–M	5.126	3.083	2.925
Eint	79.45	54.80	35.61
q(M)	0.791	0.831	0.838

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Further, the interaction energies (E_int) between the alkali metal cations and the parent molecule were calculated, and are shown in Table 1. From Table 1, it can be seen that the E_int values are in the order of 1-Li⁺ (79.45) > 1-Na⁺ (54.80) > 1-K⁺ (35.61 kcal mol⁻¹), indicating the interaction between the alkali metal cations and the parent molecule weakens with the enhancement in atomic number. The variation of E_int values could be mainly ascribed to the increasing average distance between the metal and the oxygen atom in the order of Li⁺ < Na⁺ < K⁺. In addition, the natural bond orbital (NBO) charges of 1-Li⁺, 1-Na⁺ and 1-K⁺ were calculated, and are listed in Table 1. The NBO charge of Li in 1-Li⁺ is 0.791 au, which is smaller than 0.831 au of Na in 1-Na⁺ and 0.838 au of K in 1-K⁺. In other words, the alkali metal NBO charges of 1-Li⁺, 1-Na⁺ and 1-K⁺ are enhanced with increasing the average distances between the metal cations and the oxygen atom, as well as their closest neighbors.

2. Electro-optical properties

The dipole moment (μ₀), polarizability (α₀) and first hyperpolarizability (β₀) were calculated using four DFT methods (BHandHLYP, CAM-B3LYP, LC-BLYP and M06-2X), given in Table 2 and Fig. 2. From Fig. 2, it can be seen that the μ₀ values obtained with LC-BLYP method are the smallest, while the μ₀ values obtained with BHandHLYP, CAM-B3LYP and M06-2X methods are almost the same. Similar to the μ₀ values, the α₀ and β₀ values obtained with four DFT methods follow the same trend (see Table 2). Significantly, followed by increasing the atomic number of the alkali metal, the μ₀, α₀ and β₀ values present three different trends. For example, the μ₀ values by BHandHLYP follow the order of 1-Li⁺ (1.892) < 1-Na⁺ (2.012) < 1-K⁺ (3.188 Debye), indicating that μ₀ values are enhanced with increasing the atomic number of the alkali metal, which are caused by the variation of the geometric structure when in complexation with Li⁺, Na⁺ and K⁺. From Fig. 2, one can see that the α₀ value of 1-Na⁺ is slightly larger than those of 1-Li⁺ and 1-K⁺. However, the effect on first hyperpolarizability becomes more striking with increasing the atomic number of the alkali metal. Moreover, the change of β₀ values is different from our previous works, i.e. the β₀ values increase with increasing the atomic number of the alkali metal.^34–39 Fig. 2 illustrates the relationship between β₀ values and different complexes, it is clear that the β₀ values of 1-Li⁺, 1-Na⁺ and 1-K⁺ decrease with increasing the atomic number of the alkali metal. For example, the order of β₀ values (BHandHLYP) is 1-Li⁺ (11839) > 1-Na⁺ (8734) > 1-K⁺ (7829 au). On the other hand, it can be observed from the data in Table 2 that the β_x values of 1-Li⁺ are small (changing from −66 to −119 au with four DFT methods), and the β₀ values are mainly decided by the β_y and β_z values. However, for 1-Na⁺ and 1-K⁺, the three directions (β_x, β_y and β_z) have equal contributions to the β₀ values. It can be seen that the contrasts of μ₀ and β₀ values are larger than that of α₀ values. Moreover, there are significant contrasts among the μ₀ and β₀ values of 1-Li⁺, 1-Na⁺ and 1-K⁺. Therefore, the combination of the variations of the first hyperpolarizability and dipole moment can be used as a detecting sensor for alkali metal cations.

Table 2 Dipole moment (μ₀, Debye), polarizability (α₀, au) and the first hyperpolarizability (β₀, au) of 1-Li⁺, 1-Na⁺ and 1-K⁺ calculated with four density functional methods

		1-Li^+	1-Na^+	1-K^+
BHandHLYP	μ0	1.892	2.012	3.188
	α0	409	414	409
	βx	−88	4219	−3102
	βy	−4611	1640	−2427
	βz	10904	7469	−6766
	β0	11839	8734	7829
CAM-B3LYP	μ0	1.910	2.045	3.198
	α0	416	420	416
	βx	−103	4705	−3481
	βy	−4893	1760	−2634
	βz	11749	8321	−7560
	β0	12727	9720	8730
M06-2X	μ0	1.924	2.041	3.193
	α0	417	421	416
	βx	−119	4926	−3634
	βy	−5125	1780	−2685
	βz	12423	8676	−7824
	β0	13439	10134	9035
LC-BLYP	μ0	2.023	2.251	3.419
	α0	390	397	393
	βx	−66	3739	−2610
	βy	−3513	1347	−1946
	βz	8517	6600	−5630
	β0	9214	7704	6503

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Fig. 2 (a) Relationship between the dipole moment (μ₀, Debye) and 1-Li⁺, 1-Na⁺ and 1-K⁺ with four density functional methods. (b) Relationship between the polarizability (α₀, au) and 1-Li⁺, 1-Na⁺ and 1-K⁺ with four density functional methods. (c) Relationship between the first hyperpolarizability (β₀, au) and 1-Li⁺, 1-Na⁺ and 1-K⁺ with four density functional methods.

It has been suggested that the alkali metal cations can enhance the first hyperpolarizability by decreasing the transition energy of the crucial excited state. To further explain the difference of first hyperpolarizability, a well-known two-level model is utilized. In the expression, the β₀ is proportional to the oscillator strength (ƒ₀) and the difference of dipole moment between the ground state and the crucial excited state (Δu), and is inversely proportional to the transition energy (ΔE). The transition properties were estimated with the BHandHLYP method, which are displayed in Table 3. The UV-Vis spectra are shown in Fig. 3 and the absorption maxima (λ_max) of 1-Li⁺, 1-Na⁺ and 1-K⁺ are summarized in Table 3. From Fig. 3, it can be seen that the absorption maxima of 1-Li⁺, 1-Na⁺ and 1-K⁺ produce a blue-shift with increasing the atomic number of the alkali metal, which are 391 nm for 1-Li⁺, 382 nm for 1-Na⁺ and 375 nm for 1-K⁺. Simultaneously, as shown in Table 3 and Fig. 4, the corresponding ΔE values of 1-Li⁺, 1-Na⁺ and 1-K⁺ are enhanced with increasing the atomic number of the alkali metal, and the order is 1-Li⁺ (3.172) < 1-Na⁺ (3.246) < 1-K⁺ (3.308 eV). Based on the two-level model, the larger first hyperpolarizability is associated with systems having smaller excitation energy. Therefore, ΔE is the major factor in producing the difference of first hyperpolarizability. Table 3 also reveals that the main transition is from the highest occupied molecular orbital (HOMO) to the lowest unoccupied molecular orbital (LUMO) for all the complexes. The corresponding plots of HOMO and LUMO are illustrated in Fig. S1,† displaying the charge-transfer between HOMO and LUMO character from styryl to quinoline.

Table 3 Oscillator strength (ƒ₀), and transition energy (ΔE) and crucial transition. λ_max refers to the absorption maxima of 1-Li⁺, 1-N⁺ and 1-K⁺ in UV-Vis spectra

	1-Li^+	1-Na^+	1-K^+
ƒ0	1.253	1.422	1.330
ΔE (eV)	3.172	3.246	3.308
Crucial transition	HOMO → LUMO	HOMO → LUMO	HOMO → LUMO
λmax (nm)	391	382	375

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Fig. 3 UV-Vis spectra of 1-Li⁺, 1-Na⁺ and 1-K⁺ using the BHandHLYP method.

Fig. 4 First hyperpolarizability (β₀, au) and transition energy (ΔE, eV) of 1-Li⁺, 1-Na⁺ and 1-K⁺ using the BHandHLYP method.

Conclusions

In summary, the geometric structure, natural bond orbital charge and electro-optical properties of the N-methylbenzoaza-18-crown-6-ether derivatives with alkali metal cations (1-Li⁺, 1-Na⁺ and 1-K⁺) were studied. The obtained conclusions are listed below.

(1) The results of geometric structure indicate that for each alkali metal cation, the closest neighbors are four O atoms for 1-Li⁺, five O atoms for 1-Na⁺ and six atoms (five O atoms and one N atom) for 1-K⁺. The average distance between the metal and the oxygen atom increases in the order of Li⁺ < Na⁺ < K⁺, and the interaction energies are in the order of 1-Li⁺ (79.45) >1-Na⁺ (54.80) > 1-K⁺ (35.61 kcal mol⁻¹).

(2) Interestingly, the electro-optical properties calculated using four different DFT methods show that the dipole moment (μ₀), polarizability (α₀) and first hyperpolarizability (β₀) show three different trends with increasing the atomic number of the alkali metal. The μ₀ values of 1-Li⁺, 1-Na⁺ and 1-K⁺ are enhanced with increasing the atomic number of the alkali metal, and the α₀ value of 1-Na⁺ is slightly larger than those of 1-Li⁺ and 1-K⁺. However, the β₀ values of 1-Li⁺, 1-Na⁺ and 1-K⁺ decrease with increasing the atomic number of the alkali metal.

(3) Further, the UV-Vis spectra and crucial transition energy (ΔE) were calculated with the BHandHLYP method. The results show that the absorption maxima of 1-Li⁺, 1-Na⁺ and 1-K⁺ produce a blue-shift with increasing the atomic number of the alkali metal, which are in the order of 1-Li⁺ (391) > 1-Na⁺ (382) > 1-K⁺ (375 nm). Correspondingly, the ΔE values of 1-Li⁺, 1-Na⁺ and 1-K⁺ are in the order of 1-Li⁺ (3.172) < 1-Na⁺ (3.246) < 1-K⁺ (3.308 eV). Therefore, the crucial transition energy is the major factor in producing the difference of first hyperpolarizability.

Our work theoretically predicts the electric-optical properties of the N-methylbenzoaza-18-crown-6-ether derivatives with alkali metal cations (1-Li⁺, 1-Na⁺ and 1-K⁺), indicating that the alkali metal cation recognition can be performed by combining the variation of the dipole moment and the first hyperpolarizability.

Acknowledgements

The authors gratefully acknowledge financial support from National Science Foundation of China (NSFC) (21003019), the Science and Technology Development Planning of Jilin Province (20100178, 201201062 and 20140101046JC), the Doctoral Fund of Ministry of Education of China (20100043120006). Computing Center of Jilin Province for essential support and Dr Xu acknowledges support from Hong Kong Scholars Program.

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Footnote

† Electronic supplementary information (ESI) available: The equilibrium geometries and HOMO and LUMO plots of 1-Li⁺, 1-Na⁺ and 1-K⁺ are given in supporting information. See DOI: 10.1039/c4ra02238f

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