Advantageous Units in Antimony Sulfides: Exploration and Design of

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Functional Inorganic Materials and Devices

Advantageous Units in Antimony Sulfides: Exploration and Design of Infrared Nonlinear Optical Materials Cong Hu, Bingbing Zhang, Bing-Hua Lei, Shilie Pan, and Zhihua Yang ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.8b08466 • Publication Date (Web): 12 Jul 2018 Downloaded from http://pubs.acs.org on July 12, 2018

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ACS Applied Materials & Interfaces

Advantageous Units in Antimony Sulfides: Exploration and Design of Infrared Nonlinear Optical Materials Cong Hu,1,2 Bingbing Zhang,1 Bing-Hua Lei,1,2 Shilie Pan,* 1 Zhihua Yang* 1 1

CAS Key Laboratory of Functional Materials and Devices for Special Environments, Xinjiang Technical Institute of Physics & Chemistry, CAS; Xinjiang Key Laboratory of Electronic Information Materials and Devices, 40–1 South Beijing Road, Urumqi 830011, China 2

University of Chinese Academy of Sciences, Beijing 100049, China

ABSTRACT: The exploration of infrared (IR) nonlinear optical (NLO) materials remains attractive because of the urgent requirements in the laser field. Meanwhile, the deepened cognition of structure-property relationships is necessary to help guide the exploration of IR NLO materials. So far, the family of antimony sulfides is an important system with a lot of attention, and a series of antimony sulfides are reported. However, it is urgent to be revealed how different Sb-S units, like SbS3, SbS4 and more complex combinations affect apparent properties. Here, taking ternary metal antimony sulfides for examples, the sources of some essential optical properties, such as second harmonic generation (SHG) and birefringence, are systematically analyzed through the first-principle calculations, and the mechanisms of the performances with various magnitudes are also presented to clarify the structure-property relationships. The results indicate that the SbS4 unit among antimony sulfides is an advantageous NLO active unit, which can balance the contradictory between band gap and SHG response. Introducing transition-metals in Sb-S anionic frameworks can tune the magnitude of birefringence. Besides, the substitution of cation from transition-metal to alkali metal can notably enlarge the band gap and maintain large SHG response. These design strategies are beneficial to explore potential IR NLO materials with Sb-S units.

KEYWORDS: nonlinear optical materials, advantageous units, structure-property relationships, design strategies, second harmonic generation, birefringence

INTRODUCTION Nonlinear optical (NLO) materials are vitally essential for the laser technologies, which can be used as frequency conversion devices to acquire the coherent lights of the desired frequencies with the applications of laser lithography, communication, detection and medical treatment.1-10 Based on the classification of applied wave ranges, the crystals of visible range (e.g. KH2PO4 (KDP),11 KTiOPO4 (KTP)12) and ultraviolet ranges (e.g. β-BaB2O4 (BBO),13 LiB3O5 (LBO)14) are maturely applied. The discovery of KBe2BO3F2 (KBBF) has partly satisfied the application requirement in the deep UV (DUV) range with its coherent output laser from direct sixth harmonic generation.15 In the IR range, some famous crystal, such as AgGaQ2 (Q=S, Se) and ZnGeP2 have also been successfully commercialized, but low laser damage threshold (LDT) or two-photon absorption seriously limits the extension of application.16-18

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As second-order NLO crystals should crystallize in noncentrosymmetric (NCS) space groups, several feasible strategies are proposed to guide obtaining NCS structures with NCS chromophores (NLO active units, the sources of NLO effects) especially for visible-DUV ranges: the use of (1) conjugated π configurations in anionic groups, such as (BO3)3-, (CO3)2-, (NO3)- and (B3O6)3-; (2) d0 transition-metal cations related to the second-order Jahn–Teller (SOJT) distortions, such as V5+, Nb5+, W6+ and Mo6+; (3) d10 transition-metal cations with polar displacements, such as Hg2+, Zn2+ and Cd2+; (4) stereochemical activity lone pair cations, such as Pb2+, Sb3+, Bi3+ and I5+; (5) fluorooxoborates anionic units, such as (BOF3)2-, (BO2F2)3-, (BO3F)4- and so on.19-28 In recent years, a great of efforts have been made to obtain NCS structures with high performances as potential IR NLO materials.29-35 It was found that the trigonal planar (HgSe3)4in BaHgSe2 could result in large NLO susceptibilities.36 NaSb3F10 was reported with a remarkable laser damage threshold, as high as about 1.3 GW/cm2, greatly exceeding that of commercialized AgGaS2 (25 MW/cm2).37 Combining Sb-S units with GaS4 tetrahedra, a series of NCS chain-like structures, Ln4GaSbS9 (Ln = Pr, Nd, Sm, Gd−Ho) were successfully designed with large SHG responses.38 Besides, the NLO effects of ternary metal antimony sulfides have been found long time ago, but the sources of NLO response and the structure-property relationships have rarely been concerned. Later, the discovery of the acousto-optical effect in ternary metal antimony sulfides leads the investigation of this family of compounds to other directions.39 Because of the multiple valence states, antimony could connect with sulfur in flexible coordination to form different Sb-S units, such as SbS3, SbS4, SbS5 and so on. After introducing metal cations, these various Sb-S units could appear solely to generate relatively simple isolated structures, such as isolated SbS3 in Li3SbS340 and isolated SbS4 in K3SbS441, or appear mixedly in one compound to form a complex 3D structure, such as SbS3, SbS4 and SbS5 in KSb 5S842. The flexible coordination between boron and oxygen, such as BO3, BO4, B3O6, B3O7 has proved that borate is a rich ore in NLO field,43-45 and we believe that antimony sulfide is another rich ore to explore potential NLO materials. Another reason that antimony sulfides are noteworthy is the appearance of stereochemical activity lone pair, which is considered as an efficient NLO active unit, and generally could develop a prominently large NLO response, just like in BiB2O4F46 and Pb17O8Cl1847. Therefore, to clarify the correlation and contribution of Sb-S units to the macroscopic properties is necessary to design and screen IR NLO materials with high performances. Searching in the inorganic crystal structure database (ICSD-3.7.0, the latest release of ICSDDecember 2017), we have found 25 NCS structures of ternary antimony sulfides (seeing Table S1 in the ESI). Among them, only a few do not contain A site metal cations, such as SbSI48 and (SbI3)(S8)349, and most (21 structures) are metal antimony sulfides. To explore the general correlation between the structural features and apparent diversity in performances, we have chosen a series of ternary metal antimony sulfides, Li3SbS3, Ag3SbS3, K3SbS4, Cu3SbS4 KSb5S8, and AgSbS2.40-42, 50-52 Through the first-principle calculation based on the density functional theory (DFT)53, the band gaps of these compounds are assessed, and the essential optical


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properties (SHG response and birefringence), which are the significant criterions whether one material could be applied in NLO field, are systematically discussed by comparing and analyzing apparent structural features and microscopic electron distribution with various post-processing tools, such as bonding analysis, response electron distribution anisotropy (REDA) approximation method and stereochemical activity intensity analysis for lone-pair electron (SIALEN).

THEORETICAL CALCULATION Electronic structures and optical properties calculation. The electronic structures and optical properties were theoretically simulated by the CASTEP package54, a plane wave pseudo-potential method based on the density functional theory (DFT). Here, Ceperley–Alder–Perdew–Zunger (CA-PZ)55-56 functional

under the local density approximation (LDA)

was set as the

exchange-correlation (XC) functional. The valence electrons outside ion cores in ultrasoft pseudopotential (USP) approach among the investigated elements were: Li 1s22s1, K 3s23p64s1, Cu 3d104s1, Ag 4d105s1, Sb 5s25p3 and S 3s23p4, and the energy cutoff were all no more than 850 eV, while the Monkhorst-Pack k-points used in the calculation of were 3 × 4 × 2, 4 × 4 × 4, 3 × 3 × 4, 3 × 4 × 4, 3 × 1 × 3 and 2 × 6 × 2, for Li3SbS3, Ag3SbS3, K3SbS4, Cu3SbS4 KSb5S8, and AgSbS2, respectively. Linear and nonlinear optical properties calculation. The linear optical refractive indices could be obtained by calculating dielectric functions, and birefringence was the difference of the refractive indices in various principal-axes. The SHG conversion efficiency was significantly determined by the magnitudes of the SHG coefficients when the condition of phase matching was met.57 Moreover, the SHG coefficient components were directly related to the second-order nonlinear susceptibilities, dij = χij/2. By computing the band structure results from CASTEP package, the second-order nonlinear susceptibilities with the limit of zero frequency, χαβγ(2)(0), were obtained as the sum of the contribution of the virtual-electron (VE) processes and the virtual-hole (VH) processes.58-59

Stereochemical activity analysis of lone-pairs. The intensity of Sb-5s stereochemical activity lone-pair was estimated through a revised method,60 called ‘Stereochemical activity Intensity Analysis for Lone-pair ElectroN’ (SIALEN). Using the SIALEN method, an RSIA factor was introduced to compare s orbitals with p orbitals of cations near the Femi level, which could reflect the degree of the stereochemical activity of lone-pairs. RSIA factor was the ratio of Sb-s states to Sb-p states, which was expressed as RSIA = I(Sb-s)/I(Sb-p). Here, I(Sb-s) and I(Sb-p) were the integrated partial density of states (PDOS) from a specified energy level to Femi level, and the point where the intensity of Sb-s state was same as that of Bi-p state was defined as the specified energy level.

RESULTS AND DISCUSSION Structural features and bonding analysis. As shown in Table S1 (ESI), there are various kinds of ternary metal antimony sulphides with different stoichiometric proportions. To systematically analyse their characteristics, some typical compounds are screened out, and listed in Table 1. These selected



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ternary metal antimony sulphides could be expressed as the formula AmSbnSk (A = Li, K, Cu, Ag; m = 1, 3; n = 1, 5; k = 2, 3, 4, 8). In this paper, the compounds from three types of formulas are investigated in detail, which are A3SbS3 (A = Li, Ag), A3SbS4 (A = K, Cu) and others (KSb5S8, AgSbS2), respectively.

Table 1 Classification and fundamental building units of Sb-S and A-S (A= Li, K, Cu, Ag) units Classification A3SbS3

Compound Li3SbS3

Ag3SbS3 A3SbS4

K3SbS4 Cu3SbS4

Others

KSb5S8

AgSbS2

Space group Pna21 (No. 33) R3c (No. 161) Cmc21 (No. 36) Pmn21 (No. 31) Pc (No. 7) C2 (No. 5)

Sb-S unit isolated SbS3 pyramids isolated SbS3 pyramids isolated SbS4 tetrahedra isolated SbS4 tetrahedra 3D structure with SbS3, SbS4 and SbS5 [SbS2]∞ chains

A-S unit /

AgS6 octahedra / CuS4 tetrahedra /

AgS6 octahedra

Among bond population analysis, the overlap population has provided an objective criterion for bonding between atoms that a high value of bond population indicates a covalent bond and a low value indicates an ionic bond.61 From the bond population results (Table 2), it can be found that the population values of Ag-S and Cu-S bonds are much higher than that of Li-S and K-S bonds, comparing with or even exceeding that of Sb-S bonds. Therefore, it can be easily deduced that among these antimony sulphides, the IB d10 transition-metal elements (Ag and Cu) present obvious covalent interaction when connecting with S, while IA alkali metal elements (Li, K) are prone to exhibit ionicity. As covalent interaction is closely related to SHG effect, the analysis of bond population is beneficial to explore the sources of SHG response among these NCS antimony sulphides.

Table 2 Bond length and bond population Compound Li3SbS3 Ag3SbS3 K3SbS4 Cu3SbS4 KSb5S8 AgSbS2

bond Sb-S Li-S Sb-S Ag-S Sb-S K-S Sb-S Cu-S Sb-S K-S Sb-S Ag-S

Length/Å 2.423~2.447 2.415~2.780 2.454 2.410~2.899 2.340~2.353 3.105~3.333 2.223~2.259 2.346~2.432 2.401~3.104 3.141~3.582 2.446~2.514 2.377~2.661


Population 0.35~0.42 0.06~0.15 0.43 0.10~0.42 0.71~0.77 0.02~0.19 0.45~0.56 0.27~0.44 0.03~0.53 0.02~0.08 0.22~0.42 0.25~0.51

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Among the three types of formulas (Table 1), each type contains two typical compounds, one containing ionic A site metal cations (A = Li, K) and the other containing covalent A cations (A = Cu, Ag), seeing Figs. 1a-c and Figs. 1d-f. Based on different covalent fundamental building units (FBUs), the structures of these antimony sulphides are described in two different perspectives, Sb-S units (Figs. 1a-f) and A-S (A = Cu, Ag) units (Figs. 1g-i). Besides, as the electron distribution of ionic cations (A = Li, K) is greatly local, the ionic cations are considered as interstitial role and contribute little to the main covalent frameworks.

Figure 1. Structures of ternary metal antimony sulphides AmSbnSk (A = Li, K, Cu, Ag) based on Sb-S units: Li3SbS3 (a), K3SbS4 (b), KSb5S8 (c), Ag3SbS3 (d), Cu3SbS4 (e), AgSbS2 (f), and based on A-S units: Ag3SbS3 (g), Cu3SbS4 (h), AgSbS2 (i), where (a) and (d) belong to the same family A3SbS3; (b) and (e) belong to the same family A3SbS4; while (c) and (f) present distinctive structures.

The FBUs both in Li3SbS3 (Fig. 1a) and Ag3SbS3 (Fig. 1d) are isolated SbS3 pyramids, and the difference is that the SbS3 pyramids in the former are distortedly antiparallel, while the latter contains nearly parallel SbS3 pyramids. Similarly, the formula A3SbS4 (A = K, Cu) contains another typical FBUs of antimony sulphides SbS4 tetrahedra. And these SbS4 tetrahedra are also isolated both in K3SbS4 (Fig. 1b) and Cu3SbS4 (Fig. 1e). The covalent framework in KSb5S8 (Fig. 1c) is particularly complex, which is composed of various Sb-S units, namely SbS3, SbS4 and SbS5. Viewing in the direction [1 0 -1], the 3D net structure in KSb5S8 shows a layer-like configuration, which is fit for producing a large birefringence.62 The Sb-S units in AgSbS2 (Fig. 1f) arise as infinite [SbS2]∞ chains, which are made from the consecutively connected SbS3 by sharing bridging oxygen atoms.



As mentioned above, the A-S (A = Cu, Ag) bonds in Ag3SbS3, Cu3SbS4 and AgSbS2 presents obvious covalence, so we also draw the structure figures based on A-S (A = Cu, Ag) bonds in Figs. 1g-i. The SbS3 pyramids in Ag3SbS3 are very simple and easily recognizable because of the uniform lengths of Sb-S bonds 2.454 Å, but the Ag-S bonds exhibit dispersive bond lengths with a large span, from 2.410 to 3.658 Å, forming metal-centered AgS6 octahedra (Fig. 1g) with second-order Jahn-Teller distortions,63 which are regarded as efficient NLO active units. Fig. 1h shows CuS4 tetrahedra in Cu3SbS4 locate toward -c axis, similar with the orientation of SbS4 tetrahedra, so parallel CuS4 and SbS4 tetrahedra are combined into the diamond-like structure of Cu3SbS4. As shown in Fig. 1i, the Ag-S units in AgSbS2 are also AgS6 octahedra. While Sb-S units are [SbS2]∞ chains, the Ag atoms are located in parallel with bc plane, leading to the layered distribution of AgS6 octahedra in AgSbS2. Band gaps and electronic structures. The calculated band gaps with LDA for CA-PZ functional of these compounds are shown in Table 3. Besides, the band structures are drawn in Fig. S1 in the ESI, which indicate A3SbS4 (A = K, Cu) own direct band gaps, while A3SbS3 (A = Li, Ag), KSb5S8 and AgSbS2 own indirect band gaps. Because of the inherent discontinuity exchange-correlation energy in a typical DFT calculation with LDA or GGA (generalized gradient approximation), calculated band gaps could underestimate experimental band gaps by 30% ~ 100%.64 Meanwhile, the subsequent optical property calculation is sensitive with the magnitudes of experimental optical band gaps. To achieve more accurate values of band gaps, we also adopted the non-local exchange functional HSE06,65 a widely used hybrid functional with a relatively high efficiency. To achieve larger band gaps, alkali metals are popularly introduced as cations in the design of NLO materials, because the valance electronic states of alkali metal usually stay far away from Fermi level when forming polynary compounds. Among the six compounds, alkali metal antimony sulphides show relatively large band gaps, 3.02 eV (Li3SbS3) and 3.51 eV (K3SbS4). As shown in Figs. 2a-c, the top of VBs and the bottom of CBs are mainly composed of Sb and S atoms, which immediately determine the magnitudes of band gaps. KSb5S8 is also a kind of alkali metal antimony sulphides, but obtains an obviously smaller band gap, 1.82 eV, much different from Li3SbS3 and K3SbS4 which is mainly derived from the different electron distribution. In Li3SbS3 and K3SbS4, isolated SbS3 and SbS4 form local electron distribution. After combining with ionic alkali metal, it is further hard for the local electron distribution to occur electron transitions, so Li3SbS3 and K3SbS4 perform large band gaps. Conversely, the Sb-S unit in KSb5S8 is a complex 3D net structure (Fig. 1c), and generates a delocalized electron distribution, which is in favour of the electron transferring between atoms, tending to develop a relative narrow band gap.


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Figure 2. Partial density of states (PDOS) of Li3SbS3 (a), K3SbS4 (b), KSb5S8 (c), Ag3SbS3 (d), Cu3SbS4 (e), AgSbS2 (f). Especially, the PDOS of Sb atoms near Fermi level is also drawn (g).

Table 3 Calculated and experimental band gaps and SHG coefficient Compound Li3SbS3

Ag3SbS3 K3SbS4 Cu3SbS4 KSb5S8 AgSbS2

Band gap 2.28 eV (LDA) 3.02 eV (HSE06) 0.87 eV (LDA) 2.20 eV (Exp.) 2.20 eV (LDA) 3.51 eV (HSE06) 0.68 eV (LDA) 1.93 eV (HSE06) 1.53 eV (LDA) 1.82 eV (Exp.) 1.20 eV (LDA) 1.96 eV (HSE06)

SHG coefficient 2.6 pm/V (Cal.)

9.0 pm/V (Cal.) 7.8 pm/V (Exp.) 8.3 pm/V (Cal.) 12 pm/V (Cal.) 60 pm/V (Cal.) 0.54 pm/V (Cal.)

From PDOS maps, above two different kinds of electron distributions can be easily identified. Among Li3SbS3 (Fig. 2a), K3SbS4 (Fig. 2b), and KSb5S8 (Fig. 2c), the peaks of Sb and S atoms in the same locations of energy levels represent the overlaps of Sb and S orbitals, which indicate obvious covalent interaction of Sb-S bonds. Furthermore, it is clear that the energy widths of Sb-S bonds show an obvious distinction. In KSb5S8, from -15 eV to Fermi level, three



overlap areas (-15 ~ -10 eV, -10 ~ -5 eV and -5 eV ~ Fermi level) nearly cover this whole energy range, and denote the delocalized electron distribution. On the contrary, narrow energy widths of Sb-S bonds are related to the local electron distribution. The other three compounds, which can be expressed as d10 transition-metal antimony sulphides, exhibit moderate band gaps at a same level around 2 eV: 2.20 eV (Ag3SbS3), 1.93 eV (Cu3SbS4) and 1.96 eV (AgSbS2). Compared with the large band gaps from introducing alkali metal cations, the relatively narrow band gaps are mainly owing to the covalent interaction between transition-metal atoms and sulfur atoms. And from the PDOS maps of Figs. 2d-f, a plenty part of the electron states from transition-metal locate at the top of VB as well as those from antimony and sulfur, which significantly influence the band gaps. Moreover, bond population results suggest that Ag-S and Cu-S bonds exhibit obvious characteristics of covalent bonds, and induce delocalized electron distribution. The Electron localization function (ELF) was introduced by Becke et al. to characterize the localization behaviors of electrons.66 And normally, it is easy to observe the appearance of the electron distribution of lone-pairs from the ELF maps (Fig. 3). Here, in Fig. 4 the display upper limits of ELF values had been set as the mean values, so these maps could exhibit more subtle difference of electron distribution. The spherical appearances of electron localization around K atoms of K3SbS4 in Fig. 4b are separate from the cluster of Sb-S units, indicating the ionicity of K cations. The unbroken expanse localization of Cu3SbS4 in Fig. 4a suggests that an integrated chain -Cu2-S3-Sb1-S1-Cu2- has formed by Cu-S and Sb-S covalent bonds and the electrons in the chain are easier to transfer, which is the reason why the band gap of Cu3SbS4 (1.93 eV) could not catch up with that of its similar structure K3SbS4 (3.51 eV), but is similar to that of its completely different structure KSb5S8 (1.82 eV).

Figure 3. Electron localization function (ELF) of Li3SbS3 (a), K3SbS4 (b), KSb5S8 (c), Ag3SbS3 (d), Cu3SbS4 (e), AgSbS2 (f). The apparent lobes of localized electron distributions around Sb atoms (Figs. 3a, 3c, 3d, 3f) indicate the presence of stereochemical activity (SCA) of lone pairs, called that SCA of lone pairs is turned on. Conversely, the non-localized electron distribution (Figs. 3b and 3e) denotes inertness of lone pairs, called that SCA of lone pairs is turned off.


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Figure 4. Electron localization function (ELF) of Cu3SbS4 (a) and K3SbS4 (b). The display upper limits of ELF values have been set as the mean values, so these maps exhibit subtle difference of electron distributions.

Nonlinear optical property. As a promising second-order NLO material, obtaining a large SHG response is an essential evaluation criterion. In this paper, we would take these six NCS metal antimony sulphides for examples to explore which building unit could develop a large SHG response. Among these compounds, Li3SbS3, Ag3SbS3, K3SbS4, Cu3SbS4, KSb5S8 and AgSbS2, although there are a part of structures similar, actually the six compounds crystallize in absolutely different space groups, Pna21, R3c, Cmc21, Pmn21, Pc and C2, covering from monoclinic and orthorhombic to trigonal crystal systems. Table 3 contains the calculated results of SHG coefficients, where the maximum SHG coefficient in the effective SHG formula is chosen as the evaluation of SHG response. Cu3SbS4, Ag3SbS3 and K3SbS4 obtain large SHG coefficients, 12, 9.0 and 8.3 pm/V, all of which are 20 times larger than that of KDP (KH2PO4, d36 = 0.39 pm/V). Cu3SbS4 and K3SbS4 are composed by the same Sb-S building units, isolated SbS4 tetrahedra. When replacing A site cation from transition-metal Cu to alkali metal K, SHG response decreases due to the missing part of the contribution of Cu-S bonds, but actually SHG response has missed only about 30% and still maintains a high level (≥ 20 × KDP). In turn, the band gap value has increased more than 80%, reaching a new threshold range (≥ 3 eV). Therefore, from the analysis of this couple, a promising strategy can be concluded that, in parallel SbS4 unit frameworks A site substitution from transition-metal to alkali metal tends to improve the combination property for IR NLO materials. Although the Sb atoms among Li3SbS3 and AgSbS2 own obvious stereochemical activity (SCA) lone-pairs, which are shown as lobe shape electron distribution in Figs. 3a and 3f, the SHG responses of these two antimony sulphides are far less than others, 2.6 pm/V (Li3SbS3) and 0.54 pm/V (AgSbS2). According to anionic group theory, the macroscopic NLO coefficients can be obtained by the geometric superposition of the second-order susceptibilities of anionic groups.67 So antiparallel arrangement would cause counteract of second-order susceptibilities, and results in a small SHG coefficient. There are angles between the orientations of SbS3 units, 175.7° in Li3SbS3 and 179.9° in AgSbS2, and a larger angle denotes a stronger counteract. Therefore, the structural feature of the SbS3 arrangements is in agreement with apparent SHG responses. Naturally, their SHG response could not catch up with that of the parallel SbS3 structure in Ag3SbS3 (9.0 pm/V).



Figure 5. (a) Summary of SHG responses based on various Sb-S building units; (b) Comparison of band gaps and SHG responses based on RSIA factors (The blue triangles show the magnitudes of SHG responses and the red dots represent the values of band gaps).

Based on the different Sb-S building units, the summary of SHG responses of these antimony sulphides is drawn in Fig. 5a. Among the six compounds, we find that, the SbS4 unit is prone to develop a larger SHG response than the SbS3 unit no matter whether A site cation is transition-metal or alkali metal (Cu3SbS4 ˃ Ag3SbS3, K3SbS4 ˃ Li3SbS3). Besides, the band gap of K3SbS4 (3.51 eV) is much larger than that of Ag3SbS3 (2.20 eV), but the SHG response of K3SbS4 is similar with that of Ag3SbS3 in Fig. 5a, which further indicates that the SbS4 units have more advantages. This phenomenon is in accordance with typical tetrahedral units that are frequently present in IR NLO materials, such as commercialized AgGaS2 and ZnGeP2. Chain-typed AgSbS2 exhibits the weakest NLO effect, which is only about 1 time that of KDP, but it obtains a prominent birefringence (˃ 0.3), as shown in Fig. 6. An interesting thing is that KSb5S8 owns a particularly outstanding SHG coefficient, as large as 60 pm/V, which is considered as the result of the ultra-wide delocalized electron distribution among the whole 3D net anionic framework.

Optical anisotropy. As we know, covalent bonds have the distinct characteristic of directionality and lead to anisotropic electron distribution, which is the essential source of optical anisotropy.68 From DFT calculation, the optical anisotropy of a material can be easily evaluated by the magnitude of birefringence, and the calculated results are shown in Fig. 6. It is clear that the magnitudes of birefringences present in hierarchy based on the kinds of Sb-S units. The compounds containing isolated SbS4, Cu3SbS4 and K3SbS4 obtain relatively small birefringences, 0.05 and 0.005 @1064 nm, mainly due to the minimal anisotropy of electron distribution in the SbS4 tetrahedra. However, the CuS4 tetrahedra in Cu3SbS4 exhibit larger distortions, in which the difference of four Cu-S bonds at one tetrahedron (2.368 Å ~ 2.432 Å)


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is 0.064 Å, compared with 0.036 Å of the Sb-S bonds in Cu3SbS4 and 0.013 Å of the Sb-S bonds in K3SbS4. Therefore, even if Cu3SbS4 is entirely composed of tetrahedron units, it still maintains a visible birefringence, 0.05. Both Li3SbS3 and Ag3SbS3 are made of isolated SbS3 units and the SbS3 units are almost in one plane, but their birefringences make a big difference, 0.20 and 0.10 @1064 nm, which is related to the different contributions of A site cations. Here, the electron distribution around ionic Li is nearly spherical, and its contribution can be ignored, while covalent Ag-S bonds play an important role. The SbS3 units are parallel in Ag3SbS3, and it ought to develop a larger birefringence, but distorted AgS6 octahedra locate in various orientations and form a complex 3D net structure, which would disrupt the layer-like electron distribution of Sb-S units. Besides, the SbS3 density of Ag3SbS3 is 0.0065 atom/Å3 (counting Sb atoms), smaller than 0.0073 atom/Å3 of Li3SbS3, further expanding the diversity of the birefringence. Among these antimony sulfides, chain-like AgSbS2 exhibits an especially large birefringence 0.32. The large birefringence of AgSbS2 is derived from the combined anisotropy of [SbS2]∞ chains and layer-distributed AgS6 octahedra.

Figure 6. Summary of birefringences on typical ternary metal antimony sulphides.

Figure 7. Calculated bonding electron density difference (∆ρ) of the covalent bonds along the optical principal axes, which is derived from Sb-S units and Ag-S units.



To check above analysis in quantification, we calculated the bonding electron density difference (∆ρ) of the covalent bonds along the optical principal axes by the response electron distribution anisotropy (REDA) approximation.69 As shown in Fig. 7, the Sb-S units contribute the most part of ∆ρ, which indicates that the Sb-S units are the main source of birefringence in both AgSbS2 and Ag3SbS3. The difference is that the Ag-S units contribute a positive in AgSbS2, but produce a negative in Ag3SbS3, which is the reason that AgSbS2 obtains an extraordinarily large birefringence and the birefringence of Ag3SbS3 is obviously smaller than that of Li3SbS3. Stereochemical activity of lone-pairs. There is no lob sharp electron distribution around the Sb atoms in the ELF maps Figs. 3b and 3e, indicating that the lone-pairs are inert in the two tetrahedral structures, K3SbS4 and Cu3SbS4, which is called that the stereochemical activity (SCA) of lone-pairs is turned off. The lob sharp electron distribution in Figs. 3a, 3c, 3d, 3f denotes an obvious stereochemical activity of lone-pairs, so we called that SCA is turned on. When SCA of lone-pairs is turned on, through SIALEN method, we can compare the activities of lone-pairs among these antimony sulphides by calculating the occupancy state ratio of Sb-s orbital to Sb-p orbital near the Fermi surface (shown in Fig. 2g). A larger RSIA factor denotes that the lone-pair is more active when considering the influence that lone-pair exerts on the apparent properties, such as SHG response and band gap. Here, the comparison of band gaps and SHG responses based on calculated RSIA factors is shown in Fig. 5b. In general, more active lone-pairs tend to cause a larger red-shift of the absorbing cutoff edge,70 resulting in a narrower band gap. Meanwhile, a larger RSIA factor is beneficial to develop a large SHG response. The comparison between KSb5S8 and Li3SbS3 on the values of band gaps and SHG responses is accordance with this tendency, and so is the band gap comparison between Ag3SbS3 and AgSbS2. The only exceptional one is that AgSbS2 exhibits a relatively much smaller SHG response, resulting from counteract of SHG response by the antiparallel arrangement of the SbS3 units. Furthermore, considering that the cations containing lone pairs (Pb2+, Sb3+ and Bi3+) are widely adopted as lead-based or bismuth-based perovskites for solar cells, the SIALEN method is hopeful to provide a new strategy in the design of perovskite solar cells.

CONCLUSIONS Antimony sulfides are a promising family of IR NLO materials with large SHG responses and attract extensive attentions. In recent years, although a series of antimony sulfides have been reported with excellent properties, the mechanism about how different Sb-S units exert different influences on apparent properties remains to be revealed, just like band gap, SHG response and birefringence. Here, taking these ternary metal antimony sulfides for examples, we have explored the structure-property relationship by combining first-principle calculation and post-processing tools, such as bonding analysis, response electron distribution anisotropy approximation method and stereochemical activity analysis of lone-pairs. The results indicate that the SbS4 tetrahedra are advantageous FBUs in Sb-S chromophores, which can possess a


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much larger band gap than SbS3 pyramids and the composite structure of SbS3, SbS4 and SbS5 units, while parallel SbS4 tetrahedra structure can simultaneously maintain a satisfied SHG response, as large as parallel SbS3 structure. Besides, in parallel SbS4 unit frameworks, A site substitution from transition-metal to alkali metal tends to improve the combination property as above SbS4 does. Because of the delocalized electron distribution in complex Sb-S framework, consisted by SbS3, SbS4 and SbS5 units, KSb5S8 owns an extraordinary SHG coefficient, about 60 pm/V. In addition, introducing transition-metal in Sb-S anionic groups could result in an obvious enhancement or diminishment on optical anisotropy, and the Ag-S unit is one of the sources of the remarkably large birefringence of chain-like AgSbS2 (˃ 0.3), which can provide an optional strategy when tuning the birefringence of NLO materials. These results are beneficial to explore potential antimony sulfides as IR NLO materials.

ASSOCIATED CONTENT

Supporting Information The Supporting Information is available free of charge on the ACS Publications website. Band structures of ternary metal antimony sulphides: Li3SbS3, K3SbS4, KSb5S8, Ag3SbS3, Cu3SbS4 and AgSbS2 (Figure S1). Summary of noncentrosymmetric ternary antimony sulfides (Table S1).

AUTHOR INFORMATION

Corresponding Author, * Email: [email protected], [email protected]. Notes The authors declare no competing financial interest.

ACKNOWLEDGEMENTS This work is supported by the National Natural Science Foundation of China (Grant Nos. 11774414, 11474353, 51425206), National Basic Research Program of China (Grant No. 2014CB648400), the National Key Research Project (Grant Nos. 2016YFB1102302, 2016YFB0402104), Shanghai Cooperation Organization Science and Technology Partnership Program (Grant No. 2017E01013).

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