Two-electron/24-center (2e/24c) bonding in novel diradical π-dimers.

A series of diradical π-dimers 2 with interesting pancake-shaped 2e/24c π-π bonding character were designed and investigated based on the famous phenalenyl (PLY) π-dimer with 2e/12c π-π bonding character. The position of stronger interaction between two layers of radicals was found by the Wiberg bond index (WBI) maximum component. Further, the different contributions of the interaction energy were analyzed quantitatively by energy decomposition analysis (EDA). Among these new diradical π-dimers, 2180 has the smallest layer distance and the largest interaction between two layers of radicals. The unusual PLY analogues can provide new insights into the unique features of two-electron/multicenter (2e/mc) π-π bonding.

Charge transfer and first hyperpolarizability: cage-like radicals C59X and lithium encapsulated Li@C59X (X=B, N).

Very recently, two new cage-like radicals (C59B and C59N) formed by a boron or nitrogen atom substituting one carbon atom of C60 were synthesized and characterized. In order to explore the structure-property relationships of combination the cage-like radical and alkali metal, the endohedral Li@C59B and Li@C59N are designed by lithium (Li) atom encapsulated into the cage-like radicals C59B and C59N. Further, the structures, natural bond orbital (NBO) charges, and nonlinear optical (NLO) responses of C59B, C59N, Li@C59B, and Li@C59N were investigated by quantum chemical method. Three density functional methods (BHandHLYP, CAM-B3LYP, and M05-2X) were employed to estimate their first hyperpolarizabilities (ß tot) and obtained the same trend in the ß tot value. The ß tot values by BHandHLYP functional of the pure cage-like radicals C59B (1.30 × 10(3) au) and C59N (1.70 × 10(3) au) are close to each other. Interestingly, when one Li atom encapsulated into the electron-rich radical C59N, the ß tot value of the Li@C59N increases to 2.46 × 10(3) au. However, when one Li atom encapsulated into the electron-deficient radical C59B, the ß tot value of the Li@C59B sharply decreases to 1.54 × 10(2) au. The natural bond orbital analysis indicates that the encapsulated Li atom leads to an obvious charge transfer and valence electrons distribution plays a significant role in the ß tot value. Further, frontier molecular orbital explains that the interesting charge transfer between the encapsulated Li atom and cage-like radicals (C59B and C59N) leads to differences in the ß tot value. It is our expectation that this work will provide useful information for the design of high-performance NLO materials.

"Dancing inside the ball": the structures and nonlinear optical properties of three Sc2S@C3v(8)-C82 isomers.

Recently, the crystal structures and electrochemical properties of the isomers (Sc2S "trapped" in C82) have been reported, in which the Sc2S is located inside the different positions of the C82 cage. In the present work, three isomers of endohedral metallofullerenes Sc2S@C3v(8)-C82 (A, B, and C) have been designed to explore the effect of the position of Sc2S on their interaction energies and nonlinear optical properties. Among three isomers, the Sc2S is located in different positions of the C82 cage: the angles of Sc-S-Sc in A, B, and C are 104.9, 114.8, and 115.7°, respectively. Furthermore, the analysis of natural bond orbital (NBO) charge indicates that the electron-transfer is from the Sc2S to the adjacent carbon atoms of the C82 cage. The interaction energy of B is the smallest among three isomers which is -226.2 kcal mol(-1). It was worth mentioning that their first hyperpolarizabilities (ß tot) were studied, we found that their ß tot values were related to the positions of Sc2S: C (2100) > B (1191) > A (947 au). We hope that the present work can provide a new strategy to promote the nonlinear optical properties of endohedral metallofullerenes by changing the positions of the encapsulated molecular. Graphical abstract Three isomers of endohedral metallofullerenes Sc2S@C3v(8)-C82 (A, B, and C) have been designed to explore the position effect of Sc2S on the interaction energies and nonlinear optical properties. Among three isomers, the Sc2S in B has the most stable position. Significantly, the first hyperpolarizability is related to the position of Sc2S inside the C82 cage, which provides a novel strategy to enhance the first hyperpolarizability by the Sc2S revolving inside the C82 cage.

Superalkali atoms bonding to the phenalenyl radical: structures, intermolecular interaction and nonlinear optical properties.

Due to unpaired electrons, both radicals and superalkali are investigated widely. In this work, two interesting complexes (Li3O-PLY and Li3-PLY) were constructed by phenalenyl radical and superalkali atoms. Why are they interesting? Firstly, for Li3O-PLY and Li3-PLY, although the charge transfer between superalkali atoms and PLY is similar, the sandwich-like charge distribution for Li3O-PLY causes a smaller dipole moment than that of Li3-PLY. Secondly, their UV-vis absorption show that the maximum wavelengths for Li3O-PLY and Li3-PLY display a bathochromic shift compared to PLY. Moreover, Li3-PLY has two new peaks at 482 and 633 nm. Significantly, the ß 0 values of Li3-PLY (4943-5691 a.u.) are much larger than that of Li3O-PLY (225-347 a.u.). Further, the ß HRS values of Li3O-PLY decrease slightly while ß HRS of Li3-PLY increase dramatically with increasing frequency. It is our expectation that these results might provide beneficial information for theoretical and experimental studies on complexes with superalkali and PLY radicals. Graphical Abstract Two interesting complexes (Li3O-PLY and Li3-PLY) were constructed by phenalenyl radical and superalkali atoms. We explore their structures, Wiberg bond indices, interaction energies and the static first hyperpolarizabilities (ß 0). The ß 0 values of Li3-PLY (4943-5691 a.u.) were much larger than those of Li3O-PLY (225-347 a.u.).

One lithium atom binding with P-nitroaniline: lithium salts or lithium electrides?

Recently, both lithium (Li) salts and Li electrides formed by one Li atom interacting with ligand complexes, have been widely investigated. An interesting question emerges: is the configuration of one Li atom interacting with ligand complexes a Li salt or electride? In the present work, four configurations n-Li-PNA (n = 1-4) were obtained by binding one Li atom with the p-nitroaniline (PNA) at different positions to explore this question. The results show that 1-Li-PNA and 2-Li-PNA are typical Li salts, and 4-Li-PNA is a typical Li electride. Significantly, 3-Li-PNA possesses both characteristics of Li salt and electride. At the same time, 3-Li-PNA has the largest first hyperpolarizability (2.9 × 10(6) au) by ROMP2 method compared with the other three configurations. Furthermore, the first hyperpolarizability of 3-Li-PNA is about 2600 times larger than that of PNA. Further, the vertical ionization potential (VIP) and interaction energy (E int) indicate that 3-Li-PNA is less stable than 1-Li-PNA and 2-Li-PNA (Li salts), but is more stable than 4-Li-PNA (Li electrides).

Modulating the charge transfer of D-S-A molecules: structures and NLO properties.

Very recently, the investigation of an Li atom doped effect on the "through-space" electronic interaction (S) of a donor-S-acceptor (D-S-A, 1) shows that the Li-doping effect can modulate the first hyperpolarizability of 1 ( Dyes Pigm. 2014 , 106 , 7 - 13 ). Can we further enhance the first hyperpolarizability (ßtot) of 1 by modulating the charge transfer of D-S-A molecules? The present work indicates that the ßtot value can be successfully modulated by replacing the sp(2)-hybridized CH═CH moiety connected with substituted para-cyclophane (PCP). On the other hand, the NO2 contributes more than NH2 to the ßtot value. The results of time-dependent density functional theory (TD-DFT) provide a good explanation for the variation in the ßtot value. Interestingly, the ßtot value of 3 (4.09 × 10(3) au) is larger than 1.52 × 10(3) au of 4, while the difference between the dipole moments (Δµ) of the ground state and the crucial excited state of 3 (2.93 D) is smaller than that of 4 (7.79 D). Further, the charge-transfer excitation length (D(CT)) of 3 (1.41 Å) is smaller than that of 4 (2.89 Å). Therefore, D(CT) is the major factor in determining the Δµ value.

The Effect of the different spin multiplicity on nonlinear optical properties of lithium decahydroborate dimers.

In 2009, an innovative type of lithium decahydroborate (Li@B(10)H(14)) complex with a basketlike complexant of decaborane (B(10)H(14)) was designed and studied. Theoretical investigation is very important for designing high-performance nonlinear optical (NLO) materials. In the present work, an unusual Li@B(10)H(14) dimer with different spin multiplicities was designed theoretically to explore the influence of the spin multiplicity on NLO properties: 1 (triplet), 2 (open-shell singlet) and 3 (singlet). Interestingly, the results show that the intersection angle (between cage A and cage A') follows the order of 1 (13.71°) > 2 (1.65°) > 3 (0°). As a result, the first hyperpolarizability (ß(tot)) value follows the order of 1 (19,129 a.u.) < 2 (35,992 a.u.) < 3 (77,660 a.u.). Additionally, 1, 2 and 3 of λ(max) shows an apparent red shift with three spin multiplicities in the absorption spectrum. The results of this work can be expected to provide useful information for designing high-performance NLO materials based on decaborane.

Superatoms (Li3O and BeF3) induce phenalenyl radical π-dimer: fascinating interlayer charge-transfer and large NLO responses.

Recently, the well-known phenalenyl radical π-dimer with its fascinating 2-electron/12-center (2e/12c) bond has attracted our attention. In this work, we designed two molecules, Li3OC13H9 () and BeF3C13H9 (). Interestingly, owing to the inductive effect of superatoms, an electron is transferred from Li3O to phenalenyl in , while an electron is transferred from phenalenyl to BeF3 in . Further, we employed and as building blocks to assemble two novel molecules with 2e/12c bonds: Li3O(C13H9)2BeF3 () and Li3O(C13H9)2BeF3 (). Remarkably, and with novel 2e/12c bonds exhibit a dramatic interlayer charge-transfer character, which results in a significant difference of dipole moments (Δµ: 2.6804 for and 3.8019 Debye for ) between the ground state and the crucial excited state. As a result, the static first hyperpolarizabilities (ß0: 5154 for and 12 500 au for ) are considerably larger than the values of 347 for and 328 au for . It is our expectation that the results of the present work might provide beneficial information for further theoretical and experimental studies on the fascinating properties of molecules with interlayer charge-transfer character.

The V-shaped polar molecules encapsulated into Cs (10528)-C72: stability and nonlinear optical response.

Recently, a new sulfide cluster fullerene, Sc2S@Cs (10528)-C72 containing two pairs of fused pentagons has been isolated and characterized (Chen et al., J. Am. Chem. Soc., 2012, 134, 7851). Inspired by this investigation, we propose a question: what properties will be influenced by the interaction between the encapsulated V-shaped polar molecule and C72? To answer this question, four encapsulated metallic fullerenes (EMFs) M2N@C72 (M = Sc or Y, N = S or O) along with pristine Cs-C72 (10528) were investigated by quantum chemistry methods. The results show that the Egap (3.01-3.14 eV) of M2N@C72 are significantly greater than that of pristine Cs-C72 (10528) (2.34 eV). This indicates that the stabilities of these EMFs increase by encapsulating the V-shaped polar molecule into the fullerene. Furthermore, the natural bond orbital (NBO) charge analysis indicates electron transfer from M2N to C72 cage, which plays a crucial role in enhancing first hyperpolarizability (ßtot). The ßtot follows the order of 1174 au (Y2O@C72) ≈ 1179 au (Sc2O@C72) > 886 au (Y2S@C72) ≈ 864 au (Sc2S@C72) > 355 au (C72). This indicates that the ßtot of M2N@C72 is more remarkable than that of pristine Cs-C72 (10528) due to the induction effect of the encapsulated molecule. Compared with sulfide cluster fullerenes (Y2S@C72 and Sc2S@C72), oxide cluster fullerenes (Sc2O@C72 and Y2O@C72) show much larger ßtot due to the small ionic radius and the large electronegativity of oxygen. In contrast, the metal element (scandium and yttrium) has a slight influence on the ßtot. Thus, oxide cluster fullerenes are candidates to become promising nonlinear optical materials with higher performance.

Structures and electro-optical properties of Möbius [n]Cyclacenes[13-18]: a theoretical study.

Due to the unusual properties of the Möbius cyclacenes (MC) such as π electrons, MC has drawn the extensive attention of scientists. In the present work, six [n]MC (n = 13-18, n is the number of benzenoid rings) were systematically investigated to explore the size-dependent effects on structures, electro-optical properties, and frontier molecule orbits (FMO). According to the dihedral angles (C-C-C-C), the un-twisted area and twisted area are defined, respectively. The twisted area mainly distributes on seven or eight benzenoid rings for [n]MC (n = 13-18). Further, the polarizability (α0) and first hyperpolarizability (ß0) of [n]MC (n = 13-18) were calculated with three density functional methods (BHandHLYP, Cam-B3LYP, and M06-2X). Results show that the α0 values increase linearly with increasing the number (n) of benzenoid rings. Significantly, the ß0 values are increased to zigzag with increasing the number (n) of benzenoid rings. Interestingly, when n is even (14, 16, and 18), the electron transfer is from the twisted area to the un-twisted area, but the electron transfer is from the un-twisted area to the twisted area when n is odd (13, 15, and 17).

Influence of spiral framework on nonlinear optical materials.

A series of spiral donor-π-acceptor frameworks (i.e. 2-2, 3-3, 4-4, and 5-5) based on 4-nitrophenyldiphenylamine with π-conjugated linear acenes (naphthalenes, anthracenes, tetracenes, and pentacenes) serving as the electron donor and nitro (NO2 ) groups serving as the electron acceptor were designed to investigate the relationships between the nonlinear optical (NLO) responses and the spirality in the frameworks. A parameter denoted as D was defined to describe the extent of the spiral framework. The D value reached its maximum if the number of NO2 groups was equal to the number of fused benzene rings contained in the linear acene. A longer 4-nitrophenyldiphenylamine chain led to a larger D value and, further, to a larger first hyperpolarizability. Different from traditional NLO materials with charge transfer occurring in the one-dimensional direction, charge transfer in 2-2, 3-3, 4-4, and 5-5 occur in three-dimensional directions due to the attractive spiral frameworks, and this is of great importance in the design of NLO materials. The origin of such an enhancement in the NLO properties of these spiral frameworks was explained with the aid of molecular orbital analysis.

Redox control of ferrocene-based complexes with systematically extended π-conjugated connectors: switchable and tailorable second order nonlinear optics.

The studies of geometrical structures, thermal stabilities, redox properties, nonlinear responses and optoelectronic properties have been carried out on a series of novel ferrocenyl (Fc) chromophores with the view of assessing their switchable and tailorable second order nonlinear optics (NLO). The use of a constant Fc donor and a 4,4'-bipyridinium acceptor and varied conjugated bridges makes it possible to systematically determine the contribution of organic connectors to chromophore nonlinear optical activities. The structures reveal that both the reduction reactions and organic connectors have a significant influence on 4,4'-bipyridinium. The potential energy surface maps along with plots of reduced density gradient mirror the thermal stabilities of the Fc-based chromophores. The first and second reductions take place preferentially at the 4,4'-bipyridinium moieties. Significantly, the reduction processes result in the molecular switches with large NLO contrast varying from zero or very small to a large value. Moreover, time-dependent density functional theory results indicate that the absorption peaks are mainly attributed to Fc to 4,4'-bipyridinium charge transfer and the mixture of intramolecular charge transfer within the two respective 4,4'-bipyridinium moieties coupled with interlayer charge transfer between the two 4,4'-bipyridinium moieties. This provides us with comprehensive information on the effect of organic connectors on the NLO properties.

Enhancement of second-order nonlinear optical response in boron nitride nanocone: Li-doped effect.

The unusual properties of Li-doped boron nitride nanomaterials have been paid further attention due to their wide applications in many promising fields. Here, density functional theory (DFT) calculations have been carried out to investigate the second-order nonlinear optical (NLO) properties of boron nitride nanocone (BNNC) and its Li-doped BNNC derivatives. The natural bond orbital charge, electron location function, localized orbital locator and frontier molecular orbital analysis offer further insights into the electron density of the Li-doped BNNC derivatives. The electron density is effectively bounded by the Li atom and its neighboring B atoms. The Li-doped BNNC molecules exhibit large static first hyperpolarizabilities (ß(tot)) up to 1.19×10³ a.u. for Li@2N-BNNC, 5.05×10³ a.u. for Li@2B-BNNC, and 1.08×10³ a.u. for Li@BN-BNNC, which are significantly larger than that of the non-doped BNNC (1.07×10² a.u.). The further investigations show that there are clearly dependencies of the first hyperpolarizabilities on the transition energies and oscillator strengths. Moreover, time-dependent DFT results show that the charge transfer from BNNC to Li atom becomes more pronounced as doping the Li atom to BNNC. It is also found that the frequency-dependent effect on the first hyperpolarizabilities is weak, which may be beneficial to experimentalists for designing Li-doped BNNC molecules with large NLO responses.

Isomeric thiophene-fused benzocarborane molecules--different lithium doping effect on the nonlinear optical property.

Recently, two isomeric thiophene-fused benzocarborane derivatives Tb1 and Tb2 with different locations of sulfur atoms, labeled as 1, 4 and 6, 9 of the thiophene were synthesized by Morisaki (Chem.-Eur. J., 2012, 18, 11251-11257) and Barrere (Macromolecules, 2009, 42, 2981-2987), respectively. In the present work, natural bond orbital (NBO) analysis shows that after doping one lithium atom into the isomeric structures Tb1 and Tb2, the electrons transfer to different regions in Tb1 and Tb2. For Tb1-Li, the transferred electrons mainly locate at S1, C2, C3, and S4, but for Tb2-Li, the transferred electrons mainly locate at C2, C3, C7, and C8. Significantly, the charge distribution is a crucial factor influencing the static first hyperpolarizabilities for Tb1-Li and Tb2-Li. Furthermore, the ßtot value of Tb1-Li is 6222 au, which is about 160 times larger than that of Tb1 (39 au). However, the ßtot value of Tb2-Li (498 au) is only about 5 times larger than that of the corresponding Tb2 (91 au). It is our expectation that this work could provide useful information for the development of nonlinear optical materials based on carboranes.

Strategy for enhancing second-order nonlinear optical properties of the Pt(II) dithienylethene complexes: substituent effect, π-conjugated influence, and photoisomerization switch.

The second-order nonlinear optical (NLO) properties of a series of Pt(II) dithienylethene (DTE) complexes possessing the reversible photochromic behavior have been investigated by density functional theory (DFT) combined with the analytic derivatives method. The results show that the calculated static first hyperpolarizabilities (ßtot) of the open-ring and closed-ring systems significantly increase in the range of 2.1-4.5 times through strengthening of the electron-withdrawing ability of the substituent R (R = H, CF3, NO2) and an increase of the number of thiophene rings. Moreover, there is a large enhancement of the ßtot values from the open-ring systems to the corresponding closed-ring systems. This efficient enhancement is attributed to the better delocalization of the π-electron system, the more obvious degree of charge transfer, and the larger f(os)/E(gm)(3) (f(os) is the oscillator strength, and E(gm) is the transition energy between the ground and the excited states) values in the closed forms according to the bond length alternation (BLA) and time-dependent density functional theory (TDDFT) calculations. In addition, the dispersion has less influence on the frequency-dependent first hyperpolarizabilities (ßtot(ω)) of the studied systems at the low-frequency area ω (0.000-0.040 au). Our present work would be beneficial for further theoretical and experimental studies on large second-order NLO responses of metal complexes.

Theoretical investigation on the 2e/12c bond and second hyperpolarizability of azaphenalenyl radical dimers: strength and effect of dimerization.

An increasing number of chemists have focused on the investigations of two-electron/multicenter bond (2e/mc) that was first introduced to describe the structure of radical dimers. In this work, the dimerization of two isoelectronic radicals, triazaphenalenyl (TAP) and hexaazaphenalenyl (HAP) has been investigated in theory. Results show TAP2 is a stable dimer with stronger 2e/12c bond and larger interaction energy, while HAP2 is a less stable dimer with larger diradical character. Interestingly, the ultraviolet-visible absorption spectra suggest that the dimerization induces a longer wavelength absorption in visible area, which is dependent on the strength of dimerization. Significantly, the amplitude of second hyperpolarizability (γ(yyyy)) of HAP2 is 1.36 × 10(6) a.u. that is larger than 7.79 × 10(4) a.u. of TAP2 because of the larger diradical character of HAP2. Therefore, the results indicate that the strength of radical dimerization can be effectively detected by comparing the magnitude of third order non-linear optical response, which is beneficial for further theoretical and experimental studies on the properties of complexes formed by radical dimerization.

The symmetric and asymmetric thiophene-fused benzocarborane: structures and first hyperpolarizabilities.

The unusual properties of thiophene-fused benzocarborane have attracted a lot of interest in recent years due to their wide applications in photonics and optoelectronics. In the present work, nine molecules [M, N] (M, N are labeled as the number of thiophene rings on the left and right part, respectively) on the basis of thiophene-fused benzocarborane were considered. The first hyperpolarizability (ß tot) values of three synthesized symmetric molecules [1, 1], [2, 2], [3, 3] (M=N, Chem. Eur. J 2012. 18, 11251-11257) and six asymmetric molecules [1, 2], [1, 3], [1, 4], [1, 5], [2, 3], [2, 4] (M≠N) were investigated, ß tot values of symmetric molecules show the order: 39 of [1, 1]< 800 of [2, 2]< 903 au of [3, 3], which indicate that ß tot value increases with increasing the number of thiophene ring for symmetric molecules. The other order of ß tot values can be observed: 39 of [1, 1]< 800 of [1, 2]< 3553 of [1, 3]< 7998 of [1, 4]< 13049 au of [1, 5] and 66 of [2, 2]< 3240 of [2, 3]< 8029 au of [2, 4]. Interestingly, when sum of M and N is constant, larger difference between M and N is, larger ß tot value is: 800 au of [2, 2]< 3553 au of [1, 3]; 3240 au of [2, 3] < 7998 au of [1, 4]; 903 au of [3, 3]< 8029 au of [2, 4]< 13049 au of [1, 5]. Significantly, [1, 5] with six thiophene rings has the largest ß tot value (13049 au) which is greatly larger than 903 au of [3, 3] with six thiophene rings. Furthermore, the natural bond orbital (NBO) charge populations, the nucleus-independent chemical shift (NICS), the bond length alternation (BLA) of the nine molecules and crucial transition were studied in our work. We hope that the present work will be beneficial for future theoretical and experimental studies on the electro-optical properties of thiophene-fused benzocarborane molecules.

Third-order nonlinear optical properties of molecules containing aromatic diimides: effects of the aromatic core size and a redox-switchable modification.

The third-order nonlinear optical (NLO) properties of aromatic diimide molecules have been studied for the first time using density functional theory (DFT) with a finite field (FF). This study shows that the size of the aromatic core can affect the static second hyperpolarizability (γ). Increasing the number of benzenes along the longitudinal axis can effectively improve the γ values because the degree of charge transfer along the longitudinal direction increases, whereas an increase in the number of benzenes along the perpendicular axis does not enhance the γ values. Furthermore, the NLO responses of the reduced form radical anions 1(-), 5(-) and 6(-), which were obtained by a reversible redox process, are discussed. The results show that the γ values of the radical anions are changed by the redox process. For the reduced form radical anion 6(-), the γ value is -1906.71×10(-36)esu, and its absolute value is ∼7.3 times larger than that of its neutral parent. An analysis of the BLA values demonstrates that the γ value is closely related to the conjugation of the aromatic core used in the redox process.

Theoretical investigation on switchable second-order nonlinear optical (NLO) properties of novel cyclopentadienylcobalt linear [4]phenylene complexes.

As a kind of novel organometallic complexes, the cyclopentadienylcobalt (CpCo) linear [4]phenylene complexes (4 = number of benzene rings) display efficient switchable nonlinear optical (NLO) response when CpCo reversibly migrates along the linear [4]phenylene triggered by heating or lighting. In this paper, the second-order NLO properties for CpCo linear [4]phenylene complexes were calculated by using the density functional theory (DFT) methods with four functionals. All of the functionals yield the same order of ß tot values: 1<2<4<3. The effect of solvent on second-order NLO properties has been studied using polarized continuum model (PCM) in the tetrahydrofuran (THF) solution. The solvent leads to a slight enhancement of the NLO responses for the studied complexes relevant to their NLO responses in vacuo. The electronic absorption spectra were investigated by the TDDFT methods. The TDDFT calculations indicate that the maximum absorption peaks of complexes 2-4 in the near-infrared spectrum area show the bathochromic shift together with a decreasing intensity compared to complex 1. We have also found that the cobalt (Co) atom acts as a donor in all the organometallic complexes and the d → π* and π → π* charge transfer (CT) transitions contribute to the enhancement of second-order NLO response. Furthermore, two experimentally existing complexes 1 and 3 are found to have a large difference in ß tot values. It is our expectation that this difference may stimulate the search for a new type of switchable NLO material based on CpCo linear [4]phenylene complexes.

After the electronic field: structure, bonding, and the first hyperpolarizability of HArF.

In this work, we add different strength of external electric field (E(ext)) along molecule axis (Z-axis) to investigate the electric field induced effect on HArF structure. The H-Ar bond is the shortest at E(ext) = -189 × 10(-4) and the Ar-F bond show shortest value at E(ext) = 185 × 10(-4) au. Furthermore, the wiberg bond index analyses show that with the variation of HArF structure, the covalent bond H-Ar shows downtrend (ranging from 0.79 to 0.69) and ionic bond Ar-F shows uptrend (ranging from 0.04 to 0.17). Interestingly, the natural bond orbital analyses show that the charges of F atom range from -0.961 to -0.771 and the charges of H atoms range from 0.402 to 0.246. Due to weakened charge transfer, the first hyperpolarizability (ß(tot)) can be modulated from 4078 to 1087 au. On the other hand, make our results more useful to experimentalists, the frequency-dependent first hyperpolarizabilities were investigated by the coupled perturbed Hartree-Fork method. We hope that this work may offer a new idea for application of noble-gas hydrides.