Halogen‐Rich Design Strategy: Rational Synthesis of High‐Performance Tetrahedron‐Based Chalcohalides for Advanced Infrared Optical Materials

ABSTRACT

Based on the latest anisotropic structure building units with diverse chemical bonds (ABUCB) concept, tetrahedron‐based chalcohalides constructed from the heteroanionic [MCh_4‐xX_x] tetrahedra are expected to display superior nonlinear optical (NLO) performance relative to conventional single‐anion chalcogenides. However, reported chalcohalides indicate a pronounced bias toward chalcogen‐rich (Ch‐rich) compositions. Over 95% of known chalcohalides fall into the Ch‐rich regime, leaving the intrinsic advantages of halogen‐rich (X‐rich) structures largely untapped. We reveal that this gap is not due to structural instability, but rather a dual “synthetic trap” of thermodynamic factor and stoichiometric constraint. Guided with the X‐rich design strategy, we overcame these long‐standing key constraints and realizing the first X‐rich chalcohalides: A₄Ga₄Se₂X₁₂ (X = Cl: 1, Rb; 2, Cs; X = Br: 7, Rb) together with novel A₄M₄Se₃Cl₁₀ (M = Ga: 3, Rb; 4, Cs; M = Al: 6, Rb), Cs₄Ga₄Se₄Cl₈ (5) and Cs₃Al₆Se₁₀Cl (8). The noncentrosymmetric 4 distinguishes itself among all NLO chalcohalides, exhibiting strong second‐harmonic generation response (4.27 ⨯ AgGaS₂ @ 1570 nm), wide band gap (4.05 eV), highest laser‐induced damage threshold (50 ⨯ AgGaS₂), phase‐matching compatible birefringence (0.066 @ 546 nm), and the broadest IR transparency window (0.26–25 µm).

A halogen‐rich design strategy guides the discovery of X‐rich chalcohalides, achieving advanced nonlinear optical properties.

1. Introduction

Compounds constructed from tetrahedral building units form diverse structure families, including conventional chalcogenides, halides, and heteroanionic chalcohalides. They constitute a large family of multifunctional solids with remarkable practical application value and profound fundamental research significance. Chalcohalides, incorporating both chalcogen (Ch = S, Se, Te) and halogen (X = F, Cl, Br, I) anions, feature rich structural diversity and tunable properties that stem from the distinct electronegativities, ionic radii, and bonding preferences of Ch and X. These attributes have spurred their exploration for applications spanning solid‐state electrolytes, photoluminescence, thermoelectrics, superconductivity and nonlinear optics [1, 2, 3, 4]. For instance, chalcogenides serve as important infrared nonlinear optical (IR NLO) crystals, such as commercial benchmark AgGaS₂ and AgGaSe₂, which feature classic 3D diamond‐like structures. Their structures are constructed from MCh₄ tetrahedron (M = transition metal or main group element) that is, found to determine their NLO properties [5, 6]. The density functional theory (DFT) calculations also reveal the crucial bands around the Fermi level are predominantly governed by the covalent M–Ch bonds, and thus determines their optical band gaps (E _g) (E _g = 2.58 for AgGaS₂ and 1.83 eV for AgGaSe₂) [7]. These features give rise to their practical short comings, namely a low laser‐induced damage threshold (LIDT = 25 and 11 MW•cm⁻² for AgGaS₂ and AgGaSe₂, respectively at 1.06 µm, 35 ns pulse) [8], which results in short device operational lifetimes.

Based on the “electronic structure engineer bucket effect” concept [7], the E _g of a compound is predominantly determined by the components with the minimum energy levels at the valence band maximum (VBM) and conduction band minimum (CBM) in its electronic band structure. Accordingly, the E _g of AgGaQ₂ is governed by the [MCh₄] tetrahedron which is the dominant components of VBM and CBM. Therefore, to widen the E _g, it is essential to tailor the intrinsic nature of the [MCh₄] tetrahedron by introducing ligands with higher electronegativity (e.g., X).

Previous studies have shown that Ch and X can jointly coordinate to the central metal, forming a heteroligand [MCh_4‐xX_x] tetrahedron (0 ≤ x < 4) [9], which belongs to an anisotropic structure building units with diverse chemical bonds (ABUCB) [10]. Owing to the differences in electronegativity, coordination ability, and ionic radius between Ch and X, the [MCh_4‐xX_x] tetrahedron displays distinct structural and electronic features relative to the conventional monoligand [MCh₄] and [MX₄] tetrahedra, including enhanced geometric distortion and a moderate HOMO–LUMO gap—with the latter following the trend: [MCh₄] < [MCh_4‐xX_x] < [MX₄]. These features provide a unique platform for developing high‐performance second‐harmonic generation (SHG) compounds, thus offering a chemical strategy to overcome the fundamental constraint, that is, the inverse relationship between a large second‐order nonlinear coefficient (d _ij) and a wide E _g, as well as the challenge of simultaneously achieving a large E _g and high birefringence (Δn).

Nevertheless, a systematic survey of the [MCh_4‐xX_x]‐based chalcohalide family uncovers a pronounced bias toward chalcogen‐rich (Ch‑rich) compositions (0 ≤ X/Ch ≤ 1), which account for over 95% — particularly in the IR NLO field [11, 12]—where the complementary halogen‐rich (X‑rich) structures (X/Ch > 1) remains largely underexplored (Figure 1, Table S11). Early attempts yielded only one example, the zero‐dimensional adduct SnI₄(S₈)₂ [13], leaving the construction of X‐rich chalcohalide an unresolved challenge. In most cases, the X– anions act merely as non‐coordinating counter‐ions, as exemplified in Li[LiCs₂Cl][Ga₃S₆], [Ba₃CsCl₂][Ga₅Se₁₀], and [K₄BaCl₂][In₆Se₁₁] [14, 15, 16], and exert only an indirect influence on the properties (e.g., band gap) compared to covalently bonded halogens, thus, they fall outside the scope of the present study. For these monoligand cases ([MCh₄] or [MX₄]), the X/Ch is defined as 0 or ∞ (Table S11). Strikingly, all known heteroligand A[MCh_4‐xX_x] chalcohalides (A = alkali metals, alkaline earth metals, and rare‐earth metal) exhibit exceedingly low X/Ch ratios (0.1, 0.33, and 1.0). Representative examples include Na₃SiS₃F (featuring the [SiS₃F] tetrahedral building unit, X/Ch = 0.33) [17], Ag₅PS₄Cl₂ (featuring [AgS₂Cl₂], X/Ch = 1.0) [18], Cs₃Ga₈S₁₃Cl (featuring [GaS₃Cl], X/Ch = 0.33) and CsBrHg₃P₂S₈ (featuring [HgS₃Br], X/Ch = 0.33) [19, 20].

FIGURE 1.

(a) Synthetic landscape and key synthetic parameters for A[M(Ch_4‐xX_x)] chalcohalides. Conventionally employed starting materials with key physical parameters (melting point ranges): i: chalcogenide M_aCh_b (580°C–1700°C), ii: alkali halide A_aX_b (605°C–993°C), and iii: metal halide M_aX_b (77°C–500°C). (b) Chalcogen‐rich region is defined by 0 ≤ X/Ch ≤ 1.0, and halogen‐rich region is defined by X/Ch > 1.0. For cases of conventional [MCh₄] or [MX₄], the X/Ch is defined as 0 or ∞. The X‐rich region remains a glaring blank and thus an overlooked research frontier. (c) Polar bar chart comparison of key NLO properties of chalcohalides, showing the superior and balanced performance profile of 4. Compounds 1–39 compounds (b and c): their properties are listed in Table S11 and synthesis conditions in Table S12.

Our systematic studies reveal that this phenomenon arises not from the structural instability, but from a dual synthetic trap: 1) Thermodynamic preference: conventional high‐temperature approaches thermodynamically favor Ch^2– coordination, which effectively excludes X– from the metal coordination sphere. Also, 2) Stoichiometric constraint: the common practice of using chalcogen‐excess feed ratios (mol_Ch > mol_X) further diminishes the chemical driving force for halogen incorporation into the [MCh_4‐xX_x] units. The behavior stems from the delicate interplay between reactant properties (e.g., melting points and coordination affinity toward M), reaction parameters (e.g., reaction temperature and molar loading ratios), as well as the substantially stronger coordination ability of Ch^2– relative to X– (Table S12), which arises from the stronger electrostatic attraction and higher polarizability of the divalent Ch^2– [21, 22]. For example, halides A_aX_b have high melting points (600°C–993°C), usually requiring high‐temperature reaction temperatures. Under such conditions, the stronger coordination affinity of Ch^2– competitively excludes X– from the metal coordination sphere, stabilizing Ch‑rich phases and hindering effective X– coordination. Second, a typical Ch^2—excess feeding ratio (mol_Ch > mol_X) limits X– availability and its competitive coordination ability, thus confining X– to non‐coordinating roles in the reaction. Consequently, the X‐rich region remains a glaring blank and thus an overlooked research frontier. Yet, this region, benefiting from the distinct intrinsic properties of the two types of ligands (Ch^2– and X–), serves as an ideal platform for the structural design and modulation of functional compounds, as well as the synergistic enhancement of their performance, especially for the discovery of next‐generation high‐performance IR NLO crystals.

Herein, we propose a halogen‐rich design principle that enables moderate‐temperature solid‐state reaction synthesis (<500°C) and affords the first X‐rich chalcohalide. We reveal a X/Ch ratio within the [MCh_nX_m] fragement ‐dependent structural correlation, ranging from dimeric P2₁/n‐phase Rb₄Ga₄Se₂Cl₁₂ (1), Cs₄Ga₄Se₂Cl₁₂ (2), and Rb₄Ga₄Se₂Br₁₂ (7), to trimeric Cmc2₁‐phase Rb₄Ga₄Se₃Cl₁₀ (3),Cs₄Ga₄Se₃Cl₁₀ (4), and Rb₄Al₄Se₃Cl₁₀ (6), and further to the infinite 1D chain in Pnma‐phase Cs₄Ga₄Se₄Cl₈ (5) and 2D layers in P $\overline{1}$‐phase Cs₃Al₆Se₁₀Cl (8). Notably, NCS compounds 3, 4, and 6 combine superior NLO properties, notably, 4 distinguishes itself among all known NLO chalcohalides including a large second‐harmonic generation response (4.27 ⨯ AgGaS₂ @ 1570 nm), a wide E _g (4.05 eV), a highest LIDT (50 ⨯ AgGaS₂), a desired birefringence (0.066 @ 546 nm) for phase matching, and the broadest IR transparency window (0.26–25 µm).

2. Results and Discussion

Eight new single crystals, Rb₄Ga₄Se₂Cl₁₂ (1) and Cs₄Ga₄Se₂Cl₁₂ (2), Rb₄Ga₄Se₃Cl₁₀ (3) and Cs₄Ga₄Se₃Cl₁₀ (4), Cs₄Ga₄Se₄Cl₈ (5), Rb₄Al₄Se₃Cl₁₀ (6), Rb₄Ga₄Se₂Br₁₂ (7), and Cs₃Al₆Se₁₀Cl (8) [23], were synthesized by solid‐state or hydrothermal reactions (Figure S1, Tables S1 and S2, detailed in Methods). Compounds 1, 2, and 7 are isostructural and feature [Ga₂SeX₆] dimers; compounds 3, 4, and 6 are constructed from [M₃Se₃Cl₆] trimers, while compounds 5 and 6 exist as monomers built from [GaSe₂Cl₂] and [AlSe₃Cl] tetrahedra, respectively. The observed powder x‐ray diffraction (PXRD) patterns of 1, 2 are fully assigned and match well with the simulations (Figures S2a–d), except that 3 and 4 contain detectable impurities (approximately 5%, Figures S2e,f) of centrosymmetric (CS) AGaCl₄ and Se, which is a common phenomenon, as observed in Sn₇Br₁₀S₂ [24]. As these CS impurities are SHG inert (Figure S3), thereby have no influence on the SHG response, related properties are measured on as‐synthesized polycrystalline samples. In contrast, 5–8 could not be reliably obtained as pure‐phase samples; thus, it was excluded from further property measurements.

Thermal analyses (TG‐DSC) of 1–4 show distinct endothermic events at 264°C, 271°C, 256°C, and 245°C, respectively (Figure S4). No mass loss or structural change was detected before these thermal events, confirming excellent thermal stability up to the corresponding temperatures. Furthermore, all samples exhibit superior environmental stability, with no obvious structural degradation or phase decomposition after 3 months of ambient air exposure (Figure S5). Notably, PXRD analysis of the pristine and heated samples (Figure S6) reveals that heating 3 and 4 (X/Ch = 2) to only 256°C and 245°C (well below their respective synthesis temperatures of 400°C and 350°C), respectively, for 18 h, triggers their predominate decomposition into compounds 1 or 2, which possess a higher X/Ch ratio (X/Ch = 6). This temperature‐dependent structural evolution clearly reveals that X‐rich chalcohalides tend to spontaneously decompose into Ch‐rich compounds at elevated temperatures. Additionally, energy‐dispersive spectroscopy (EDS) microanalysis confirmed the presence of all constituent elements (Cs/Rb, Ga, Se, and Cl) and revealed their homogeneous spatial distribution, corroborating the phase purity (Figure S7).

The structure of NCS 4 is discussed as a representative example. The single‐crystal x‐ray diffraction data reveal 4 crystallizing in the polar orthorhombic space group Cmc2₁ (No. 36), with cell parameters a = 11.3250(5), b = 14.2651(6), and c = 17.3516(7) Å (Table S1). The crystallographically independent ions can be assigned to specific Wyckoff 4a and 8b sites (Table S3). All Ga atoms are four‐fold coordinated in a tetrahedral geometry. Ga1 (4a site) is coordinated exclusively to Cl atoms, with Ga─Cl bond lengths of 2.158–2.183 Å, forming a [GaCl₄]– tetrahedron; in contrast, Ga2 (4a site) and Ga3 (8b site) feature a heteroligand coordination sphere, distorted [GaSe₂Cl₂]^3– tetrahedron, with Ga–Cl (2.229–2.247 Å) and Ga–Se (2.340–2.353 Å) bonds. This structural distinction arises from the differences in electronegativity and coordination ability between Cl and Se. This [GaSe₂Cl₂] unit is classified as an ABUCB, which further fuses via corner‐sharing into a [Ga₃Se₃Cl₆]^3– trimer (Figure 2a). To the best of our knowledge, [Ga₃Se₃Cl₆]^3– represents a functional building unit with the highest X/Ch ratio to date (Figure 1). These trimers and [GaCl₄]– tetrahedra are arranged into a pseudo‐layer pattern (Figure 2b) that exhibits a macroscopic polarization along the c direction imposed by the the Cmc2₁ crystallographic symmetry (Figure 2c), with Cs⁺ ions occupying the interlayer space as charge‐balancing cations (Figure S8). The bond valence sum (BVS) calculations of 3, 4, and 6 (Tables S3–S5) yield chemically reasonable values for all atoms in both compounds. Raman spectra (Figures 4a and S9) provide additional confirmation, verifying the presence of the same key structural units. The detailed bond lengths (Tables S6–S8) are consistent with those reported, such as [Cs₆Br][NaGa₆Se₁₂] (Cs─Se bond: 3.638–4.165 Å) [25], Cs₃Ga₈S₁₃Cl (Cs–Cl bond: 3.101–3.828 Å) [19], Cs₉Ga₈Se₁₂Cl₉ (Ga–Se bond: 2.373–2.398 Å) [19], and (Hg_9.75As_5.5)(GaCl₄)₃ (Ga‐Cl bond: 2.158–2.223 Å) [26].

FIGURE 2.

Novel structure of trimeric Cs₄Ga₄Se₃Cl₁₀ (4). (a) Structural building units: conventional [GaCl₄]– and anisotropic heteroligand [Ga₃Se₃Cl₆]³⁻ trimer. (b) Pseudo‐layer view with labeled Ga atom serial numbers and unit cell. (c) Crystal packing view along (100); arrows denote dipole moments (small black: [GaCl₄]–, medium yellow: [Ga₃Se₃Cl₆]³⁻). Overall polarization is shown by a large arrow along the c‐axis, imposed by the Cmc2₁ crystallographic symmetry.

FIGURE 4.

Comprehensive characterization of 4. (a) Raman spectrum. (b) UV/Vis‐NIR spectrum; inset: experimental E _g. (c) FTIR spectrum showing a broad IR transparency. (d) Comparison of optical transparency window among all reported NLO chalcohalides (see Table S11 for details). (e) SHG intensity versus AgGaS₂ under 1570 nm incident light, and phase‐matching curves as a function of particle size (particle size error: ±10 to ±31 µm). (f) Thermal evolution of lattice parameters (error bars smaller than symbol sizes).

Figure 3 shows the structural change as the X/Ch ratio decreases, from 1 (X/Ch = 6:1) to 8 (X/Ch = 1:3). The high X/Ch ratio in 1/2/7 enforces the heteroligand [GaSeX₃]^2– coordination environment, however, the strong coordination of Se promotes the dimerization of [Ga₂SeX₆]^2–, which generates an inversion center, the resulting P2₁/n space group is SHG inert (Figure 3a). In 3/4/6 with Cl/Se = 2:1, a desired heteroligand coordination is also achieved in the [Al/Ga₃Se₃Cl₆]^3– trimer. Interestingly, with the help of secondary building unit [27], conventional monoligand [Al/GaCl₄]– tetrahedron, compounds 3, 4, and 6 adopt NCS structures of Cmc2₁ symmetry (Figure 3b). Crucially, the heteroligand tetrahedron within the trimers exhibits severe geometric distortion compared to the monoligand tetrahedron. For instance, in 4, the bond length distortion (Δd) of [GaSe₂Cl₂]^3– reaches 22.93 × 10⁻³, about five times that of [GaCl₄]– (4.49 × 10⁻³, Table S9). Such pronounced local structural distortion destroys centrosymmetry and generates a large local dipole moment, where 2₁ screw axis propagates the inherent polarity (Figure 2c). As the X/Ch ratio further decreases, the [GaSe₂Cl₂]^3– tetrahedron in 5 (Cl/Se = 1:1) extends into a zig‐zag chain via Se‐sharing, whereas the [AlSe₃Cl]⁴⁻ tetrahedron in 8 (Cl/Se = 1:3) forms a two‐dimensional layer. In both Ch‐rich compounds, the inherent packing periodicity facilitates the formation of an inversion center, thus leading to the CS Pnma for 5 and P $\overline{1}$ for 8, respectively (Figure 3c,d). Thus, this series of eight compounds offers experimental insights into the correlation between macroscopic symmetry and compositional control. Specifically, the structural variations observed are associated with the Cl/Se ration, and the emergence of NCS state is linked to the designed stoichiometry that favors the formation of highly distorted heteroligand polyhedra and an intrinsically asymmetric lattice, providing a practical handle for subsequent experimental exploration in similar systems.

FIGURE 3.

Structural symmetry changes as the X/Ch ratio decreases. (a) Structure of isostructural 1/2/7: a CS (P2₁/n) structure featuring a discrete [Ga₂SeX₆]^2– dimer with a high X/Ch ratio of 6:1. (b) Structure of isostructural 3/4/6: a a NCS (Cmc2₁) structure featuring a discrete [Al/Ga₃Se₃Cl₆]^3– trimer with a moderate X/Ch ratio of 2:1. (c) Structure of 5: a CS (Pnma) structure featuring a one‐dimensional chain of [GaSe₂Cl₂]³⁻ tetrahedra with a low X/Ch of 1:1. (d) Structure of 8: a CS (P $\overline{1}$) structure featuring a two‐dimensional layer of [AlSe₃Cl]⁴⁻ tetrahedra with the lowest X/Ch of 1:3. Black ball: Se; green ball: Cl; yellow ball: Br.

Optical property measurements reveal that 1–4 exhibit exceptionally wide E _g and a broad transparency window (Figures 4b,c and S10). 1–4 possess ultrawide E _g (4.04–4.21 eV) that significantly surpass those of commercial benchmarks (AgGaS₂, 2.58 eV; AgGaSe₂, 1.83 eV; ZnGeP₂, 1.75 eV) [7, 28], as well as other representative chalcohalides: [CsBa₂Cl][Ga₄S₈] (3.35 eV) and LiPb₃GeS₄Cl₃ (2.81 eV) [29, 30]. These data confirm that X‐rich chemistry is a robust design principle for achieving wide E _g. Fundamentally, highly electronegative halogens introduce deep‐lying states that dilute the high‐energy chalcogen p‐orbitals. This effectively suppresses the upward dispersion of the valence band maximum (VBM), leading to a widened E _g, as further corroborated by our DFT calculations. Owing to their wide E _g, their transparency windows span from approximately 0.25–25 µm, fully covering the 3–5 µm and 8–12 µm atmospheric windows, representing the broadest transparency among reported NLO chalcohalides (Figure 4d). Critically, SHG measurements under 1570 nm laser irradiation highlight the outstanding nonlinear performance of 3 and 4. Theoretical calculations reveal that 3 and 4 possess comparable static SHG coefficients (Table S13). Figure S11 displays a modest PM SHG response of 3 (∼ 1.17 times that of AgGaS₂) In comparison, 4 having better crystallinity (as evidenced by its sharper and higher intensity PXRD peaks, and lower R _exp in Rietveld refinement, Figure S2), delivers a strong SHG efficiency of ∼ 4.27 times that of AgGaS₂ at the largest particle size range of 150–212 µm, in a phase matching behavior (Figure 4e). This SHG intensity surpasses most chalcohalides, with only a few exceptions: SbSI (5.7 times that of AgGaS₂) [31], Hg₃AsSe₄Br (6.2 times), and Hg₃AsSe₄I (8.8 times) [32]. Overall, 4 achieves an outstanding performance balance by uniquely combining an ultra‐wide E _g, record‐breaking broadband transparency, and a strong SHG response.

The LIDT of 4, as evaluated by the R‐on‐1 method [33], was determined to be 282.86 MW cm⁻² (Table S10). This value represents a 50‐fold enhancement over AgGaS₂ (5.68 MW cm⁻²) and surpasses that of most chalcohalides, including Li[LiCs₂Cl][Ga₃S₆] (4.1 times that of AgGaS₂) [14] and Sn₇Br₁₀S₂ (6.3 times) [24]. The Rb analogue, 3 exhibits a lower LIDT of 82.13 MW cm⁻² (∼14.5 times), consistent with its inferior crystallinity.

Thermal analysis reveals a very low thermal expansion anisotropy (I _TEA = 0.31 for 4, 0.11 for 3), significantly lower than that of AgGaS₂ (1.60) [34] (Figures 4f andS12). In compounds, the smallest thermal expansion coefficient (α _L) is observed along the c‐axis, a direction defined by the alternating pseudo‐layers of [Ga₃Se₃Cl₆]^3– trimers and [GaCl₄]– tetrahedra. This structural feature facilitates effective thermal stress dissipation, thereby contributing to the high LIDT.

As a fundamental optical property, the experimental Δn of 1–4 was measured using polarizing microscopy. The high‐quality crystals with optical anisotropy, evidenced by the characteristic four‐fold extinction patterns (Figure S13), yielded experimental Δn values at 546 nm of 0.058 (1), 0.053 (2), 0.064 (3), and 0.066 (4). These results align well with the theoretical values obtained from first‐principles calculations (Figures 5a andS14). A well‐established principle is that a sufficient but not excessive Δn is a critical prerequisite for achieving PM in IR NLO materials; an insufficient Δn can preclude the PM by standard angle or temperature tuning methods, while an excessively high Δn can narrow the angular acceptance and thus degrade the conversion efficiency, with the optimal range typically being 0.04–0.10 [35]. Importantly, the theoretical Δn_cal of 4 is 0.06 @ 1 µm, which falls within the desired range and larger than those of key commercial benchmarks in the IR region (e.g., AgGaS₂: 0.053, ZnGeP₂: 0.048, and AgGaSe₂: 0.020) [8, 36]. This suitable birefringence enables the observed PM capability and strong SHG response (Figure 1c and Table S11).

FIGURE 5.

Electronic structure and property evaluation of 4. (a) Calculated refractive indices and birefringence. (b) Theoretical electronic band structure. (c) Orbital‐projected density of states. Partial charge density distribution for the VBM (d) and CBM (e). (f) Evolution of the dominant static SHG coefficient d ₁₅ as a function of the energy cutoff. (g) ELF maps on the (1 ‐1 1) plane (1.5562 Å from origin; top) and the (0 ‐1 46) plane (11.3249 Å from origin; bottom) (h) Calculated polarizability anisotropy (δ), hyperpolarizability (|β _max|), and HOMO–LUMO gaps of the [Ga/Se/Cl] anionic units, illustrating the functional superiority of the [Ga₃Se₃Cl₆]^3– trimer.

To gain deeper insight into the origin of the optical properties, DFT theoretical calculations were carried out. The electronic structure indicated an indirect E _g of 2.73 eV for 4 (Figure 5b), which is smaller than the experimental value (4.05 eV) due to the well‐known systematic underestimation of E _g by standard DFT functionals, arising from the self‐interaction error and the missing derivative discontinuity in the exchange–correlation potential (Figure S16) [37, 38]. The similar systematic discrepancies are observed for 1–3 and 5–8 (Figure S15). The density of states (DOS) analyses for 4 (Figure 5c) reveal the VBM near Fermi level (E _F) is dominated by Se 4p orbitals with negligible contribution from Cl. Highly electronegative Cl atoms substantially lower VBM via their localized 3p states, which are situated in the lower‐energy VB‐II region, thus broadening the VB width and increasing the E _g. The conduction band minimum (CBM) is primarily composed of Ga 4s and Se 4p states, with negligible contribution from Ga 3d, 4p, Cl 3s, 3p, and Cs 5p orbitals. The band edges are governed by Ga–Se interactions and the VB is broadened by deep Cl states, which is consistent across other compounds in this series (Figure S15). The spatial localization of these frontier orbitals is visualized by the partial charge density distributions (Figures 5 and S17). The electron densities at VBM and CBM are highly confined within the isolated building units of [Al/Ga₃Se₃Cl₆]^3– trimers and [Al/GaCl₄]– tetrahedra.

The cutoff‐energy‐dependent static d _ij is calculated (Table S13). The sharp variations in d ₁₅ for 3 and 4 happen in the energy regions of VB‐I and CB‐I (Figures 5f and S18). Given that the VB‐I corresponds to Se 4p orbitals and the CB‐I to Ga 4s and Se 4p orbitals, the [Ga₃Se₃Cl₆]^3– trimer, the sole building unit featuring Ga–Se bonds, is identified as the key structural motifs driving the second‐order nonlinear polarization. Furthermore, the electron localization function (ELF) analyses (Figures 5g and S19) provide direct visual evidence that the strong SHG response originates from the covalent Ga–Se bonds and the stereochemically active lone pairs on Se atoms, the latter feature is seen as the Se 4p states in the DOS (Figure 5c). The presence of these lone pairs verifies that each Se atom is covalently bonded to only two Ga atoms, consistent with the valence shell electron pair repulsion model for a Se^2– anion. The spherical distributions around Rb⁺ and Cs⁺ cations confirm their negligible roles in second‐order susceptibility.

The [Ga₃Se₃Cl₆]^3– trimer also exhibits a significant geometry distortion, as quantified by its largest bond “flexibility index” (F) [39] (Table S14). This structural flexibility facilitates the formation of strong induced dipole oscillations. Moreover, bond‐valence calculations [40] reveal that the vector components of dipole moment are aligned cooperatively along the crystallographic c‐axis (Tables S15–S17 and Figure S20).

To quantitatively evaluate the molecular‐scale optical properties of monomeric, dimeric, and trimeric [GaCl₄]– and [GaSe₄]^5–, [Ga₂SeCl₆]^2–, [Ga₃Se₃Cl₆]^3– tetrahedral building units, their HOMO‐LUMO gap, polarizability (δ), and hyperpolarizability (|β _max|) are calculated (Figure 5h). As shown, the [Ga₃Se₃Cl₆]^3– trimer achieves a synergistic enhancement and balance in these key properties and significantly outperforming the others. A similar trend is also observed for the [Ga/S/Cl] moieties (Figure S21). Thus, the halogen‐rich design principle we propose exhibits universal validity, and its extension from the selenides reported herein to other chalcogenides (e.g., sulfides) is anticipated.

3. Conclusion

In summary, we propose a halogen‐rich design strategy for moderate‐temperature solid‐state synthesis, affording the first halogen‐rich chalcohalides A₄Ga₄Se₂X₁₂ (X = Cl: 1, Rb; 2, Cs; X = Br: 7, Rb), and novel A₄M₄Se₃Cl₁₀ (M = Ga: 3, Rb; 4, Cs; M = Al: 6, Rb), Cs₄Ga₄Se₄Cl₈ (5) and Cs₃Al₆Se₁₀Cl (8). The X/Ch ratio within the [MCh_nX_m] fragement‐dependent structural evolution was demonstrated across the series: from dimeric 1/2/7, to trimeric 3/4/6, and further to infinite 1D chain 5 and 2D layer 8. Notably, 3 – 6 are NLO active and 4 distinguishes itself among all NLO chalcohalides, exhibiting a strong SHG response (4.27 times that of AgGaS₂), a wide E _g (4.05 eV), a high LIDT (50 times that of AgGaS₂), phase‐matching compatible birefringence (0.066 @ 546 nm), and the broadest IR transparency window (0.26–25 µm). Our work establishes X‐rich design strategy for the rational design and synthesis of high‐performance IR NLO materials, and this method is directly transferable to the discovery of new phases in other anion‐competitive systems.

Author Contributions

Wen‐Li Zhao: methodology, data curation, investigation, formal analysis, writing – original draft. Rui‐Xi Wang: methodology, data curation. Shuang Zhao: software, data curation. Cui‐Er Deng: investigation. Li‐Ming Wu: conceptualization, supervision, writing – original draft, writing – review and editing, methodology, funding acquisition. Ling Chen: conceptualization, methodology, supervision, funding acquisition, project administration, writing – original draft, writing – review and editing.

Conflicts of Interest

The authors declare no conflicts of interest.

Supporting information

The authors have cited additional references within the Supporting Information [S1–S60]. Supporting File 1: anie72779‐sup‐0001‐Data.zip.

Supporting File 2: anie72779‐sup‐0002‐SuppMat.docx.

Data Availability Statement

The data that support the findings of this study are available in the Supporting Information of this article.