Point-to-volume engineering enables enhanced birefringence and a wide bandgap in hybrid halide ultraviolet nonlinear optical crystals

Abstract

Ultraviolet nonlinear optical (UV NLO) crystals are important for advanced photonics, yet their development is hindered by the inherent trade-off among strong SHG response, a wide bandgap and large birefringence. Herein, guided by systematic theoretical screening, the “two-in-one” flexible π-conjugated (C₄H₁₃N₅)²⁺ (MF) group was identified as a prospective functional building unit (FBU) owing to its superior polarizability anisotropy and hyperpolarizability. Its initial combination with Cl⁻ yielded C₄H₁₃N₅Cl₂ (MFC), which exhibits a wide band gap (4.64 eV) and a high SHG response (2.8 × KH₂PO₄ (KDP)), yet a small birefringence of 0.02@546 nm. To address this limitation, we implemented a point-to-volume substitution strategy, replacing the discrete Cl⁻ anions in MFC with distorted [ZnCl₄]²⁻ tetrahedra, yielding a novel zero-dimensional (0D) organic–inorganic hybrid halide (C₄H₁₃N₅)ZnCl₄ (MFZC). This structural evolution simultaneously enhances most of the key optical properties: bandgap widening to 4.72 eV, birefringence enhancement to 0.09 at 546 nm, and retention of a strong SHG response of 2.2 × KDP. Theoretical and structural analyses indicate that the improved properties originate from the synergistic alignment of organic MF cations and inorganic [ZnCl₄]²⁻ tetrahedral FBUs. This work provides an effective strategy for engineering hybrid halide materials with concurrently optimized linear and nonlinear optical properties.

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Introduction

Nonlinear optical (NLO) crystals are indispensable for frequency conversion in solid-state lasers,^1,2 enabling the generation of coherent light and extending the operational wavelength into the short-wavelength ultraviolet (UV) region.^3–5 Their functionality is critical for key applications including precision micromachining, modern medical treatment, and information storage.^6–9 However, high-performance commercial UV NLO materials are rather scarce, with representative ones including β-BaB₂O₄ (β-BBO),¹⁰ LiB₃O₅ (LBO),¹¹ and KBe₂BO₃F₂ (KBBF).¹² Excellent UV NLO materials must achieve an effective balance among large second-harmonic generation (SHG) effects, a wide bandgap and appropriate birefringence.^13–15 These properties, however, are mutually constrained, making their concurrent optimization within a single crystal a persistent challenge. To achieve balance, researchers are paying increasing attention to the rational structure design of such materials.¹⁶

The rational design of structural motifs and the deliberate choice of their assembly modes serve as the key background for optimizing NLO properties. Inorganic π-conjugated groups, such as (BO₃)³⁻,¹⁷ (NO₃)⁻,¹⁸ and (B₃O₆)³⁻,¹⁹ serve as superior UV NLO-active building units and exhibit strong polarizability anisotropy (δ) and large hyperpolarizability tensor (β_|max|). These features have enabled the development of notable NLO crystals, including KBBF,¹² RE(OH)₂NO₃ (RE = La, Y, Gd),²⁰ and Ba₂Mg(B₃O₆)₂ (BMBO).²¹ However, the growth of inorganic NLO crystals is typically associated with high costs, substantial energy consumption, and prolonged processing times.²² Studies have shown that organic π-conjugated groups, such as (C₃N₃S₃H_x)^x−3 (x = 0–3),^23–26 [C(NH₂)₃]⁺ (Gua⁺),^2,27 (DAMS⁺),²⁸ etc., outperform their structurally similar inorganic counterparts in both second-order polarizability and optical anisotropy.¹⁶ For example, the large delocalized π-electron systems of Cd(SCN)₂(C₄H₆N₂)₂ (10 × KDP, E_g = 4.74 eV),²⁹ ZnBr(C₆H_3.5FNO₂)₂ (1.7 × KDP, E_g = 4.2 eV),³⁰ (C₅H₆N₂O₂)ZnCl₂ (3.5 × KDP, E_g = 5.19 eV),³¹ and [C(NH₂)₃]₃PO₄·2H₂O (1.5 × KDP, E_g = 4.2 eV)² can effectively balance the critical performance metrics indispensable for short-wave UV NLO crystals.

The coupling of functional groups (e.g., dimeric [B₂O₅]⁴⁻ and [P₂O₇]⁴⁻) is recognized as an effective strategy for enhancing SHG efficiency.³² However, achieving precise and controllable coupling in inorganic systems remains synthetically challenging,³³ whereas such coupling can be more readily and predictably realized in organic frameworks.³⁴ Inspired by reported examples such as M₄Mg₄(P₂O₇)₃ (M = K, Rb),³³ NH[C(NH₂)₂]₂(NO₃)₂,¹⁶ {N[C(NH₂)₂]₂}₂CO₃,¹⁶ and [C₂N₄H₇O][NH₂SO₃],³² we have identified a flexible “two-in-one” organic group, metformin ([C₄H₁₃N₅]²⁺, abbreviated MF), which is formed by combining planar [C(NH₂)₃]⁺ and [C(NH₂)₃(CH₃)₂] through a shared nitrogen atom. Theoretical calculations reveal that the π-conjugated MF cation exhibits favorable δ values and a large β_|max|, exceeding those of well-known building units such as [BO₃]³⁻,¹⁷ (NO₃)⁻,¹⁸ (C₂N₄OH₇)⁺,³² etc. (Fig. 1). These results demonstrate that the MF moiety represents a highly promising functional building block for the design of nonlinear optical crystals.

Fig. 1 Calculated gaps between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), polarizability anisotropy (δ), and the maximum absolute value of hyperpolarizability (β_|max|) of typical functional groups.

Based on the anionic group theory,³⁵ the rational introduction of halide anions or their assembled metal-halide polyhedral units serves as a key molecular design strategy for developing high-performance NLO crystals. Halide anions (Cl⁻, Br⁻, and I⁻), with their high electronegativity and strong polarizability, can effectively widen the optical bandgap and enhance the macroscopic polarization of the crystal lattice, such as Mg₂PO₄Cl³⁶ and Ba₃P₃O₁₀Cl.³⁷ When coordinated with metal cations with stereochemically active lone pairs (Pb²⁺, Sb³⁺, and Te⁴⁺) or d¹⁰ electron configurations (Cd²⁺ and Zn²⁺), they form structurally distorted metal-halogen polyhedra, which not only break the structural symmetry but also provide a large microscopic second-order susceptibility. Examples include (L-ipp)(L-pro)PbI₃,³⁸ (C₅H₆N₂O₂)ZnBr₂,³¹ and [DASH]Cd₂Cl₆.²⁸

Guided by this strategy, we have successfully synthesized C₄H₁₃N₅Cl₂ (MFC) through the rational integration of the distinctive merits of organic cations (C₄H₁₃N₅)²⁺ (1) (Fig. 1). Although MFC was initially reported in 2023,³⁹ its optical properties have not yet been systematically investigated. Meanwhile, by employing a novel point-to-volume substitution strategy—replacing the discrete Cl⁻ ions in MFC with [ZnCl₄]²⁻ tetrahedral units—we have obtained a new UV NLO crystal (C₄H₁₃N₅)ZnCl₄ (MFZC). Both MFC and MFZC exhibit wide bandgaps (>4.6 eV) and strong SHG responses (>2 × KDP). Notably, the birefringence value of MFZC exhibits a 4.5 times enhancement relative to that of MFC because MFZC features a significantly higher degree of structural ordering compared with MFC. Here, we present a systematic investigation into the synthesis, crystal structures, optical properties, theoretical calculations, and structure-property relationships of MFC and MFZC.

Results and discussion

The colorless and transparent crystals of MFC (rod-shaped) and MFZC (block-shaped) were obtained via slow solvent evaporation at room temperature (Fig. 2a). Their crystal structures were confirmed by single-crystal X-ray diffraction (SCXRD) analysis, and detailed crystallographic data are summarized in Tables S1–S5 (SI). Both MFC and MFZC crystallize in the monoclinic polar noncentrosymmetric (NCS) space group P2₁ (No. 4) and feature zero-dimensional (0D) structures (Fig. 2c and d). The phase purities of MFC and MFZC were confirmed by powder X-ray diffraction (PXRD) analysis (Fig. S1).

Fig. 2 (a) The synthesis of MFC and MFZC. (b) Functional motifs in MF. The crystal structures of (c) MFC and (d) MFZC. Hirshfeld surfaces for (e) MFC and (h) MFZC. Modular description of functional motifs for (f) MFC and (g) MFZC.

For MFC, its asymmetric unit contains one protonated MF cation and two free Cl⁻ anions (Fig. S2). The MF unit exhibits a “two-in-one” flexible configuration, comprising planar [CN₃H₅] and [C₃N₃H₈] groups (Fig. 2b). The dihedral angle between them, denoted as α, is 63.01° in MFC. As shown in Fig. S3, the organic MF molecules and Cl⁻ anions are interconnected via hydrogen bonds in the ab-plane, forming a pseudo-2D structure. The layers stack along the c-axis, resulting in a pseudo-3D network framework. Along the c-axis, the organic molecules MF exhibit an alternating -ABAB- arrangement. The dihedral angles between adjacent organic cations in layer A and layer B were determined to be β₁ = 80.48° (between two [CN₃H₅] planes) and β₂ = 77.76° (between two [C₃N₃H₈] planes), respectively, with an interlayer distance of 7.50 Å (Fig. 2f). Within layer A or layer B, adjacent organic cations aligned along the b-axis exhibit a dihedral angle of 0° and an interatomic spacing of 5.79 Å (Fig. 2f). The organic MF cation is tilted relative to the (001) crystal plane with a dihedral angle (γ) of 86.37° (Fig. S7a). To further evaluate the interplay of molecular interactions in the structure of MFC, we employed Hirshfeld surface (HS) analysis and mapped d_norm, which are presented in Fig. 2e. The red areas on the Hirshfeld surface correspond to significant H⋯Cl contacts (Fig. 2e). The percentage contribution of H⋯Cl interaction is 45.6% for MFC (Fig. 2e and S6a).

In contrast to MFC, the Cl⁻ anions in MFZC are not free ions but coordinate to Zn atoms, forming tetrahedral [ZnCl₄]²⁻ units. The asymmetric unit of MFZC consists of one such [ZnCl₄]²⁻ tetrahedron and one protonated MF cation (Fig. S4). The dihedral angle (α) within the MF unit decreases from 63.01° to 53.15°. MFZC also adopts a pseudo-layered structure parallel to the ab plane, wherein the (C₄H₁₃N₅)²⁺ cations and [ZnCl₄]²⁻ anions are interconnected by [N–H⋯Cl] and [C–H⋯Cl] hydrogen bonds, with the H⋯Cl distances ranging from 2.47 to 2.79 Å (Fig. S5 and Table S5). These pseudo-layers stack along the c direction to form the entire 3D network of MFZC (Fig. S5). Similar to MFC, the organic moieties MF in MFZC adopt an alternating “ABAB” arrangement along the c-axis, with an interlayer distance of 7.91 Å (Fig. 2g). Notably, within the organic MF cations in MFZC, the [C₃N₃H₈] adopts a zig-zag arrangement with β₂ = 76.17°, whereas [CN₃H₅] groups exhibit β₁ = 15.12° and an interatomic spacing of 6.92 Å. The H⋯Cl ratio of these hydrogen bonds is higher in MFZC than in MFC (Fig. 2e and h). These enhanced hydrogen-bonding interactions impose strong structural constraints on the cationic framework, effectively restricting the relative orientation between adjacent organic planes and reducing the dihedral angles. This ordered alignment significantly enhances the overall birefringence of MFZC (Fig. 2g). Additionally, the MF cations are oriented off the (001) crystal plane with a dihedral angle of γ₂ = 80.28° for MFZC, which is smaller than that of MFC (γ₁ = 86.37°) (Fig. S7b). This structural feature further enhances the optical anisotropy of MFZC. The red regions in the 2D fingerprint plots of hydrogen bonds correspond to H⋯Cl contacts, accounting for 65.7% of the total interaction. This proportion, which is greater than MFC (45.6%), underscores the critical role of hydrogen bonds in stabilizing the structure framework (Fig. 2h and S6b).

The UV-vis-NIR diffuse reflectance spectra demonstrate that the UV cutoff edge of MFC is located at 250 nm, while MFZC shows a blue-shifted edge at approximately 240 nm (Fig. 3a and b). The corresponding optical bandgap values were determined to be 4.64 eV for MFC and 4.72 eV for MFZC, consistent with the colorless and transparent appearance of the crystals (Fig. 2a). Notably, the bandgap of MFZC surpasses that of previously reported hybrid Zn-based halide NLO crystals including (4-AMP)ZnX₄·H₂O (X = Cl, Br),⁵ (3-AMP)ZnBr₄,⁴⁰ (C₄H₁₁N₂)ZnI₃ ⁴¹ and (C₆H₅N₂)₂ZnCl₄.⁴² The NCS structures of MFC and MFZC motivated the evaluation of their SHG responses at 1064 nm using the Kurtz−Perry method,⁴³ with commercially available KDP serving as the reference. As shown in Fig. 3d and e, MFC and MFZC exhibit strong SHG responses, reaching 2.8 × and 2.2 × KDP, respectively. Furthermore, as the particle size increases, their SHG intensities increase significantly, indicating that they both exhibit phase-matching behaviors. Notably, MFC demonstrates more outstanding SHG properties than the majority of metal-free materials, such as C₅H₆N₃O₂I,⁴⁴ C(NH₂)₃(I₃O₈)(HI₃O₈)(H₂I₂O₆)(HIO₃)₄·3H₂O⁴⁵ and [C₅H₆O₂N₃]₂[IO₃]₂.⁴⁶ In addition, MFZC demonstrates better SHG performance than most similar organic–inorganic zinc-based hybrid materials, like (C₁₄H₁₄N₂)ZnCl₄,⁴⁷ (C₆H₁₆N₂)₃Zn₃Br₁₂·2H₂O,⁴⁸ (C₄H₁₁N₂)ZnCl₃ ⁴¹ and (C₁₃N₃H₁₄)₂ZnBr₄ ⁴⁹ (Fig. 3g and Table S6). The wide bandgaps and strong SHG responses of MFC and MFZC make them promising UV NLO crystals.

Fig. 3 (a and b) UV-vis spectra of MFC (a) and MFZC (b). (c and f) Triaxial ellipsoid of three principal refractive indices at 546 nm for (c) MFC and (f) MFZC. (d) Size-dependent SHG responses of MFC, MFZC and KDP under 1064 nm laser radiation. (e) SHG intensities of MFC, MFZC and KDP at 1064 nm. (g) Comparison of bandgaps, SHG efficiency and birefringence in organic–inorganic hybrid zinc-based materials. (h) The calculated birefringence values of MFC and MFZC.

To clarify the structure-property relationships of MFC and MFZC, the hyperpolarizability of organic moieties and density functional theory (DFT) calculations were conducted. The organic moieties in MFC and MFZC exhibit the anticipated anisotropy in polarizability, and their hyperpolarizabilities follow the descending order of β_x > β_y > β_z (Fig. 4a and c). As MFC and MFZC are polar crystals, their polar axes are aligned parallel to the crystallographic b-axis along the 2₁ screw axis, a feature dictated by the symmetry of their crystal structures. Consequently, the combined polarizability components along the 2₁ screw axis contribute to the second-order nonlinear optical response.⁵⁰ As illustrated in Fig. 4b and d, the hyperpolarizability components of MFC and MFZC along the 2₁ screw axis yield values of θ₁ = 37.56 and θ₂ = 38.38, respectively. Furthermore, compared with MFZC, MFC exhibits a larger hyperpolarizability of the organic (C₄H₁₃N₅)²⁺ molecules (Fig. 1), together with larger dihedral angles β₁ and β₂ between adjacent layers (β₁ = 80.48° and β₂ = 77.76° for MFC and β₁ = 15.12° and β₂ = 76.17° for MFZC) (Fig. 2). These factors collectively contribute to the slightly higher SHG intensity of MFC relative to MFZC. Meanwhile, the electronic structure analysis indicates that both MFC and MFZC exhibit indirect bandgaps, with calculated values of 3.62 eV for MFC and 3.77 eV for MFZC (Fig. 4e and h), where the little underestimation relative to experimental values is attributed to the well-known limitation of the generalized gradient approximation (GGA) in treating exchange-correlation energy discontinuities.^51,52 Since the optical properties of crystalline materials are predominantly determined by electronic transitions near the band edges, we analyzed their total (TDOS) and partial density of states (PDOS) near the Fermi level (E_f = 0 eV). The results show that the valence band maximum (VBM) of MFC is dominated by Cl 3p states, while that of MFZC receives an additional contribution from Zn 3d orbitals. In contrast, the conduction band minimum (CBM) of both compounds is primarily composed of C 2p and N 2p states from the organic MF cation. Therefore, the linear and nonlinear optical properties of MFC and MFZC arise from the synergistic interplay between their organic and inorganic components. Frontier molecular orbital analysis further supports this finding (Fig. 4f and i): the highest occupied molecular orbital (HOMO) is localized on Cl atoms in MFC and extends on both Zn 3d and Cl 3p in MFZC, whereas the lowest unoccupied molecular orbital (LUMO) in both compounds is dominated by the C 2p and N 2p orbitals of the organic MF cation. To gain an in-depth understanding of the microscopic mechanism underlying the NLO properties, the maps of electron localization function (ELF) were studied (Fig. 4g and j). Notably, the electron cloud density around MF in MFC and MFZC exhibits obvious π-conjugated structural features. In addition, there is a significant electron cloud distribution around the Cl⁻ ions in MFC and MFZC. Consequently, the MF cations and Cl⁻/[ZnCl₄]²⁻ anions significantly contribute to their linear and nonlinear optical properties.

Fig. 4 (a and c) Distribution of the first hyperpolarizability values of organic cations MFC and MFZC, respectively. Angle (θ) between the β_max vector and the crystal polar 2₁ axis in MFC (b) and MFZC (d). Calculation results: (e and h) calculated band structure and DOS diagrams of (e) MFC and (h) MFZC. (f and i) The HOMO (blue sector) and LUMO (red sector) maps of (f) MFC and (i) MFZC. (g and j) The ELF diagrams of (g) MFC and (j) MFZC.

The birefringence values of MFC and MFZC were further evaluated through the first-principles theoretical calculations (Fig. S8 and S9). At 546 nm, the three principal refractive indices of MFC and MFZC are illustrated in Fig. 3c and f. Specifically, the refractive indices of MFC follow the order of n_a > n_b > n_c, whereas those of MFZC exhibit the sequence n_c > n_a > n_b. Their birefringence values are calculated to be 0.02 and 0.09 at 546 nm, respectively (Fig. 3h). It is worth noting that the birefringence of MFZC is 4.5 times higher than that of MFC, because (i) the organic (C₄H₁₃N₅)²⁺ cations of MFZC possess a larger polarizability anisotropy than those of MFC (Fig. 1). (ii) The dihedral angle (α) within the MF moiety decreases from 63.01° in MFC to 53.15° in MFZC. (iii) The dihedral angles between adjacent organic cations in the A and B layers of MFC are determined to be β₁ = 80.48° and β₂ = 77.76°, respectively. In contrast, for the organic MF cations in MFZC, the corresponding dihedral angles are β₁ = 15.12° and β₂ = 76.17° (Fig. 2). (iv) The MF cation exhibits an orientation deviation from the (001) plane, with the dihedral angle γ₂ = 80.28° for MFZC being lower than γ₁ = 86.37° for MFC (Fig. S7). Furthermore, the birefringence of MFZC is larger than those of some commercial crystals and zinc-based hybrid halide crystals, such as MgF₂ (0.012@532 nm),⁵³ LiNbO₃ (0.089@546 nm),⁵⁴ and (4-AMP)ZnX₄·H₂O (X = Cl, Br) (0.069@546 nm and 0.053@546 nm, respectively).⁵ Therefore, these data demonstrate that the birefringence values of MFC and MFZC are predominantly governed by MF moieties, highlighting that the coupling of π-conjugated groups represents a meaningful strategy for manipulating the macroscopic optical anisotropy of materials.

Conclusions

In conclusion, this work demonstrates that the metformin cation MF is a promising NLO-active functional motif and reports the synthesis of new MFZC via a point-to-volume substitution strategy from MFC. MFZC exhibits strong SHG response and a wide optical bandgap. Moreover, the successful introduction of [ZnCl₄]^2- tetrahedral units and the favorable arrangement of organic cations collectively enhance the optical anisotropy of MFZC, much higher than that of MFC. Theoretical calculation and structural analysis demonstrate that the optical properties of MFC and MFZC are synergistically affected by both organic MF cations and inorganic halogen ions/metal-halide anions. This work offers not only a promising UV NLO material, but also an effective strategy for the rational design of novel SHG materials.

Author contributions

This work was conceptualized by Jiajing Wu. Experimentation was performed by Ruo-Nan Li. Software analysis was performed by Wen-Dong Yao. Besides, Jiajing Wu and Sheng-Ping Guo contributed to funding acquisition and supervision. The first draft of the manuscript was prepared by Jiajing Wu and Ruo-Nan Li, and the final draft was edited by all the authors.

Conflicts of interest

The authors declare that they have no conflict of interest.

Data availability

The data supporting this article have been included as part of the supplementary information (SI). Supplementary information: additional tables and pictures. See DOI: https://doi.org/10.1039/d6sc00466k.

CCDC 2521794 C₄H₁₃N₅Cl₂ and 2522224 (C₄H₁₃N₅)ZnCl₄ contain the supplementary crystallographic data for this paper.^55a,b

Acknowledgements

This work was supported by the National Natural Science Foundation of China (22505217 and 22371246), the Natural Science Foundation of Jiangsu Province (Grant No. BK20220558), the Yangzhou University Science and Technology Innovation Fund (2022CXJ029), the start-up fund of Yangzhou University (Grant No. 137012279) and the Lvyangjinfeng Talent Program of Yangzhou (YZLYJFJH2021YXBS085).

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