Simultaneously Enhanced Bond Energies and Nonlinear Optical

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Superatom Compounds under Oriented External Electric Fields: Simultaneously Enhanced Bond Energies and Nonlinear Optical Responses Wei-Ming Sun, Chunyan Li, Jie Kang, Di Wu, Ying Li, Bi-Lian Ni, Xiang-Hui Li, and Zhi-Ru Li J. Phys. Chem. C, Just Accepted Manuscript • Publication Date (Web): 27 Mar 2018 Downloaded from http://pubs.acs.org on March 27, 2018

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The Journal of Physical Chemistry

Superatom Compounds under Oriented External Electric Fields: Simultaneously Enhanced Bond Energies and Nonlinear Optical Responses Wei-Ming Suna, Chun-Yan Lia, Jie Kang,a Di Wuc, Ying Lic, Bi-Lian Nia, Xiang-Hui Lib, Zhi-Ru Lic a

The Department of Basic Chemistry, The School of Pharmacy, Fujian Medical University, Fuzhou 350108, People’s Republic of China. b

Medical Technology and Engineering College, Fujian Medical University Fuzhou 350004, People’s Republic of China. c Laboratory of Theoretical and Computational Chemistry, Institute of Theoretical Chemistry, Jilin University, Changchun 130023, People’s Republic of China.

ABSTRACT: It has recently been demonstrated that oriented external electric fields (OEEFs) can serve as future smart reagents and effectors in chemistry. Consequently, the effect of OEEFs on the geometric structures, electronic properties, bonding properties, and NLO responses of three typical superatom compounds, i.e., (NLi4)(BF4) and (BLi6)X (X = BeF3 and BF4) has been systemically investigated by ab initio computations in this work. The computational results reveal that the (NLi4)(BF4) possesses almost the same performance as the traditional alkali metal halide under the same OEEFs. It is found that the vertical ionization potential, bond energy, and first hyperpolarizability of (NLi4)(BF4) can be gradually enhanced by increasing the imposed OEEF from zero to the critical external electric field (Fc) along the charge transfer direction (NLi4→BF4). In particular, the first hyperpolarizability of (NLi4)(BF4) is greatly enlarged from 2.84103 au to 1.36107 au (for 4790 fold) by increasing OEEF from 0 to 121×10−4 au. Moreover, a similar effect is also observed for (BLi6)X. Consequently, this work reveals an effective approach to simultaneously enhance the bond energies and NLO responses of superatom compounds through imposing OEEFs along the charge transfer direction.



Corresponding author.

E-mail address: [email protected] 1

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1. INTRODUCTION For more than a century, the Periodic Table of elements continues to serve as the foundation for the synthesis of materials with desired properties. Nevertheless, in a pioneering work, Khanna and Jena1 proposed that atomic clusters with unique electronic structures can mimic the chemical behavior of individual atoms. Hence, they named such unusual clusters as “superatoms” and considered them as a three-dimensional (3D) expansion of the conventional Periodic Table.2,3 Studies in the past decades have greatly expanded the scope of superatoms and yielded plentiful exciting results.4-12 More importantly, it is established that superatoms can maintain their identity, much in the same way as ordinary atoms, when assembled into an extended nanostructure,13 and thereby they offer the exciting prospect of serving as novel building blocks for cluster-assembled compounds and nanomaterials with tailored properties for a great variety of potential technologies.14-17 Up to now, a large number of novel compounds using superatoms as building blocks have been synthesized and characterized by experimental and theoretical workers.4,5,13,18-29 Among them, the “supersalts”,18-24 a special kind of superatom compounds formed by combining superalkalis30 and superhalogens31, have attracted great interests because of their potential applications in nonlinear optical (NLO) materials,19,20 high energy density materials,22 energy storage and energy conversion materials23. For example, Khanna and coworkers have theoretically constructed a new type of unique superatom compound by combining superhalogen Al13 and superalkalis (K3O and Na3O).18 Wu and coworkers have presented the theoretical evidence for a series of superatom compounds, including (BLi6)X (X = F, LiF2, BeF3, and BF4),19 (BF4)M (M = Li, FLi2, OLi3, NLi4),20 (Li3)(SH) (SH = LiF2, BeF3, and BF4)21. Among them, (BLi6)X and (BF4)(NLi4) have been predicted to be stable NLO molecules in view of their large bond energies and considerable first hyperpolarizabilities. In another respect, it is known that the oriented external electric fields (OEEFs) plays an important role in chemistry. For instance, OEEFs can affect the H-bonding and

π-stacking

interactions,32

cause

structural

distortions33

2


and

molecular

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isomerization,34-36 induce proton transfer37–40 and mutation of DNA,41,42 control metal-ligand binding,43,44 elicit spin-crossover transitions45 and spin-polarized conductivity,46,47 promote electron transfer and redox reactions,48–50 and activate click reactions.51 In particular, Shaik and coworkers have successfully utilized OEEFs to catalyze and control a variety of non-redox reactions, such as Diels–Alder reaction,52 enzymatic-like bond-activation reaction,53 hydrogen abstraction reaction,54 and the catalytic cycle of the enzyme cytochrome P450.55 They proposed that an OEEF along the reaction axis will catalyze nonpolar reactions by orders of magnitude, control regioselectivity and induce spin-state selectivity. More recently, the elegant experiment of an OEEF-catalyzed Diels–Alder reaction56 showed that these theoretical predictions are reachable with the help of already accessible techniques.37,56-58 Hence, Shaik et al.59 proposed that the OEEFs have the potential of becoming smart catalysts or inhibitors of non-redox reactions and as controllers of reaction mechanisms. Inspired by the above facts, we want to know whether OEEF can be utilized to modulate the electronic properties and NLO responses of superatom compounds. Consequently, the performance of three superatom compounds, including (NLi4)(BF4) and (BLi6)X (X = BeF3 and BF4), under varying OEEFs has been systemically investigated in the present work. Here, we will mainly solve the following problems: (1) Do the superatom compounds possess the same performance as traditional alkali metal halide under the same OEEFs? (2) How the geometric structures, electronic properties, bonding properties, and NLO responses of superatom compounds evolve with the varying strength of OEEFs? (3) Can OEEF be utilized to enhance the bond energies and NLO responses of superatom compounds? (4) If increasing OEEF can indeed enlarge the bond energies and NLO responses of superatom compounds, does a critical external electric field (Fc, the maximum electric field that the structure can withstand) exist for each superatom compound? (5) What is the detailed mechanism of the enhancement of bond energies and NLO responses of superatom compounds under the chosen OEEFs? 3



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2. COMPUTATIONAL METHODS The MP2 method has been widely applied to study the structures and properties of superatom compounds.19-21,24 Thus, the equilibrium geometries with all real frequencies of the studied superatom compounds under a series of OEEFs were obtained by the second-order MP2 method in conjunction with the aug-cc-pVDZ basis set. As for the direction of OEEFs, the formal physics convention that positive field is the direction a positive test charge would move was used in this work. To be specific, the keyword “Field = z + n” (n > 0) was used for imposing positive electric field on (NLi4)(BF4), whereas “Field = z - n” (n > 0) was used for applying positive electric field on (BLi6)X (X = BeF3 and BF4). The first hyperpolarizabilities (β0) and natural bond orbital (NBO) charges of these compounds are calculated at the MP2/aug-cc-pVTZ level. Herein, the β0 values were calculated by the finite-field approach, in which the total energy of a molecular system in the presence of a homogeneous electric field can be expressed as follows: 1 1 E  E 0   F   F F   F F F  2 6

(1)

where E0 is the molecular total energy without the electric field, and Fα is the electric field component along α direction; μα, ααβ, and βαβγ are the dipole moment, the polarizability, and the first hyperpolarizability, respectively. Herein, the static mean first hyperpolarizability (β0) are defined as follows:

 (  x 2  y 2  z )2 1/2

(2)

0

3 where  i  (  iii   ijj   ikk ) , i, j, k = x, y, z. 5

In

addition,

the

TD-DFT

calculations

were

performed

at

the

M06-2X/aug-cc-pVTZ level to obtain the oscillator strengths (f0), transition energies (E), and the difference of the dipole moments (μ) between the ground state and crucial excited state for the studied systems. The vertical ionization potential (VIP) of each compound, defined as the total energy difference between the ionized and the neutral compound with the same geometry as the neutral, was obtained at the MP2/aug-cc-pVTZ level. The intramolecular interaction energies (Eint) between the 4


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superalkali and superhalogen subunits of these studied compounds were also calculated at the MP2/aug-cc-pVTZ level. We used the counterpoise procedure60 to eliminate the basis set superposition error (BSSE) effect given as follows,61 Eint  EAB ( X AB )  EA ( X AB )  EB ( X AB )

(3)

where the whole basis set, XAB, was used for the subunit energy (EA and EB) calculations. And then, the bond energies (Eb) of these studied compounds are defined as the negative of Eint. All the above calculations were performed by using the GAUSSIAN 09 program package.62 Dimensional plots of molecular configurations and orbitals were generated with the GaussView program.63

3. RESULTS AND DISCUSSION 3.1 Performance of (NLi4)(BF4) under OEEFs To detect how OEEFs affect the geometric structures, electronic properties, bonding properties, and NLO responses of superatom compounds, the reported global minimum of the supersalt (NLi4)(BF4)20 was firstly chosen as an example and has been optimized both in the absence of external perturbation and under the influence of twenty-one OEEFs with strengths ranging from -80×10−4 to 121×10−4 au (1 au = 5.142  109 V/cm). All the external electric fields have been applied parallel to the charge transfer direction (NLi4 → BF4) in both directions, that is, positive fields (F > 0) with the direction of NLi4 → BF4 and negative fields (F < 0) with the direction of NLi4 ← BF4 (see Figure 1). Our computational test demonstrates that the critical positive electric field (Fc) for (NLi4)(BF4) is 121×10−4 au because a larger positive electric field (≥122×10−4 au) will destroy its geometric structure. Under the above OEEFs, the variations of selective geometric parameters, NBO charges on the superalkali units, the highest occupied molecular orbital (HOMO)−lowest unoccupied molecular orbital (LUMO) gaps, Eb values, Wiberg bond index, VIP, and β0 values of (NLi4)(BF4) were gathered in Table 1, while the rest geometric parameters and total energies are listed in Table S1 of the Supporting Information. It is reported that the 5



superalkali and superhalogen subunits can behave as single alkali metal atoms and halogen atoms, respectively, when they are interacting with each other in the superatom compounds.19,20 Thus, for comparison, the behavior of the traditional alkali-halide LiF under the same OEEFs has also been studied. In the following subsections, the changing trends of geometric features, electronic properties, bonding properties, and NLO responses of (NLi4)(BF4) and LiF under the varying OEEFs are discussed in detail.

Figure 1 Geometric structures of (NLi4)(BF4) and LiF without an electric field. Cartesian axis, atomic numbering, the direction of inherent μz, and the direction of the positive and negative electric fields (F, in 10-4 au) are also shown.

6


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Table 1. Changes of Symmetry Points, Bond Lengths of Li2-F3 (RLi2-F3, in Å), NBO Charges on Superalkali Units (QSA, in |e|), μz (in debye), HOMO-LUMO Gaps (in eV), Vertical Ionization Potentials (VIP, in eV), Bond Energies (Eb, in kcal/mol), Wiberg Bond Index (WBI) of the Li2-F3 Bond, and the First Hyperpolarizability (β0, in au) with the Oriented External Electric Field (OEEF, in 10−4 au) for (NLi4)(BF4). OEEF

Symmetry

RLi2-F3

QSA

μz

Gap

VIP

Eb

WBI

β0

-80 -70 -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90 100 110 121

C3v C3v C3v C3v C3v C3v C3v C3v C3v C3v C3v C3v C3v C3v C3v C3v C3v C3v C3v C3v C3v

1.985 1.974 1.962 1.952 1.942 1.933 1.924 1.916 1.908 1.899 1.893 1.886 1.879 1.872 1.865 1.859 1.853 1.847 1.841 1.835 1.828

0.866 0.864 0.859 0.861 0.858 0.855 0.852 0.851 0.847 0.847 0.846 0.845 0.843 0.838 0.838 0.835 0.833 0.832 0.834 0.831 0.832

10.200 9.859 9.521 9.189 8.861 8.536 8.213 7.888 7.568 7.245 6.945 6.641 6.315 5.981 5.659 5.333 5.003 4.669 4.328 3.979 3.557

4.21 4.56 4.91 5.27 5.62 5.97 6.31 6.58 6.45 6.14 5.73 5.50 4.79 4.31 3.83 3.34 2.85 2.36 1.88 1.39 0.85

5.55 5.65 5.75 5.85 5.96 6.06 6.16 6.27 6.38 6.48 6.59 6.71 6.82 6.93 7.05 7.16 7.28 7.41 7.53 7.66 7.80

106.6 108.7 110.7 112.6 114.6 116.6 118.5 120.5 122.4 124.4 126.3 128.2 130.1 132.1 134.1 136.1 138.1 140.1 142.2 144.2 146.6

0.0615 0.0626 0.0636 0.0647 0.0656 0.0666 0.0674 0.0682 0.0690 0.0699 0.0705 0.0711 0.0717 0.0724 0.0729 0.0734 0.0737 0.0741 0.0743 0.0744 0.0742

5.68102 7.91102 1.02103 1.26103 1.51103 1.79103 2.10103 2.44103 2.84103 3.31103 3.87103 4.55103 5.38103 6.42103 7.81103 9.72103 1.25104 1.70104 2.55104 4.93104 1.36107

Figure 2. Evolution of (a) the Li2-F3 bond lengths and (b) μz as a function of the oriented external electric field (OEEF, in 10-4 au) for the (NLi4)(BF4) and LiF (inset) compounds. 7



A. Geometric Characteristics Figure 1 displays the optimized C3v-symmetric (NLi4)(BF4) without any OEEF at the MP2/aug-cc-pVDZ level, where the bond length of Li2-F3 is 1.908 Å and the angles of θ and φ are 93.47°and 111.15°, respectively. Under different OEEFs, this structure preserves its C3v geometry, where the superalkali and superhalogen subunits retain their structural integrities. Even so, the applied OEEFs also have certain influence on the geometric structure of (NLi4)(BF4), which has been clearly displayed in Figures 2a and S2. From Figure S2, it can be observed that the bond lengths of N–Li2 and B-F3 of (NLi4)(BF4) are slightly elongated, whereas the Li2-F3 and B-F4 bonds are gradually reduced with the OEEF changing from -80×10−4 to 121×10−4 au. It is found that, under the external electric fields, the variation of bond length is more obvious for Li2-F3 (ca. 0.17 Å), while the change in bond length is less than 0.07 Å for the other bonds, indicating that the OEEFs have substantial effects on the Li-F bonds formed between the NLi4 and BF4 subunits of (NLi4)(BF4). As is revealed in Figure 2a, the Li-F bond of LiF exhibits almost the same dependence on OEEF. To be specific, the Li2-F3 and Li-F bonds are gradually shortened under the increasing positive OEEF along the charge transfer direction. This is reasonable considering the fact that the F− anion tends to move towards the positive pole while the Li+ cation tends to move towards the negative pole of the applied electric field, leading to the contraction of the bridging bonds between the (super)halogen anion and (super)alkali cation in the ionic compounds. When taking the other geometric parameters into account, as shown in Figure S2, it is found that the distance between the B and N atoms of (NLi4)(BF4) is generally increased with the applied OEEF changing from -80×10−4 to 121×10−4 au. This can be understood by the fact that the B center of BF4-unit carries positive charge and the N center of NLi4-unit has negative charge, which gradually makes them move to the opposite direction as the imposed OEEF varies from -80×10−4 to 121×10−4 au. As the Li2-F3 bonds are shortened, the elongation of B-N distances leads to the synchronous stretch of the N–Li2 and B-F3 bonds. Meanwhile, the angle of θ is gradually reduced, 8


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whereas the angle of φ is slightly enlarged under the variation of OEEF. B. Electronic Properties To explore the effect of OEEFs on the charge transfer in (NLi4)(BF4) and LiF compounds, NBO analyses were performed and the related results are listed in Tables 1, S2 and S3 and plotted in Figure S3. From Table 1 and Figure S3a, it can be seen that the general changing trend of NBO charges on the NLi4 unit (QSA) of (NLi4)(BF4) is decreased from 0.866 to 0.831|e| with the OEEF changing from -80×10−4 to 121×10−4 au, which is similar to the varying tendency of QLi for LiF (see Figure S3b). This indicates that the charge transfer from (super)alkali to (super)halogen in these ionic compounds is gradually weakened by enlarging positive electric fields along the charge transfer direction, but is gradually enhanced by increasing the negative electric fields with the opposite direction. Moreover, from Table S2, it is observed that the NBO charges on the Li1 and F4 atoms of (NLi4)(BF4) change more obviously as compared with the other atoms in each superatom subunit. In addition, our computations reveal that only the μz component makes contribution to the dipole moment of (NLi4)(BF4) or LiF, as the μx and μy are zero. As shown in Figure 1, the inherent μz points from (super)halogen to (super)alkali with the same direction as the negative field. Consequently, as shown in Table 1 and Figure 2b, the μz of (NLi4)(BF4) is gradually enlarged from 7.568 to 10.200 D under the increasing negative OEEF, whereas it is gradually reduced to 3.557 D under the increasing positive field. As a result, an excellent linear relationship between μz and electric field (F) was obtained, and the resulting linear equation is μz = -0.032 F + 7.580 with R2 = 0.99978 (F in 10-4 au). The same case is also true for the LiF compound, whose μz decreases from 6.994 to 6.338 D with the linear equation of μz = -0.0032 F + 6.723 (F in 10-4 au, R2 = 0.99933) under the same OEEFs. This phenomenon can be attributed to the fact that the increasing positive electric field not only gradually shortens the Li-F bonds but also weakens the charge transfer from Li to F (see Figures 2a and S3b), jointly leading to the decrease of μz as the magnitude of dipole moment is equal to the separated charge multiplied by the distance between the 9



charges (μ = q· d). The HOMO–LUMO gap of cluster is considered to be an important electronic property in chemistry, which can represent its ability to participate in chemical reactions to some degree. Moreover, the HOMO–LUMO gap is also closely related to the band gap in solid-state physics, serving as an important indicator to predict the conductivity of cluster-assembled materials. As shown in Table 1, the HOMO-LUMO gap of (NLi4)(BF4) without external electric field is as large as 6.45 eV, exhibiting its intrinsic insulator properties. The dependence of HOMO–LUMO gaps of (NLi4)(BF4) and LiF compounds on OEEF is plotted in Figure S3. From Figure S3c, it is observed that the HOMO–LUMO gap of (NLi4)(BF4) increases from 4.21 to 6.58 eV with the negative OEEF decreasing from -80×10−4 to -10×10−4 au, and then gradually reduces from 6.45 to 0.58 eV with the increasing positive electric field from 0 to 121×10−4 au. This variation of HOMO–LUMO gap suggests that our work may provide an effective method to control the energy gaps of superatom compounds. Similar varying trend of HOMO–LUMO gap is also observed for LiF, but the difference is that the peak value of gap appears at OEEF = -40×10−4 au for LiF (see Figure S3d). To deeply understand the origin of the change of energy gaps, the variations of HOMO and LUMO energies of (NLi4)(BF4) as a function of OEEF are shown in Figure S4 of Supporting Information. From this figure, it is observed that, regardless of which direction of the OEEF is adopted, the increasing electric field strength leads to the quickly decrease of LUMO level. As the HOMO level decreases slowly and linearly under the same OEEFs, the change tendency of the HOMO-LUMO gap of (NLi4)(BF4) accords well with the variation of LUMO level. In other words, the change rule of HOMO-LUMO gap of (NLi4)(BF4) mainly depends on the evolution of LUMO level under the varying OEEFs. Among various electronic properties, the vertical ionization potential (VIP) is considered to be an important parameter for estimating the electronic stability of clusters. Thus, the VIP values of (NLi4)(BF4) and LiF compounds under the chosen OEEFs have been also calculated and are listed in Tables 1 and S3, respectively. To 10


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better visualize the results, the dependences of VIP on OEEF for (NLi4)(BF4) and LiF are also plotted in Figure 3. It noted that the VIP values of (NLi4)(BF4) and LiF linearly increase with the imposed OEEF changing from -80×10−4 to 121×10−4 au, demonstrating that the electronic stability of such compounds can be gradually enhanced by applying increased positive electric fields along the charge transfer direction.

Figure 3. Dependences of (a) VIP and (b) Eb on the oriented external electric field (OEEF, in 10-4 au) for the (NLi4)(BF4) and LiF (inset) compounds.

C. Bonding Properties The bond energy (Eb) is considered to a crucial parameter to evaluate the strength of electrostatic interaction between the cation and anion in ionic superatom compounds.19,20 Herein, the dependences of the Eb values of (NLi4)(BF4) and LiF compounds on OEEF are plotted in Figure 3b. It is observed that the Eb value of (NLi4)(BF4) gradually increases with the imposed OEEF changing from -80×10−4 to 121×10−4 au, and an excellent linear relationship between Eb and electric field (F) is obtained with the linear equation of Eb = 0.197 F + 122.417 (R2 = 0.99989 and F in 10-4 au). This indicates that the strength of electrostatic interaction between the NLi4+ and BF4− subunits in (NLi4)(BF4) can be enhanced by employing a larger electric field along the charge transfer direction, resulting in a more stable supersalt where the superalkali and superhalogen subunits are more tightly bound. From the inset picture of Figure 3b, the same case is also observed for the traditional LiF compound. 11



How to understand the effect of OEEFs on the electrostatic interaction between the NLi4+ and BF4− units in the (NLi4)(BF4) compound? This may be related to the fact that the Li-F bonds linking the NLi4+ and BF4− subunits together in (NLi4)(BF4) are gradually shortened with changing OEEF from -80×10−4 to 121×10−4 au (see Figure 2a). According to the Coulomb’s law,64 the electrostatic interaction between two point charges is inversely proportional to the square of the distance between them. Hence, the electrostatic interaction between the Li+ and F− of the bridging Li-F bonds in (NLi4)(BF4) gradually increases when the Li-F bond lengths decrease. Also, this can be further confirmed by the increasing Wiberg bond index (WBI) of bridging Li-F bonds under the changing OEEF from -80×10−4 to 121×10−4 au (see Figure S3e). Similarly, the dependence of Eb of the LiF compound on OEEF can also be understood by the decreasing Li-F bonds and the increasing WBI values (see Figures 2 and S3f). D. NLO Responses It is reported that the (NLi4)(BF4) compound exhibits relatively large NLO response among the BF4-M (M = Li, FLi2, OLi3, and NLi4) series.20 However, the field-free first hyperpolarizability (β0) of 2.84103 au for (NLi4)(BF4) is not large enough; this suggests that this compound can not serve as a good NLO molecule in the absence of an external electric field. One interesting question therefore emerges: can the NLO response of this compound be enhanced by imposing appropriate OEEFs? Consequently, the β0 values of (NLi4)(BF4) under the chosen OEEFs have been calculated and listed in Table 1. To better visualize the results, the dependence of the β0 value of (NLi4)(BF4) on electric field is exhibited in Figure 4. As shown in Figure 4, the β0 value of (NLi4)(BF4) gradually increases along with the imposed OEEF changing from -80×10−4 to 121×10−4 au, indicating that the NLO response of (NLi4)(BF4) can be modulated by changing the magnitude and direction of an applied OEEF. To be specific, the field-free β0 value (2.84103 au) of (NLi4)(BF4) is greatly enlarged to 1.36107 au (4790 fold increase) via imposing an OEEF of 121×10−4 au along the charge transfer direction, whereas it is reduced to 12


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5.68102 au under OEEF of -80×10−4 au against the charge transfer direction. It is also noted that, under positive electric fields, the β0 of (NLi4)(BF4) is slowly increased in the range of low fields, but is quickly enlarged in the range of high fields, indicating that the enhanced effect of positive fields on β0 is more obvious for the larger electric fields. This case is quite different to LiF, for which β0 almost linearly increases with the electric field changes from -80×10−4 to 121×10−4 au (see Figure S5).

Figure 4. Dependence of the first hyperpolarizability (β0) on the oriented external electric field (OEEF, in 10-4 au) for the (NLi4)(BF4) compound. The inset is the change of β0 under the fields ranging from 115×10−4 to 121×10−4 au with the step size of 1×10−4 au.

As shown in Table 1, the β0 of (NLi4)(BF4) is sharply increased from 4.93104 to 1.36107 au when the imposed OEEF is changed from 110×10−4 au to the critical electric field (121×10−4 au). Thus, we focused our attention on the variation of β0 values under this OEEF range. The β0 values of (NLi4)(BF4) for fields ranging from 115×10−4 to 121×10−4 au (with a step size of 1×10−4 au) have been calculated and are shown in Table S4 and Figure 4. Similar to the above case, the β0 of (NLi4)(BF4) is slowly increased in the range of low fields (115×10−4~120×10−4 au), but is greatly enlarged from 120×10−4 to 121×10−4 au, indicating that the enhanced effect of electric field on β0 is gradually enlarged with the increase of OEEF. Additionally, it can be 13



seen from Table S4 that there is a prominent tensor component (βz) that makes the dominant contribution to the β0 values of (NLi4)(BF4) under the applied fields ranging from 0 to 117×10−4 au. In contrast, when the applied fields is larger than 117×10−4 au, more than one component contributes to the β0 value. How to understand the dependence of β0 value on the chosen OEEFs? We may find some clues from the two-level model proposed by Oudar and Chemla65,66. For the static case, the expression of the two-level model is employed as follows:

0 

  f 0 E 3

where ΔE, f0, and Δµ are the transition energy, oscillator strength, and the difference in the dipole moment between the ground state and crucial excited state, respectively. According to the two-level expression, β0 is proportional to f0 and Δµ, whereas is inversely proportional to the third power of ΔE and thus ΔE is usually considered to be the decisive factor on β0. Herein, the ΔE, f0, and Δµ values of (NLi4)(BF4) under the applied electric fields are presented in Table S4 and the change trend of ΔE is illustrated in Figure S6. As shown in Figure S6, it can be clearly seen that the ΔE values of (NLi4)(BF4) exhibit a decreased trend as the OEEF changes from -80×10−4 to 121×10−4 au, which justifies the increasing tendency of corresponding β0 values. Moreover, the greatly large Δµ value of 50.273 D at OEEF = 121×10−4 au can also contribute to the remarkably large β0 of (NLi4)(BF4) under this electric field. Accordingly, the combination of the smallest ΔE and largest Δµ is responsible for the largest β0 value of (NLi4)(BF4) under its critical electric field. 3.2 Performance of (BLi6)X (X = BeF3 and BF4) under OEEFs Based on the above analyses, we gained a significative conclusion that imposing an increasing OEEF along the charge transfer direction of (NLi4)(BF4) is an effective approach to simultaneously enhance its bond energy and first hyperpolarizability. Can this conclusion be extended to the other superatom compounds? The performance of (BLi6)X (X = BeF3 and BF4) under the OEEFs ranging from 0 to Fc along the charge transfer direction has therefore also been investigated. The Fc values of (BLi6)(BeF3) 14


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and (BLi6)(BF4) are found to be 95×10−4 and 93×10−4 au, respectively. The geometric structures of (BLi6)X (X = BeF3 and BF4) are shown in Figure 5, and the geometric parameters and relevant properties are summarized in Tables 2 and S5.

Figure 5 Geometric structures of (BLi6)X (X = BeF3 and BF4) without an external electric field. Cartesian axis, atomic numbering, the direction of inherent μz, and the direction of applied electric field (F, in 10-4 au) are also shown.

Computationl results reveal that both of (BLi6)(BeF3) and (BLi6)(BF4) preserve their C3v-symmetric structures under the chosen external electric fields, where the superalkali and superhalogen subunits always retain their structural integrities under the varying OEEF. The evolution of the geometric parameters of (BLi6)X (X = BeF3 and BF4) under the varying OEEFs has been plotted in Figures S7 and S8, respectively. Similar to (NLi4)(BF4), the Li2-F3 bonds linking the superalkali and superhalogen units together in (BLi6)X are gradually shortened with the increasing electric fields. Also, it is found that the B-Be and B-B distances of (BLi6)(BeF3) and (BLi6)(BF4) are generally increased with the increase of OEEF. Moreover, it can be observed from Figures S7 and S8 that the structural changes of BLi6 unit under the varying OEEFs are the same for (BLi6)X. That is, regardless of whether the superhalogen unit is BeF3 or BF4 for (BLi6)X, the B-Li2 bond length is gradually increased, whereas the bond length of B-Li1 and the angle of θ are reduced as the electric field increases.

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Table 2. Changes of Symmetry Points, Bond Lengths of Li2-F3 (RLi2-F3, in au), μz (in debye), NBO Charges on Superalkali Units (QSA, in |e|), HOMO-LUMO Gaps (in eV), Bond Energies (Eb, in kcal/mol), Wiberg Bond Index (WBI), Vertical Ionization Potentials (VIP, in eV), and the First Hyperpolarizability (β0, in au) with Oriented External Electric Field (OEEF, in 10−4 au) for (BLi6)X (X = BeF3 and BF4). Compounds (BLi6)(BeF3)

OEEF 0 10 20 30 40 50 60 70 80 95

Symmetry C3v C3v C3v C3v C3v C3v C3v C3v C3v C3v

RLi2-F3 1.814 1.813 1.813 1.812 1.810 1.808 1.803 1.803 1.802 1.795

μz -5.083 -3.931 -2.744 -1.565 -0.378 0.8572 2.1459 3.5939 5.5795 21.277

QSA 0.883 0.871 0.861 0.854 0.846 0.841 0.838 0.830 0.827 0.817

Gap 5.10 4.85 4.43 3.98 3.53 3.09 2.64 2.21 1.82 1.56

Eb 132.4 134.6 137.2 140.1 143.1 146.3 149.4 152.9 156.3 161.9

WBI 0.0789 0.0786 0.0786 0.0786 0.0788 0.0792 0.0792 0.0797 0.0805 0.0823

VIP 5.54 5.51 5.63 5.72 5.82 5.92 6.04 6.13 6.25 6.43

β0

(BLi6)(BF4)

0 10 20 30 40 50 60 70 80 93

C3v C3v C3v C3v C3v C3v C3v C3v C3v C3v

1.881 1.874 1.865 1.858 1.851 1.845 1.839 1.833 1.829 1.820

-5.818 -4.925 -3.991 -3.025 -2.016 -0.965 0.163 1.4143 3.0009 11.616

0.819 0.819 0.817 0.815 0.815 0.814 0.813 0.812 0.811 0.807

5.03 4.87 4.52 4.09 3.66 3.22 2.79 2.37 1.97 1.60

121.1 124.5 127.8 131.1 134.5 137.9 141.3 144.8 148.4 153.1

0.0736 0.0737 0.0739 0.0741 0.0742 0.0744 0.0746 0.0749 0.0754 0.0764

5.48 5.59 5.69 5.84 5.98 6.12 6.26 6.41 6.56 6.76

5.93103 9.01103 1.35104 1.99104 2.87104 4.12104 6.21104 1.10105 2.56105 4.15105

16


1.01104 1.53104 2.13104 2.92104 3.96104 5.41104 8.41104 1.65105 3.63105 1.47106

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The NBO computations show that, similar to (NLi4)(BF4), the NBO charges on the BLi6 subunits of (BLi6)X decrease with the increasing OEEF (see Figure S9a), indicating that the charge transfer from superalkali to superhalogen in (BLi6)X can be weakened by exposing them to electric fields along the charge transfer direction. It is noted that the decreasing tendency of QSA is more obvious for (BLi6)(BeF3) as compared with (BLi6)(BF4), implying that the effect of electric field on the charge transfer of the former is much larger than that of the latter. As for μz, a similar variation is observed for the (BLi6)X compounds (see Figure S9b). To be specific, the magnitudes of μz for (BLi6)X are firstly reduced with the increasing OEEF until the directions of inherent μz are reversed, and then they are gradually increased as the electric field increases. In particular, it can be seen from Table 2 that the μz values of (BLi6)X are enlarged by ca. 4 times with the OEEF changing from 80×10−4 au to their respective Fc, whereas they are almost linearly increased under the lower OEEFs from 0 to 80×10−4 au (see Figure S9b).

Figure 6. Dependence of (a) VIP and (b) Eb on the oriented external electric field (F, in 10-4 au) for the (BLi6)X (X = BeF3 and BF4) compounds.

From Figure S9c, it is observed that the HOMO–LUMO gaps of (BLi6)X gradually decrease with the increasing electric fields, suggesting that their energy gaps can also be manipulated by changing the imposed OEEF. When the variations of HOMO and LUMO energies of (BLi6)X are taken into consideration, it can be seen from Figure S10 that both of HOMO and LUMO energy levels are decreased with the increasing OEEF, but the decrease of the LUMO is much obvious than that of the 17



HOMO, leading to reduced tendency of the HOMO-LUMO gaps. It is worth mentioning that the gaps of (BLi6)(BeF3) and (BLi6)(BF4) are 1.56 and 1.60 eV, respectively, even when they are exposed to their Fc. These values are comparable to the experimental HOMO−LUMO gap of 1.57 eV for the kinetically stable C60,67 suggesting that the chemical stabilities of (BLi6)(BeF3) and (BLi6)(BF4) continue to be large under the Fc. In addition, as shown in Table 2 and Figure 6a, the calculated VIP values of (BLi6)X (X = BeF3 and BF4) increase with increasing electric field with only one exception at OEEF = 10×10−4 au for (BLi6)(BeF3); this further demonstrates that the electronic stability of such compounds can be enhanced by the application of electric field along the charge transfer direction. Turn to the bond energy (Eb), it is found that this parameter almost linearly increases with the increase of imposed OEEF for (BLi6)(BeF3) and (BLi6)(BF4), indicating that the strength of ionic bonds between the BLi6+ and BeF3−/BF4− subunits in these two compounds can be gradually enhanced by employing an increasing OEEF along the same direction as charge transfer. This is further confirmed by the generally increasing trend of Wiberg bond indexes (WBI) of the bridging Li2-F3 bonds under the increasing OEEF (see Figure S9d). Thus, this work provides an effective strategy to enhance the interaction between cationic superalkali and anionic superhalogen units in such supersalts.

Figure 7. Dependence of the first hyperpolarizability (β0) on the oriented external electric field (F, in 10-4 au) for the (BLi6)X (X = BeF3 and BF4) compounds.

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We now turn to the key question of this study: can the NLO responses of (BLi6)X (X = BeF3 and BF4) also be enhanced by exposing them to OEEFs? Consequently, the β0 values of (BLi6)X under the varying OEEFs have been obtained and listed in Table 2. To clearly display the results, the relationship between β0 and OEEF for (BLi6)X is also illustrated in Figure 7. It is notable that the β0 values of (BLi6)X gradually increase with the increasing OEEF, indicating that their NLO responses can be substantially enhanced by introducing an OEEF along the charge transfer direction. Here, the increased trend of β0 values for (BLi6)X can also be well understood by the corresponding decrease in ∆E values when the applied electric field increases (see Table S6 and Figure S11); this demonstrates that the ∆E is the decisive factor determining the NLO responses of such superatom compounds. Similar to (NLi4)(BF4), the β0 values of (BLi6)X also slowly increase under the lower electric fields, while quickly increasing under relatively higher fields. This further confirms the conclusion that the enhanced effect of OEEFs on β0 is more obvious for larger electric fields. In particular, as shown in Table 2 and Figure 7, the β0 of (BLi6)(BeF3) is greatly increased from 1.01104 to 1.47106 au (146 fold), while the β0 of (BLi6)(BF4) is enlarged from 5.93103 to 4.15105 au (70 fold) when the imposed electric field increases from 0 to the critical electric field (Fc). Additionally, it can be seen from Table S6 that the tensor component βz always makes the dominant contribution to the β0 values of (BLi6)X under the applied OEEFs. 4. CONCLUSIONS In the present work, the evolution of geometric structures, electronic properties, bonding properties, and NLO responses of (NLi4)(BF4) and (BLi6)X (X = BeF3 and BF4) under the varying OEEFs has been studied in detail by ab initio computations. Our results demonstrate that the OEEFs have substantial effect on the geometric and electronic properties, bonding properties, and NLO responses of the (NLi4)(BF4), and that these effects are almost the same as for traditional alkali metal halides. It is found that the HOMO–LUMO gaps of the studied compounds can be modulated by changing the magnitude and direction of OEEFs. In particular, the bond energies and 19



first hyperpolarizabilities can be gradually enhanced by increasing OEEF along the charge transfer direction from zero to the critical external electric field (Fc) along the charge transfer direction. This indicates that imposing an increasing OEEF along the charge transfer direction of superatom compounds is an effective approach to simultaneously enhance their bond energies and NLO responses. Despite that imposing extremely high electric field on clusters is a great challenge, it is hoped that this work could not only offer theoretical insights into the effect of OEEFs on the structures, electronic properties, and NLO responses of superatom compounds, but also attract more research interests and efforts of experimentalist in the application of OEEFs to modulate the desired properties of superatom compounds.

Supporting Information Effect of OEEFs on geometric parameters, β0, f0, ΔE, and Δμ for (NLi4)(BF4) and (BLi6)X. Charge distribution and WBI within NLi4+ and BF4− of (NLi4)(BF4). Dependence of QSA, HOMO-LUMO gaps, and WBI on OEEF for LiF, (NLi4)(BF4), and (BLi6)X. Dependence of HOMO and LUMO energy levels as well as ∆E on OEEF for (NLi4)(BF4) and (BLi6)X. Dependence of β0 on OEEF as well as the changes of symmetry points, bond length, μz, QLi, HOMO-LUMO gaps, VIP, Eb, WBI, and β0, with OEEF for LiF. Optimized structures of BeF3−, BF4−, NLi4+, and BLi6+. Cartesian coordinates of field-free (NLi4)(BF4) and (BLi6)X.

Acknowledgements This work was supported by the National Natural Science Foundation of China (21303066, 21375017, 21573089, 21603032), Natural Science Foundation of Fujian Province (2016J05032, 2016J01771), State Key Development Program for Basic Research of China (2013CB834801), Academic Foundation for Professor of Fujian Medical University (JS14008, JS14009). The authors also acknowledge the National Supercomputing Center in Shenzhen for providing computational resources.

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Simultaneously Enhanced Bond Energies and Nonlinear Optical

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