Bridging Motifs Induced Ordered Arrangement Contributing Large Birefringence for Hg₄BiQ₂Cl₅ (Q═S, Se)

ABSTRACT

Chalcogenide birefringent materials are key for polarization applications in the middle and far‐infrared region, yet their performance remains constrained by bottlenecks birefringence and bandgap. Due to their remarkable polarizability anisotropy, the linear [HgQ₂] (Q═S, Se) units are recognized as promising birefringence functional motifs. Therefore, Hg₄BiQ₂Cl₅ (Q═S (1), Se (2)) containing [HgQ₂] units were synthesized and studied. Their structural difference caused by the congener substitution induces the bridging motifs transformed from extremely distorted [HgS₂Cl₂] tetrahedron to [HgSe₂Cl] planar triangle, resulting in structural dimensionality transition from {[Hg₇S₄Cl₂]} _n layers in 1 to {[Hg₈Se₄Cl₂]²⁺} _n chains in 2. This structure reorganization optimizes the coplanar alignment of the {[Hg₃Q₂]} _n chains, leading to a remarkable enhancement in optical anisotropy. In both structures, the {[BiCl₅]²⁻} _n chains constructed by vertex‐shared [BiCl₆] octahedra occupy the voids within the frameworks. Experimental and theoretical calculation results reveal that 2 exhibits a large birefringence of 0.45@ 546 nm that surpasses all known commercial birefringent crystals, and also one of the largest ones for diverse chalcogenides. This study demonstrates that regulating structural dimensionality through bridging motifs can effectively optimize the spatial arrangement of linear functional motifs, providing a clear structural design paradigm for the development of high‐performance birefringent crystals.

By replacing the bridging motifs from the [HgS₂Cl₂] tetrahedra with the [HgSe₂Cl] planar triangles, the dimensional transition in the structures were successfully induced, optimizing the coplanar alignment of the linear [HgQ₂] and [Hg₂Q₂] functional motifs. Consequently, Hg₄BiSe₂Cl₅ achieves a giant birefringence value of 0.45@546 nm, surpassing all known commercial crystals, while maintaining a moderate bandgap greater than 2.5 eV. Theoretical calculations clarify that its exceptional performance originates from the extremely high polarizability anisotropy of the linear [HgSe₂] and [Hg₂Se₂] units, as well as the precise spatial arrangement of the functional motifs regulated by the bridging motifs.

1. Introduction

Birefringence, a property to exhibit different refractive indices depending on the polarization direction of incident light, lies at the heart of optical anisotropy [1, 2, 3, 4, 5]. It serves as the fundamental physical basis for manipulating the polarization state, phase, and propagation direction of light. Since Huygens first observed this phenomenon in calcite during the 17th century, the pursuit of high‐performance birefringent materials has been a key driver in the advancement of optical technologies [6, 7, 8, 9, 10, 11, 12]. These materials form the cornerstone of modern polarization optics and are widely employed in polarizers, wave plates, phase retarders, optical isolators, as well as laser and optical communication systems [13, 14, 15, 16, 17, 18, 19, 20].

To meet the demands across different spectral ranges and device applications, the family of birefringent materials has become highly diverse. Traditional oxide crystals such as CaCO₃, YVO₄, and TiO₂ excel in the ultraviolet and visible region [21, 22, 23, 24], but their extension into the middle to far‐infrared (MFIR) is limited by phonon absorption. Fluorides like MgF₂ offer broad transparency windows, yet their birefringences are generally low [24]. While emerging organic‐inorganic hybrid materials exhibit large optical anisotropy and favorable crystal growth characteristics [25, 26, 27], their thermal and chemical stability often poses challenges for practical applications. Consequently, research focus has gradually shifted toward material systems capable of simultaneously achieving large birefringence, wide infrared transparency, and good stability in the MFIR region. Among diverse candidates, chalcogenides have become a focal point due to their unique potential. By incorporating functional units with exceptionally high polarizability anisotropy, such as chain‐like [Q _x ] (Q═S, Se, Te; x = 1–6) [28, 29, 30], linear [AQ₂] (A = Cu, Ag, Hg) [31−33], [BQ₃] (B = Cu, Ag, Hg, B) planar triangle [34, 35], or units with stereochemically active lone‐pair (SCALP) electrons like [DQ₃] (D = As, Sb, Bi) [36, 37], and combining them with low dimensional structural designs such as chains or layers, these materials achieve highly directional electron cloud distribution, resulting in pronounced macroscopic optical anisotropy at the molecular level.

The research paradigm in this field has evolved from traditional trial‐and‐error screening toward rational design based on structure‐properties relationships. The core of this approach lies in the directional control of microscopic polarizability through “functional motif” engineering [38, 39]. However, introduction of functional motifs with high polarizability anisotropy and induction of their directional alignment remain significant challenges. Guided by the functional motif theory, we employed Gaussian calculations to screen for anionic groups with large polarizability anisotropy (Figure 1). Among the candidates, the linear [HgQ₂] (Q═S, Se) units were identified as particularly promising due to their significant anisotropy polarizability. Based on this consideration, we sieved and studied two chalcohaldies Hg₄BiQ₂Cl₅ (Q═S (1), Se (2)) [40, 41]. They adopt similar structures where {[BiCl₅]²⁻} _n chains are nested within the voids of a low dimensional framework. Crucially, the bridging motifs of distorted [HgS₂Cl₂] tetrahedron and [HgSe₂Cl] planar triangle facilitate the parallel alignment of the {[Hg₃Q₂]} _n zig−zag chains. This architectural control results in large experimental birefringence of 0.36@546 nm for 1 and 0.45@546 nm for 2. Notably, the latter surpasses those of commercial birefringent crystals. To elucidate the origin of the enhanced optical anisotropy, an in‐depth structural analysis was performed, complemented by the first‐principles theoretical calculations.

FIGURE 1.

Open in figure viewer (a) An overview of common chalcogenide birefringent functional motifs. (b) Polarizability anisotropy and HOMO‐LUMO gap of chalcogenide birefringent functional motifs.

2. Results and Discussion

Polycrystalline powder samples of 1 and 2 were synthesized using the high‐temperature solid‐state reactions. Their phase purity and chemical compositions were confirmed by PXRD (Figure S1) and EDS (Figure S2) analysis, respectively. Structural analysis indicates that 1 and 2 possess similar {[Hg₃Q₂]} _n zig−zag chains, which are constructed from corner‐shared linear [HgQ₂] and [Hg₂Q₂] units (Figure 2a). Their primary structural difference stems from the bridging motifs that connect these chains. 1 crystallizes in the chiral space group P2₁. In 1, the {[Hg₃S₂]} _n chains are interconnected via [HgS₂Cl₂] bridging motifs, stacking along the a‐axis to from the {[Hg₇S₄Cl₂]} _n layers (Figure 2b,c). These layers stack orderly to form the framework of the structure, and the {[BiCl₅]²⁻} _n chains fill the interlayer spaces within this framework (Figure 2d,e). The centrosymmetric structure (P2₁/c) of 2 can be evolved from that of 1. When S is substituted by Se, the bridging motif changes from [HgS₂Cl₂] tetrahedron to [HgSe₂Cl] triangle. Consequently, the {[Hg₇S₄Cl₂]} _n layers transform to {[Hg₈Se₄Cl₂]²⁺} _n chains (Figure 2f,g). These chains pack alternately to construct the basic framework of 2, and the {[BiCl₅]²⁻} _n chains fill the interchain voids within this framework. As shown in Figure 2d,h, this change is accompanied by a displacement of the bridging motif from site A ([HgS₂Cl₂] tetrahedron) to site B ([HgSe₂Cl] triangle), which is accompanied by the transformation of symmetry. The bond valence sum calculation values are consistent with those previously reported in the literature (Tables S3–S5) [42]. Furthermore, we analyzed the fundamental building motifs in 1 and 2 (Figure S3) using the same methodology as in our previous works [43, 44], and the result reveals that the [Hg₇S₄Cl₂] unit adopts an irregular hexagonal geometry lacking symmetry center. In contrast, the [Hg₈S₄Cl₂] unit can be conceptually dissected into [Hg₆Se₄Cl₂] and [Hg₄Se₄Cl₂] units, both of which are the parallelogram owning symmetry center. Consequently, the space group shifts from the noncentrosymmetric P2₁ (1) to the centrosymmetric P2₁/c (2). This transformation highlights the regulatory role of bridging motifs on their structural dimensionality and symmetry.

FIGURE 2.

Open in figure viewer Structural comparison for 1 and 2. (a) [HgS₂Cl₂] tetrahedron, [HgSe₂Cl] planar triangle, linear [HgQ₂] unit, lnear [Hg₂Q₂] unit and {[Hg₃Q₂]} _n zig−zag chain. (b) {[Hg₇S₄Cl₂]} _n chain along a‐axis. (c) {[Hg₇S₄Cl₂]} _n layer parallel with the bc plane. (d) The structure of 1 along the b‐axis. (e) {[BiCl₅]²⁻} _n chain along the c‐axis. (f,g) {[Hg₈Se₄Cl₂]²⁺} _n chain and its arrangement along the c‐axis. (h) The structure of 2 along the a‐axis.

Statistical analysis of the ICSD reveals 52 reported Hg‐based chalcohalides. Based on the structural motifs, they can be categorized into five groups: linear [HgQ _m X _n ] (Q═S, Se, Te; X═Cl, Br; m + n = 2) units, triangular or highly distorted tetrahedral [HgQ _m X _n ] (Q═S, Se, Te; X = Cl, Br, I; m + n = 3, 4) units, distorted [HgQ₃X] (Q═S, Se; X═Cl, Br, I) tetrahedra, and [HgS₄] tetrahedra or [HgS₄Cl₂] octahedra. Notably, structures containing linear [HgQ₂] units account for 38.5％ of the total (Figure S5). Given the exceptionally high polarizability anisotropy of linear [HgQ₂] units, we conducted a detailed structural analysis of chalcohalides containing them. These structures can be generally divided into three types based on their compositions: (I) structures solely composed of isolated linear [HgQ₂] units; (II) layered structures formed by corner‐sharing linear [HgQ₂] units; (III) structures containing both [HgQ₂] and [HgQ _m X _n ] (Figure S3). It is worth noting that [HgQ₂] units are almost exclusively parallelly arranged. In contrast, in structures containing only linear [HgQ₂] units, these units are mostly unparallelly arranged, suggesting that the presence of other [HgQ _m X _n ] units facilitates the parallel alignment of the linear [HgQ₂] units. However, the [HgQ _m X _n ] units in known structures often exhibit overlapping arrangements, which is detrimental for large birefringence. While in 1 and 2, the [HgS₂Cl₂] and [HgSe₂Cl] units not only avoid such overlap but also effectively induce the parallel alignment of both [HgQ₂] and [Hg₂Q₂] units. This unique structural feature accounts for the large birefringences of 1 and 2.

The experimental bandgaps were determined to be 2.73/2.63 eV for 1/2 (Figure S6). The birefringences of 1 and 2 were analyzed (Figure 3a). The crystal orientation of 1 and 2 was determined using APEX3 software (Figure 3b; Figure S7c), showing that the (00$\overline{1}$) plane coincides with the polarized light plane during measurement. Optical interference color and complete extinction were observed for 2 under crossed polarizers at different rotation angles (Figure 3c–g). After confirming complete extinction of the crystal, the platform was fixed and rotated 45 °, and then a Berek compensator (Figure 3h) was inserted. The compensator's screw axis was adjusted until extinction was achieved, yielding readings of B = 17.8 and R = 17.5 for 2 (Figure 3i,j), and B = 9.0 and R = 8.5 for 1 (Figure S7a,b). The corresponding optical path differences were 6151.15/1524.67 nm, and the thicknesses of the tested samples were 13.577/4.189 µm (Figure 3k; Figure S7d). The calculated birefringences are 0.36/0.45@546.1 nm for 1/2 (Figure 3i; Figure S8a). The three principal refractive indices for both compounds at λ = 546 nm are presented in Figure 3m and Figure S8b. The close agreement between theoretical and experimental birefringences confirms the reliability of measurements. Their birefringences are higher than those of commercial birefringent crystals (Figure 3n).

FIGURE 3.

Open in figure viewer (a) Schematic diagram of polarizing interference method. (b) the crystal orientation of the 2. (c–g) Optical interference color and complete extinction observed for 2 under crossed polarizers at different rotation angles. (h) Optical interference color for 2 under crossed polarizers at Berek compensator. (l) The birefringence curve of 2 calculated based on DFT. (m) The ellipsoidal refractive index of 2 at 546 nm. (n) Birefringence comparison of 2 with representative commercial birefringent crystals [21, 45, 46, 47].

A summary of chalcohalides with birefringence data is shown in Figure 4a and Table S7, which reveals a striking predominance: nearly all chalcohalides exhibiting birefringence larger than 0.15 are Hg−based ones. This underscores the exceptional capability of this chemical system for generating high‐birefringence crystals. Specific functional motifs within these structures are identified as key contributors to enhanced optical anisotropy. Linear units such as [HgQ₂] and [Hg₂Q₂] units, and planar triangular like [HgQ₃] units, are recognized as favorable structural motifs for boosting birefringence. To elucidate the structure‐properties relationship, we compiled the structural and optical information for chalcohalides containing these motifs (Figure 4b; Table S8). For low dimensional Hg−Based chalcohalides with birefringence data unavailable, DFT calculations were performed to supplement the missing birefringence information. The results indicate that while materials containing the linear [HgQ₂] units generally possess appreciable birefringences, their values typically do not surpass 0.3. In contrast, Hg−based chalcohalides incorporating either the linear [Hg₂Q₂] or planar triangular [HgQ₃] units consistently demonstrate birefringence above 0.3. This superior performance is attributed to their characteristic low dimensional structures. In these chalcohalides, the linear [HgQ₂], [Hg₂Q₂] and triangular [HgQ₃] units are oriented within the same (or nearly) crystallographic plane. It is worth noting that in this system, 1 and 2 exhibit extremely large birefringences.

FIGURE 4.

Open in figure viewer (a) Birefringences of reported chalcohalides. (b) Birefringences of Hg−based chalcohalides.

This work demonstrates that 1 and 2 achieves an excellent balance between large birefringence (Δn > 0.3) and moderate bandgap (E _g > 2.5 eV), highlighting their potential as MFIR birefringent materials (Figure 5a). To elucidate the origin of their wonderful optical properties, the polarizability anisotropy and (Highest occupied molecular mrbital) HOMO‐(Lowest unoccupied molecular orbital) LUMO gaps of key functional motifs in 1 and 2 were calculated (Figure 5b; Figure S9). The results indicate that the linear [Hg₂Q₂] units exhibit strong optical anisotropy. Meanwhile, the [HgS₂Cl₂] tetrahedron and [HgSe₂Cl] planar triangle possess large HOMO‐LUMO gaps, which contribute to the relatively large bandgaps of 1 and 2. More importantly, these units act as bridging motifs that regulate the spatial arrangement of the {[Hg₃S₂]} _n zig−zag chains. In 1, the chains exhibit a dihedral angle of ∼8.9° between them, whereas in 2, the {[Hg₃S₂]} _n zig−zag chains are perfectly coplanar (Figure S10). This structural distinction, combined with the inherently higher polarizability anisotropy of the linear [HgSe₂] and [Hg₂Se₂] units, collectively leads to superior in‐plane alignment of the functional motifs and a more pronounced birefringence in 2. This work demonstrates that the strategic selection of bridging motifs is an effective approach to tuning the arrangement of structural units, thereby synergistically optimizing birefringence and bandgap. We also considered the possibility that the substitution of S with the larger Se atoms may be the cause of the structural transformation. However, Hg₄InS₂Cl₅ and Hg₄BiSe₂Cl₅ contain a similar [HgQ₂Cl] (Q═S, Se) bridging unit and crystallize in the same P2₁/c structure, despite their different chalcogen compositions [32]. This observation indicates that when the bridging unit remains unchanged, chalcogen substitution does not necessarily alter the structure, thereby indirectly supporting the conclusion that the bridging motif is the dominant factor governing the structural change in this system. As shown in Figure S11,  1 exhibits a clear and reproducible SHG response with an intensity of approximately 0.12 × AGS, which further confirms the structural accuracy of 1.

FIGURE 5.

Open in figure viewer (a) Comparison of birefringences and bandgaps of Hg−based chalcohalides. (b) The microscopic polarizability anisotropy of Hg−based functional motifs in chalcogenides. (c) PDOS of 2. (d,e) The HOMO and LUMO of 2. (f,g) The electron localization function (ELF) slices of 2.

The calculated indirect bandgaps for 1 and 2 (Figure S12) are both 2.52 eV, which align well with the experimental values. Their partial density of states (PDOS) plots (Figure 5c; Figure S13) reveal that the valence band maximum (VBM) is predominantly contributed from the 3p/4p orbitals of S/Se, and the 3p orbitals of Cl. The conduction band minimum (CBM) is primarily occupied by the 6s orbitals of Hg, the 6p orbitals of Bi and the 3p/4p orbitals of S/Se. Thus, the [HgS₂Cl₂] and [HgSe₂Cl] bridging motifs are the motifs determining the optical bandgap, in line with what we have envisioned.

Due to the highly similar optical characteristics of 1 and 2, the following discussion will focus on 2 as a representative. Frontier molecular orbital analysis of the linear [HgSe₂] and [Hg₂Se₂] units demonstrates that the electron density of HOMO is dumbbell‐shaped and exhibits pronounced delocalization along the directions of the Hg−Hg and Hg−Se bonds (Figure 5d,e). In contrast, the electron cloud of LUMO is distributed perpendicularly to this axis. This obvious spatial separation and anisotropic distribution of the HOMO and LUMO endow these functional motifs with exceptionally high polarizability anisotropy. Further analysis indicates that the HOMO primarily derives from the p orbitals of Se, while the LUMO receives contribution from the s and p orbitals of Hg. Such an electronic distribution renders the response of the linear [HgSe₂] and [Hg₂Se₂] units to an external electric field strongly directionally dependent. Consequently, the parallel alignment of these units within the crystallographic plane allows their polarizability anisotropy to superimpose, thereby giving rise to the observed giant birefringence. As shown in the ELF plots in Figure 5f,g, the electron cloud density around the linear [HgSe₂] and [Hg₂Se₂] units differs markedly and is more concentrated than the charge density around the [BiCl₆] octahedra, indicating a pronounced delocalized character of the electron distribution in these units. This feature implies that the {[Hg₃Se₂]} _n zig−zag chains play a crucial role in the birefringence of 2.

3. Conclusion

In this study, the substitution of the bridging unit from [HgS₂Cl₂] to [HgSe₂Cl] successfully induces a dimensional transition from {[Hg₇S₄Cl₂]} _n layer to {[Hg₈Se₄Cl₂]²⁺} _n chain. This structural reorganization optimizes the alignment of the linear [HgQ₂] and [Hg₂Q₂] units, enabling a geometric superposition of their polarizability anisotropy. Consequently, 2 achieves a birefringence of 0.45@546 nm, surpassing all known commercial birefringent crystals while maintaining good optical transparency across a broad spectral range. Theoretical calculations and analyses reveal that the giant birefringence originates from two key factors. First, the linear [HgSe₂] and [Hg₂Se₂] units possess extremely high polarizability anisotropy, characterized by marked spatial separation and strongly directional distribution of their HOMO and LUMO orbitals. Second, the [HgSe₂Cl] bridging motif precisely regulates the arrangement of the {[Hg₃Se₂]} _n zig−zag chains, rendering them perfectly coplanar and thereby achieving the optimal orientation of the functional motifs. This work not only reports two promising birefringent materials, more importantly, elucidates and validates a design paradigm that “bridging motifs” can effectively modulate structural dimensionality and symmetry to optimize the spatial organization of functional motifs, providing rational design of high performance birefringent materials.In this study, the substitution of the bridging unit from [HgS₂Cl₂] to [HgSe₂Cl] successfully induces a dimensional transition from {[Hg₇S₄Cl₂]} _n layer to {[Hg₈Se₄Cl₂]²⁺} _n chain. This structural reorganization optimizes the alignment of the linear [HgQ₂] and [Hg₂Q₂] units, enabling a geometric superposition of their polarizability anisotropy. Consequently, 2 achieves a birefringence of 0.45@546 nm, surpassing all known commercial birefringent crystals while maintaining good optical transparency across a broad spectral range. Theoretical calculations and analyses reveal that the giant birefringence originates from two key factors. First, the linear [HgSe₂] and [Hg₂Se₂] units possess extremely high polarizability anisotropy, characterized by marked spatial separation and strongly directional distribution of their HOMO and LUMO orbitals. Second, the [HgSe₂Cl] bridging motif precisely regulates the arrangement of the {[Hg₃Se₂]} _n zig−zag chains, rendering them perfectly coplanar and thereby achieving the optimal orientation of the functional motifs. This work not only reports two promising birefringent materials, more importantly, elucidates and validates a design paradigm that “bridging motifs” can effectively modulate structural dimensionality and symmetry to optimize the spatial organization of functional motifs, providing rational design of high performance birefringent materials.

Conflicts of Interest

The authors declare no conflicts of interest.

Supporting information

Supporting File 1: smll73990‐sup‐0001‐SuppMat.docx.

Supporting File 2: smll73990‐sup‐0002‐cif.zip.

Data Availability Statement

The data that supports the findings of this study are available in the supplementary material of this article.