From poor-active to high performance via heteroleptic tetrahedra engineering: rational design of non-π-conjugated hybrids for phase-matchable ultraviolet nonlinear optics

Abstract

In the exploration of new second-harmonic generation (SHG) crystals, non-π-conjugated organic–inorganic metal halides (OIMHs), particularly Zn/Cd-based OIMHs, have long been overlooked. This is primarily due to the high symmetry and low polarizability of both metal-halide anions (typically regular tetrahedra or octahedra) and non-π-conjugated organic cations. Herein, we report two novel SHG-active non-π-conjugated OIMHs: (H₂DABCO)CdI₄ and (PIP)·CdI₃(HDABCO), where DABCO = C₆H₁₂N₂ (1,4-diaza[2.2.2]bicyclooctane) and PIP = C₄H₁₀N₂ (piperazine). (H₂DABCO)CdI₄ (P2₁2₁2₁), with discrete (H₂DABCO)²⁻ cations and (CdI₄)²⁻ anions, exhibits a poor SHG performance, including a small birefringence of 0.02@546 nm, weak and non-phase-matchable SHG response (0.3 × KH₂PO₄, KDP), and a narrow bandgap of 3.84 eV. However, by constructing higher-polarizability [CdI₃(HDABCO)] heteroleptic tetrahedra through organic–metal coordination bonds and incorporating PIP units, the two modules are assembled into the polar space group Cc via hydrogen bonding. Consequently, (PIP)·CdI₃(HDABCO) demonstrates a dramatically enhanced SHG effect (2.1 × KDP), which is sevenfold higher than that of (H₂DABCO)CdI₄, and achieves phase-matchability. Additionally, (PIP)·CdI₃(HDABCO) exhibits good thermal stability (180 °C), a short λ_cutoff edge (273 nm) and wide bandgap (4.05 eV), indicating its potential as a high-performance ultraviolet SHG crystal.

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Jin Chen

Dr Jin Chen received his PhD from the Fujian Institute of Research on the Structure of Matter, Chinese Academy of Sciences in 2021, under the supervision of Prof. Mao Jianggao. He then joined Fujian Normal University as an Associate Professor in the College of Chemistry and Materials Science. His research focuses on designing organic–inorganic hybrid crystals by optimizing the microscopic physical properties of functional building blocks and assembling them via non-covalent interactions like hydrogen and halogen bonds. The goal is to explore novel high-performance second-order nonlinear optical and birefringent crystals. He has published over 20 papers in journals including Acc. Chem. Res. and Angew. Chem., Int. Ed. Outside of his research commitments, he is a new father who enjoys every moment spent with his family.

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Introduction

Nonlinear optical (NLO) materials, particularly crystals exhibiting second-harmonic generation (SHG), are indispensable components in advanced photonic technologies, including laser frequency conversion, optical communication, and polarization control.^1–5 While established inorganic crystals like KBe₂BO₃F₂ (KBBF), β-BaB₂O₄ (BBO), and KH₂PO₄ (KDP) remain crucial,^6–8 significant research efforts are directed towards discovering novel materials with enhanced performance or complementary properties.⁹ A prominent direction in recent years has involved organic–inorganic hybrid compounds.^10–13 Many high-performance examples leverage organic π-conjugated units, which act as chromophores possessing intrinsically higher hyperpolarizabilities compared to traditional inorganic NLO-active groups (e.g., [BO₃]³⁻ and [NO₃]⁻). This design strategy has successfully yielded materials with strong SHG responses, often significantly exceeding that of KDP, as exemplified by KLi(HC₃N₃O₃)·2H₂O (5.3 × KDP),¹⁴ [C(NH₂)₃]₂[B₃O₃F₄(OH)] (1.4 × KDP),¹⁵ (C₅H₆ON)(H⁺₂PO₄)⁻ (3 × KDP),¹⁶ and α-(C₂H₅N₄)(NO₃) (3.5 × KDP).¹⁷

Organic–inorganic metal halides (OIMHs) have emerged as a promising class of NLO materials due to their synthetic versatility, tunable structures combining organic flexibility with inorganic functionality, and propensity for facile single-crystal growth.^18–22 A prevalent strategy for achieving strong SHG responses in OIMHs involves incorporating organic cations with extended π-conjugation or elements with stereochemically active lone pair electrons (e.g., Pb²⁺, Sn²⁺, Sb³⁺, and Bi³⁺). Examples such as (C₇H₁₀N)PbBr₃ (10.9 × urea),²³ Cs₃Pb₂(CH₃COO)₂X₅ (X = I and Br; 4 and 8 × KDP, respectively),²⁴ and (C₅H₅NO)(Sb₂OF₄) (12 × KDP)²⁵ demonstrate the effectiveness of this approach. However, OIMHs constructed from non-π-conjugated organic components and d¹⁰ transition metal cations (e.g., Zn²⁺ and Cd²⁺) represent a less explored but potentially advantageous alternative. These d¹⁰ cations exhibit moderate polarizability and lack low-energy d–d transitions, which is conducive to achieving wide optical bandgaps essential for avoiding laser damage and extending transparency into the ultraviolet region.^26–28 Furthermore, the introduction of non-π-conjugated organic ligands can facilitate the formation of diverse and highly distorted metal-centered coordination polyhedra. Our group's previous work highlights that engineering such pronounced polyhedral distortion (e.g., in Org-M–X units) can significantly enhance polarizability anisotropy and microscopic hyperpolarizability, leading to strong macroscopic NLO effects even without π-conjugated moieties, as demonstrated in H₁₁C₄N₂CdI₃ (6.0 × KDP, E_g = 4.10 eV)²⁹ and (C₄H₁₁N₂)ZnBr₃ (2.5 × KDP, E_g = 5.53 eV).³⁰

Building on this strategy, we initially investigated (H₂DABCO)CdI₄, incorporating the non-π-conjugated diamine 1,4-diazabicyclo[2.2.2]octane (DABCO). Although crystallizing in a noncentrosymmetric space group, this compound exhibited only a weak, non-phase-matchable SHG response (≈0.3 × KDP) and small birefringence (Δn_cal = 0.02@546 nm). This limited performance is attributed to the relatively low distortion of the homoleptic [CdI₄] tetrahedra and the modest polarizability anisotropy of the (H₂DABCO)²⁺ cation. To overcome these limitations and test the hypothesis that increasing polyhedral distortion enhances NLO properties, we strategically introduced piperazine (PIP) alongside DABCO. This led to the successful synthesis of a new OIMH, (PIP)·CdI₃(HDABCO), crystallizing in the polar space group Cc. Crucially, this modification results in the formation of heteroleptic [CdNI₃] tetrahedra where one iodide is replaced with a nitrogen atom from the HDABCO⁺ ligand. These highly distorted [CdNI₃] units align effectively within the polar structure. Consequently, (PIP)·CdI₃(HDABCO) displays substantially improved NLO properties compared to its precursor: a strong and phase-matchable SHG response (≈2.1 × KDP), a significantly larger birefringence (Δn ≈ 0.06@546 nm), and a wide bandgap (4.05 eV), validating the effectiveness of enhancing polyhedral distortion in non-π-conjugated OIMHs for achieving high-performance NLO crystals.

Experiments

Materials and synthesis

CdO (>99%), Y₂O₃ (>99%), C₆H₁₂N₂ (1,4-diaza[2.2.2]bicyclooctane, 99%), C₄H₁₀N₂ (piperazine, 99%) and HI (55–58 wt%) were used as purchased from Adamas-beta. For the synthesis of (H₂DABCO)CdI₄, the following starting materials were used: CdO (128.4 mg, 1 mmol), C₆H₁₂N₂ (224.4 mg, 2 mmol), HI (1 mL), and H₂O (2 mL). The mixture was placed in Teflon pouches (23 mL), sealed in an autoclave, heated at 120 °C for 72 hours, and then cooled to 30 °C at a rate of 1.88 °C h⁻¹. For the synthesis of (PIP)·CdI₃(HDABCO), the starting materials comprised CdO (128.4 mg, 1 mmol), Y₂O₃ (112.9 mg, 0.5 mmol), C₆H₁₂N₂ (224.4 mg, 2 mmol), C₄H₁₀N₂ (172.3 mg, 2 mmol), HI (1 mL), and H₂O (2 mL). The mixture was placed in Teflon pouches (23 mL), sealed in an autoclave, heated at 110 °C for 72 hours, and then cooled to 30 °C at a rate of 1.67 °C h⁻¹.

Single crystal structure determination

Single-crystal X-ray diffraction data for the title compounds were collected on a Rigaku XtaLAB Synergy-DW dual-wavelength CCD diffractometer with Cu Kα radiation (λ = 1.54184 Å) at 298 K. Data reduction was performed with CrysAlisPro, and absorption correction based on the multi-scan method was applied.³¹ The structures of title compounds were determined by the direct methods and refined by full-matrix least-squares fitting on F² using SHELXL-2014.³² All of the non-hydrogen atoms were refined with anisotropic thermal parameters. The structure was checked for missing symmetry elements using PLATON,³³ and none was found. Crystallographic data and structural refinements of the compounds are listed in Tables S1–S4 (ESI†).

Powder X-ray diffraction

Powder X-ray diffraction (PXRD) patterns were recorded on a Rigaku Ultima IV diffractometer with graphite-monochromated Cu Kα radiation in the 2θ range of 10–70°, with a step size of 0.02°.

Energy-dispersive X-ray spectroscopy

Microprobe elemental analyses and elemental distribution maps were obtained using a field-emission scanning electron microscope (Phenom LE) equipped with an energy-dispersive X-ray spectrometer (EDS, Phenom LE).

Thermal analysis

The data thermogravimetric analysis (TG) and differential thermal analysis (DTA) were performed with a Rigaku TG-DTA 8121 unit under an Ar atmosphere, at a heating rate of 10 °C min⁻¹ in the range from 30 to 800 °C.

Optical measurements

The infrared (IR) spectra were recorded on a Bruker-VERTEX 70 in the range from 4000 to 400 cm⁻¹. The ultraviolet-visible (UV-vis) spectra in the range of 200–2000 nm were recorded on a PerkinElmer Lambda 750 UV-vis-NIR spectrophotometer. The reflectance spectra were converted into absorption spectra by using the Kubelka–Munk function.³⁴

Second harmonic generation measurements

Powder SHG measurements were carried out with a Q switch Nd:YAG laser generating radiation at 1064 nm according to the method of Kurtz and Perry.³⁵ Crystalline (H₂DABCO)CdI₄ and (PIP)·CdI₃(HDABCO) samples were sieved into distinct particle-size ranges (45–63, 63–75, 75–105, 105–150, 150–210 and 210–300 μm). Sieved KH₂PO₄ (KDP) samples in the same particle-size ranges were used as references.

Computational method

The electronic structures and optical properties were studied using a plane-wave pseudopotentials method within the density functional theory (DFT) implemented in the total energy code CASTEP.^36,37 For the exchange and correlation functional, we chose Perdew–Burke–Ernzerhof (PBE) in the generalized gradient approximation (GGA).³⁸ The interactions between the ionic cores and the electrons were described by the norm-conserving pseudopotential.³⁹ The following orbital electrons were treated as valence electrons: C-2s²2p², N-2s²2p³, I-5S²5P⁵, Cd-4d¹⁰5s², and H-1s¹. The numbers of plane waves included in the basis sets were determined by a cutoff energy of 700 eV. During the SCF and optical-property calculations of the two compounds, the k-point separation was set to 0.04 Å⁻¹ to perform the numerical integration of the Brillouin zone, and the corresponding k-point samplings are 3 × 2 × 2 and 3 × 1 × 2 for (H₂DABCO)CdI₄ and (PIP)·CdI₃(HDABCO), respectively.

Formula of the octahedra distortion degree (Δd)

In a distorted octahedra [MX_n], n is the coordination number of M, d_n is each individual M–X bond length, and d is the average bond length.

Results and discussion

The crystal structures of title compounds were successfully resolved by single-crystal X-ray diffraction (SCXRD), and the crystallographic data are summarized in Table S1 (ESI†). Powder X-ray diffraction (PXRD) analysis of the single crystals and refined PXRD data confirmed their phase purity (Fig. S1, ESI†). The EDS results indicated that the Cd : I ratios are 6.89 : 29.51 and 4.92 : 15.73, respectively, which are consistent with structural calculations (1 : 4 and 1 : 3 for (H₂DABCO)CdI₄ and (PIP)·CdI₃(HDABCO), respectively) (Fig. S2, ESI†). Thermal behaviors (TG-DTA) indicate the thermal stabilities of (H₂DABCO)CdI₄ and (PIP)·CdI₃(HDABCO), at around 310 °C and 180 °C, respectively (Fig. S3, ESI†). For (H₂DABCO)CdI₄, the protonated [H₂DABCO]²⁺ cation began to decompose at about 310 °C. With the increase of temperature, the [CdI₄]²⁻ anion gradually de-iodized. For (PIP)·CdI₃(HDABCO), the piperazine ring in its structure began to decompose at 180 °C, and the protonated [H₂DABCO]²⁺ cation began to decompose at 310 °C, accompanied by the volatilization of iodine vapor. The infrared spectra (Fig. S4, ESI†) of the title compounds show that the absorption peaks at 1344–1381 cm⁻¹ correspond to the stretching vibration of C–N bonds, and the absorption peaks at 2876–3005 cm⁻¹ correspond to the stretching vibration of C–H bonds, respectively. In compounds (H₂DABCO)CdI₄ and (PIP)·CdI₃(HDABCO), the N–H stretching vibration peaks are at 3072 and 3225 cm⁻¹, respectively.^40,41 For (PIP)·CdI₃(HDABCO), the strong peak at 490 cm⁻¹ corresponds to the stretching vibration of Cd–N.⁴² The detailed peak assignment in the infrared spectrum is presented in Table S5 (ESI†). A single crystal of (PIP)·CdI₃(HDABCO) exhibits white-yellow light under UV illumination (Fig. S5b, ESI†), corresponding to its photoluminescence–photoexcitation (PL–PLE) spectrum (Fig. S5c, ESI†). The PLE spectrum shows distinct excitation peaks at 330 and 390 nm, with the corresponding emission peaks at 530 and 560 nm in the PL spectra. As the excitation wavelength increases, a redshift in the emission spectrum can be observed.

Crystal structures

(H₂DABCO)CdI₄ crystallizes in a noncentrosymmetric space group P2₁2₁2₁ (No. 19) with one cationic H₁₆C₆N₂²⁺ (H₂DABCO²⁺) bridged ring and one anionic CdI₄²⁻ tetrahedron (Fig. 1a and Fig. S6a, ESI†) in each asymmetric unit. In the H₂DABCO²⁺, each C and N atom exhibits sp³ hybridization, with C–C/C–N distances of 1.47(4)–1.50(3) Å and 1.46(3)–1.54(4) Å, respectively, which is consistent with those of previously reported compounds. Each Cd²⁺ cation bonds with four I⁻ anions to form a CdI₄²⁻ tetrahedron, with the Cd–I distances ranging from 2.751(3) Å to 2.8061(19) Å and I–Cd–I angles of 102.73(6)–116.70(8)°, which are comparable with reported OIMHs with CdI₄ units, such as PIPCdI₄,⁴³ [C₆H₅CH₂CH₂NH₃]₂[CdI₄],⁴⁴ and (C₆H₁₄N₂)[CdI₄].⁴⁵ Neighboring H₂DABCO²⁺ and CdI₄²⁻ groups are isolated from each other and arranged in a quasi-two-dimensional (quasi-2D) [H₂DABCOCdI₄] layer (Fig. S6b, ESI†), parallel to the bc plane. These pseudo-layers stack along the a-axis to form the entire 3D network. (Fig. 1b).

Fig. 1 Views of the asymmetric unit (a) and the 3D structure (b) of (H₂DABCO)CdI₄; the CdI₃(HDACBO) heteroleptic tetrahedra (c), 1D [(PIP)·CdI₃(HDABCO)] chain (d) and overall architecture of (PIP)·CdI₃(HDABCO) (e).

(PIP)·CdI₃(HDABCO) crystallizes in the polar space group Cc (No. 9). Its asymmetric unit comprises one HCACBO⁺ cation, one PIP central molecule, one Cd²⁺ cation, and three I⁻ anions. Both HDACBO⁺ and PIP have sp³ hybridized C/N atoms, with C–C and C–N bond lengths of 1.51(3)–1.53(3) Å and 1.46(3)–1.51(2) Å, respectively. Notably, each Cd atom is coordinated to the HBACBO⁺ unit via Cd–N bonds and to three I atoms via Cd–I bonds, forming CdI₃(HDACBO) heteroleptic tetrahedra (Fig. 1c and Fig. S6c, ESI†). The Cd–N bond length (2.301(13) Å) is significantly shorter than the Cd–I bond lengths (2.7251(19)–2.7597(17) Å). The bond angles of N–Cd–I and I–Cd–I are 99.8(4)–108.8(3)° and 110.29(6)–116.71(7)°, respectively, consistent with known OIMHs containing Org-Cd–I heteroleptic units. Adjacent PIP molecules are connected by N(4)–H(4D)⋯N(3) hydrogen bonds, forming 1D [PIP] chains parallel to the c-axis (Fig. S6d, ESI†). Subsequently, each CdI₃(HDACBO) heteroleptic tetrahedra is successively attached to the sides of the [PIP] chains in an alternating “up” and “down” manner via N(1)–H(1)⋯N(3) hydrogen bonds, resulting in the formation of the neutral 1D [(PIP)·CdI₃(HDABCO)] chain (Fig. 1d). These 1D chains are parallel to each other within the ac plane, forming a 2D pseudo-layer. Finally, the overall architecture of (PIP)·CdI₃(HDABCO) is constructed through the interlacing of these 2D pseudo-layers along the b-direction. (Fig. 1e)

Structure comparison

A comparison of the structural features between the two title compounds is instructive for understanding their significant differences in optical properties. Both compounds crystallize in non-centrosymmetric (NCS) space groups; however, we propose that the distinct structural characteristics of (PIP)·CdI₃(HDABCO), specifically the heteroleptic coordination environment and the incorporation of non-π-conjugated PIP groups, contribute to its enhanced polarity and structural asymmetry. In (H₂DABCO)CdI₄, each Cd²⁺ ion coordinates with four I⁻ anions, forming a nearly regular CdI₄ tetrahedral unit possessing a calculated dipole moment of approximately 3.10 D. In contrast, the 1 : 3 ratio of Cd to I in (PIP)·CdI₃(HDABCO) necessitates the participation of the N atom from the HDABCO⁺ cation in coordination with the Cd²⁺ center. This results in the formation of a highly distorted heteroleptic CdNI₃ tetrahedral unit, which exhibits a substantially larger dipole moment of approximately 6.75 D, reflecting increased local asymmetry. Furthermore, the spatial arrangement of these Cd-centered tetrahedra critically influences the overall polarity of the compounds. Within the unit cell of (H₂DABCO)CdI₄, the dipole moments of the four constituent CdI₄ tetrahedra effectively cancel each other along all crystallographic axes (a, b, and c). Consequently, despite its NCS structure, (H₂DABCO)CdI₄ is effectively nonpolar, with a net unit cell dipole moment close to zero. Conversely, in (PIP)·CdI₃(HDABCO), the dipole moments of the CdNI₃ tetrahedra align such that they largely cancel along the b axis but constructively add along the a and c axes. This vectorial summation yields a significant net dipole moment of approximately 17.45 D for the unit cell, confirming its polar nature alongside its non-centrosymmetry. Detailed dipole moment calculations are provided in Table S7 (ESI†). Finally, the degree of polyhedron distortion (Δd), calculated using formula (1), further quantifies the structural differences. The CdI₄ tetrahedron in (H₂DABCO)CdI₄ shows minimal distortion (Δd = 7.8 × 10⁻⁵), whereas the heteroleptic CdNI₃ tetrahedron in (PIP)·CdI₃(HDABCO) exhibits a markedly higher distortion (Δd = 5.4 × 10⁻³). This clearly demonstrates that engineering a heteroleptic coordination environment involving a Cd–N bond in (PIP)·CdI₃(HDABCO) significantly enhances the distortion of the Cd-centered polyhedron.

UV transmission and bandgaps

The optical properties of the title compounds were investigated using ultraviolet-visible (UV-vis) diffuse reflectance spectroscopy (Fig. 2). From the spectra, the absorption cutoff edges for (H₂DABCO)CdI₄ and (PIP)·CdI₃(HDABCO) were determined to be 294 nm and 273 nm, respectively. These correspond to relatively wide optical bandgaps (E_g) of 3.84 eV and 4.05 eV. Such wide bandgaps imply significant transparency extending into the short-wavelength UV region (<300 nm), which is advantageous for potential applications in UV nonlinear optics (NLO). Importantly, these E_g values exceed those of numerous reported NLO organic–inorganic metal halides (OIMHs), particularly systems based on heavier post-transition metal cations such as Pb²⁺, Sn²⁺, Sb³⁺, and Bi³⁺. For comparison, reported bandgaps include 2.36 eV for (C₈N₂H₂₂)(PbI₄),⁴⁶ 2.55 eV (X = I) and 3.26 eV (X = Br) for Cs₃Pb₂(CH₃COO)₂X₅,²⁴ 3.09 eV for Sn[(C₇H₃NO₄)(H₂O)],⁴⁷ 3.47 eV for (C₉H₁₄N)SbCl₄,⁴⁸ 2.91 eV for MAGeBr₃,⁴⁹ and values generally below 3.6 eV for many bismuth-based analogues (e.g., 2.29–3.52 eV reported for (C₆H₅(CH₂)₄NH₃)₄BiX₇ phases, X = Br and I⁵⁰). The wider transparency window observed in the title compounds highlights their potential suitability for frequency conversion or other NLO processes operating in the UV spectrum.

Fig. 2 UV-vis diffuse reflectance spectra (a) and bandgaps (b) of the title compounds (curve 1 for (H₂DABCO)CdI₄ and 2 for (PIP)·CdI₃(HDABCO), respectively). The DOS plots for (H₂DABCO)CdI₄ (c) and (PIP)·CdI₃(HDABCO) (d).

Density functional theory (DFT) calculations indicate that both (H₂DABCO)CdI₄ and (PIP)·CdI₃(HDABCO) possess direct bandgaps. The theoretical bandgaps calculated using the Perdew–Burke–Ernzerhof generalized gradient approximation (GGA-PBE) functional are 3.24 eV and 3.69 eV, respectively (Fig. S7, ESI†). As anticipated, these values underestimate the experimental bandgaps, a common characteristic of the GGA-PBE functional. To correct for this underestimation and better align the calculated electronic structure with experimental observations, scissor operators of 0.60 eV for (H₂DABCO)CdI₄ and 0.36 eV for (PIP)·CdI₃(HDABCO) were applied. Analysis of the calculated density of states (DOS) (Fig. 3c and d) provides insights into the orbital contributions near the band edges. For both compounds, the valence band maximum (VBM) is predominantly composed of I-5p orbitals, with minor contributions from C-2p orbitals originating from the organic cations. The conduction band minimum (CBM) is primarily derived from Cd-5s and Cd-4p states, along with contributions noted from I-5s orbitals and smaller admixtures of I-5p and C-2p states. This orbital composition, with the VBM dominated by iodide p-orbitals and the CBM dominated by cadmium s/p-orbitals, highlights that the electronic transitions across the fundamental bandgap primarily involve the inorganic framework. Consequently, the bandgap characteristics of both compounds are largely governed by the electronic structure of their respective Cd-centered tetrahedral units ([CdI₄] and [CdNI₃]).

Fig. 3 Oscilloscope traces of the SHG signals (150–210 μm) with 1064 nm laser radiation (a) and phase-matching curves (b), KDP was used as the reference for the SHG measurements.

SHG properties

The noncentrosymmetric crystal structures of the title compounds enable second-harmonic generation (SHG), which was investigated using the Kurtz–Perry powder method with 1064 nm laser radiation (Fig. 3). For (H₂DABCO)CdI₄, the SHG intensity exhibited an irregular dependence on the particle size (Fig. 3a and b), characteristic of non-phase-matchable (NPM) behavior. The maximum observed SHG intensity was relatively weak, approximately 0.3 times that of potassium dihydrogen phosphate (KDP). This NPM behavior and modest response are consistent with the minimal distortion of the [CdI₄] tetrahedra and the likely cancellation of SHG tensor components within the P2₁2₁2₁ space group. In stark contrast, (PIP)·CdI₃(HDABCO) displayed clear phase-matchable (PM) characteristics, with its SHG intensity increasing with the particle size before reaching saturation (Fig. 3c and d). This indicates that efficient SHG conversion is achievable in this material. At the optimal particle size range of 150–210 μm, its SHG intensity reached approximately 2.1 times that of KDP, significantly outperforming (H₂DABCO)CdI₄ (≈7 times stronger).

Notably, the SHG efficiency of 2.1 × KDP for (PIP)·CdI₃(HDABCO) surpasses those of many previously reported Cd-based NLO OIMHs, which typically exhibit responses below 1.0 × KDP (e.g., (C₅H₁₄NO)CdCl₃: 0.4 × KDP;⁵¹ [(CH₃)₃NCH₂Cl]CdCl₃: 0.73 × KDP;⁵² (C₁₃N₃H₁₄)₂CdBr₄: 0.98 × KDP⁵³). Moreover, its performance compares favorably even with several high-performance NLO OIMHs incorporating other d¹⁰ or stereo-chemically active lone pair (SCALP) cations, such as (C₅H₆N)SbF₂SO₄ (1.6 × KDP),¹⁹ [C₈N₂H₂₂]_1.5[Bi₂I₉] (1.29 × KDP),⁵⁴ and ZnBr(C₆H_3.5FNO₂)₂ (1.7 × KDP).⁵⁵ A detailed comparison of SHG efficiencies and bandgaps for relevant compounds is provided in Table S8 (ESI†), indicating that (PIP)·CdI₃(HDABCO) achieves this strong SHG response (2.1 × KDP) while maintaining a wide optical bandgap (4.05 eV).

Structure–property relationship analysis

To understand the phase-matching (PM) capabilities and the origin of the NLO responses, the birefringence (Δn) and electronic structures of the title compounds were investigated using density functional theory (DFT). Both (H₂DABCO)CdI₄ (orthorhombic, P2₁2₁2₁) and (PIP)·CdI₃(HDABCO) (monoclinic, Cc) are biaxial crystals. Their theoretical birefringence was estimated from the calculated principal refractive indices (Fig. 4a and b and Fig. S8, ESI†). For (H₂DABCO)CdI₄, the refractive indices follow n[001] ≈ n[100] > n[010], yielding a relatively small calculated birefringence Δn = n[001] − n[010] ≈ 0.02 at 546 nm. In contrast, (PIP)·CdI₃(HDABCO) exhibits significantly larger anisotropy, with a calculated birefringence of Δn ≈ 0.06 at 546 nm. This difference in birefringence directly impacts the phase-matching conditions. The shortest calculated wavelengths for type-I phase-matched second-harmonic generation (λ_SHG_min) are approximately 878 nm for (H₂DABCO)CdI₄ and 468 nm for (PIP)·CdI₃(HDABCO). Since the SHG wavelength corresponding to the 1064 nm fundamental laser used in experiments is 532 nm, these calculations predict that (PIP)·CdI₃(HDABCO) (λ_SHG_min ≈ 468 nm < 532 nm) should be phase-matchable, whereas (H₂DABCO)CdI₄ (λ_SHG_min ≈ 878 nm > 532 nm) should not. This theoretical prediction is fully consistent with the experimental observation of the phase-matchable behavior for (PIP)·CdI₃(HDABCO) and non-phase-matchable behavior for (H₂DABCO)CdI₄ (Fig. 3a). Analysis of the frontier molecular orbitals provides further insight. For (H₂DABCO)CdI₄ (Fig. 4c and d), the highest occupied molecular orbital (HOMO) is primarily localized on the I-5p orbitals within the [CdI₄] tetrahedron, while the lowest unoccupied molecular orbital (LUMO) is predominantly associated with the organic (H₂DABCO)²⁺ cation. This spatial separation between the HOMO and LUMO might relate to its optical properties. In (PIP)·CdI₃(HDABCO) (Fig. 4e and f), while the HOMO shows contributions influenced by the organic components and associated hydrogen bonding, the LUMO is distinctly localized on the inorganic [CdNI₃] framework. Crucially, the LUMO distribution reflects the significant distortion of the [CdNI₃] tetrahedron, exhibiting considerable electron density anisotropy. This anisotropy within the inorganic NLO-active unit likely underlies the larger birefringence and the strong, phase-matchable SHG response observed experimentally for (PIP)·CdI₃(HDABCO).

Fig. 4 Calculated birefringence and refractive index dispersion curves for the fundamental and second-harmonic light of (H₂DABCO)CdI₄ (a) and (PIP)·CdI₃(HDABCO) (b). The type-I phase matching wavelengths in different planes were evaluated based on the calculated refractive index, in which we consider the type-I phase matching conditions of n(ω) = n(2ω). HOMO (c) and LUMO (d) for (H₂DABCO)CdI₄ and the HOMO (e) and LUMO (f) for (PIP)·CdI₃(HDABCO).

Comparing the two compounds reveals significant enhancements in the optical properties for (PIP)·CdI₃(HDABCO) over (H₂DABCO)CdI₄: the calculated birefringence is approximately three times larger (Δn ≈ 0.06 vs. 0.02@546 nm), and the experimental SHG response is roughly seven times stronger (≈2.1 vs. 0.3 × KDP). This marked improvement underscores the effectiveness of modifying the inorganic coordination environment. To investigate the structure–property relationship, we calculated the distortion parameter (Δd) for the cadmium-centered coordination polyhedra. The [CdNI₃] tetrahedron in (PIP)·CdI₃(HDABCO) exhibits a significantly higher distortion (Δd = 5.4 × 10⁻³) compared to the [CdI₄] tetrahedron in (H₂DABCO)CdI₄ (Δd = 7.8 × 10⁻⁵). This difference, nearly two orders of magnitude, arises from the heteroleptic nature of the [CdNI₃] unit, which incorporates a Cd–N bond facilitated by the HDABCO ligand, contrasting with the homoleptic [CdI₄] unit. Given that the organic units PIP and H₂DABCO²⁺ are non-π-conjugated, their direct contributions to birefringence are expected to be negligible. Therefore, the substantially larger birefringence observed in (PIP)·CdI₃(HDABCO) can be primarily attributed to the pronounced distortion of its [CdNI₃] inorganic framework. This comparison highlights that engineering highly distorted heteroleptic coordination environments, such as the [CdNI₃] tetrahedron here, is a promising strategy for enhancing optical anisotropy and achieving strong, phase-matchable SHG responses in materials while potentially maintaining wide optical bandgaps.

To further understand the structural origins of the contrasting SHG responses, we analyzed the dipole moments of the inorganic units and the net dipole moments of the unit cells. The calculated dipole moment of the heteroleptic [CdNI₃] tetrahedron in (PIP)·CdI₃(HDABCO) (6.75 D) is significantly larger than that of the homoleptic [CdI₄] tetrahedron in (H₂DABCO)CdI₄ (3.10 D). More importantly, the spatial arrangement and alignment of these polar units within the crystal lattices lead to vastly different net dipole moments per unit cell: 17.45 D for (PIP)·CdI₃(HDABCO) compared to a near-zero value of 6.13 × 10⁻⁵ D for (H₂DABCO)CdI₄. This near-cancellation of the local dipoles in (H₂DABCO)CdI₄ contrasts sharply with the constructive alignment in (PIP)·CdI₃(HDABCO), resulting in much greater macroscopic polarization potential in the latter. A more effective metric for comparing materials with different unit cell sizes is the dipole moment per unit volume (dipole density). Calculating this value reveals a dramatic difference: (PIP)·CdI₃(HDABCO) exhibits a dipole density of 9.01 × 10⁻³ D Å⁻³, which is over five orders of magnitude larger than that of (H₂DABCO)CdI₄ (3.72 × 10⁻⁸ D Å⁻³) (Table S7, ESI†). This vast difference in the dipole density directly correlates with the experimentally measured SHG intensities: (PIP)·CdI₃(HDABCO) (≈2.1 × KDP) ≫ (H₂DABCO)CdI₄ (≈0.3 × KDP).

We investigated this correlation further by calculating the dipole density for several other Cd-based OIMHs (Table S9, ESI†). The results largely support this hypothesis, showing a positive trend between the dipole density and SHG response for several compounds. For instance, comparing (PIP)·CdI₃(HDABCO) (9.01 × 10⁻³ D Å⁻³, 2.1 × KDP) with (C₁₃N₃H₁₄)₂CdBr₄ (6.98 × 10⁻³ D Å⁻³, 0.98 × KDP)⁵³ illustrates this trend. However, deviations can occur if the organic cations themselves possess significant polarity or specific orientations that contribute to the overall dipole moment. For example, [(CH₃)₃NCH₂Cl]CdCl₃ exhibits a moderate SHG response (0.73 × KDP)⁵² despite a relatively low calculated dipole density originating solely from the Cd-polyhedra (6.87 × 10⁻⁴ D Å⁻³). This suggests a potential additional contribution from the polar C–Cl bond on the organic cation, oriented favorably within the structure. Extending this analysis to OIMHs based on other d¹⁰ cations (Zn²⁺ and Hg²⁺, Table S9, ESI†) further corroborates the general trend: higher dipole densities tend to correlate with stronger SHG responses. In summary, our theoretical analysis indicates that for OIMHs featuring metal-centered polyhedra and relatively simple organic components, the dipole moment per unit volume serves as a valuable indicator, positively correlating with the SHG intensity. This finding provides a useful guideline for rapidly assessing the potential SHG performance of new OIMH candidates and offers valuable theoretical insights into the structure–property relationships governing the NLO behavior in this material class.

Conclusions

In summary, we report a new organic–inorganic metal halide (OIMH), (PIP)·CdI₃(HDABCO), developed by strategically incorporating piperazinium (PIP) units and creating heteroleptic [CdNI₃] tetrahedra within the crystal structure, building upon the simpler (H₂DABCO)CdI₄ featuring homoleptic [CdI₄] units. This targeted structural modification yields a polar compound with markedly enhanced NLO properties compared to its precursor. Specifically, (PIP)·CdI₃(HDABCO) demonstrates a strong phase-matchable second-harmonic generation (SHG) response (≈2.1 × KDP, a 7-fold increase), a significantly larger birefringence suitable for phase matching (Δn ≈ 0.06@546 nm, a 3-fold increase), combined with a wide optical bandgap (4.05 eV) and good thermal stability (180 °C). The structure–property analysis pinpoints the origin of these superior NLO characteristics to the pronounced distortion of the heteroleptic [CdNI₃] tetrahedra and their effective alignment within the polar Cc space group, which maximizes macroscopic polarization. Crucially, these high-performance NLO properties are achieved using only non-π-conjugated organic cations, highlighting that heteroleptic tetrahedra engineering is a potent strategy for developing advanced OIMH NLO materials. This work validates the promise of exploring heteroleptic (e.g., N- or O-hybrid) metal-halide frameworks as a fruitful direction for discovering new, high-performance semi-organic NLO crystals.

Author contributions

Ming-Chang Wang and Mo-Fan Zhuo: conceptualization, methodology, writing – original draft, data curation, and visualization; Zhi Lin, Jia-Jia Li and Miao-Bin Xu: formal analysis; Yun-Xia Hu and Jia-Min Lian: data curation; Ke-Zhao Du and Jin Chen: writing – review & editing and supervision.

Data availability

CCDC 2435361 and 2435362 contain the supplementary crystallographic data for this paper.† Other data are available from the authors upon request. The experimental or computational data can be obtained via contacting the corresponding author.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

Our work has been supported by the National Natural Science Foundation of China (No. 22205037 and 22373014) and the Natural Science Foundation of Fujian Province (2023J01498).

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Footnote

† Electronic supplementary information (ESI) available. CCDC 2435361 and 2435362. For ESI and crystallographic data in CIF or other electronic format see DOI: https://doi.org/10.1039/d5tc01362c

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