Large Second-Harmonic Generation Responses Achieved by the

Article Cite This: Chem. Mater. 2017, 29, 9200-9207

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Large Second-Harmonic Generation Responses Achieved by the Dimeric [Ge2Se4(μ-Se2)]4− Functional Motif in Polar Polyselenides A4Ge4Se12 (A = Rb, Cs) Bin-Wen Liu,† Min-Yi Zhang,† Xiao-Ming Jiang,* Shu-Fang Li, Hui-Yi Zeng, Guo-Qiang Wang, Yu-Hang Fan, Yong-Fei Su, Chunsen Li,* Guo-Cong Guo,* and Jin-Shun Huang State Key Laboratory of Structural Chemistry, Fujian Institute of Research on the Structure of Matter, Chinese Academy of Sciences, Fuzhou, Fujian 350002, P. R. China S Supporting Information *

ABSTRACT: Two new polar polyselenides Rb4Ge4Se12 (1) and Cs4Ge4Se12 (2) with rarely reported dimeric [Ge2Se4(μ-Se2)]4− units were synthesized. They present large second-harmonic generation (SHG) intensities of 7.5 and 6.5 times that of the benchmark AgGaS2 with type I phase-matching behavior, high laser-induced damaged thresholds, a wide transmission region and congruently melting behavior, making them excellent candidates for IR nonlinear optical (NLO) applications. The SHG functional motifs of both compounds are determined to be [Ge2Se4(μ-Se2)]4− unit by time-dependent density functional theory calculation, which further reveals that charge transfers from the lone pairs of terminal Se atoms to the five σ* orbitals of five-membered ring Ge2Se3 have a predominant contribution to the total SHG effect.

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pucker layer 2/∞[Ge2Se5]2− in Na2Ge2Se5,29 and 3D diamondlike framework 3/∞[CdGeS4]2− in Li2CdGeS4.30 Additionally, a higher level of polyanionic versatility can be obtained because chalcogenide anions can also be condensed with Q−Q bonds adopting various binding modes in molecular and polymeric complexes. 31,32 Therefore, through Q−Q bonding, the [GeQ4]4− tetrahedral units have the potential to produce an even greater family of compounds, which may possess interesting structures and promising properties. The incorporation of Q−Q bonds in NLO metal chalcogenides may be beneficial to larger macroscopic second-harmonic generation (SHG) efficiency of the whole compound owing to two facts. First, Q−Q bonds are much more covalent than metal−Q bonds with significant ionicity, and are normally more easily polarizable and contribute more to SHG efficiency compared with ionic bonds.33 Second, the formation of Q−Q bonds of MQ4 (M = metal) units usually reduce their symmetry from perfect nonpolar Td to a polar one and make the MQ4 units possess a nonzero dipole moment, which is an important source of SHG efficiency. SHG functional motifs of NLO materials can be defined as structural building units and their topology order that are essential for the generation of SHG efficiency.34 The determination of SHG functional motif is very important for the rational design of NLO materials. Although many IR NLO candidates were

INTRODUCTION Infrared nonlinear optical (NLO) materials are highly attractive in all-solid-state lasers for the generation of coherent tunable radiation in the IR region, a spectral range of importance for molecular spectroscopy, atmospheric sensing, and various optoelectronic devices.1−5 Comparing with the well-known oxide-based NLO crystals, such as BaB2O 4,6 LiB3 O5 ,7 KH2PO4,8 and KTiOPO4,9 which have been widely used in the ultraviolet (UV) and visible regions, the number of available NLO materials that can be applied in the IR region is limited. Currently, the typical IR NLO materials are mainly chalcopyrite semiconductors such as AgGaS2,10 AgGaSe211 and ZnGeP2.12 These crystals exhibit wide infrared transparency and high nonlinearity, but all of them suffer from defects like strong twophoton absorption and poor laser damage thresholds, which seriously limit their high power laser applications.13 Thus, exploring new excellent IR NLO materials is a pressing and important topic in NLO materials chemistry. Recently, significant efforts have been made on discovering new IR NLO materials.14−20 Chalcogermanates are a rich resource for IR NLO materials mainly because Ge prefers to adopt acentric tetrahedral coordination with chalcogen atoms [GeQ4]4− (Q = S, Se, Te). Some chalcogenide clusters composed of [GeQ4]4− tetrahedral units, such as dimeric [Ge2Q6]4− and [Ge2Q7]6−,21−24 trimeric [Ge3Q9]6−,25 and adamantine-like [Ge4Q10]4−,26 can be assembled by bridging a variety of metal or nonmetal ions into discrete and extended structures, such as discrete molecule [GeS4]4− in Na2BaGeS4,27 1D zigzag chain 1/∞[(Ga/Ge)3Se9]7.5− in PbGa2GeSe6,28 2D © 2017 American Chemical Society

Received: July 20, 2017 Revised: September 20, 2017 Published: October 5, 2017 9200

DOI: 10.1021/acs.chemmater.7b03046 Chem. Mater. 2017, 29, 9200−9207

Article

Chemistry of Materials explored and considerable studies on their crystal structures and NLO performances were accomplished in the past decades,35 their SHG functional motifs are far from clear. Guided by these ideas, our exploration in chalcogermanates leads to the discovery of two new ternary polar polyselenides A4Ge4Se12 (A = Rb, Cs). Their most striking structural features is the rarely reported dimeric [Ge2Se4(μ-Se2)]4− building units, which are assembled in such a manner that gives rise to the net macroscopic polarity along the c direction. They exhibit strong SHG responses of 7.5 and 6.5 times that of commercial AgGaS2 with phase-matching behavior at the incident 1910 nm laser, large laser-induced damaged thresholds (LIDTs), wide optical transparency region, and congruent melting behavior, which comprehensively make them excellent candidates for IR NLO applications. Meanwhile, theoretical calculations were performed to investigate the structural origin of their strong SHG effects.

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Table 1. Crystal Data and Structure Refinement Parameters for 1 and 2

EXPERIMENTAL SECTION

Syntheses. All of the following chemicals were used as received without further purification: barium metal (99.9%, Aladdin Chemistry Co. Ltd.), germanium powder (99.99%, Aladdin Chemistry Co. Ltd.), selenium powder (99.99%, Aladdin Chemistry Co. Ltd.), rubidium chloride (99.9%, Aladdin Chemistry Co. Ltd.), and cesium chloride (99.9%, Aladdin Chemistry Co. Ltd.). Given the easily oxidized barium element and hygroscopic rubidium chloride and cesium chloride, all starting reactants were handled inside an Ar-filled glovebox with controlled oxygen and moisture levels below 0.1 ppm. A stoichiometric mixture of the starting materials Ba, Ge, Se, and ACl (A = Rb, Cs) as a reactive flux with a molar ratio of 1:4:12:8 was loaded into a sealed silica tube evacuated to 10−4 Torr. The tubes were then placed into a temperature-controlled muffle furnace, slowly heated to 750 °C maintaining that temperature for 96 h, and finally slowly cooled down to 350 °C before switching off the furnace. The products were washed by distilled water to remove the excess RbCl or CsCl, and red single crystals of title compounds were hand-picked under microscope for properties measurement. Several attempts to synthesize the compound without adding Ba as a reactant failed to obtain the desired products. The additional reactant Ba may play the reaction promoter role in the formation of title compounds. Energy-Dispersive Analyses by X-ray (EDX). EDX was performed with an EDX-equipped Hitachi S-3500 SEM spectrometer on the crystals that were used for X-ray single-crystal diffraction. The measurements confirmed the presence of A (A = Rb, Cs), Ge and Se in an approximate molar ratio of 1.0:1.1:3.0 and 1.0:1.0:3.1 for 1 and 2, respectively, which agree well with the results from single-crystal X-ray diffraction (Figure S1). Single-Crystal X-ray Diffraction. Single crystals of both title compounds were selected and mounted on the tips of glass fibers for X-ray diffraction. Intensity data sets were collected on a Rigaku Pilatus CCD diffractometer equipped with a graphite-monochromated Mo− Kα radiation (λ = 0.71073 Å) at 293 K. The structures were solved by direct methods and refined by full-matrix least-squares method on F2 with anisotropic thermal parameters for all atoms. All the calculations were performed with the Siemens SHELXTL version 5 package of crystallographic software.36 The parameters for data collection and the details of the structure refinement are presented in Table 1. Selected bond distances are listed in Table S1. Further details on the crystal structures investigation may be obtained from the Fachinformationszentrum Karlsruhe, 76344 Eggenstein-Leo-poldshafen, Germany (fax: (+49)7247-808-666; E-mail: crysda-ta@fiz-karlsruhe.de), on quoting the depository number ICSD-432588 for 1, ICSD-432589 for 2. Powder X-ray Diffraction (XRD). The powder XRD measurements were performed on the ground crystals of 1 and 2 with an automated Rigaku MiniFlex II X-ray diffractometer equipped with a diffracted monochromator set for Cu−Kα radiation (λ = 1.54057 Å). The operating 2θ angle ranges from 5 to 65°. The observed powder XRD patterns were in agreement with the simulated ones (Figure S2).

a

empirical formula

Rb4Ge4Se12 (1)

Cs4Ge4Se12 (2)

Fw space group a (Å) b (Å) c (Å) V (Å3) Z Dcalcd (g cm−3) μ (mm−1) GOF on F2 R1a (I > 2σ (I)) wR2b (I > 2σ (I)) R1a (all data) wR2b (all data) Flack x Δρmax/Δρmin, (e Å−3)

1579.76 Pna21 14.870(8) 13.800(8) 12.445(6) 2554(2) 4 4.109 29.327 1.054 0.0473 0.0938 0.0680 0.1038 0.00(4) 1.626/−1.032

1769.52 Pna21 15.193(6) 13.944(5) 12.845(5) 2721.4(2) 4 4.319 25.687 1.002 0.0388 0.0767 0.0550 0.0831 0.00(2) 2.133/−0.796

R = Σ∥Fo| − |Fc∥/Σ|Fo|, bwR = (Σ(w(Fo2−Fc2)2)/Σ(w(Fo2)2))1/2.

Infrared and UV−Vis−NIR Diffuse Reflectance Spectroscopy. The optical diffuse reflectance spectra (220−2500 nm) of powder samples of 1 and 2 were obtained by using a Perkin−Elmer Lambda 900 UV−Vis−NIR spectrophotometer equipped with an integrating sphere attachment. The absorption spectra were calculated from the reflection spectra using the Kubelka−Munk formula.37 IR spectra were recorded on a Nicolet Magana 750 FT−IR spectrophotometer range from 400 to 4000 cm−1, with the samples embedded in KBr matrices. Differential Thermal Analysis (DTA). Thermal properties of both title compounds were investigated by differential scanning calorimetric analysis using the TGA/DSC Mettler Toledo thermal analyzer. Polycrystalline samples (23.4 mg for 1 and 20.2 mg for 2) were placed in sealed silica tubes and then subjected to a heating/ cooling cycle at a rate of 5 °C/min. Reproducibility of the results was confirmed by running two heating/cooling cycles. Melted residues were analyzed by powder XRD after each cycle. SHG Measurements. The powder SHG measurements of 1 and 2 were investigated under a laser irradiation at 1910 nm using a modified Kurtz-Perry powder technique.38 Microcrystalline samples were sieved into several distinct particle size ranges (30−40, 40−50, 50−75, 75− 100, 100−125, 125−150, and 150−200 μm) for the SHG phasematching measurements. And cylinder AgGaS2 single crystals, provided by Anhui Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, were ground and sieved in the same ranges serving as the reference. The frequency-doubling signal (955 nm) was detected by an Andor’s DU420A-BR-DD CCD. Powder LIDT Measurements.39−42 The powder LIDTs measurements of 1 and 2 were performed on the microcrystalline sample (75− 100 μm) using the focused high-power 1064 nm laser beam with a pulse width τp of 10 ns and a repetition rate of 1 Hz. The microcrystalline sample of AgGaS2 with a similar particle size was used as the reference. The power of the laser beam was measured by a Nova II sensor display with a PE50-DIF-C energy sensor. An optical concave lens was used to adjust the diameter of the laser beam to obtain different intensities. The measurements were performed by gradually increasing the laser power until the color of the sample changed, at which the laser power was defined as the damage threshold. Areas of the damaged spots were then measured to estimate the value of LIDT. Computational Procedure. Calculations of electronic band structures were performed for 1 and 2 based on the structures determined by single-crystal X-ray diffraction. The CASTEP code43 on the basis of density functional theory was used to calculate band structures and densities of state (DOS) using a plane-wave expansion of the wave functions and norm-conserving pseudo potentials,44,45 in which the orbital electrons of Rb 4s24p65s1, Cs 5s25p66s1, Ge 4s24p2, and Se 4s24p4 were treated as valence electrons. The number of plane 9201

DOI: 10.1021/acs.chemmater.7b03046 Chem. Mater. 2017, 29, 9200−9207

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Chemistry of Materials waves included in the basis was determined using a cutoff energy of 400 eV, and the numerical integration of the Brillouin zone was performed using a 2 × 2 × 2 Monkhorst−Pack k-point sampling, for both compounds. The complex dielectric function ε(ω) = ε1(ω)+iε2(ω) was calculated, of which the imaginary part ε2(ω) generated the other optical constants via the Kramers−Kroning transform.46,47 The second-order susceptibilities are expressed in terms of the first-order susceptibilities as ma χijk(2) (ω3 , ω1, ω2) = 2 3 χii(1) (ω3)χjj(1) (ω1)χkk(1) (ω2), which are derived Ne from a classical anharmonic oscillator (AHO) model.48 The m, e, and N are the electron mass, electron charge and number density of atoms, respectively, and the parameter a characterizes the nonlinearity of the response. To further investigate the SHG functional motifs in both compounds, we obtained several calculation models with increasing levels of complexity from their structures by getting rid of connections at appropriate positions, and the dangling bonds are saturated by methyl groups. Geometric optimizations were performed by the hybrid density functional B3LYP49 and 6-311+G* basis set. The excitations were calculated using the time-dependent density functional theory (TDDFT) with the 6-311++g** basis sets. The calculations were performed using Gaussian 03 program package.50 The NLO properties were calculated by employing the sum-overstate (SOS) method51,52 developed by Cheng’s group.53,54 The compact expression of the tensor component of polarizability and the frequency-dependent first-order hyperpolarizability obtained from transition moment, dipole moment and transition energy, can be written as follows βijk =

1 P(i , j , k ; − ωpol , ω1, ω2) 4ℏ2 ⎡ ⎤ (μi )gm (μj̅ )mn (μk )gn ⎥ ∑ ∑⎢ ⎣ (ωmg − ωpol − i Γmg )(ωng − ω1 − i Γng ) ⎥⎦ m≠g n≠g ⎢

Figure 1. (a) Ball-and-stick structure of 2 viewed slightly skewed from the b-axis. (b) Single 1∞[Ge4Se12]4− chain built of dimeric [Ge2Se4(μSe2)]4− units by sharing Se4 and Se10 atoms. The [Ge2Se4(μ-Se2)]4− unit is identified by the blue-dotted circle.

All Ge atoms in both compounds are tetrahedrally coordinated by three bridged Se atoms with Ge−Se bond lengths of 2.379(1)−2.410(1) Å and one terminal Se atom with Ge−Se bond lengths of 2.243(1)−2.257(2) Å. The GeSe4 tetrahedra moieties are distorted from the ideal geometry evidenced by the Se−Ge−Se angles ranging from 95.68(7) to 119.08(8)°. Both Ge−Se bond distances and Se−Ge−Se bond angles observed in 1 and 2 are in agreement with those in Na2Ge2Se5, and BaGa2GeSe6.57 The Se−Se bond lengths ranging from 2.350(1) Å to 2.356(1) Å, are consistent with those in Cs2SnAs2Q9 (Q = S, Se)58, APSe5 (A= K, Rb)59 and A2P2Se5 (A= Rb, Cs).60 In addition, the coordination circumstances of Rb+ and Cs+ are shown in Figure S3 with atom distances marked, and the Rb (and Cs)−Se distances are also reasonable.61 Differential Thermal Analysis. The DTA measurement results of 1 and 2 are shown in Figure 2a, b, as can be seen,

(1)

For the first-order nonlinear response, we are interested in the vector component along the ground state dipole moment direction (βvec) and the total hyper-Rayleigh scattering (HRS) first hyperpolarizability (βtot). These are defined as βvec = (μ1β1 + μ2 β2 + μ3 β3)/|μ|

(2)

βtot = (βx2 + βy2 + βz2)1/2

(3)

Here, the HRS quantities are reported for the static case (λ = ∞) as well as accounting for frequency dispersion (λ = 1064 nm). Natural bond orbital (NBO)55 analysis was performed using the NBO 3.1 embedded in Gaussian 03 program package to estimate natural atomic charges.

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RESULTS AND DISCUSSION Crystal Structures. Both polyselenides 1 and 2 crystallize in the polar orthorhombic space group Pna21 (No. 33). As they are isostructural, the following discussion will mainly focus on Cs-salt. As shown in Figure 1a, its structure features infinite one-dimensional polyanionic 1∞[Ge4Se12]4− chains extending along the b direction, separated by the counter Cs+ cations. Two GeSe4 tetrahedra are coupled by sharing a Se atom and a diselenide Se2 linkage to form a dimeric [Ge2Se4(μ-Se2)]4− unit; the [Ge2Se4(μ-Se2)]4− units are further linked by sharing Se4 and Se10 atoms with alternating [Ge(1)Ge(4)Se5(μSe2)]4− and [Ge(2)Ge(3)Se5(μ-Se2)]4− to generate the 1D 1 4− chains (Figure 1b). The asymmetrically bridged ∞[Ge4Se12] ditetrahedral [Ge2Se4(μ-Se2)]4− polyanions are first discovered in solid-state inorganic compounds; before this, only two organic−inorganic hybrids have been reported, namely, (enH 2 )[{Mn(en) 2 (enH)} 2 (μ-en)](Ge 2 Se 7 ) 2 and Mn[(dien)2]2Ge2Se7.56

Figure 2. DTA curves reveal the melting and recrystallization events of (a) 1 and (b) 2. (c) UV−Vis diffuse reflectance spectra. (d) IR spectra of 1 and 2. 9202

DOI: 10.1021/acs.chemmater.7b03046 Chem. Mater. 2017, 29, 9200−9207

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Chemistry of Materials

which are even greater than commercial used AgGaSe2 (χ(2) = 66 pm/V),63 and recently discovered IR-NLO materials, such as CsM3Se 6 (M = Ga/Sn, In/Sn),64 SnGa4 Se7 ,65 and Na2Hg3Sn2S8.66 The powder LIDTs of 1 and 2 and AgGaS2 measured by the single pulse powder LIDT method are shown in Figure 3b and Table S3. The LIDTs estimated for both compounds are 4.5 MW cm−2, namely, three times that of AgGaS2 (1.5 MW cm−2). Exploring new materials with both large SHG and high LIDTs in IR-NLO material science and laser technology is important and challenging. These experimental results indicate that compounds 1 and 2 may be good candidates for IR-NLO applications. Meanwhile, the high electropositive alkali metals in NLO metal chalcogenides usually form strong ionic bonds with surrounding anions and may result in high LIDTs, as bond energy of ionic bonds are normally higher than those of covalent bonds.39 Therefore, IR NLO chalcogenides with large SHG efficiency and high LIDT may be created by the combinations of Q−Q bonds and high electropositive alkali metals. Structure−Property Relationships. The net dipole moment of a NLO material is positively associated with its macroscopic SHG efficiency. The dipole moments of [Ge2Se4(μ-Se2)]4− units in the structures of 1 and 2 were calculated using the bond-valence approach proposed by Poeppelmeier et al.67,68 The dipole moments are listed in Table S4 and their directions are marked in Figure 4. The

both one endothermic peak upon heating and one exothermic peak on the cooling curve are found in two cycles. Powder XRD patterns of the residue from one melting/recrystallization cycle are in agreement with those before melting (Figure S2), indicating these phases are congruently melting. Comparing to the well-known IR-NLO materials, such as AgGaS2 (melting point 996 °C) and AgGaSe2 (melting point 850 °C), compounds 1 and 2 have relatively lower melting temperatures of 345 and 452 °C, respectively. The congruent-melting and low melting point behavior makes it feasible to using Bridgman method to grow bulk crystals, which are needed for further physical property studies and practical application in IR NLO optics. Infrared and UV−Vis−NIR Diffuse Reflectance Spectroscopy. The UV−Visible−NIR diffuse reflectance spectra of the solid samples in Figure 2c give the absorption edges at 2.10 and 2.15 eV for 1 and 2, respectively, consistent with the observed red color of the crystals. Additionally, the IR transmission spectra of 1 and 2 are depicted in Figure 2d, together with UV−Visible−NIR diffuse reflectance spectra, indicating that no bond absorption in a broad spectral range from 0.6 to 25 μm occurs, which covers the important band ranges of 3−5 and 8−14 μm of atmospheric transparent windows. These results suggest that they may be suitable for a variety of NLO applications in longer wavelength (mid- and farIR) regions. Powder SHG vs LIDT. Given that the NCS structure features title compounds, the powder SHG measurements were performed at a laser irradiation of 1910 nm, by a modified Kurtz powder method. The measured SHG signals of ground crystals of both compounds and the reference AgGaS2 as a function of particle size are shown in Figure 3a and Figure S4.

Figure 4. Ball-and-stick representations of 2 in the bc-plane, the Cs+ cations have been removed for clarity. The black arrows show the local dipole moments of [Ge2Se4(μ-Se2)]4− units, which show that a net macroscopic polarization along the c direction.

Figure 3. (a) Phase-matching results for 1 and 2. Inset: SHG signals of 1, 2, and AgGaS2 with the particle size of 150−200 um at the incident laser with wavelength of 1910 nm and pulse width of 10 ns. (b) Relative LIDTs and relative SHG intensities of 1 and 2 and AgGaS2 at the incident laser with wavelength of 1064 nm and pulse width of 10 ns.

dipoles of [Ge2Se4(μ-Se2)]4− units cancel out completely in the a and b directions, leaving the net nonzero dipole moments in the c direction. Therefore, the NCS packing of the polyanionic 1/∞[Ge4Se12]4− chains and the in-phase alignment of the dipoles of [Ge2Se4(μ-Se2)]4− units may be responsible for the large SHG observed in both compounds. A perfect GeSe4 tetrahedron has zero static dipole moment because of its nonpolar point group Td; however, the GeSe4 units in the title compounds are highly distorted and possess significantly nonzero dipole moment resulting from the combination of nonequivalent coordination of Se atoms (namely, bridged and terminal Se atoms) and the formation of Se−Se bonds. Obviously, the different cation size of Rb+ (ionic radius: 1.63 Å) and Cs+ cations (ionic radius: 1.78 Å) affect the interactions between the anionic and cationic groups, resulting in the

Their SHG intensities increase with the increasing particle size and then reach a plateau at the maximum value after a certain particle size. Such correlation is consistent with a phasematching behavior according to the rule proposed by Kurtz and Perry. The measured SHG intensities of 1 and 2 are 7.5 and 6.5 times that of AgGaS2 (d36 = 13.7 pm/V)62 for the nonlinear frequency-doubling signals at 955 nm induced by the incident laser at 1910 nm (see inset of Figure 3a). According to Kurtz and Perry powder method, the absolute second-order susceptibility χ(2) was calculated using χ(2) = χref(2) (I2ω/ I2ωref)1/2 for the phase-matchable case, where I2ω and I2ωref are the measured SHG intensities for the samples of 1 and 2 and reference AgGaS2, respectively.59 Therefore, the estimated χ(2)eff values are 75.0 and 69.3 pm/V for 1 and 2, respectively, 9203

DOI: 10.1021/acs.chemmater.7b03046 Chem. Mater. 2017, 29, 9200−9207

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Chemistry of Materials different distortion of their frameworks,69 and consequently the different SHG intensities of 1 and 2. Electronic Structure Calculations. The calculated energy band diagrams in Figure S5 show that compounds 1 and 2 are direct band gap materials with band gaps of 1.830 and 1.836 eV. As can be seen from the total and partial DOS presented in Figure 5, for both compounds, the conductive band near its

Figure 7. (a) Three different models in TDDFT calculation. For the clarity of the presentation of calculation results, the Ge and Se atoms in the three models are renumbered, such as Ge(1, 2) and Se (1−6) in model II, which are different from the corresponding atom numbers used for crystal structure description. (b) Convergence behavior of βtot with the number of excited states of studied conformers.

Figure 5. Total and DOS of 1(a) and 2(b), whereas the Se(t), Se(b1) and Se(b2) represent the terminal Se, Se−Se boned Se, and bridging Se atoms, respectively.

containing only a GeSe4 tetrahedron; model-II is a medium one containing a [Ge2Se4(μ-Se2)]4− unit in which two Ge atoms (Ge1 and Ge2) and three Se atoms (Se3, Se4 and Se5) constitute a five-membered ring; model-III is an extension of the [Ge2Se4(μ-Se2)]4− unit with one neighboring Se atom and two neighboring Ge atoms added. By employing TDDFT combined with SOS method, we investigate the behavior of the convergence in the summation of the excited states for the studied conformers to obtain reliable results. Figure 7b shows all first-order hyperpolarizabilities of the studied conformers converged within 300 states. Therefore, all the discussions are based on the truncated SOS method with 300 excited states. The calculated static and dynamic (λ = 1064 nm) first-order hyperpolarizabilities (FOHP) are listed in Table 2. The order of

bottom is mostly composed of Se(b2)-4p states (here the terminal Se(3, 5, 9, 11) atoms, Se−Se bonded Se(2, 6, 8, 12) atoms, and bridged Se(1, 4, 7,10) atoms are labeled as t, b1, and b2, respectively), as well as a small portion of Se(b1)-4p, Se(b2)-4s, and Se(t)-4p states. The valence band close to the Fermi level originates predominately from Se-4p states with the contribution order of Se(t)-4p > Se(b1)-4p > Se(b2)-4p. Therefore, their optical absorptions can mainly be ascribed to the charge transfer from Se-4p states to Ge-4p and Se-4p states, and the electronic structure around the band edges is thus mainly derived from the GeSe4 groups, which provide the dominant states in the optical matrix elements describing the virtual excitations responsible for the SHG effect in 1 and 2. Particularly, Se(t)-4p states make the largest contribution to the valence band close to the Fermi level, indicating that the terminal Se atoms in NLO materials can be beneficial to the larger SHG effect. The title compounds have three independent second-order dielectric tensor elements under the restriction of Kleinman symmetry because they belong to mm2 point group symmetry. As shown in Figure 6, the calculated SHG coefficients d15, d24,

Table 2. First-Order Hyperpolarizabilities β (× 10−30 cm5/ esu) of the Studied Conformer Models conformer

model I

model II

model III

β (static) β (1064 nm)

7.69 12.68

12.47 131.65

11.72 111.70

amplitudes of dynamic FOHP is in accordance with those in the static case, namely, β(I)