Unprecedented [Hg3Se2]2- cluster drives giant optical anisotropy and broad infrared transparency

Unprecedented [Hg3Se2]2- cluster drives giant optical anisotropy and broad infrared transparency | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Unprecedented [Hg3Se2] 2- cluster drives giant optical anisotropy and broad infrared transparency Shilie Pan, Qixian Ren, Chen Cui, Xinchen Chen, Yabo Wu, Ran An, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6232980/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 06 Jan, 2026 Read the published version in Nature Communications → Version 1 posted You are reading this latest preprint version Abstract Optical anisotropy, as the core physical property for polarization manipulation, has always posed a significant challenge in the design of functional optical materials regarding its regulation mechanism and performance optimization. In the mid-far infrared (IR) region, optical materials that possess both large birefringence and wide transparent range are extremely scarce. In this study, we synthesized Hg 9 Ga 4 Se 4 Cl 16 (HGSC), a tridymite-like topological structure incorporating well-aligned linear [Hg 3 Se 2 ] units. HGSC exhibits an exceptional birefringence of 0.808 at 546 nm, which is 67 times higher than that of commercial MgF 2 , while also possessing the broadest transparency window among Hg-based chalcogenide single crystals (0.4 to 25 µm). Theoretical calculations reveal that the significant birefringence of HGSC originates from the well-aligned [Hg 3 Se 2 ] clusters, which exhibit the highest optical anisotropy (𝛿 = 430) among all known birefringence-active functional units. This study presents a new bifunctional unit for the design of optical materials that combine both a wide IR transparency range and exceptional birefringence. Furthermore, as the first selenide to feature [Hg 3 ] 2+ atomic multinuclear clusters, HGSC compounds offer significant potential for applications in thermoelectric, magnetism, and low-temperature superconductivity. Physical sciences/Chemistry/Materials chemistry Physical sciences/Materials science/Materials for optics infrared optical materials linear units birefringence Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Introduction Birefringent materials achieve polarization separation by exploiting the angular difference in the total internal reflection of ordinary (o) and extraordinary (e) lights, and have been widely used as polarization modulators in optical imaging, remote sensing, and laser communication systems 1-5 . Over the past few decades, a variety of birefringent materials have been developed, including commercially available crystals such as YVO 4 , TiO 2 , CaCO 3 , MgF 2 , and α-BaB 2 O 4 6-10 . However, the intrinsic absorption above 5 μm wavelength hinders their utilization in the mid-far-infrared (IR) regions. Furthermore, birefringent materials with large optical anisotropy are advantageous for achieving polarization devices with high extinction ratios, stability, and miniaturization 11-14 . Therefore, it is urgent to find optical materials with both a wide IR transparency range and a large birefringence 15 . The IR optical transparency of a material is primarily determined by its phonon modes. In contrast, optical anisotropy is influenced by its electronic structure and response 16-19 . It is crucial to develop novel functional units that can simultaneously broaden the IR transparency range while enhancing optical anisotropy, which remains a significant challenge in material design. Recently, various strategies have been developed to enhance the optical anisotropy of materials, such as introducing planar π-conjugated units 20,21 , linear units 22-28 , or elements containing stereo electronic lone pairs (As 3+ , Sb 3+ , Sn 2+ ) 29,30 . Among them, mercury is a unique element capable of forming multinuclear metal anion clusters, with linear arrangements of Hg atoms proven to be effective in enhancing optical anisotropy 31,32 . Our group had analyzed the potential mechanisms underlying the enhanced birefringence, the polarization anisotropy of the linear clusters is superior to that of traditional functional modules, with [Hg 2 I 2 ] exhibiting the highest polarization anisotropy 33 . Kong et al. reported linear [Hg 2 O 2 ] as a novel birefringence-active structural unit, successfully constructing a layered structure with significant anisotropic characteristics. This strategy effectively mitigated the mutual cancellation of anisotropic effects, resulting in the compounds Hg 4 (Te 2 O 5 )(SO 4 ) and Hg I 2 Hg II (Te 2 O 4 ) 2 (HPO 4 ) 2 exhibiting notable birefringence values of 0.542 and 0.444 at a wavelength of 546 nm, respectively 34,35 . Our group has revealed that the incorporation of well-aligned linear [Hg 2 S 2 ] clusters significantly enhances the optical anisotropy of the Hg 4 InS 2 Cl 5 compound, achieving the highest experimentally observed birefringence of 0.35 for Hg-based thiohalides at a wavelength of 546 nm 36 . Owing to relativistic effects, the 6 s orbital of Hg contracts significantly, causing Hg 2+ to favor electronic rearrangements and the formation of multinuclear clusters such as Hg 2 2+ and Hg 3 2+ . This suggests that the coordination form Q-Hg-Hg-Hg-Q (Q = S, Se) may also be viable. Moreover, as a heavy metal element, Hg exhibits lower metal bond stiffness compared to typical transition metals, resulting in lower optical phonon energies in Hg-rich compounds and consequently reducing high-frequency IR absorption. The choice of anion is equally important in designing optical materials with a wide IR transparency range. To avoid the multinuclear absorption of oxygenated acid salts in the near-IR region, chalcogenides were chosen as the study system. We have investigated Hg-based compounds in the ICSD database, and to the best of our knowledge, no reports on the synthesis and properties of the [Hg 3 Q 2 ] unit to date. The design and synthesis of multinuclear clusters with Hg 3 2+ are a promising approach for further exploration. In this paper, we designed and synthesized the Hg-based thiohalides Hg 9 Ga 4 Se 4 Cl 16 (HGSC) with ultra-large birefringence, and millimeter-sized single crystals were grown by using the chemical vapor transport method (CVT). Notably, this represents the first synthesis of the linear [Hg 3 Se 2 ] unit. As a new birefringent gain unit with linear geometry, [Hg 3 Se 2 ] anionic multinuclear cluster exhibits the largest polarization anisotropy (𝛿 = 430) to date, thereby producing an exceptionally significant birefringence gain. The calculated birefringence of the HGSC compound at 546 nm is 0.808, and it also possesses significant birefringence ( ∆n = 0.4) in the mid-far-IR region. Theoretical calculations indicate that the remarkable birefringence in HGSC compound originates from the well-arranged linear [Hg 3 Se 2 ] units. The high-density arrangement of mixed-valence Hg atoms in HGSC compounds gives them an exceptionally broad IR transparency range from 0.4 to 25 µm, which is the widest reported among Hg-based chalcogenide single crystals. We also reported in detail the synthesis, structure, and optical properties of HGSC. Furthermore, the synthesis of [Hg 3 Se 2 ] unit not only provides a new functional unit with linear geometric coordination but also its unique three-mercury atom cluster structure allows for further filling of the conduction band through orbital overlap, bringing about unique optical or electronic properties. This study, through systematic experimental characterization and theoretical calculations, reveals the structure-property relationship of the linear [Hg 3 Se 2 ] functional unit, not only providing a significant theoretical basis for elucidating the structure-property correlation in IR birefringent materials but also laying a material foundation for the development of new high-performance mid-far-IR optical devices. Results and Discussion Crystal structure of Hg 9 Ga 4 Se 4 Cl 16 . The crystal structure of HGSC was analyzed and refined using single-crystal X-ray diffraction (SXRD) data. HGSC crystallizes in the monoclinic space group P 2 1 / c (no. 14). In the asymmetric unit, there are five independent crystallographic Hg atoms, two Ga atoms, two Se atoms, and eight Cl atoms (Supplementary Tables 1–5). The crystal structure of HGSC consists of three distinct linear units that are interconnected through shared Se atoms, forming a unique tridymite-like topology. This breakthrough led to the successful synthesis of the first tridymite-like topology incorporating [HgSe 2 ], [Hg 2 Se 2 ], and [Hg 3 Se 2 ] units. The Hg-Se bond length in [Hg 3 Se 2 ] is 2.610 Å, which is longer than the average values in [Hg 2 Se 2 ] (2.558 Å) and [HgSe 2 ] (2.448 Å). This increase in bond length can be attributed to the larger induced dipole moments of the multinuclear clusters [Hg 3 Se 2 ] and [Hg 2 Se 2 ] compared to the [HgSe 2 ] unit. The Hg-Hg-Hg bond angle is 174.57 °, consistent with the known bond angle of Hg 3 2+ . The geometries of [Hg 2 Se 2 ] and [HgSe 2 ] are consistent with previously reported Hg-based thiohalides (Fig. 1 a). The [Hg 3 Se 2 ] and [HgSe 2 ] units form one-dimensional helical channels along the b -axis through bridging Se atoms (Fig. 1 b). The [Hg 2 Se 2 ] and [HgSe 2 ] units form a Hg 8 Se 6 chair-like conformation through vertex-sharing (Fig. 1 c). The one-dimensional helical chains and chair-like conformations alternate in a reverse parallel stacking along the c -axis, forming two channels of different sizes, with the [Hg 3 Se 2 ] and [Hg 2 Se 2 ] units serving as the boundaries of the larger and smaller channels, respectively (Fig. 1 d). Weak electrostatic interactions within the multinuclear cluster structure retain [GaCl 4 ] within the cavities of the framework, and the entire three-dimensional framework is formed through axial rotational symmetry around the central Hg atoms (Fig. 1 e). The coordination angles between Ga and Cl atoms range from 104.7 to 114.2 °, close to ideal tetrahedral coordination. The Ga-Cl bond lengths are consistent with the reported range. It is worth noting that this study marks the first successful synthesis of the linear [Hg 3 Se 2 ] unit. Typically, ordered arrangements of linear units can exhibit significant optical anisotropy, which is beneficial for achieving maximum birefringence in optical material design. Furthermore, owing to its complex structure, the information complexity parameters, including information content ( I G ), total information content ( I G , total), maximum structural information content ( I G , max), and information density (ρ inf .), are 5.569 bits/atom, 6014.52 bits/unit-cell, 7.0444 bits/atom, and 1.678 bits/Å 3 , respectively, calculated based on the formulas from the literature 37 . The information complexity of HGSC is greater than that of most inorganic chalcogenides, resulting in a smaller first Brillouin zone for its phonon dispersion. This leads to the folding of high-frequency acoustic phonon modes into the optical phonon regime, resulting in phonon dispersion flattening and a significant reduction in phonon group velocities near the zone boundaries. This phenomenon may give rise to unique optical, electrical, and thermal properties, with particular advantages for thermoelectric applications. High-purity HGSC polycrystalline powder samples were synthesized via a stoichiometric solid-state reaction method. The powder X-ray diffraction (PXRD) pattern of the sample matches well with the theoretical one (Supplementary Fig. 1). Single crystals of HGSC were grown using the chemical vapor transport (CVT) method in sealed quartz tubes at 950 C °. Figure 2 a presents a schematic representation of crystal growth via CVT. In this process, Hg 2 Cl 2 served dual functions as both the transport agent and reagent, which was found to be particularly effective for the CVT growth of the target compound. This approach created a mercury-rich environment, which prevented the decomposition of the target product. As a result, millimeter-sized single crystals were obtained, with the (001) plane as the preferential growth facet (Fig. 2 b). The chemical composition of the obtained single crystals was verified by energy-dispersive X-ray spectroscopy (EDS), which confirms the presence of Hg, Ga, Se, and Cl (Fig. 2 c). The optical bandgap of HGSC was determined using UV-Vis-NIR diffuse reflectance spectroscopy on polycrystalline powder. The Kubelka-Munk transformation of the reflectance data yielded an optical bandgap of 2.559 eV for HGSC (Fig. 2 d). To gain insights into the lattice vibrations and chemical bond vibrational modes of HGSC, Raman spectroscopy was performed. Figure 2 e displays the Raman spectrum of HGSC in the range of 20 to 4000 cm − 1 , revealing eight distinct Raman-active vibrational modes. Vibrational bands associated with Hg-Hg-Hg, Hg-Hg, Hg-Se, and Ga-Cl bonds were identified. Raman shifts at 102.6 and 129.8 cm − 1 are attributed to Hg 3 2+ , while the peak at 174.55 cm − 1 corresponds to Hg 2 2+ , consistent with previously reported values for Hg 3 (AsF 6 ) 2 , confirming the presence of Hg 3 2+ and Hg 2 2+ in the compound 38 , 39 . X-ray photoelectron spectroscopy (XPS) was conducted to analyze the chemical and electronic states of HGSC (Supplementary Fig. 2). In the analysis of the Hg4f 5/2 and Hg4f 7/2 peaks, we observed six distinct peaks and determined their binding energy positions to be 105.0, 103.9, and 104.3 eV (Hg4f 5/2 ) and 101.1, 99.8, and 100.4 eV (Hg4f 7/2 ), respectively. These peaks are attributed to the oxidation states of Hg 0 , Hg + , and Hg 2+ (Fig. 2 f) 40 – 42 . It is worth noting that in the Hg 3 − x AsF 6 compound, the presence of linear Hg 3 2+ with mixed valence states has been reported to exhibit superconductivity at 4 K 43 , 44 . According to the Lewis acids and bases theory 45 , since Se 2− has a lower electronegativity than F − , the basicity of Se 2− is softer than that of F − , leading to a more stable combination of soft acids (Hg 2 2+ ) with soft bases (Se 2− ). This makes the HGSC with retained linear mercury atom clusters promising candidates for more stable low-temperature superconducting materials. Considering the electronic properties of mercury with multiple valence states, we investigated the luminescent properties (PL) of HGSC. Under excitation at 300–485 nm, PL excitation at room temperature (298 K) was measured. The optimal emission wavelength is approximately 332 nm, with HGSC exhibiting a super-broadband green emission at 501 nm (Supplementary Fig. 3). The ultra-broad emission band spans nearly the entire visible spectrum, demonstrating its exceptional potential for applications in spectral lighting and advanced optoelectronic devices 46 – 48 . The fully filled 5 d orbitals of Hg effectively prevent d-d electronic transitions, thereby avoiding absorption in the visible and IR regions 49 . Additionally, as a heavy metal element, Hg-based compounds exhibit low lattice vibration frequencies, leading to weak absorption of far-IR light. To experimentally validate this, we conducted transmission spectroscopy tests on HGSC single-crystal with the (001) surface exposed. The results indicate that the short-wavelength transparency cutoff edge of HGSC is located at 0.4 µm, while its IR transparency extends up to 25 µm (Fig. 2 g), covering a broad spectral range from near UV to far IR. This range includes the important atmospheric windows at 3–5 µm and 8–14 µm. The exceptionally broad optical transparency range can be attributed to the unique valence states of Hg in the enriched [Hg 3 Se 2 ] and [Hg 2 Se 2 ] units, typically assigned as 0 and + 1, respectively. These valence states contribute to a high proportion of heavy elements in the compound, effectively suppressing multiphonon absorption in the near-IR region. To investigate the anisotropic properties of HGSC crystals, we conducted detailed observations using the ZEISS Axio Scope 5 polarizing microscope. Figure 3 a illustrates a schematic diagram of the polarizing microscope setup. When linearly polarized light is incident on the HGSC crystal, its polarization state transforms into elliptical polarization due to the birefringence effect. The HGSC single crystal exhibits strong birefringence, as evidenced by periodic brightness variations under different polarization angles (Fig. 3 b). At a polarization angle of 0 °, the tested crystal achieves complete extinction (perpendicular to the polarization direction), and as the polarization angle increases, the light intensity gradually rises. At a polarization angle of 45 °, the brightness reaches its maximum (parallel to the polarization direction). Further rotation of the measured crystal results in periodic changes in the brightness of the interference colors every 45 °. Supplementary Video 1 provides recorded images of the HGSC crystal, indicating that the HGSC crystal exhibits notable optical anisotropy. The laser-induced damage threshold is one of the key parameters for evaluating the performance of birefringent materials. We investigated the laser damage behavior of HGSC single crystals using a picosecond pulse laser. As shown in Supplementary Fig. 4, when the laser output energy ranges from 0.4 to 2.4 mJ, the HGSC crystal exhibits no detectable damage. However, when the energy is increased to 2.8 mJ, micro-cracks begin to appear at the edges of the crystal. Further increasing the energy to 4.0 mJ results in noticeable cracks in the crystal. Experimental results based on picosecond laser irradiation indicate that HGSC crystals exhibit excellent resistance to laser damage, exceeding that of AgGaS₂ by a factor of 3.5. To elucidate the structural-property relationship of the titled compound, the electronic structure was investigated through first-principles calculations. As shown in Fig. 3 f, the valence band maximum (VBM) and conduction band minimum (CBM) of HGSC are located at different high-symmetry points, indicating that HGSC is an indirect bandgap semiconductor. Due to the well-known underestimation of bandgaps in DFT calculations caused by exchange-correlation energy discontinuities, the calculated bandgap is 2.11 eV, which is lower than the experimental value of 2.559 eV. Figure 3 g illustrates the total density of states (TDOS) and partial density of states (PDOS) of HGSC. The Hg 5 d orbitals are mainly concentrated between − 8 and − 6 eV, while the valence band region near the Fermi level (-5 to 0 eV) is predominantly occupied by Hg 6 s , 6 p orbitals, Ga 4 p orbitals, Se 4 p orbitals, and Cl 3 p orbitals. The conduction band region from the Fermi energy level to 4.0 eV is mainly occupied by Hg 6 s and 6 p orbitals, Se 4 s and 4 p orbitals, with a minor contribution from Cl 3 s orbitals. Therefore, the optical properties of HGSC are primarily determined by the Hg 6 s and 6 p orbitals, Se 4 p , and Cl 3 p orbitals. Based on the formula ε(ω) = ɛ 1 (ω) + iε 2 (ω) and n 2 (ω) = ε(ω) , the birefringence properties were calculated, resulting in refractive indices n (010) > n (100) > n (001) for HGSC. The birefringence (Δ n ) values are 0.808 at 546 nm and 0.443 at 1064 nm (Fig. 3 h). Since the birefringence of optical materials not only depends on the functional unit but also on the arrangement and configuration of the building units 50 , the unique structural feature of the HGSC compound, characterized by three near-parallel alignment units vertically assembled, significantly reduces anisotropic mutual cancellation, thus enhancing the superposition of the polarizability vector. Figure 3 i shows that the maximum refractive index direction of the HGSC compound is aligned with the arrangement direction of the linear [Hg 3 Se 2 ] units. This fully demonstrates that the significant optical anisotropy in the HGSC compound originates from the preferential arrangement of the linear [Hg 3 Se 2 ] units. At the microscopic level, the polarization anisotropy of all linear units in the Hg-based chalcogenides was calculated using Gaussian 09 51 . To make a comprehensive comparison, we also calculated some emerging linear birefringence units (Fig. 3 j). Prior to this, the highest reported polarization anisotropy is for the [Hg 2 I 2 ] unit. The linear [Hg 3 Se 2 ] unit, as a new functional unit in the Hg-based chalcogenides family, exhibits the highest polarization anisotropy ( δ = 430) among all known birefringence-active units to date. The visualization results of the electronic localization function (ELF) for HGSC were calculated using first principles calculations (Supplementary Fig. 5). In functional units with linear coordination, the charge distribution around the atoms is highly uneven, and the deformation of the electron clouds leads to a more localized electron distribution, resulting in a more significant electron displacement polarization. Thus, the linear [Hg 3 Se 2 ] unit possesses the characteristics of the most promising functional unit for achieving giant birefringence. To validate the phase retardation effect of transmitted light 52 , 53 , the evolution of the polarization state of linearly polarized light passing through an HGSC crystal was systematically investigated (Fig. 4 a). The polarization modulation characteristics of linearly polarized light with a wavelength of 1064 nm passing through an HGSC crystal with a thickness of 70.5 µm were experimentally observed. To establish a comprehensive polarization state characterization system, the intensity distributions of the horizontal linear polarization state under crystal-free conditions, as well as the polarization states corresponding to rotations of 30, 60, and 90 °, were observed (Figs. 4 b, 4 d, 4 f). By rotating the polarizing prism, the elliptical polarization states of the output light from the (001) crystal plane were precisely measured (Figs. 4 c, 4 e, 4 g). Their Jones vectors, E 0 , E 1 , E 2 , and E 3 , are explained in Supplementary Equations 1–4. The crystal can be regarded as a phase retardation plate, and the general Jones matrix of a phase retardation plate can be expressed as: $$\:{J}_{R}\left(\phi\:,\left.\theta\:\right)\right.=\left(\begin{array}{cc}\text{cos}\frac{\phi\:}{2}+i\text{sin}\frac{\phi\:}{2}\text{cos}2\theta\:&\:i\text{sin}\frac{\phi\:}{2}\text{sin}2\theta\:\\\:i\text{sin}\frac{\phi\:}{2}\text{sin}2\theta\:&\:\text{cos}\frac{\phi\:}{2}-i\text{sin}\frac{\phi\:}{2}\text{cos}2\theta\:\end{array}\right)$$ Where φ represents the phase retardation induced by birefringence, and θ denotes the rotation angle of the polarization principal axis. In the HGSC crystal with the (001) crystal orientation, this phase retardation primarily arises from the phase superposition of polarization components due to the refractive index difference between the x and y directions ( n x ≠ n y ) Based on crystal optics theory, the phase parameters corresponding to rotations of 30, 60, and 90 ° can be expressed as ( φ,θ )、( φ,θ + 30 °)、and ( φ,θ + 60 °) respectively, where φ and θ are undetermined parameters that can be obtained by solving the subsequently established system of equations. According to the above parameter relationships, the Jones matrix expressions corresponding to the three rotation angles (30, 60, and 90 °) can be expressed as J 1 , J 2 , and J 3 (Supplementary Equations 5–7). Based on the theoretical analysis above, the following matrix equations were derived: J 1 ·E 0 = E 1 , J 2 ·E 0 = E 2 , J 3 ·E 0 = E 3 . By solving this system of equations, the average value of the phase retardation φ was determined to be 2.79 + m ·2 π (where m is an integer). According to the phase retardation formula induced by birefringence, φ = Δ k·z = 2π·(n y - n x )·z/λ ( z = 70.5 µm ) represents the crystal thickness, and λ = 1064 nm is the incident laser wavelength).The experimental value of n y −n x is 0.052, which shows good agreement with the theoretically predicted value of 0.046 for the (001) crystal plane. The phase retardation effect confirms that the HGSC crystal exhibits significant birefringence, further validating the reliability in polarization modulation devices. To fully elucidate the unique potential of HGSC as a birefringent material in the mid-to far IR region, we compared the IR transparency ranges of previously reported Hg-based chalcogenide single crystals. HGSC exhibits exceptional optical properties, spanning the atmospheric transmission windows of the mid-to-far-IR spectrum, and has the broadest transmission range among Hg-based chalcogenide single crystals to date (Fig. 5 a). Figure 5 b demonstrates the significant birefringence of HGSC, with Δ n ≈ 0.808 in the visible spectrum and Δ n ≈ 0.4 in the mid-to-far IR region. These birefringence values are 67 times higher than that of the commercial material MgF 2 (0.012@546 nm) and 2.6 times higher than that of TiO 2 (0.306@546 nm), the leading commercial birefringent material, in the visible spectrum. These findings highlight the potential of HGSC for advanced optical applications. Discussion In this study, we successfully synthesized a novel compound, HGSC, featuring a unique tridymite-like topological structure incorporating linear [Hg 3 Se 2 ] functional units. HGSC exhibits an exceptional birefringence of 0.808 at 546 nm, which is 67 times higher than that of the commercial infrared birefringent material MgF 2 . Furthermore, the incorporation of the heavy metal element Hg grants HGSC an exceptionally broad infrared transparency range from 0.4 to 25 µm, the widest reported among Hg-based chalcogenide single crystals.Theoretical calculations reveal that the pronounced birefringence of HGSC originates from the well-aligned linear [Hg 3 Se 2 ] units. Notably, the [Hg 3 Se 2 ] unit exhibits the highest polarization anisotropy among all known birefringence-active units to date. This study represents the first successful synthesis and demonstration of the [Hg 3 Se 2 ] multinuclear cluster as a structural unit capable of significantly enhancing the optical anisotropy of materials.These findings provide critical insights into the structure-property relationships governing birefringence and offer valuable guidance for the design of next-generation birefringent materials with high applicability in mid-to-far infrared optical technologies. Materials The reagents including Hg 2 Cl 2 (Aldrich, 99.9%), HgCl 2 (Aexchem, 99.99%), HgSe (Aldrich, 99.99%), Ga 2 Se 3 , (Aldrich, 99.999%) are analytical grade from commercial sources without further purification. Synthesis and crystal growth The millimeter-sized HGSC single crystals were grown using the chemical vapor transport method (CVT). A mixture of HgCl 2 (1.3085 g, 3 mmol), Hg 2 Cl 2 (3.0334 g, 4 mmol), HgSe (0.4491 g, 1 mmol), and Ga 2 Se 3 (1.2091 g, 2 mmol). The mixtures of raw materials were put into quartz tubes and sealed using a methane-oxygen under a high vacuum of 10 − 3 Pa. The sealed tube is transferred to a computer-controlled furnace, and the temperature distribution is as follows: The furnace temperature gradually increases to 400°C within 12 h. It is then dwelled at 400°C for 7 h, followed by an increase to 950°C within 30 h, and kept at this temperature for 4 days. Subsequently, the temperature is reduced to 300°C at a rate of 2°C/h, and finally gradually cooled down to room temperature within 10 h. Through the above process, pale yellow tridymite-like topological structure can be obtained Characterization High-optical quality crystal (HGSC, 0.091 × 0.068 × 0.092 mm 3 ) was selected under a polarizing microscope and used for single-crystal X-ray data collection. Single-crystal XRD data were collected on a Bruker SMART APEX Ⅴ CCD diffractometer using Mo Kα radiation (λ = 0.71073 Å) at room temperature. Data integration, cell refinement, and absorption corrections were carried out with the program SADABS 54 . The structure was solved by direct methods and refined on F 2 by full-matrix least-squares techniques using the program suite SHELXTL 55 . Solutions were checked for missed symmetry using PLATON 56 . The crystal data give R int = 0.0605 and the structure solution parameters are R 1 = 0.0462, wR 2 = 0.1114, GOF = 1.095. Powder XRD data were collected with a Bruker D2 PHASER diffractometer (Cu Kα radiation with λ = 1.5418 Å, 2 θ = 5 to 70 °, scan step width = 0.02 °, and counting time = 1 s/step). IR spectroscopy was measured on a Shimadzu IR Affinity-1 Fourier transform IR spectrometer in the 400–4000 cm − 1 range. X-ray photoelectron Spectroscopy of HGSC powder samples was collected on a Thermo Scientific ESCALAB 250Xi spectrometer equipped with a monochromatic Al Kα X-ray source. Samples were analyzed under high vacuum (Pa < 10 − 9 mbar). Survey scans and high-resolution scans were collected. Binding energies of all scans were corrected according to the C 1 s binding energy at 284.8 eV. The optical diffuse-reflectance spectra of HGSC were recorded at room temperature on a Shimadzu SolidSpec-3700DUV spectrophotometer. The measured wavelength range is 200–2600 nm. To figure out the experimental band gap ( E g ), the diffuse reflection data were converted into absorption data by the Kubelka-Munk function F(R ) = K / S = (1 − R ) 2 /2 R , where R represents the reflection coefficient, K is the absorption value, and S is the scattering coefficient. To verify the presence of Hg 3 2+ and Hg 2 2+ , selected HGSC crystals were placed on a glass slide and then irradiated with a 532 nm laser. Raman spectra were recorded in the range of 40-4000 cm − 1 using a LABRAM HR Evolution spectrometer equipped with a CCD detector. The integration time was set to 5 seconds, and the laser intensity was maintained at 25%. To determine the chemical compositions, the EDS spectra and mappings of the compounds were tested on a field emission scanning electron microscope (FE-SEM, JEOL JSM-7610F Plus, Japan) equipped with an energy-dispersive X-ray spectrometer (Oxford, X-Max 50). The birefringence of HGSC was measured using a polarizing microscope (ZEISS Axio Scope.5 pol) equipped with a Berek compensator under a light source with an average wavelength of 546.1 nm. The interference color in the measurement was classified as first-, second-, or higher-order to ensure the accuracy of the measurement, as their boundary lines were relatively clear compared to subsequent interference colors. Crystals with high optical quality were selected for scanning under the polarizing microscope. The LIDT of HGSC single crystals were measured through a picosecond pulsed laser (1064 nm, 10 Hz, 5 ns). The input laser intensities were raised from 5 mJ until damage occurred, and the laser energy E was recorded. Computational methods The electronic structures, density of states, and birefringence of the title compounds were evaluated in the plane-wave pseudopotential method implemented in the CASTEP software based on Density Functional Theory (DFT) 57 . HGSC was optimized by the Perdew − Burke − Ernzerhof (PBE) exchange-correlation of generalized gradient approximation (GGA) 58 , while the following orbital electrons were preserved as valence electrons: Hg 6 s 2 5 d 10 , Ga 4 s 2 4 p 1 , Se 4 s 2 4 p 4 , and Cl 3 s 2 3 p 5 , respectively. The plane-wave cutoff energy for HISC was set to 800 eV during the calculation, and Monkhorst-Pack k -point meshes (2 × 3 × 1) with a density of less than 0.04 Å −1 in the Brillouin zone (BZ) were adopted. The default values of the CASTEP code were used on the aspect of the other calculation parameters and convergence criteria 59 . To calculate the birefringence, the complex dielectric function, ε(ω) = ε 1 (ω) + iε 2 (ω) was computed from the PBE wave functions. The imaginary portion of the dielectric function ε 2 may be estimated upon the electronic structures, and its real part is determined using the Kramers − Kronig transform, which was used to derive the refractive indices and finally get the birefringence Δ n , the optical properties were scissor-corrected. Anisotropy of the polarizability (Δ α ) was calculated by the Gaussian 09 revision D.01 program. The GaussView5 software visualizes the output file 60 . $$\:\varDelta\:\varvec{\alpha\:}=\sqrt{\frac{1}{2}\left[{\left({\varvec{\alpha\:}}_{\varvec{x}\varvec{x}}-{\varvec{\alpha\:}}_{\varvec{y}\varvec{y}}\right)}^{2}+{\left({\varvec{\alpha\:}}_{\varvec{x}\varvec{x}}-{\varvec{\alpha\:}}_{\varvec{z}\varvec{z}}\right)}^{2}+{\left({\varvec{\alpha\:}}_{\varvec{y}\varvec{y}}-{\varvec{\alpha\:}}_{\varvec{z}\varvec{z}}\right)}^{2}+6\left({{\varvec{\alpha\:}}_{\varvec{x}\varvec{y}}}^{2}+{{\varvec{\alpha\:}}_{\varvec{x}\varvec{z}}}^{2}+{{\varvec{\alpha\:}}_{\varvec{y}\varvec{z}}}^{2}\right)\right]}$$ Where, αij (i, j = x, y, z) represents an independent element of the polarization tensor. Declarations Data availability All the characterization data and experimental protocols are provided in this article and its Supplementary Information. The X-ray crystallographic coordinates for structures reported in this study have been deposited at the Cambridge Crystallographic Data Centre (CCDC), under deposition numbers 2428275. These data can be obtained free of charge from The Cambridge Crystallographic Data Centre via www.ccdc.cam.ac.uk/ data_request/cif. Acknowledgements This work is financially supported by National Natural Science Foundation (NSFC) of China (62305382, 52302011, 22335007, 22361132544), Natural Science Foundation of the Xinjiang Uygur Autonomous Region (2023D01A04, 2022D01B206), Shanghai Cooperation Organization Science and Technology Partnership Program (2023E01001), the Xinjiang Major Science and Technology Project (2021A01001). Y. W. and C. C. thanks the support from Tianchi Plan of Xinjiang Uygur Autonomous Region. Author contributions Q. X. Ren was responsible for single crystal growth, experimental implementation, auxiliary characterization, and the drafting of the manuscript; X. C. 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Supplementary Files checkcif.pdf Dataset 1 Hg9Ga4Se4Cl16.cif Dataset 2 SupportingInformation.docx Supporting Information Video1.mp4 Video 1 Cite Share Download PDF Status: Published Journal Publication published 06 Jan, 2026 Read the published version in Nature Communications → Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6232980","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":430953484,"identity":"0f768342-52b1-4cae-a69e-8a57c6df88b3","order_by":0,"name":"Shilie 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Hg\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e9\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003eGa\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e4\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003eSe\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e4\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003eCl\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e16\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003e.\u003c/strong\u003e \u003cstrong\u003ea\u003c/strong\u003e Coordination environment of mercury atoms in HGSC. \u003cstrong\u003eb\u003c/strong\u003e A one-dimensional helical channel along the \u003cem\u003eb\u003c/em\u003e-axis. \u003cstrong\u003ec\u003c/strong\u003e A chair-like conformation of Hg\u003csub\u003e8\u003c/sub\u003eSe\u003csub\u003e6\u003c/sub\u003e along the \u003cem\u003eb\u003c/em\u003e-axis. \u003cstrong\u003ed\u003c/strong\u003e The helical channels and chair-like conformations are stacked in an alternating manner along the \u003cem\u003ec\u003c/em\u003e-axis in a reverse parallel arrangement. \u003cstrong\u003ee\u003c/strong\u003e Crystal structure of HGSC along the \u003cem\u003eb\u003c/em\u003e-axis.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-6232980/v1/d85e46bcdf318d220e5fe0ab.png"},{"id":79809503,"identity":"55cda368-a6d3-4193-b245-4698df23b0d5","added_by":"auto","created_at":"2025-04-03 06:17:17","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":2662256,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eOptical properties of Hg\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e9\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003eGa\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e4\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003eSe\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e4\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003eCl\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e16\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003e. a\u003c/strong\u003e Schematic diagram of the growth of HGSC single crystals via CVT. \u003cstrong\u003eb\u003c/strong\u003e XRD pattern of naturally grown (001) crystal face. \u003cstrong\u003ec\u003c/strong\u003e The elemental mapping of HGSC. The scale bar is 50 μm. \u003cstrong\u003ed\u003c/strong\u003e UV-Vis-NIR diffuse-reflectance spectrum of HGSC sample. \u003cstrong\u003ee\u003c/strong\u003e Non-polarized Raman spectroscopy of the HGSC sample. \u003cstrong\u003ef\u003c/strong\u003e XPS spectrum of HGSC sample. \u003cstrong\u003eg\u003c/strong\u003e Transmission spectrum of the (001) face.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-6232980/v1/47a8a7b1df393039e36059a5.png"},{"id":79810280,"identity":"aee019ee-c835-4ed7-89c5-af0feb6c4d5f","added_by":"auto","created_at":"2025-04-03 06:25:17","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":2584819,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eOptical anisotropy observation and calculation of Hg\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e9\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003eGa\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e4\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003eSe\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e4\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003eCl\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e16\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003e. a\u003c/strong\u003e Schematic diagram of polarizing microscope. \u003cstrong\u003eb\u003c/strong\u003e Transmitted images under orthogonally polarized light at different rotation angles. \u003cstrong\u003ec\u003c/strong\u003e The thickness of HGSC for the birefringence measurement. \u003cstrong\u003ed,e\u003c/strong\u003e The positive and negative rotation of compensatory. \u003cstrong\u003ef\u003c/strong\u003e The electronic band structure of HGSC. \u003cstrong\u003eg\u003c/strong\u003e TDOS and PDOS plots for HGSC. \u003cstrong\u003eh\u003c/strong\u003e Calculated refractive indices and birefringence of HGSC. \u003cstrong\u003ei\u003c/strong\u003e Diagrammatic sketch of functional modules in an optical indicatrix for HGSC (\u003cem\u003eN\u003c/em\u003e\u003csub\u003e\u003cem\u003eg\u003c/em\u003e\u003c/sub\u003e \u0026gt; \u003cem\u003eN\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e \u0026gt; \u003cem\u003eN\u003c/em\u003e\u003csub\u003e\u003cem\u003em\u003c/em\u003e\u003c/sub\u003e). \u003cstrong\u003ej\u003c/strong\u003e Contrasting the anisotropy of the polarizability of linear units.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-6232980/v1/c050fd8df61b3baf83c9f8f3.png"},{"id":79810278,"identity":"18e6c3f9-e49c-4f8d-90b8-deee65a58ff5","added_by":"auto","created_at":"2025-04-03 06:25:17","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":972208,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003ea \u003c/strong\u003eSchematic illustration showing the polarization state change of the linear polarized light passing through the HGSC crystal. \u003cstrong\u003eb,d,f\u003c/strong\u003e Schematic diagram of polarization state for input/output light corresponding. \u003cstrong\u003ec,e,g\u003c/strong\u003e Schematic diagram of polarization state for output light corresponding to (b),(d) and (f), respectively.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-6232980/v1/ca3881b20e17b13ebb7810af.png"},{"id":79809507,"identity":"758058ee-730e-4537-8949-23c357a8de74","added_by":"auto","created_at":"2025-04-03 06:17:17","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":826139,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003ea\u003c/strong\u003e The comparison of birefringence and IR transmission ranges of Hg-based chalcogenide single crystals (dark blue: high optical transparency regions; light blue: transparent regions with significant optical absorption). \u003cstrong\u003eb\u003c/strong\u003e Comparison of birefringence of commercial optical materials with HGSC in the IR region.\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-6232980/v1/b31bbbced74d4f3e07f8a149.png"},{"id":99676276,"identity":"575f5b1a-e11d-4351-baac-49499cc88461","added_by":"auto","created_at":"2026-01-07 08:06:51","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":8356997,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6232980/v1/b4d67e70-2ac3-44ac-9564-27ab2ab07087.pdf"},{"id":79810633,"identity":"20b88266-3583-4b92-bf89-e8e7f2f71a29","added_by":"auto","created_at":"2025-04-03 06:33:17","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":84731,"visible":true,"origin":"","legend":"Dataset 1","description":"","filename":"checkcif.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6232980/v1/b5c23a276c8c26e81ae0f38a.pdf"},{"id":79809502,"identity":"763370c8-06d3-4bca-92c4-cdc6755d5ef5","added_by":"auto","created_at":"2025-04-03 06:17:17","extension":"cif","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":1119556,"visible":true,"origin":"","legend":"Dataset 2","description":"","filename":"Hg9Ga4Se4Cl16.cif","url":"https://assets-eu.researchsquare.com/files/rs-6232980/v1/258a13b7e8e57d30413830b8.cif"},{"id":79809508,"identity":"fbe831b9-9653-4df1-8895-de667131f723","added_by":"auto","created_at":"2025-04-03 06:17:17","extension":"docx","order_by":3,"title":"","display":"","copyAsset":false,"role":"supplement","size":6188230,"visible":true,"origin":"","legend":"Supporting Information","description":"","filename":"SupportingInformation.docx","url":"https://assets-eu.researchsquare.com/files/rs-6232980/v1/aac4cfa724c298e78c965c6f.docx"},{"id":79809516,"identity":"2ca2c40c-7d8d-425c-bd43-5a84fdaca8dd","added_by":"auto","created_at":"2025-04-03 06:17:17","extension":"mp4","order_by":4,"title":"","display":"","copyAsset":false,"role":"supplement","size":17586415,"visible":true,"origin":"","legend":"Video 1","description":"","filename":"Video1.mp4","url":"https://assets-eu.researchsquare.com/files/rs-6232980/v1/aecf8dabfc7467b0fff23b56.mp4"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"\u003cp\u003eUnprecedented [Hg3Se2]\u003csup\u003e2-\u003c/sup\u003e cluster drives giant optical anisotropy and broad infrared transparency\u003c/p\u003e","fulltext":[{"header":"Introduction","content":"\u003cp\u003eBirefringent materials achieve polarization separation by exploiting the angular difference in the total internal reflection of ordinary (o) and extraordinary (e) lights, and have been widely used as polarization modulators in optical imaging, remote sensing, and laser communication systems\u003csup\u003e1-5\u003c/sup\u003e. Over the past few decades, a variety of birefringent materials have been developed, including commercially available crystals such as YVO\u003csub\u003e4\u003c/sub\u003e, TiO\u003csub\u003e2\u003c/sub\u003e, CaCO\u003csub\u003e3\u003c/sub\u003e, MgF\u003csub\u003e2\u003c/sub\u003e, and \u0026alpha;-BaB\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e\u003csup\u003e6-10\u003c/sup\u003e. However, the intrinsic absorption above 5 \u0026mu;m wavelength hinders their utilization in the mid-far-infrared (IR) regions. Furthermore, birefringent materials with large optical anisotropy are advantageous for achieving polarization devices with high extinction ratios, stability, and miniaturization\u003csup\u003e11-14\u003c/sup\u003e. Therefore, it is urgent to find optical materials with both a wide IR transparency range and a large birefringence\u003csup\u003e15\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eThe IR optical transparency of a material is primarily determined by its phonon modes. In contrast, optical anisotropy is influenced by its electronic structure and response\u003csup\u003e16-19\u003c/sup\u003e. It is crucial to develop novel functional units that can simultaneously broaden the IR transparency range while enhancing optical anisotropy, which remains a significant challenge in material design. Recently, various strategies have been developed to enhance the optical anisotropy of materials, such as introducing planar \u0026pi;-conjugated units\u003csup\u003e20,21\u003c/sup\u003e, linear units\u003csup\u003e22-28\u003c/sup\u003e, or elements containing stereo electronic lone pairs (As\u003csup\u003e3+\u003c/sup\u003e, Sb\u003csup\u003e3+\u003c/sup\u003e, Sn\u003csup\u003e2+\u003c/sup\u003e)\u003csup\u003e29,30\u003c/sup\u003e. Among them, mercury is a unique element capable of forming multinuclear metal anion clusters, with linear arrangements of Hg atoms proven to be effective in enhancing optical anisotropy\u003csup\u003e31,32\u003c/sup\u003e. Our group had analyzed the potential mechanisms underlying the enhanced birefringence, the polarization anisotropy of the linear clusters is superior to that of traditional functional modules, with [Hg\u003csub\u003e2\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e] exhibiting the highest polarization anisotropy\u003csup\u003e33\u003c/sup\u003e. Kong et al. reported linear [Hg\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e2\u003c/sub\u003e] as a novel birefringence-active structural unit, successfully constructing a layered structure with significant anisotropic characteristics. This strategy effectively mitigated the mutual cancellation of anisotropic effects, resulting in the compounds Hg\u003csub\u003e4\u003c/sub\u003e(Te\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e5\u003c/sub\u003e)(SO\u003csub\u003e4\u003c/sub\u003e) and Hg\u003csup\u003eI\u003c/sup\u003e\u003csub\u003e2\u003c/sub\u003eHg\u003csup\u003eII\u003c/sup\u003e(Te\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e)\u003csub\u003e2\u003c/sub\u003e(HPO\u003csub\u003e4\u003c/sub\u003e)\u003csub\u003e2\u003c/sub\u003e exhibiting notable birefringence values of 0.542 and 0.444 at a wavelength of 546 nm, respectively\u003csup\u003e34,35\u003c/sup\u003e. Our group has revealed that the incorporation of well-aligned linear [Hg\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e2\u003c/sub\u003e] clusters significantly enhances the optical anisotropy of the Hg\u003csub\u003e4\u003c/sub\u003eInS\u003csub\u003e2\u003c/sub\u003eCl\u003csub\u003e5\u003c/sub\u003e compound, achieving the highest experimentally observed birefringence of 0.35 for Hg-based thiohalides at a wavelength of 546 nm\u003csup\u003e36\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eOwing to relativistic effects, the 6\u003cem\u003es\u003c/em\u003e orbital of Hg contracts significantly, causing Hg\u003csup\u003e2+\u003c/sup\u003e to favor electronic rearrangements and the formation of multinuclear clusters such as Hg\u003csub\u003e2\u003c/sub\u003e\u003csup\u003e2+\u003c/sup\u003e and Hg\u003csub\u003e3\u003c/sub\u003e\u003csup\u003e2+\u003c/sup\u003e. This suggests that the coordination form Q-Hg-Hg-Hg-Q (Q = S, Se) may also be viable. Moreover, as a heavy metal element, Hg exhibits lower metal bond stiffness compared to typical transition metals, resulting in lower optical phonon energies in Hg-rich compounds and consequently reducing high-frequency IR absorption. The choice of anion is equally important in designing optical materials with a wide IR transparency range. To avoid the multinuclear absorption of oxygenated acid salts in the near-IR region, chalcogenides were chosen as the study system. We have investigated Hg-based compounds in the ICSD database, and to the best of our knowledge, no reports on the synthesis and properties of the [Hg\u003csub\u003e3\u003c/sub\u003eQ\u003csub\u003e2\u003c/sub\u003e] unit to date. The design and synthesis of multinuclear clusters with Hg\u003csub\u003e3\u003c/sub\u003e\u003csup\u003e2+\u003c/sup\u003e are a promising approach for further exploration.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eIn this paper, we designed and synthesized the Hg-based thiohalides Hg\u003csub\u003e9\u003c/sub\u003eGa\u003csub\u003e4\u003c/sub\u003eSe\u003csub\u003e4\u003c/sub\u003eCl\u003csub\u003e16\u003c/sub\u003e(HGSC) with ultra-large birefringence, and millimeter-sized single crystals were grown by using the chemical vapor transport method (CVT). Notably, this represents the first synthesis of the linear [Hg\u003csub\u003e3\u003c/sub\u003eSe\u003csub\u003e2\u003c/sub\u003e] unit. As a new birefringent gain unit with linear geometry, [Hg\u003csub\u003e3\u003c/sub\u003eSe\u003csub\u003e2\u003c/sub\u003e] anionic multinuclear cluster exhibits the largest polarization anisotropy (𝛿 = 430) to date, thereby producing an exceptionally significant birefringence gain. The calculated birefringence of the HGSC compound at 546 nm is 0.808, and it also possesses significant birefringence (\u003cem\u003e∆n\u003c/em\u003e = 0.4) in the mid-far-IR region. Theoretical calculations indicate that the remarkable birefringence in HGSC compound originates from the well-arranged linear [Hg\u003csub\u003e3\u003c/sub\u003eSe\u003csub\u003e2\u003c/sub\u003e] units. The high-density arrangement of mixed-valence Hg atoms in HGSC compounds gives them an exceptionally broad IR transparency range from 0.4 to 25 \u0026micro;m, which is the widest reported among Hg-based chalcogenide single crystals. We also reported in detail the synthesis, structure, and optical properties of HGSC. Furthermore, the synthesis of [Hg\u003csub\u003e3\u003c/sub\u003eSe\u003csub\u003e2\u003c/sub\u003e] unit not only provides a new functional unit with linear geometric coordination but also its unique three-mercury atom cluster structure allows for further filling of the conduction band through orbital overlap, bringing about unique optical or electronic properties. This study, through systematic experimental characterization and theoretical calculations, reveals the structure-property relationship of the linear [Hg\u003csub\u003e3\u003c/sub\u003eSe\u003csub\u003e2\u003c/sub\u003e] functional unit, not only providing a significant theoretical basis for elucidating the structure-property correlation in IR birefringent materials but also laying a material foundation for the development of new high-performance mid-far-IR optical devices.\u003c/p\u003e"},{"header":"Results and Discussion","content":"\u003cp\u003e\u003cstrong\u003eCrystal structure of Hg\u003c/strong\u003e \u003csub\u003e\u0026nbsp;\u003cstrong\u003e9\u003c/strong\u003e\u0026nbsp;\u003c/sub\u003e \u003cstrong\u003eGa\u003c/strong\u003e \u003csub\u003e\u0026nbsp;\u003cstrong\u003e4\u003c/strong\u003e\u0026nbsp;\u003c/sub\u003e \u003cstrong\u003eSe\u003c/strong\u003e \u003csub\u003e\u0026nbsp;\u003cstrong\u003e4\u003c/strong\u003e\u0026nbsp;\u003c/sub\u003e \u003cstrong\u003eCl\u003c/strong\u003e \u003csub\u003e\u0026nbsp;\u003cstrong\u003e16\u003c/strong\u003e\u0026nbsp;\u003c/sub\u003e. The crystal structure of HGSC was analyzed and refined using single-crystal X-ray diffraction (SXRD) data. HGSC crystallizes in the monoclinic space group \u003cem\u003eP\u003c/em\u003e2\u003csub\u003e1\u003c/sub\u003e/\u003cem\u003ec\u003c/em\u003e (no. 14). In the asymmetric unit, there are five independent crystallographic Hg atoms, two Ga atoms, two Se atoms, and eight Cl atoms (Supplementary Tables 1\u0026ndash;5). The crystal structure of HGSC consists of three distinct linear units that are interconnected through shared Se atoms, forming a unique tridymite-like topology. This breakthrough led to the successful synthesis of the first tridymite-like topology incorporating [HgSe\u003csub\u003e2\u003c/sub\u003e], [Hg\u003csub\u003e2\u003c/sub\u003eSe\u003csub\u003e2\u003c/sub\u003e], and [Hg\u003csub\u003e3\u003c/sub\u003eSe\u003csub\u003e2\u003c/sub\u003e] units. The Hg-Se bond length in [Hg\u003csub\u003e3\u003c/sub\u003eSe\u003csub\u003e2\u003c/sub\u003e] is 2.610 \u0026Aring;, which is longer than the average values in [Hg\u003csub\u003e2\u003c/sub\u003eSe\u003csub\u003e2\u003c/sub\u003e] (2.558 \u0026Aring;) and [HgSe\u003csub\u003e2\u003c/sub\u003e] (2.448 \u0026Aring;). This increase in bond length can be attributed to the larger induced dipole moments of the multinuclear clusters [Hg\u003csub\u003e3\u003c/sub\u003eSe\u003csub\u003e2\u003c/sub\u003e] and [Hg\u003csub\u003e2\u003c/sub\u003eSe\u003csub\u003e2\u003c/sub\u003e] compared to the [HgSe\u003csub\u003e2\u003c/sub\u003e] unit. The Hg-Hg-Hg bond angle is 174.57 \u0026deg;, consistent with the known bond angle of Hg\u003csub\u003e3\u003c/sub\u003e\u003csup\u003e2+\u003c/sup\u003e. The geometries of [Hg\u003csub\u003e2\u003c/sub\u003eSe\u003csub\u003e2\u003c/sub\u003e] and [HgSe\u003csub\u003e2\u003c/sub\u003e] are consistent with previously reported Hg-based thiohalides (Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003ea). The [Hg\u003csub\u003e3\u003c/sub\u003eSe\u003csub\u003e2\u003c/sub\u003e] and [HgSe\u003csub\u003e2\u003c/sub\u003e] units form one-dimensional helical channels along the \u003cem\u003eb\u003c/em\u003e-axis through bridging Se atoms (Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003eb). The [Hg\u003csub\u003e2\u003c/sub\u003eSe\u003csub\u003e2\u003c/sub\u003e] and [HgSe\u003csub\u003e2\u003c/sub\u003e] units form a Hg\u003csub\u003e8\u003c/sub\u003eSe\u003csub\u003e6\u003c/sub\u003e chair-like conformation through vertex-sharing (Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003ec). The one-dimensional helical chains and chair-like conformations alternate in a reverse parallel stacking along the \u003cem\u003ec\u003c/em\u003e-axis, forming two channels of different sizes, with the [Hg\u003csub\u003e3\u003c/sub\u003eSe\u003csub\u003e2\u003c/sub\u003e] and [Hg\u003csub\u003e2\u003c/sub\u003eSe\u003csub\u003e2\u003c/sub\u003e] units serving as the boundaries of the larger and smaller channels, respectively (Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003ed). Weak electrostatic interactions within the multinuclear cluster structure retain [GaCl\u003csub\u003e4\u003c/sub\u003e] within the cavities of the framework, and the entire three-dimensional framework is formed through axial rotational symmetry around the central Hg atoms (Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003ee). The coordination angles between Ga and Cl atoms range from 104.7 to 114.2 \u0026deg;, close to ideal tetrahedral coordination. The Ga-Cl bond lengths are consistent with the reported range. It is worth noting that this study marks the first successful synthesis of the linear [Hg\u003csub\u003e3\u003c/sub\u003eSe\u003csub\u003e2\u003c/sub\u003e] unit. Typically, ordered arrangements of linear units can exhibit significant optical anisotropy, which is beneficial for achieving maximum birefringence in optical material design. Furthermore, owing to its complex structure, the information complexity parameters, including information content (\u003cem\u003eI\u003c/em\u003e\u003csub\u003e\u003cem\u003eG\u003c/em\u003e\u003c/sub\u003e), total information content (\u003cem\u003eI\u003c/em\u003e\u003csub\u003e\u003cem\u003eG\u003c/em\u003e\u003c/sub\u003e, total), maximum structural information content (\u003cem\u003eI\u003c/em\u003e\u003csub\u003e\u003cem\u003eG\u003c/em\u003e\u003c/sub\u003e, max), and information density (\u0026rho;\u003csub\u003einf\u003c/sub\u003e.), are 5.569 bits/atom, 6014.52 bits/unit-cell, 7.0444 bits/atom, and 1.678 bits/\u0026Aring;\u003csup\u003e3\u003c/sup\u003e, respectively, calculated based on the formulas from the literature\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e37\u003c/span\u003e\u003c/sup\u003e. The information complexity of HGSC is greater than that of most inorganic chalcogenides, resulting in a smaller first Brillouin zone for its phonon dispersion. This leads to the folding of high-frequency acoustic phonon modes into the optical phonon regime, resulting in phonon dispersion flattening and a significant reduction in phonon group velocities near the zone boundaries. This phenomenon may give rise to unique optical, electrical, and thermal properties, with particular advantages for thermoelectric applications.\u003c/p\u003e\n\u003cp\u003eHigh-purity HGSC polycrystalline powder samples were synthesized via a stoichiometric solid-state reaction method. The powder X-ray diffraction (PXRD) pattern of the sample matches well with the theoretical one (Supplementary Fig. 1). Single crystals of HGSC were grown using the chemical vapor transport (CVT) method in sealed quartz tubes at 950 C \u0026deg;. Figure \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003ea presents a schematic representation of crystal growth via CVT. In this process, Hg\u003csub\u003e2\u003c/sub\u003eCl\u003csub\u003e2\u003c/sub\u003e served dual functions as both the transport agent and reagent, which was found to be particularly effective for the CVT growth of the target compound. This approach created a mercury-rich environment, which prevented the decomposition of the target product. As a result, millimeter-sized single crystals were obtained, with the (001) plane as the preferential growth facet (Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003eb). The chemical composition of the obtained single crystals was verified by energy-dispersive X-ray spectroscopy (EDS), which confirms the presence of Hg, Ga, Se, and Cl (Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003ec). The optical bandgap of HGSC was determined using UV-Vis-NIR diffuse reflectance spectroscopy on polycrystalline powder. The Kubelka-Munk transformation of the reflectance data yielded an optical bandgap of 2.559 eV for HGSC (Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003ed).\u003c/p\u003e\n\u003cp\u003eTo gain insights into the lattice vibrations and chemical bond vibrational modes of HGSC, Raman spectroscopy was performed. Figure \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003ee displays the Raman spectrum of HGSC in the range of 20 to 4000 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e, revealing eight distinct Raman-active vibrational modes. Vibrational bands associated with Hg-Hg-Hg, Hg-Hg, Hg-Se, and Ga-Cl bonds were identified. Raman shifts at 102.6 and 129.8 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e are attributed to Hg\u003csub\u003e3\u003c/sub\u003e\u003csup\u003e2+\u003c/sup\u003e, while the peak at 174.55 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e corresponds to Hg\u003csub\u003e2\u003c/sub\u003e\u003csup\u003e2+\u003c/sup\u003e, consistent with previously reported values for Hg\u003csub\u003e3\u003c/sub\u003e(AsF\u003csub\u003e6\u003c/sub\u003e)\u003csub\u003e2\u003c/sub\u003e, confirming the presence of Hg\u003csub\u003e3\u003c/sub\u003e\u003csup\u003e2+\u003c/sup\u003e and Hg\u003csub\u003e2\u003c/sub\u003e\u003csup\u003e2+\u003c/sup\u003e in the compound\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e38\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e39\u003c/span\u003e\u003c/sup\u003e. X-ray photoelectron spectroscopy (XPS) was conducted to analyze the chemical and electronic states of HGSC (Supplementary Fig.\u0026nbsp;2). In the analysis of the Hg4f\u003csub\u003e5/2\u003c/sub\u003e and Hg4f\u003csub\u003e7/2\u003c/sub\u003e peaks, we observed six distinct peaks and determined their binding energy positions to be 105.0, 103.9, and 104.3 eV (Hg4f\u003csub\u003e5/2\u003c/sub\u003e) and 101.1, 99.8, and 100.4 eV (Hg4f\u003csub\u003e7/2\u003c/sub\u003e), respectively. These peaks are attributed to the oxidation states of Hg\u003csup\u003e0\u003c/sup\u003e, Hg\u003csup\u003e+\u003c/sup\u003e, and Hg\u003csup\u003e2+\u003c/sup\u003e (Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003ef)\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e40\u003c/span\u003e\u0026ndash;\u003cspan class=\"CitationRef\"\u003e42\u003c/span\u003e\u003c/sup\u003e. It is worth noting that in the Hg\u003csub\u003e3\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eAsF\u003csub\u003e6\u003c/sub\u003e compound, the presence of linear Hg\u003csub\u003e3\u003c/sub\u003e\u003csup\u003e2+\u003c/sup\u003e with mixed valence states has been reported to exhibit superconductivity at 4 K\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e43\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e44\u003c/span\u003e\u003c/sup\u003e. According to the Lewis acids and bases theory\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e45\u003c/span\u003e\u003c/sup\u003e, since Se\u003csup\u003e2\u0026minus;\u003c/sup\u003e has a lower electronegativity than F\u003csup\u003e\u0026minus;\u003c/sup\u003e, the basicity of Se\u003csup\u003e2\u0026minus;\u003c/sup\u003e is softer than that of F\u003csup\u003e\u0026minus;\u003c/sup\u003e, leading to a more stable combination of soft acids (Hg\u003csub\u003e2\u003c/sub\u003e\u003csup\u003e2+\u003c/sup\u003e) with soft bases (Se\u003csup\u003e2\u0026minus;\u003c/sup\u003e). This makes the HGSC with retained linear mercury atom clusters promising candidates for more stable low-temperature superconducting materials. Considering the electronic properties of mercury with multiple valence states, we investigated the luminescent properties (PL) of HGSC. Under excitation at 300\u0026ndash;485 nm, PL excitation at room temperature (298 K) was measured. The optimal emission wavelength is approximately 332 nm, with HGSC exhibiting a super-broadband green emission at 501 nm (Supplementary Fig.\u0026nbsp;3). The ultra-broad emission band spans nearly the entire visible spectrum, demonstrating its exceptional potential for applications in spectral lighting and advanced optoelectronic devices\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e46\u003c/span\u003e\u0026ndash;\u003cspan class=\"CitationRef\"\u003e48\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eThe fully filled 5\u003cem\u003ed\u003c/em\u003e orbitals of Hg effectively prevent \u003cem\u003ed-d\u003c/em\u003e electronic transitions, thereby avoiding absorption in the visible and IR regions\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e49\u003c/span\u003e\u003c/sup\u003e. Additionally, as a heavy metal element, Hg-based compounds exhibit low lattice vibration frequencies, leading to weak absorption of far-IR light. To experimentally validate this, we conducted transmission spectroscopy tests on HGSC single-crystal with the (001) surface exposed. The results indicate that the short-wavelength transparency cutoff edge of HGSC is located at 0.4 \u0026micro;m, while its IR transparency extends up to 25 \u0026micro;m (Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003eg), covering a broad spectral range from near UV to far IR. This range includes the important atmospheric windows at 3\u0026ndash;5 \u0026micro;m and 8\u0026ndash;14 \u0026micro;m. The exceptionally broad optical transparency range can be attributed to the unique valence states of Hg in the enriched [Hg\u003csub\u003e3\u003c/sub\u003eSe\u003csub\u003e2\u003c/sub\u003e] and [Hg\u003csub\u003e2\u003c/sub\u003eSe\u003csub\u003e2\u003c/sub\u003e] units, typically assigned as 0 and +\u0026thinsp;1, respectively. These valence states contribute to a high proportion of heavy elements in the compound, effectively suppressing multiphonon absorption in the near-IR region.\u003c/p\u003e\n\u003cp\u003eTo investigate the anisotropic properties of HGSC crystals, we conducted detailed observations using the ZEISS Axio Scope 5 polarizing microscope. Figure \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003ea illustrates a schematic diagram of the polarizing microscope setup. When linearly polarized light is incident on the HGSC crystal, its polarization state transforms into elliptical polarization due to the birefringence effect. The HGSC single crystal exhibits strong birefringence, as evidenced by periodic brightness variations under different polarization angles (Fig. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003eb). At a polarization angle of 0 \u0026deg;, the tested crystal achieves complete extinction (perpendicular to the polarization direction), and as the polarization angle increases, the light intensity gradually rises. At a polarization angle of 45 \u0026deg;, the brightness reaches its maximum (parallel to the polarization direction). Further rotation of the measured crystal results in periodic changes in the brightness of the interference colors every 45 \u0026deg;. Supplementary Video 1 provides recorded images of the HGSC crystal, indicating that the HGSC crystal exhibits notable optical anisotropy.\u003c/p\u003e\n\u003cp\u003eThe laser-induced damage threshold is one of the key parameters for evaluating the performance of birefringent materials. We investigated the laser damage behavior of HGSC single crystals using a picosecond pulse laser. As shown in Supplementary Fig.\u0026nbsp;4, when the laser output energy ranges from 0.4 to 2.4 mJ, the HGSC crystal exhibits no detectable damage. However, when the energy is increased to 2.8 mJ, micro-cracks begin to appear at the edges of the crystal. Further increasing the energy to 4.0 mJ results in noticeable cracks in the crystal. Experimental results based on picosecond laser irradiation indicate that HGSC crystals exhibit excellent resistance to laser damage, exceeding that of AgGaS₂ by a factor of 3.5.\u003c/p\u003e\n\u003cp\u003eTo elucidate the structural-property relationship of the titled compound, the electronic structure was investigated through first-principles calculations. As shown in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003ef, the valence band maximum (VBM) and conduction band minimum (CBM) of HGSC are located at different high-symmetry points, indicating that HGSC is an indirect bandgap semiconductor. Due to the well-known underestimation of bandgaps in DFT calculations caused by exchange-correlation energy discontinuities, the calculated bandgap is 2.11 eV, which is lower than the experimental value of 2.559 eV. Figure\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003eg illustrates the total density of states (TDOS) and partial density of states (PDOS) of HGSC. The Hg 5\u003cem\u003ed\u003c/em\u003e orbitals are mainly concentrated between \u0026minus;\u0026thinsp;8 and \u0026minus;\u0026thinsp;6 eV, while the valence band region near the Fermi level (-5 to 0 eV) is predominantly occupied by Hg 6\u003cem\u003es\u003c/em\u003e, 6\u003cem\u003ep\u003c/em\u003e orbitals, Ga 4\u003cem\u003ep\u003c/em\u003e orbitals, Se 4\u003cem\u003ep\u003c/em\u003e orbitals, and Cl 3\u003cem\u003ep\u003c/em\u003e orbitals. The conduction band region from the Fermi energy level to 4.0 eV is mainly occupied by Hg 6\u003cem\u003es\u003c/em\u003e and 6\u003cem\u003ep\u003c/em\u003e orbitals, Se 4\u003cem\u003es\u003c/em\u003e and 4\u003cem\u003ep\u003c/em\u003e orbitals, with a minor contribution from Cl 3\u003cem\u003es\u003c/em\u003e orbitals. Therefore, the optical properties of HGSC are primarily determined by the Hg 6\u003cem\u003es\u003c/em\u003e and 6\u003cem\u003ep\u003c/em\u003e orbitals, Se 4\u003cem\u003ep\u003c/em\u003e, and Cl 3\u003cem\u003ep\u003c/em\u003e orbitals. Based on the formula \u003cem\u003e\u0026epsilon;(\u0026omega;) = ɛ\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e(\u0026omega;)\u0026thinsp;+\u0026thinsp;i\u0026epsilon;\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e(\u0026omega;)\u003c/em\u003e and \u003cem\u003en\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e\u003cem\u003e(\u0026omega;) = \u0026epsilon;(\u0026omega;)\u003c/em\u003e, the birefringence properties were calculated, resulting in refractive indices \u003cem\u003en\u003c/em\u003e\u003csub\u003e(010)\u003c/sub\u003e\u0026thinsp;\u0026gt;\u0026thinsp;\u003cem\u003en\u003c/em\u003e\u003csub\u003e(100)\u003c/sub\u003e\u0026thinsp;\u0026gt;\u0026thinsp;\u003cem\u003en\u003c/em\u003e\u003csub\u003e(001)\u003c/sub\u003e for HGSC. The birefringence (\u0026Delta;\u003cem\u003en\u003c/em\u003e) values are 0.808 at 546 nm and 0.443 at 1064 nm (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003eh). Since the birefringence of optical materials not only depends on the functional unit but also on the arrangement and configuration of the building units\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e50\u003c/span\u003e\u003c/sup\u003e, the unique structural feature of the HGSC compound, characterized by three near-parallel alignment units vertically assembled, significantly reduces anisotropic mutual cancellation, thus enhancing the superposition of the polarizability vector.\u003c/p\u003e\n\u003cp\u003eFigure\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003ei shows that the maximum refractive index direction of the HGSC compound is aligned with the arrangement direction of the linear [Hg\u003csub\u003e3\u003c/sub\u003eSe\u003csub\u003e2\u003c/sub\u003e] units. This fully demonstrates that the significant optical anisotropy in the HGSC compound originates from the preferential arrangement of the linear [Hg\u003csub\u003e3\u003c/sub\u003eSe\u003csub\u003e2\u003c/sub\u003e] units. At the microscopic level, the polarization anisotropy of all linear units in the Hg-based chalcogenides was calculated using Gaussian 09\u003csup\u003e51\u003c/sup\u003e. To make a comprehensive comparison, we also calculated some emerging linear birefringence units (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003ej). Prior to this, the highest reported polarization anisotropy is for the [Hg\u003csub\u003e2\u003c/sub\u003eI\u003csub\u003e2\u003c/sub\u003e] unit. The linear [Hg\u003csub\u003e3\u003c/sub\u003eSe\u003csub\u003e2\u003c/sub\u003e] unit, as a new functional unit in the Hg-based chalcogenides family, exhibits the highest polarization anisotropy (\u003cem\u003e\u0026delta;\u003c/em\u003e\u0026thinsp;=\u0026thinsp;430) among all known birefringence-active units to date. The visualization results of the electronic localization function (ELF) for HGSC were calculated using first principles calculations (Supplementary Fig.\u0026nbsp;5). In functional units with linear coordination, the charge distribution around the atoms is highly uneven, and the deformation of the electron clouds leads to a more localized electron distribution, resulting in a more significant electron displacement polarization. Thus, the linear [Hg\u003csub\u003e3\u003c/sub\u003eSe\u003csub\u003e2\u003c/sub\u003e] unit possesses the characteristics of the most promising functional unit for achieving giant birefringence.\u003c/p\u003e\n\u003cp\u003eTo validate the phase retardation effect of transmitted light\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e52\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e53\u003c/span\u003e\u003c/sup\u003e, the evolution of the polarization state of linearly polarized light passing through an HGSC crystal was systematically investigated (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003ea). The polarization modulation characteristics of linearly polarized light with a wavelength of 1064 nm passing through an HGSC crystal with a thickness of 70.5 \u0026micro;m were experimentally observed. To establish a comprehensive polarization state characterization system, the intensity distributions of the horizontal linear polarization state under crystal-free conditions, as well as the polarization states corresponding to rotations of 30, 60, and 90 \u0026deg;, were observed (Figs.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003eb, \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003ed, \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003ef). By rotating the polarizing prism, the elliptical polarization states of the output light from the (001) crystal plane were precisely measured (Figs.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003ec, \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003ee, \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003eg). Their Jones vectors, \u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e, and \u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sub\u003e, are explained in Supplementary Equations 1\u0026ndash;4.\u003c/p\u003e\n\u003cp\u003eThe crystal can be regarded as a phase retardation plate, and the general Jones matrix of a phase retardation plate can be expressed as:\u003c/p\u003e\n\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\n \u003cdiv class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e$$\\:{J}_{R}\\left(\\phi\\:,\\left.\\theta\\:\\right)\\right.=\\left(\\begin{array}{cc}\\text{cos}\\frac{\\phi\\:}{2}+i\\text{sin}\\frac{\\phi\\:}{2}\\text{cos}2\\theta\\:\u0026amp;\\:i\\text{sin}\\frac{\\phi\\:}{2}\\text{sin}2\\theta\\:\\\\\\:i\\text{sin}\\frac{\\phi\\:}{2}\\text{sin}2\\theta\\:\u0026amp;\\:\\text{cos}\\frac{\\phi\\:}{2}-i\\text{sin}\\frac{\\phi\\:}{2}\\text{cos}2\\theta\\:\\end{array}\\right)$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eWhere \u003cem\u003e\u0026phi;\u003c/em\u003e represents the phase retardation induced by birefringence, and \u003cem\u003e\u0026theta;\u003c/em\u003e denotes the rotation angle of the polarization principal axis. In the HGSC crystal with the (001) crystal orientation, this phase retardation primarily arises from the phase superposition of polarization components due to the refractive index difference between the x and y directions (\u003cem\u003en\u003c/em\u003e\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e\u0026ne; n\u003c/em\u003e\u003csub\u003e\u003cem\u003ey\u003c/em\u003e\u003c/sub\u003e) Based on crystal optics theory, the phase parameters corresponding to rotations of 30, 60, and 90 \u0026deg; can be expressed as (\u003cem\u003e\u0026phi;,\u0026theta;\u003c/em\u003e)、(\u003cem\u003e\u0026phi;,\u0026theta;\u003c/em\u003e\u0026thinsp;+\u0026thinsp;30 \u0026deg;)、and (\u003cem\u003e\u0026phi;,\u0026theta;\u003c/em\u003e\u0026thinsp;+\u0026thinsp;60 \u0026deg;) respectively, where \u003cem\u003e\u0026phi;\u003c/em\u003e and \u003cem\u003e\u0026theta;\u003c/em\u003e are undetermined parameters that can be obtained by solving the subsequently established system of equations. According to the above parameter relationships, the Jones matrix expressions corresponding to the three rotation angles (30, 60, and 90 \u0026deg;) can be expressed as \u003cem\u003eJ\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eJ\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e, and \u003cem\u003eJ\u003c/em\u003e\u003csub\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sub\u003e (Supplementary Equations 5\u0026ndash;7).\u003c/p\u003e\n\u003cp\u003eBased on the theoretical analysis above, the following matrix equations were derived: \u003cem\u003eJ\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e\u0026middot;E\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eJ\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e\u0026middot;E\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eJ\u003c/em\u003e\u003csub\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e\u0026middot;E\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sub\u003e. By solving this system of equations, the average value of the phase retardation \u003cem\u003e\u0026phi;\u003c/em\u003e was determined to be 2.79\u0026thinsp;+\u0026thinsp;\u003cem\u003em\u003c/em\u003e\u0026middot;2\u003cem\u003e\u0026pi;\u003c/em\u003e (where \u003cem\u003em\u003c/em\u003e is an integer). According to the phase retardation formula induced by birefringence, \u003cem\u003e\u0026phi;\u0026thinsp;=\u003c/em\u003e\u0026thinsp;\u0026Delta;\u003cem\u003ek\u0026middot;z\u0026thinsp;=\u0026thinsp;2\u0026pi;\u0026middot;(n\u003c/em\u003e\u003csub\u003e\u003cem\u003ey\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e- n\u003c/em\u003e\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e)\u0026middot;z/\u0026lambda;\u003c/em\u003e (\u003cem\u003ez\u003c/em\u003e\u0026thinsp;=\u0026thinsp;70.5 \u0026micro;m\u003cem\u003e)\u003c/em\u003e represents the crystal thickness, and \u003cem\u003e\u0026lambda;\u003c/em\u003e\u0026thinsp;=\u0026thinsp;1064 nm is the incident laser wavelength).The experimental value of \u003cem\u003en\u003c/em\u003e\u003csub\u003e\u003cem\u003ey\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e\u0026minus;n\u003c/em\u003e\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003e is 0.052, which shows good agreement with the theoretically predicted value of 0.046 for the (001) crystal plane. The phase retardation effect confirms that the HGSC crystal exhibits significant birefringence, further validating the reliability in polarization modulation devices.\u003c/p\u003e\n\u003cp\u003eTo fully elucidate the unique potential of HGSC as a birefringent material in the mid-to far IR region, we compared the IR transparency ranges of previously reported Hg-based chalcogenide single crystals. HGSC exhibits exceptional optical properties, spanning the atmospheric transmission windows of the mid-to-far-IR spectrum, and has the broadest transmission range among Hg-based chalcogenide single crystals to date (Fig. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003ea). Figure \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003eb demonstrates the significant birefringence of HGSC, with \u0026Delta;\u003cem\u003en\u003c/em\u003e\u0026thinsp;\u0026asymp;\u0026thinsp;0.808 in the visible spectrum and \u0026Delta;\u003cem\u003en\u003c/em\u003e\u0026thinsp;\u0026asymp;\u0026thinsp;0.4 in the mid-to-far IR region. These birefringence values are 67 times higher than that of the commercial material MgF\u003csub\u003e2\u003c/sub\u003e (0.012@546 nm) and 2.6 times higher than that of TiO\u003csub\u003e2\u003c/sub\u003e (0.306@546 nm), the leading commercial birefringent material, in the visible spectrum. These findings highlight the potential of HGSC for advanced optical applications.\u003c/p\u003e\n\u003ch3\u003eDiscussion\u003c/h3\u003e\n\u003cp\u003eIn this study, we successfully synthesized a novel compound, HGSC, featuring a unique tridymite-like topological structure incorporating linear [Hg\u003csub\u003e3\u003c/sub\u003eSe\u003csub\u003e2\u003c/sub\u003e] functional units. HGSC exhibits an exceptional birefringence of 0.808 at 546 nm, which is 67 times higher than that of the commercial infrared birefringent material MgF\u003csub\u003e2\u003c/sub\u003e. Furthermore, the incorporation of the heavy metal element Hg grants HGSC an exceptionally broad infrared transparency range from 0.4 to 25 \u0026micro;m, the widest reported among Hg-based chalcogenide single crystals.Theoretical calculations reveal that the pronounced birefringence of HGSC originates from the well-aligned linear [Hg\u003csub\u003e3\u003c/sub\u003eSe\u003csub\u003e2\u003c/sub\u003e] units. Notably, the [Hg\u003csub\u003e3\u003c/sub\u003eSe\u003csub\u003e2\u003c/sub\u003e] unit exhibits the highest polarization anisotropy among all known birefringence-active units to date. This study represents the first successful synthesis and demonstration of the [Hg\u003csub\u003e3\u003c/sub\u003eSe\u003csub\u003e2\u003c/sub\u003e] multinuclear cluster as a structural unit capable of significantly enhancing the optical anisotropy of materials.These findings provide critical insights into the structure-property relationships governing birefringence and offer valuable guidance for the design of next-generation birefringent materials with high applicability in mid-to-far infrared optical technologies.\u003c/p\u003e"},{"header":"Materials","content":"\u003cdiv class=\"Section2\"\u003e\n \u003cp\u003eThe reagents including Hg\u003csub\u003e2\u003c/sub\u003eCl\u003csub\u003e2\u003c/sub\u003e (Aldrich, 99.9%), HgCl\u003csub\u003e2\u003c/sub\u003e (Aexchem, 99.99%), HgSe (Aldrich, 99.99%), Ga\u003csub\u003e2\u003c/sub\u003eSe\u003csub\u003e3\u003c/sub\u003e, (Aldrich, 99.999%) are analytical grade from commercial sources without further purification.\u003c/p\u003e\n\u003c/div\u003e\n\u003ch3\u003eSynthesis and crystal growth\u003c/h3\u003e\n\u003cp\u003eThe millimeter-sized HGSC single crystals were grown using the chemical vapor transport method (CVT). A mixture of HgCl\u003csub\u003e2\u003c/sub\u003e (1.3085 g, 3 mmol), Hg\u003csub\u003e2\u003c/sub\u003eCl\u003csub\u003e2\u003c/sub\u003e (3.0334 g, 4 mmol), HgSe (0.4491 g, 1 mmol), and Ga\u003csub\u003e2\u003c/sub\u003eSe\u003csub\u003e3\u003c/sub\u003e (1.2091 g, 2 mmol). The mixtures of raw materials were put into quartz tubes and sealed using a methane-oxygen under a high vacuum of 10\u003csup\u003e\u0026minus;\u0026thinsp;3\u003c/sup\u003e Pa. The sealed tube is transferred to a computer-controlled furnace, and the temperature distribution is as follows: The furnace temperature gradually increases to 400\u0026deg;C within 12 h. It is then dwelled at 400\u0026deg;C for 7 h, followed by an increase to 950\u0026deg;C within 30 h, and kept at this temperature for 4 days. Subsequently, the temperature is reduced to 300\u0026deg;C at a rate of 2\u0026deg;C/h, and finally gradually cooled down to room temperature within 10 h. Through the above process, pale yellow tridymite-like topological structure can be obtained\u003c/p\u003e\n\u003ch3\u003eCharacterization\u003c/h3\u003e\n\u003cp\u003eHigh-optical quality crystal (HGSC, 0.091 \u0026times; 0.068 \u0026times; 0.092 mm\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e) was selected under a polarizing microscope and used for single-crystal X-ray data collection. Single-crystal XRD data were collected on a Bruker SMART APEX Ⅴ CCD diffractometer using Mo K\u0026alpha; radiation (\u0026lambda;\u0026thinsp;=\u0026thinsp;0.71073 \u0026Aring;) at room temperature. Data integration, cell refinement, and absorption corrections were carried out with the program SADABS\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e54\u003c/span\u003e\u003c/sup\u003e. The structure was solved by direct methods and refined on \u003cem\u003eF\u003c/em\u003e\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e by full-matrix least-squares techniques using the program suite SHELXTL\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e55\u003c/span\u003e\u003c/sup\u003e. Solutions were checked for missed symmetry using PLATON\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e56\u003c/span\u003e\u003c/sup\u003e. The crystal data give \u003cem\u003eR\u003c/em\u003e\u003csub\u003eint\u003c/sub\u003e = 0.0605 and the structure solution parameters are \u003cem\u003eR\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.0462, \u003cem\u003ewR\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.1114, GOF\u0026thinsp;=\u0026thinsp;1.095. Powder XRD data were collected with a Bruker D2 PHASER diffractometer (Cu K\u0026alpha; radiation with \u0026lambda;\u0026thinsp;=\u0026thinsp;1.5418 \u0026Aring;, 2\u003cem\u003e\u0026theta;\u003c/em\u003e\u0026thinsp;=\u0026thinsp;5 to 70 \u0026deg;, scan step width\u0026thinsp;=\u0026thinsp;0.02 \u0026deg;, and counting time\u0026thinsp;=\u0026thinsp;1 s/step). IR spectroscopy was measured on a Shimadzu IR Affinity-1 Fourier transform IR spectrometer in the 400\u0026ndash;4000 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e range. X-ray photoelectron Spectroscopy of HGSC powder samples was collected on a Thermo Scientific ESCALAB 250Xi spectrometer equipped with a monochromatic Al \u003cem\u003eK\u0026alpha;\u003c/em\u003e X-ray source. Samples were analyzed under high vacuum (Pa\u0026thinsp;\u0026lt;\u0026thinsp;10\u003csup\u003e\u0026minus;\u0026thinsp;9\u003c/sup\u003e mbar). Survey scans and high-resolution scans were collected. Binding energies of all scans were corrected according to the C 1\u003cem\u003es\u003c/em\u003e binding energy at 284.8 eV. The optical diffuse-reflectance spectra of HGSC were recorded at room temperature on a Shimadzu SolidSpec-3700DUV spectrophotometer. The measured wavelength range is 200\u0026ndash;2600 nm. To figure out the experimental band gap (\u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003eg\u003c/em\u003e\u003c/sub\u003e), the diffuse reflection data were converted into absorption data by the Kubelka-Munk function \u003cem\u003eF(R\u003c/em\u003e)\u0026thinsp;=\u0026thinsp;\u003cem\u003eK\u003c/em\u003e/\u003cem\u003eS\u003c/em\u003e = (1\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003eR\u003c/em\u003e)\u003csup\u003e2\u003c/sup\u003e/2\u003cem\u003eR\u003c/em\u003e, where \u003cem\u003eR\u003c/em\u003e represents the reflection coefficient, \u003cem\u003eK\u003c/em\u003e is the absorption value, and S is the scattering coefficient. To verify the presence of Hg\u003csub\u003e3\u003c/sub\u003e\u003csup\u003e2+\u003c/sup\u003e and Hg\u003csub\u003e2\u003c/sub\u003e\u003csup\u003e2+\u003c/sup\u003e, selected HGSC crystals were placed on a glass slide and then irradiated with a 532 nm laser. Raman spectra were recorded in the range of 40-4000 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e using a LABRAM HR Evolution spectrometer equipped with a CCD detector. The integration time was set to 5 seconds, and the laser intensity was maintained at 25%. To determine the chemical compositions, the EDS spectra and mappings of the compounds were tested on a field emission scanning electron microscope (FE-SEM, JEOL JSM-7610F Plus, Japan) equipped with an energy-dispersive X-ray spectrometer (Oxford, X-Max 50). The birefringence of HGSC was measured using a polarizing microscope (ZEISS Axio Scope.5 pol) equipped with a Berek compensator under a light source with an average wavelength of 546.1 nm. The interference color in the measurement was classified as first-, second-, or higher-order to ensure the accuracy of the measurement, as their boundary lines were relatively clear compared to subsequent interference colors. Crystals with high optical quality were selected for scanning under the polarizing microscope. The LIDT of HGSC single crystals were measured through a picosecond pulsed laser (1064 nm, 10 Hz, 5 ns). The input laser intensities were raised from 5 mJ until damage occurred, and the laser energy \u003cem\u003eE\u003c/em\u003e was recorded.\u003c/p\u003e\n\u003ch3\u003eComputational methods\u003c/h3\u003e\n\u003cp\u003eThe electronic structures, density of states, and birefringence of the title compounds were evaluated in the plane-wave pseudopotential method implemented in the CASTEP software based on Density Functional Theory (DFT)\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e57\u003c/span\u003e\u003c/sup\u003e. HGSC was optimized by the Perdew\u0026thinsp;\u0026minus;\u0026thinsp;Burke\u0026thinsp;\u0026minus;\u0026thinsp;Ernzerhof (PBE) exchange-correlation of generalized gradient approximation (GGA)\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e58\u003c/span\u003e\u003c/sup\u003e, while the following orbital electrons were preserved as valence electrons: Hg 6\u003cem\u003es\u003c/em\u003e\u003csup\u003e\u003cem\u003e\u003cspan class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/em\u003e\u003c/sup\u003e5\u003cem\u003ed\u003c/em\u003e\u003csup\u003e\u003cem\u003e\u003cspan class=\"CitationRef\"\u003e10\u003c/span\u003e\u003c/em\u003e\u003c/sup\u003e, Ga 4\u003cem\u003es\u003c/em\u003e\u003csup\u003e\u003cem\u003e\u003cspan class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/em\u003e\u003c/sup\u003e4\u003cem\u003ep\u003c/em\u003e\u003csup\u003e\u003cem\u003e\u003cspan class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/em\u003e\u003c/sup\u003e, Se 4\u003cem\u003es\u003c/em\u003e\u003csup\u003e\u003cem\u003e\u003cspan class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/em\u003e\u003c/sup\u003e4\u003cem\u003ep\u003c/em\u003e\u003csup\u003e\u003cem\u003e\u003cspan class=\"CitationRef\"\u003e4\u003c/span\u003e\u003c/em\u003e,\u003c/sup\u003e and Cl 3\u003cem\u003es\u003c/em\u003e\u003csup\u003e\u003cem\u003e\u003cspan class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/em\u003e\u003c/sup\u003e3\u003cem\u003ep\u003c/em\u003e\u003csup\u003e\u003cem\u003e\u003cspan class=\"CitationRef\"\u003e5\u003c/span\u003e\u003c/em\u003e\u003c/sup\u003e, respectively. The plane-wave cutoff energy for HISC was set to 800 eV during the calculation, and Monkhorst-Pack \u003cem\u003ek\u003c/em\u003e-point meshes (2 \u0026times; 3 \u0026times; 1) with a density of less than 0.04 \u0026Aring;\u003csup\u003e\u0026minus;1\u003c/sup\u003e in the Brillouin zone (BZ) were adopted. The default values of the CASTEP code were used on the aspect of the other calculation parameters and convergence criteria\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e59\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eTo calculate the birefringence, the complex dielectric function, \u003cem\u003e\u0026epsilon;(\u0026omega;) = \u0026epsilon;\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e(\u0026omega;)\u0026thinsp;+\u0026thinsp;i\u0026epsilon;\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e(\u0026omega;)\u003c/em\u003e was computed from the PBE wave functions. The imaginary portion of the dielectric function \u003cem\u003e\u0026epsilon;\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e may be estimated upon the electronic structures, and its real part is determined using the Kramers\u0026thinsp;\u0026minus;\u0026thinsp;Kronig transform, which was used to derive the refractive indices and finally get the birefringence \u0026Delta;\u003cem\u003en\u003c/em\u003e, the optical properties were scissor-corrected.\u003c/p\u003e\n\u003cp\u003eAnisotropy of the polarizability (\u0026Delta;\u003cem\u003e\u0026alpha;\u003c/em\u003e) was calculated by the Gaussian 09 revision D.01 program. The GaussView5 software visualizes the output file\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e60\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e\n\u003cdiv class=\"Equation\"\u003e\n \u003cdiv class=\"mathdisplay\" name=\"EquationSource\"\u003e$$\\:\\varDelta\\:\\varvec{\\alpha\\:}=\\sqrt{\\frac{1}{2}\\left[{\\left({\\varvec{\\alpha\\:}}_{\\varvec{x}\\varvec{x}}-{\\varvec{\\alpha\\:}}_{\\varvec{y}\\varvec{y}}\\right)}^{2}+{\\left({\\varvec{\\alpha\\:}}_{\\varvec{x}\\varvec{x}}-{\\varvec{\\alpha\\:}}_{\\varvec{z}\\varvec{z}}\\right)}^{2}+{\\left({\\varvec{\\alpha\\:}}_{\\varvec{y}\\varvec{y}}-{\\varvec{\\alpha\\:}}_{\\varvec{z}\\varvec{z}}\\right)}^{2}+6\\left({{\\varvec{\\alpha\\:}}_{\\varvec{x}\\varvec{y}}}^{2}+{{\\varvec{\\alpha\\:}}_{\\varvec{x}\\varvec{z}}}^{2}+{{\\varvec{\\alpha\\:}}_{\\varvec{y}\\varvec{z}}}^{2}\\right)\\right]}$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eWhere, \u003cem\u003e\u0026alpha;ij\u003c/em\u003e (i, j\u0026thinsp;=\u0026thinsp;x, y, z) represents an independent element of the polarization tensor.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eData availability\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAll the characterization data and experimental protocols are provided in this article and its Supplementary Information. The X-ray crystallographic coordinates for structures reported in this study have been deposited at the Cambridge Crystallographic Data Centre (CCDC), under deposition numbers 2428275. These data can be obtained free of charge from The Cambridge Crystallographic Data Centre via www.ccdc.cam.ac.uk/ data_request/cif.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgements\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis work is financially supported by National Natural Science Foundation (NSFC) of China (62305382, 52302011, 22335007, 22361132544), Natural Science Foundation of the Xinjiang Uygur Autonomous Region (2023D01A04, 2022D01B206), Shanghai Cooperation Organization Science and Technology Partnership Program (2023E01001), the Xinjiang Major Science and Technology Project (2021A01001). Y. W. and C. C. thanks the support from Tianchi Plan of Xinjiang Uygur Autonomous Region.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor contributions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eQ. X. Ren was responsible for single crystal growth, experimental implementation, auxiliary characterization, and the drafting of the manuscript; X. C. Chen was in charge of laser performance testing and experimental data analysis and fitting; R. An and Z. H. Yang handled electronic structure calculations and theoretical simulations of optical properties; C. Cui was responsible for the design and guidance of optical experiments; Y. B. Wu and S. L. Pan oversaw the design of the research plan and provided overall guidance for the research work. All authors discussed the results and provided feedback on the manuscript.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interests\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eKats MA et al (2012) Giant birefringence in optical antenna arrays with widely tailorable optical anisotropy. \u003cem\u003eProc. Natl. Acad. Sci.\u003c/em\u003e 109, 12364\u0026ndash;12368\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eNiu SY et al (2018) Giant optical anisotropy in a quasi-one-dimensional crystal. Nat Photonics 12:392\u0026ndash;396\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZhou Y et al (2024) A solution-processable natural crystal with giant optical anisotropy for efficient manipulation of light polarization. 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Comput Phys Commun 180:2582\u0026ndash;2615\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"nature-portfolio","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"","title":"Nature Portfolio","twitterHandle":"","acdcEnabled":false,"dfaEnabled":false,"editorialSystem":"ejp","reportingPortfolio":"","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"infrared optical materials, linear units, birefringence","lastPublishedDoi":"10.21203/rs.3.rs-6232980/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6232980/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eOptical anisotropy, as the core physical property for polarization manipulation, has always posed a significant challenge in the design of functional optical materials regarding its regulation mechanism and performance optimization. In the mid-far infrared (IR) region, optical materials that possess both large birefringence and wide transparent range are extremely scarce. In this study, we synthesized Hg\u003csub\u003e9\u003c/sub\u003eGa\u003csub\u003e4\u003c/sub\u003eSe\u003csub\u003e4\u003c/sub\u003eCl\u003csub\u003e16\u003c/sub\u003e (HGSC), a tridymite-like topological structure incorporating well-aligned linear [Hg\u003csub\u003e3\u003c/sub\u003eSe\u003csub\u003e2\u003c/sub\u003e] units. HGSC exhibits an exceptional birefringence of 0.808 at 546 nm, which is 67 times higher than that of commercial MgF\u003csub\u003e2\u003c/sub\u003e, while also possessing the broadest transparency window among Hg-based chalcogenide single crystals (0.4 to 25 µm). Theoretical calculations reveal that the significant birefringence of HGSC originates from the well-aligned [Hg\u003csub\u003e3\u003c/sub\u003eSe\u003csub\u003e2\u003c/sub\u003e] clusters, which exhibit the highest optical anisotropy (𝛿 = 430) among all known birefringence-active functional units. This study presents a new bifunctional unit for the design of optical materials that combine both a wide IR transparency range and exceptional birefringence. Furthermore, as the first selenide to feature [Hg\u003csub\u003e3\u003c/sub\u003e]\u003csup\u003e2+\u003c/sup\u003e atomic multinuclear clusters, HGSC compounds offer significant potential for applications in thermoelectric, magnetism, and low-temperature superconductivity.\u003c/p\u003e","manuscriptTitle":"Unprecedented [Hg3Se2]2- cluster drives giant optical anisotropy and broad infrared transparency","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-04-03 06:17:12","doi":"10.21203/rs.3.rs-6232980/v1","editorialEvents":[],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"nature-communications","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"NCOMMS","sideBox":"Learn more about [Nature Communications](http://www.nature.com/ncomms/)","snPcode":"","submissionUrl":"https://mts-ncomms.nature.com/","title":"Nature Communications","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"Nature Communications","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"0a9bcc3d-9489-41e7-92d6-7b25fe3e8383","owner":[],"postedDate":"April 3rd, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":46612049,"name":"Physical sciences/Chemistry/Materials chemistry"},{"id":46612050,"name":"Physical sciences/Materials science/Materials for optics"}],"tags":[],"updatedAt":"2026-01-07T08:06:37+00:00","versionOfRecord":{"articleIdentity":"rs-6232980","link":"https://doi.org/10.1038/s41467-025-66148-2","journal":{"identity":"nature-communications","isVorOnly":false,"title":"Nature Communications"},"publishedOn":"2026-01-06 05:00:00","publishedOnDateReadable":"January 6th, 2026"},"versionCreatedAt":"2025-04-03 06:17:12","video":"","vorDoi":"10.1038/s41467-025-66148-2","vorDoiUrl":"https://doi.org/10.1038/s41467-025-66148-2","workflowStages":[]},"version":"v1","identity":"rs-6232980","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6232980","identity":"rs-6232980","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}