A nonlinear optical switch induced by an external electric field: inorganic alkaline-earth alkalide.

Exploring a new type of nonlinear optical switch molecule with excess electron character is extremely important for promoting the application of excess electron compounds in the nonlinear optical (NLO) field. Here, we report external electric field (EEF) induced second-order NLO switch molecules of inorganic alkaline-earth alkalides, M(NH3)6Na2 (M = Mg or Ca). The centrosymmetric structure of M(NH3)6Na2 is destroyed in the presence of an EEF, and then a long-range charge transfer process occurs. It has been found that excess electrons are gradually transferred from one Na atom to the other Na atom through the inorganic metal cluster M(NH3)6. Finally, the excess electrons are completely located on one of the two Na atoms. In particular, the electronic contribution of the static first hyperpolarizability (β e 0) for M(NH3)6Na2 exhibits a large significant difference when the EEF is switched on. The β e 0 value of M(NH3)6Na2 is 0 when EEF = 0, while the peak β e 0 values are 5.95 × 106 (a.u.) for Mg(NH3)6Na2 (EEF = 58 × 10-4 (a.u.)) and 1.83 × 107 (a.u.) for Ca(NH3)6Na2 (EEF = 53 × 10-4 (a.u.)). This work demonstrates that the compounds M(NH3)6Na2 can serve as potential candidates for NLO switches. This journal is © The Royal Society of Chemistry.

Introduction

After the second harmonic generation (SHG)[1] phenomenon was discovered in the 1960s and some inorganic crystals (i.e. LiNbO3 and KTiPO4)[2] were widely used in commercial nonlinear optical (NLO) devices, NLO materials gained enormous attention and became an active research field, owing to their broad applications.[3-9] Up to now, various types of strategies have been proposed to enhance (hyper)polarizability coefficients, i.e., designing organic molecules with a donor–acceptor architecture,[10,11] spin-polarization molecules with singlet diradical character,[12-14] importing diffuse excess electrons into a molecular system to form excess electron compounds, etc. Excess electron compounds have been proven to serve as potential candidates for NLO materials with excellent NLO responses.[15-20]

In recent years, studies on excess electron compounds have gained plentiful attention.[21-29] Alkalides and electrides are typical representatives of excess electron compounds, where anion sites are occupied by anionic alkalis and trapped electrons, respectively.[21-23,30-33] At room temperature, stable organic alkalides have been synthesized by Dye et al.[33] Normally, an alkalide can be obtained by doping two alkali atoms into a suitable ligand, one of them acting as an anion and the other providing an excess of electrons. In addition, the first alkaline–earth based alkalide Ba2+(H5Azacryptand[2.2.2]−)Na−·2MeNH2 was synthesized by Dye and his co-workers.[34] Some alkaline–earth alkalides with large NLO responses have been reported by Li et al., suggesting that an alkaline–earth with alkali atoms can also form an alkalide, where an alkaline–earth atom instead of an alkali atom provides the excess electrons.[35]

Stable magnesium and calcium ammines are well known to exhibit new and interesting properties. The inorganic metal cluster Ca(NH3)6 can be obtained by dissolving calcium in ammonia and its structure has been determined by experimental methods.[36-40] However, inorganic magnesium ammine Mg(NH3)6 has not been obtained so far.[41] Nevertheless, with the existence of Cl− counterions, Mg(NH3)6Cl2 can be obtained.[42-46] Li's group[35] used M(NH3)6 (M = Mg, Ca) to theoretically design a series of novel alkalide molecules with double alkali anions M(NH3)6Na2 and they found that those compounds had large static first hyperpolarizability (electronic contribution βe0) values ranging from 0 to 1.23 × 105 (a.u.). It was noticed that one of the isomers with centrosymmetry (with D3d point group) of M(NH3)6Na2 was the most stable, but its βe0 value was zero. The isomers with centrosymmetry M(NH3)6Na2 may be considered as potential NLO switches by breaking their symmetry with external stimulation, i.e. light irradiation,[47] redox reaction,[48] pH variation, ion recognition,[49] external electric field (EEF), and so on.[19,20,50]

On the one hand, among the above-mentioned external stimulators, EEF plays an important role in chemistry. For instance, Nakano et al. have shown that singlet diradical molecules induced by EEF can produce giant static second hyperpolarizability.[51,52] Bai et al. suggested that benzene has a large βe0 value after the centrosymmetric structure has been broken by switching on a large EEF.[53] Sun et al. demonstrated that the βe0 value of superatom compounds can be greatly improved by 4790 times by imposing an EEF along the direction of charge transfer.[54] Furthermore, EEF is also used to probe other properties, such as the Π stacking interaction,[55] proton transfer,[56] metal–ligand bonding, chemical reactions etc.[57]

On the other hand, NLO switches with a large difference in NLO properties in the presence of external stimulator triggering have attracted more and more attention in recent years,[19,20,50] because of their excellent potential applications in signal processing, data storage and optical frequency converters etc.[3-9] In the presence of EEF triggering, NLO switches of the organic electride molecule K(1)⋯calix[4]pyrrole⋯K(2) with βe0 values ranging from 0 (EEF = 0 (a.u.)) to 3.147 × 106 (a.u.) (EEF = 8 × 10−4 (a.u.)) and the all-metal electride molecules e− + M2+(Ni@Pb12)2−M2+ + e− (M = Be, Mg or Ca) with βe0 values ranging from 0 (EEF = 0 (a.u.)) to 2.2 × 106 (a.u.) (EEF = 30 × 10−4 (a.u.)), as well as Be6Li8 and Be6Li14, were reported by Li and Hou et al.[19,20,50]

It is worth noticing that the above-mentioned NLO molecular switches are all electride molecules.[19,20,50] To the best of our knowledge, NLO switch molecules of an inorganic alkaline–earth alkalide have not been reported yet. Obviously, exploring new NLO switches with excess electrons is extremely necessary for promoting excess electron applications in the NLO field, which is the target of this work. With this motivation, we theoretically investigate the effects of EEF on the geometries, molecular orbitals and NLO properties of previously reported[35] novel alkaline–earth alkalide molecules M(NH3)6Na2 (M = Mg, Ca) (see Fig. 1) in this work.

Fig. 1

The optimized geometrical structure of M(NH3)6Na2 (M = Mg or Ca) at the CAM-B3LYP/6-311++G(2d,2p) level.

Computational details

All quantum chemistry calculations were executed by the Gaussian16 program package (revision B.01).[58] The Coulomb-attenuated hybrid exchange–correlation functional CAM-B3LYP has been proposed[59,60] and successfully applied to calculate (hyper)polarizabilities for charge transfer systems.[20,35,61-65] What is more, this method has been confirmed to give a better performance for calculating hyperpolarizability in the presence of EEF.[19] Furthermore, this functional can also provide molecular geometries close to experimental geometrical parameters.[66] Therefore, geometrical optimization, frequency calculation, natural population analysis charge, interaction energy, electronic contributions of the polarizability and the static first hyperpolarizability were performed at the CAM-B3LYP/6-311++G(2d,2p) level.[67] The oscillator strength of the crucial excited state (f0), the excited energy of the crucial excited state (ΔE), and the difference in transition dipole moment between the ground state and the crucial excited state (Δμ) were calculated at the TD-CAM-B3LYP/6-311++G(2d,2p) level.[68] It should be mentioned that f0 and Δμ were obtained with Gaussian16, while Δμ was obtained with the free and open source Multiwfn program package (revision 3.6).[69]

The interaction energies (Eint) are defined by eqn (1):where EM(NH, E(NH and ENa correspond to the energies of M(NH3)6Na2, (NH3)6Na2 and Na2.

The electronic contributions of the polarizability αe and the static first hyperpolarizability βe0 are defined by eqn (2)–(4):where

Results and discussion

EEF effects on geometries

The equilibrium geometries of M(NH3)6Na2 (M = Mg or Ca) were obtained at the CAM-B3LYP/6-311++G(2d,2p) level and are depicted in Fig. 1. It should be noted that the direction of the imposed EEF is along the z-axis with a magnitude of 0 to 68 × 10−4 (a.u.). If the strength of the imposed EEF is larger than 63 × 10−4 (a.u.), the geometry of Mg(NH3)6Na2 will be destroyed, whereas, if EEF is larger than 68 × 10−4 (a.u.), the geometry of Ca(NH3)6Na2 will be destroyed. Given that Ca(NH3)6Na2 (−37.43 kcal mol−1) shows a larger interaction compared with Mg(NH3)6Na2 (−35.02 kcal) in the absence of EEF, the largest EEF thresholds are different. The point group of M(NH3)6Na2 will be changed from D3d (EEF = 0) to C3V (EEF ≠ 0). For a good visualization of the variable relationships between geometrical parameters and EEF, they are plotted in Fig. 2, and the related geometrical parameters have been collected in Tables S1 and S2.†

Fig. 2

The geometrical parameters (Å) with different magnitudes of the external electric field (EEF, a.u., 10−4) for M(NH3)6Na2 (M = Mg or Ca) at the CAM-B3LYP/6-311++G(2d,2p) level.

From Fig. 2, for both Mg(NH3)6Na2 and Ca(NH3)6Na2, one can see that the distance R1(Na1–H1) is equal to R4(Na2–H2), and R2(N1–Mg) is equal to R3(N2–Mg) when EEF = 0. While, if EEF is not equal to 0, R1 ≠ R4, R2 ≈ R3 and L(Na1–Na2) is elongated. It should be noticed that the variation in L, R1, and R4 is small when EEF is less than 40 × 10−4 (a.u.). But, L, R1 and R4 are all drastically elongated when EEF is greater than 50 × 10−4 (a.u.). In terms of an electro-optical device, it is expected that the geometry should retain its integrity. Therefore, EEF switches on the range from 0 to 40 × 10−4 (a.u.) for Mg(NH3)6Na2 and Ca(NH3)6Na2, which is conducive to the development of a reversible switch.

EEF effects on the highest occupied molecular orbitals

The highest occupied molecular orbitals (HOMOs) (see Fig. 3) of M(NH3)6Na2 (M = Mg or Ca) clearly display that the electron cloud is mainly distributed on the two Na atoms or one of two Na atoms, which suggests that M(NH3)6Na2 compounds have some excess electrons. In addition, the charges by the natural population analysis on Na atoms are negative (−0.695 to −0.776|e| for M = Mg, −0.787 to −1.055|e| for M = Ca, see Table S3†), which further suggests that M(NH3)6Na2 compounds exhibit an alkalide character. From Fig. 3, one can see that when EEF = 0, the two excess electrons are distributed on the two Na atoms and exhibit centrosymmetry. The excess electrons are gradually transferred from one Na to the other Na atom with an increase in the EEF strength, resulting in the symmetry of the HOMOs for M(NH3)6Na2 being broken. When EEF > 20 × 10−4 (a.u.), the excess electrons located on one of the two Na atoms (the electric cloud of the large part is excess electrons of Na, the electronic cloud of the small part is the lone pair of N atoms of the NH3 clusters), which demonstrates that a long-range charge transfer process is occurring through the inorganic metal cluster M(NH3)6 and this process may bring about a large NLO response.

Fig. 3

The highest occupied molecular orbital (HOMO) with different magnitudes of external electric field (EEF, a.u., 10−4) for M(NH3)6Na2 (M = Mg or Ca) at the CAM-B3LYP/6-311++G(2d,2p) level.

EEF effects on nonlinear optical properties

The βe0 values of M(NH3)6Na2 (M = Mg or Ca) with and without EEF were calculated. To better visualize the results, the relationships between the βe0 values of M(NH3)6Na2 and EEF have been plotted in Fig. 4 and 5.

Fig. 4

The electronic contribution of the static first hyperpolarizability (βe0, a.u.) and the excited energy with different magnitudes of external electric field (EEF, a.u., 10−4) for Mg(NH3)6Na2 at the CAM-B3LYP/6-311++G(2d,2p) level.

Fig. 5

The electronic contribution of the static first hyperpolarizability (βe0, a.u.) and the excited energy with different magnitudes of external electric field (EEF, a.u., 10−4) for Ca(NH3)6Na2 at the CAM-B3LYP/6-311++G(2d,2p) level.

As shown in Fig. 4, the βe0 of Mg(NH3)6Na2 first increases to the peak value of 5.95 × 106 (a.u.) for EEF = 58 × 10−4 (a.u.), and then rapidly reduces to 2.79 × 106 (a.u.) for EEF = 63 × 10−4 (a.u.), indicating that the βe0 value exhibits a large difference without and with EEF. It should be noticed that the βe0 value of Mg(NH3)6Na2 slowly increases when EEF is less than 40 × 10−4 (a.u.), but βe0 greatly increases when the EEF is between 40 × 10−4 and 58 × 10−4 (a.u.). Fig. 4 clearly displays that the βe0 value sharply increases from 2.84 × 105 (a.u.) to 5.95 × 106 (a.u.) when EEF is in the range of 40 × 10−4 to 58 × 10−4 (a.u.). Therefore, we focus our attention on variation in βe0 over this range of EEF. The βe0 value of Mg(NH3)6Na2 for this range of EEF was recalculated (EEF with a step size 1 × 10−4 (a.u.)) and the results are plotted in Fig. 4 (inset). The βe0 of Mg(NH3)6Na2 slowly increases when EEF is in the range between 40 × 10−4 and 45 × 10−4 (a.u.), and βe0 increases significantly when EEF is within the range from 46 × 10−4 to 58 × 10−4 (a.u.).

To better understand the change in βe0 with the EEF switched on, a simplified two-level calculation is performed,[70]where Δμ, f0, and ΔE denote the difference in transition dipole moment between ground state and crucial excited state, the oscillator strength of the crucial excited state and the excited energy of the crucial excited state. From eqn (5), one can see that βe0 depends on three quantities: Δμ, f0 and ΔE. Obviously, ΔE is the decisive factor for βe0, since βe0 is proportional to the inverse of its cube. While, sometimes the other two factors also cannot be neglected. Thus, we provide criteria for choosing the crucial excited state using values of these three quantities. The related Δμ, f0, and ΔE values of the crucial excited state are collected in Table S4,† where one can clearly see a better inverse relationship between βe0 and ΔE, which is plotted in Fig. 4 (inset). To be specific, ΔE exhibits a decreasing trend with increasing EEF, which demonstrates why βe0 increases with increasing EEF. In addition, Fig. 4 also displays that Mg(NH3)6Na2 holds high excited energies (1.4816 eV to 1.5356 eV) when EEF is between 40 × 10−4 and 45 × 10−4 (a.u.), but low excited energies (0.3722 eV to 0.8384 eV) when EEF is between 46 × 10−4 and 58 × 10−4 (a.u.). The reason for this is that the crucial excited states are located at high excited state S6 for EEF ranging from 40 × 10−4 to 45 × 10−4 (a.u.) and low excited state S1 for EEF ranging from 40 × 10−4 to 45 × 10−4 (a.u.). This explains why βe0 slowly increases at first, and then quickly increases when EEF is within the range of 40 × 10−4 to 58 × 10−4 (a.u.). In addition, one can see from Fig. 4 that the βe0 values rapidly decrease after presenting a maximum, which is due to ΔE increasing with increasing EEF; the excited energy increased to 1.6794 eV.

For the case of Ca(NH3)6Na2, from Fig. 5 one can clearly see that βe0 value of Ca(NH3)6Na2 gradually increases to 3.11 × 105 (a.u.) when EEF is less than 40 × 10−4 (a.u.), and then dramatically increases to the largest βe0 value of 1.83 × 107 (a.u.) for EEF = 53 × 10−4 (a.u.), rapidly decreasing to 2.99 × 105 (a.u.) for EEF = 68 × 10−4 (a.u.). Here, we mainly focus on discussing the variation in βe0 with EEF ranging from 40 × 10−4 to 53 × 10−4 (a.u.). The corresponding βe0 (EEF with a step size of 1 × 10−4 (a.u.)) was calculated and is given in Fig. 5 (inset).

How can we understand the variation in βe0 with changing EEF? It is likely that we will find some clues from eqn (4). Fig. 5 clearly shows the relationship between βe0 and ΔE. When EEF continuously increases, the βe0 value of Ca(NH3)6Na2 increases with decreasing ΔE (1.4617 to 0.2155 eV). Furthermore, Fig. 5 also illustrates that ΔE dramatically decreases. The reason for this is that the crucial excited state goes from high excited state S6 for EEF ranging from 40 × 10−4 to 47 × 10−4 (a.u.) to low excited state S1 for EEF within in the range of 48 × 10−4 to 53 × 10−4 (a.u.), which explains why βe0 increases slowly at first and then rapidly increases in this EEF range (40 × 10−4 to 53 × 10−4 (a.u.)). Therefore, ΔE is a decisive factor for the variation of βe0 with changing EEF. Similarly, the βe0 values dramatically decrease after exhibiting a peak value, owing to ΔE increasing with increasing EEF, which increased to 1.7838 eV.

In the above discussions, we have obtained a qualitative explanation for the relationship between βe and the external electric field according to the simplified two-level equation. In order to obtain a quantitative explanation for this, hyperpolarizability density analysis is a good choice.[71,72] Hyperpolarizability density ρ is defined by the electronic density of a spatial point r in the presence of an external field F, namely, by the Taylor expansion of energy with respect to an external field:

From eqn (6), βe can be obtained by the following formula:where

The first hyperpolarizability density maps (see Fig. 6) are plotted with the free and open source Multiwfn program.[69] One can see from Fig. 6 that the electronic contribution on the first hyperpolarizability mainly originates from the upper Na atom under high EEF. Furthermore, the values of βe increase with increasing EEF, which explains why the total βe0 values increase with increasing EEF.

Fig. 6

Diagrams of hyperpolarizability density −ρ(2) (EEF = 58 × 10−4 for Mg(NH3)6Na2 and EEF = 53 × 10−4 for Ca(NH3)6Na2) and the relationships between βe and the external electric field.

For a good illustration of the performance of M(NH3)6Na2 (M = Mg or Ca) in a nonlinear optical switch, we further compared the electronic contribution of the first hyperpolarizability value between the current work and previous reports for a nonlinear optical switch. It was found that the inorganic alkaline–earth alkalides M(NH3)6Na2 (M = Mg or Ca), with βe0 values of 0 to 5.95 × 106 (a.u.) and 0 to 1.83 × 107 (a.u.) for Mg(NH3)6Na2 and Ca(NH3)6Na2, respectively, show a better performance than organic electride K(1)⋯calix[4]pyrrole⋯K(2) with a βe0 of 0 to 3.15 × 106(a.u.),[19] all-metal electride e− + M2+(Ni@Pb12)2−M2+ + e− (M = Be, Mg or Ca) with βe0 ranging from 0 to 2.20 × 106 (a.u.)[20] or all-metal electride Be6Li8 with the largest βe0 value of 5.54 × 104 (a.u.) and Be6Li14 with the largest βe0 value 5.0 × 106 (a.u.).[50] Furthermore, M(NH3)6Na2 also showed a better NLO performance than the organic compound benzene with the largest βe0 value of 3.9 × 105 (a.u.) in the presence of EEF.[53]

Furthermore, some NLO switch molecules have been synthesized in the presence of external stimulator triggering: e.g. an acido-triggered second-order NLO switch photochromic cyclometallated platinum(ii) complex,[73] a temperature-induced symmetry-breaking phase transition NLO switch[74] and so forth. Experimental investigations further demonstrate the possibility of the synthesis of a stimulator introduced NLO switch.

In terms of applications of nonlinear optical switches, stability is also an important issue. Thus, to characterize the stability of compounds with a high external electric field, we further calculated the interaction energy between M(NH3)6 (M = Mg or Ca) and Na atoms in the range of a high external electric field. The calculated results showed that the ranges of interaction energy for Mg(NH3)6Na2 and Ca(NH3)6Na2 are −27.70 to −35.19 and −29.17 to −36.93 kcal mol−1 (see Fig. 7), respectively, which demonstrates that M(NH3)6Na2 (M = Mg or Ca) compounds are stable over the range of a high external electric field. Mg(NH3)6Na2 still has a large interaction energy of −7.71 kcal mol−1 under a working external electric field, it should be revised that Mg(NH3)6Na2 still has a large interaction energy −27.71 kcal mol−1 under a working external electric field. Thus, this compound also is relatively stable under a working external electric field with the largest value of βe0.

Fig. 7

The interaction energy between M(NH3)6 (M = Mg or Ca) and Na atoms under different external electric fields (EEF, a.u., 10−4) for Ca(NH3)6Na2 at the CAM-B3LYP/6-311++G(2d,2p) level.

To better understand the frequency dependence behavior of M(NH3)6Na2 (M = Mg or Ca), we further calculated the electronic contribution of the polarizability (αe0) dispersion curve of M(NH3)6Na2 (EEF = 58 × 10−4 (a.u.) for M = Mg, EEF = 53 × 10−4 (a.u.) for M = Ca) with an optical frequency (ω) ranging from 0 to 0.5 eV, and the relationships between αe0 and ω are plotted in Fig. 8. This clearly shows that there are pole points with their positions close to 0.3722 eV and 0.2155 eV for Mg(NH3)6Na2 and Ca(NH3)6Na2, respectively. When ω is calculated to be close to the pole points, it will generate a very large electronic contribution of dynamic (hyper)polarizabilities.

Fig. 8

The electronic contribution of the polarizability dispersion curve for M(NH3)6Na2 (M = Mg or Ca) at the CAM-B3LYP/6-311++G(2d,2p) level.

In addition, the nuclear relaxation contribution of the static first hyperpolarizability βnr0 also plays a key role in NLO properties.[75,76] Thus, we further calculated the βnr0 of M(NH3)6Na2 by using the field induced coordinates (FICs) method which was proposed by Luis's group, and the results are given in Table 1. For more detailed information on FICs, readers are recommended to read ref. 77–79. One can clearly see that βnr0 exhibits a large contribution with 3.84 × 106 (a.u.) and 4.01 × 106 (a.u.) for Mg(NH3)6Na2 and Ca(NH3)6Na2, respectively, which indicates that the nuclear relaxation contribution to the NLO properties of M(NH3)6Na2 is also a significant component.

The electron (βe0, a.u.) and nuclear relaxation (βnr0, a.u.) contributions of the static first hyperpolarizability of M(NH3)6Na2 at the CAM-B3LYP/6-311++G(2d,2p) level

EEF (a.u., ×10−4)	Mg(NH3)6Na2		EEF (a.u., ×10−4)	Ca(NH3)6Na2
	β e 0	β nr 0		β e 0	β nr 0
58	5.95 × 106	3.84 × 106	53	1.83 × 107	4.01 × 106

Conclusions

In this work, we have designed NLO switch molecules, Mg(NH3)6Na2 and Ca(NH3)6Na2, by a theoretical study. Our computational results demonstrate that the inorganic alkaline–earth alkalide M(NH3)6Na2 (M = Mg or Ca) can serve as a potential candidate for a NLO switch. The results highlight the following points:

(1) The centrosymmetric structure of M(NH3)6Na2 is destroyed in the presence of an EEF, and then a long-range transfer process occurs.

(2) The electronic contribution of the static first hyperpolarizability (βe0) is very sensitive to the EEF. The βe0 exhibits a significant difference when the EEF is switched on. The peak βe0 value is 5.95 × 106 (a.u.) for Mg(NH3)6Na2 and 83 × 107 (a.u.) for Ca(NH3)6Na2.

(3) The electronic contribution of the polarizability curve for M(NH3)6Na2 (EEF = 58 × 10−4 (a.u.) for M = Mg, EEF = 53 × 10−4 (a.u.) for M = Ca) with optical frequency ranging from 0 to 0.5 eV was obtained. The pole points are 0.3722 eV and 0.2155 eV for M = Mg and M = Ca, respectively.

(4) The nuclear relaxation contribution of the static first hyperpolarizability plays a key role in the NLO properties of M(NH3)6Na2.

In general, we hope that this work can provide a theoretical reference for designing NLO switches and motivate experimental chemists to synthesize them in the near future.

Conflicts of interest

There are no conflicts to declare.