From H12C4N2CdI4 to H11C4N2CdI3: a highly polarizable CdNI3 tetrahedron induced a sharp enhancement of second harmonic generation response and birefringence

In this study, we identify a novel class of second-order nonlinear optical (NLO) crystals, non-π-conjugated piperazine (H10C4N2, PIP) metal halides, represented by two centimeter-sized, noncentrosymmetric organic–inorganic metal halides (OIMHs), namely H12C4N2CdI4 (P212121) and H11C4N2CdI3 (Cc). H12C4N2CdI4 is the first to be prepared, and its structure contains a CdI4 tetrahedron, which led to a poor NLO performance, including a weak and non-phase-matchable second harmonic generation (SHG) response of 0.5 × KH2PO4 (KDP), a small birefringence of 0.047 @1064 nm and a narrow bandgap of 3.86 eV. Moreover, H12C4N2CdI4 is regarded as the model compound, and we further obtain H11C4N2CdI3via the replacement of CdI4 with a highly polarizable CdNI3 tetrahedron, which results in a sharp enhancement of SHG response and birefringence. H11C4N2CdI3 exhibits a promising NLO performance including 6 × KDP, 4.10 eV, Δn = 0.074 @1064 nm and phase matchability, indicating that it is the first OIMH to simultaneously exhibit strong SHG response (>5 × KDP) and a wide bandgap (>4.0 eV). Our work presents a novel direction for designing high-performance NLO crystals based on organic–inorganic halides and provides important insights into the role of the hybridized tetrahedron in enhancing the SHG response and birefringence.

To overcome this challenge, our efforts are focused on the non-p-conjugated organic moiety-Cd 2+ /Zn 2+ -I − system.In the beginning, a noncentrosymmetric OIMH, H 12 C 4 N 2 CdI 4 , has been hydrothermally prepared.But our experimental results show that this compound has a small bandgap (3.86 eV) along with a weak and non-phase-matchable SHG response (0.5 × KDP).Such an undesired NLO performance could be attributed to the high symmetry and weak anisotropy of the CdI 4 tetrahedron.To the best of our knowledge, this phenomenon is reminiscent of metal sulfates based on a tetrahedral SO

Single crystal structure determination
Single-crystal X-ray diffraction data for the title compounds were collected on an Xcalibur, Eos, Gemini diffractometer with Mo Ka radiation (l = 0.71073 Å) at 293 K and a Rigaku XtaLAB Synergy-DW dual-wavelength CCD diffractometer with Cu Ka radiation (l = 1.54184Å) at 109 K. Data reduction was performed with CrysAlisPro, and absorption correction based on the multi-scan method was applied. 51The structures of H 12 C 4 N 2 CdI 4 and H 11 C 4 N 2 CdI 3 were determined by the direct methods and rened by full-matrix least-squares tting on F 2 using SHELXL-2014. 52All of the non-hydrogen atoms were rened with anisotropic thermal parameters.The structure was checked for missing symmetry elements using PLATON, and none were found. 53The Flack parameters rened for H 12 C 4 N 2 CdI 4 and H 11 C 4 N 2 CdI 3 are 0.45 (12) and −0.01(2), respectively, indicating the correctness of their absolute structures.In addition, twinning was observed in H 12 C 4 N 2 CdI 4 and H 11 C 4 N 2 CdI 3 , and the twin laws of these compounds were (−1.0, 0.0, 0.0, 0.0, −1.0, 0.0, 0.0, 0.0, −1.0) and (−1.0, 0.0, 0.0, 0.0, −1.0, 0.0, 0.0, 0.0, −1.0), respectively.Crystallographic data and structural renements of the compounds are listed in Tables S2-S6.†

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

Thermal analysis
Thermogravimetric analysis (TGA) was 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) spectrum was recorded on a Thermo Fisher Nicolet 5700 FT-IR spectrometer in the form of KBr pellets in the range from 4000 to 400 cm −1 .
The ultraviolet-visible-infrared (UV-vis-IR) spectrum in the range of 200-800 nm was recorded on a PerkinElmer Lambda 750 UV-vis-NIR spectrophotometer.The reectance spectrum was converted into an absorption spectrum by using the Kubelka-Munk function. 54econd 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. 55Crystalline H 12 C 4 N 2 CdI 4 and H 11 C 4 N 2 CdI 3 samples were sieved into distinct particle-size ranges (50-70, 70-100, 100-140, 140-200, 200-250 and 250-325 mm).Sieved KH 2 PO 4 (KDP) samples in the same particle-size ranges were used as references.

Elemental analysis
The elemental content was measured on a Vario EL Cube elemental analyzer from Elementar Analysensysteme GmbH, Germany.The combustion temperature was 800 °C (Table S7 †).

Energy-dispersive X-ray spectroscopy
Microprobe elemental analyses were performed and the elemental distribution maps were obtained on a eld-emission scanning electron microscope (Phenom LE) equipped with an energy-dispersive X-ray spectroscope (EDS, Phenom LE).

Computational method
The electronic structures and optical properties were obtained using a plane-wave pseudopotential method within density functional theory (DFT) implemented in the total energy code CASTEP. 56,57For the exchange and correlation functional, we chose Perdew-Burke-Ernzerhof (PBE) in the generalized gradient approximation (GGA). 58The interactions between the ionic cores and the electrons were described by the normconserving pseudopotential. 59The following orbital electrons were treated as valence electrons: I-5s 2 5p 5 , Cd-4s24p 6 5s 2 , H-1s 1 , C-2s 2 2p 2 and N-2s 2 2p 3 .The numbers of plane waves included in the basis sets were determined at 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 2 × 4 × 2 for H 12 C 4 N 2 CdI 4 and H 11 C 4 N 2 CdI 3 , respectively.Aer the principal axis transformation, the k-point sampling of H 11 C 4 N 2 CdI 3 changes to 2 × 3 × 2 when the k-point separation is 0.04 Å −1 .The other parameters and convergent criteria were the default values of the CASTEP code. 56,57he calculations of second-order NLO susceptibilities were based on length-gauge formalism within the independent particle approximation. 60,61The second-order NLO susceptibility can be expressed as where the subscript L denotes the length gauge, and c abc inter, c abc intra and c abc mod give the contributions to c abc L from interband processes, intraband processes, and the modulation of interband terms by intraband terms, respectively.The convergence test of the SHG coefficient upon k-point sampling and empty bands with H 11 C 4 N 2 CdI 3 as an example was carried out (Table S9 †), and we found that the SHG coefficient gradually converges when the k-point separation is not more than 0.04 Å −1 (2 × 3 × 2) and the quantity of the empty bands is not less than 2 times that of valence bands (280 bands).So the choice of k-point sampling and the empty band number during the optical property calculation is reasonable.

Results and discussion
In order to investigate the differences in the synthesis conditions of H ] layer (Fig. 1c), parallel to the ac plane.These pseudo-layers stack along the b direction to form the entire 3D network of H 12 C 4 N 2 CdI 4 (Fig. 1d).H 11 C 4 N 2 CdI 3 crystallizes in the polar space group Cc (No. 9), with an asymmetric unit including one protonated-piperazine group, one Cd, and three I atoms (Fig. 2a).In the chair-shaped  2a).Neighboring H 11 C 4 N 2 CdI 3 molecules are interconnected in a quasi-1D zigzag chain along the cdirection, which is further arranged in quasi-2D layers parallel to the bc plane (Fig. 2b).These quasi-2D layers are stacked upward along the a-axis, resulting in the structure of H 11 C 4 N 2 CdI 3 (Fig. 2c).

Structural comparison
It is interesting to compare the structural differences of the title compounds to further understand why H 11 C 4 N 2 CdI 3 is a polar compound while H 12 C 4 N 2 CdI 4 is not.Firstly, we believe that the distinct coordination environments of Cd 2+ ions play a key role.In     3a).These values are higher than those of previously reported NLO organic-inorganic halides, including (H 7 C 3 N 6 )(H 6 C 3 N 6 )HgCl 3 (225 °C), 16 (CH 3 NH 3 )GeBr 3 (500 K), 30 67 and (CH 3 NH 3 )GeBr 3 (2.91 eV). 30

SHG properties
Since both H 12 C 4 N 2 CdI 4 and H 11 C 4 N 2 CdI 3 are noncentrosymmetric, their SHG effects are measured according to the method of Kurtz and Perry. 55For H 12 C 4 N 2 CdI 4 , as shown in Fig. S5, † the measurement result reveals unwanted non-phase matchable NLO properties, in which the SHG intensity of the crystalline samples exhibits an initial increase, followed by a subsequent decrease as the particle size increased.The maximum value, which is approximately 90 mm, is observed to be about 0.5 times that of KH 2 PO 4 (KDP).This phenomenon is reminiscent of the behavior exhibited by traditional phosphate and sulfate compounds, where the CdI 4 tetrahedron exhibits minimal distortion, and its optical anisotropy is mutually canceled within the P2 1 2 1 2 1 space group.Conversely, as shown in Fig. 3c and d, the SHG intensity gradually increased and saturated with increasing particle size, indicating that H 11 C 4 N 2 CdI 3 exhibits phase-matching NLO properties.The SHG effect of H 11 C 4 N 2 CdI 3 is about six times that of KDP, measured at a particle size of 150-210 mm.
It is interesting to investigate the structure-property relationship among the title compounds and formerly reported Cdcentered NLO OIMHs, such as [(CH 3 ) 3 NCH 2 Cl]CdCl 3 , 46   Herein, we use the calculated birefringence (Dn) and phase matching wavelength based on the relations between the wavelength and refractive index under both fundamental and harmonic conditions (Fig. 6).Both of them are biaxial crystals with three principal optical axes, i.e., X, Y, and Z.For the orthorhombic crystal H 12 C 4 N 2 CdI 4 , the calculated refractive index curves aer structure optimization show the order of n c > n a > n b in the low-frequency range, and to satisfy the biaxial condition n X > n Y > n Z , the transformation of c / X , a / Y , and b / Z is performed and a correct order of n X > n Y > n Z is shown in Fig. 6a.For the monoclinic crystal H 11 C 4 N 2 CdI 3 , the crystallographic axes and principal dielectric axes are not consistent with each other in the ac plane, so the principal dielectric axes in the ac plane must be determined aer structure optimization and before the optical calculation.According to the principal axis transformation method in our previous work, the rotation angle q between the Fig. 4 SHG response and energy bandgap of representative NLO organic-inorganic halides.Red ball: compound containing both a pconjugated organic group and SCALP cation, red triangle: compound containing a p-conjugated organic group but without a SCALP cation, blue ball: compound without a p-conjugated organic group but with a SCALP cation, blue triangle: other compounds.original coordinate axes (i.e.ykb, zkc) and the principal dielectric axes is found to be 25.179°. 70Aer the principal axis transformation and based on the principal dielectric coordinate system, the calculated refractive index curves show an order of n X > n Y > n Z and satisfy the biaxial condition.S12.† For H 12 C 4 N 2 CdI 4 , it has three non-zero independent SHG tensors with the same value of 0.12 pm V −1 , which is about 0.3 times that of KDP (0.39 pm V −1 ), being consistent with the experimental value (0.5 × KDP).More importantly, for H 11 C 4 N 2 CdI 3 , its largest independent SHG tensor is d 11 = 2.74 pm V −1 , about 7 times larger than that of KDP, which is agreement with the experimental result (6 × KDP).To explore the origin of the better SHG effect of H 11 C 4 N 2 CdI 3 , we further calculated the SHG density distribution of the d 11 tensor (Fig. 7).In the VB, the main source of the SHG effect is the I-5p states.In addition, there are small contributions from the Cd 5s states and the N-2p states from the Cd-N bond.The maximum source in the CB is the Cd-5s orbitals, followed by the I-5s orbitals and the N-2p orbitals in the Cd-N bond.Furthermore, the contributions of each unit to the SHG response are calculated, and the CdNI 3 tetrahedron has a contribution as high as 97.96%.Therefore, we believe that the distorted CdNI 3 tetrahedron is the primary origin of the outstanding SHG effect of H 11 C 4 N 2 CdI 3 .

Conclusions
In H 11 C 4 N 2 -ring, C-N and C-C distances are 1.49(2)-1.532(17)Å and 1.462(17)-1.509(19)Å, respectively, and the bond angles are in the range of 108.7(11)-114.5(9)°,which are consistent with those of previously reported piperazine compounds. 62,63Each Cd 2+ cation connects with one N atom and three I atoms to form a N-hybrid polyhedron, a CdNI 3 tetrahedron.The length of Cd-N (2.300(11) Å) is smaller than those of Cd-I (2.7393(12)-2.7518(11)Å), and the bond angles of N-Cd-I and I-Cd-I are 100.8(3)-104.0(3)°and112.80(3)-117.07(4)°,respectively.Furthermore, one H 11 C 4 N 2 -ring is connected with one CdNI 3 tetrahedron via the corner-sharing of N atoms, forming a H 11 -C 4 N 2 CdI 3 molecule (Fig. H 12 C 4 N 2 CdI 4 , the molar ratio of Cd to I is 4, which results in each Cd 2+ ion being surrounded by only four I atoms, forming a nearly undistorted CdI 4 tetrahedron.In contrast, in H 11 C 4 N 2 CdI 3 , Cd: I is 3, which enables the N atom on the H 10 C 4 N 2 unit to participate in Cd 2+ coordination, forming a distorted CdNI 3 tetrahedron.Secondly, the calculated dipole moments of the CdI 4 and CdNI 3 units are 3.27 and 5.94 D (Table S10 †), respectively, indicating that CdNI 3 exhibits more anisotropy, favoring the formation of a polar structure.Finally,

Fig. 1
Fig. 1 Views of the structures of the CdI 4 tetrahedron (a), the chair shaped H 2 PIP 2+ cation (b), the quasi-2D H 12 C 2 N 4 CdI 4 layer along the b-axis (c) and H 12 C 2 N 4 CdI 4 along the a-axis (d).

Fig. 2
Fig. 2 Views of the structures of the H 11 C 4 N 2 CdI 3 molecule (a), the quasi-2D H 11 C 4 N 2 CdI 3 layer along the a-axis (b) and H 11 C 4 N 2 CdI 3 along the b-axis.
conjugated organic groups are sp3 hybridized, which makes them more likely to form coordination bonds with Cd 2+ cations in nonp-conjugated OIMHs.Therefore, many of them feature an O/Nhybridized polyhedron.In (H 10 C 4 NO) 2 Cd 2 Cl 6 , neighbouring CdCl 6 and CdCl 4 O 2 octahedra are bridged into a 1D chain via edge-sharing.L/D-C 12 H 20 N 6 O 4 Cd 2 Cl 5 contains a CdOCl 4 trigonal bipyramid, and each pair of them is formed into a Cd 2 O 2 Cl 6 dimer via edge-sharing.Importantly, these Cd-O-Cl polyhedra feature larger dipole moments (1.14-5.03D) that a CdCl 6 octahedron.However, for example, the undesired arrangement of CdOCl 4 groups leads to a small net dipole moment (1.19-1.20 D) and weak SHG response in L/D-C 12 H 20 N 6 O 4 Cd 2 Cl 5 (∼0.2 × KDP).Most importantly, in this work, H 12 C 4 N 2 CdI 4 and H 11 C 4 N 2 CdI 3 involve CdI 4 (3.27D) and CdNI 3 (5.94D) tetrahedra, respectively, in which the polarization magnitudes of CdNI 3 tetrahedra are mutually superimposed along the a-and c-axes resulting in a large net dipole moment of H 11 C 4 N 2 CdI 3 (17.09D) (Table S10 †).Accordingly, compared with previously reported Cd-centered OIMHs and H 12 C 4 N 2 CdI 4 , H 11 C 4 N 2 CdI 3 features a far large SHG response (6 × KDP).Besides, importantly, compared with recently reported NLO OIMHs with SCALP or other d 10 -TM cations such as (C 4 H 10 NO) PbBr 3 (0.81 × KDP), 65 [C(NH 2 ) 3 ]SbF 4 (2 × KDP), 32 [N(CH 3 ) 4 ] HgBrI 2 (4.5 × KDP), 68 (H 7 C 3 N 6 )(H 6 C 3 N 6 )HgCl 3 (5.8× KDP), 16 a-(CN 3 H 6 ) 3 Cu 2 I 5 (1.8 × KDP), 19 (CH 3 NH 3 )GeBr 3 (5.3× KDP) 30 and (C 20 H 20 P)CuCl 2 (1.1 × KDP), 69 H 11 C 4 N 2 CdI 3 has a stronger SHG response (6 × KDP).Furthermore, the SHG responses and bandgaps of selected organic-inorganic halides are summarized in Fig. 4 and Table S11 † (the relevant references are provided in the ESI †).Unlike other NLO crystals, H 11 C 4 N 2 CdI 3 simultaneously exhibits both a strong SHG effect (>5 × KDP) and wide bandgap (>4.0 eV), which makes it promising as a high-performance ultraviolet NLO crystal.Structure-property relationship analysis The calculated bandgaps of H 12 C 4 N 2 CdI 4 and H 11 C 4 N 2 CdI 3 are provided in Fig. S6, † indicating that they are direct bandgap compounds with values of 3.895 and 4.102 eV for H 12 C 4 N 2 CdI 4 and H 11 C 4 N 2 CdI 3 , respectively, being comparable to the results from measurement (3.86 and 4.10 eV).Partial density of states (PDOS) of H 12 C 4 N 2 CdI 4 and H 11 C 4 N 2 CdI 3 is presented in Fig. 5a and b, respectively.The PDOS plots of both compounds are similar.The contribution to the valence band maximum (VBM) mainly comes from the I-p orbitals, as well as a small portion of the Cd-p orbitals.For the conduction band minimum (CBM), the contribution sizes rank in the order of Cd-s, I-p, and I-s orbitals.It is worth noting that in H 11 C 4 N 2 CdI 3 , a small amount of N-p orbitals also contributes to the VBM, which is consistent with the existence of the Cd-N bond.Therefore, we believe that the bandgaps of H 12 C 4 N 2 CdI 4 and H 11 C 4 N 2 CdI 3 are determined by the Cd-centered tetrahedra.

Fig. 5
Fig. 4 SHG response and energy bandgap of representative NLO organic-inorganic halides.Red ball: compound containing both a pconjugated organic group and SCALP cation, red triangle: compound containing a p-conjugated organic group but without a SCALP cation, blue ball: compound without a p-conjugated organic group but with a SCALP cation, blue triangle: other compounds.Fig. 5 The density of states of H 12 C 4 N 2 CdI 4 and H 11 C 4 N 2 CdI 3 (b).

Fig. 6
Fig. 6 Refractive index dispersion curves for fundamental and second-harmonic light of H 12 C 4 N 2 CdI 4 (a) and H 11 C 4 N 2 CdI 3 (b), as well as the calculated birefringence (c).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 condition of n(u) = n(2u).
3 × KDP) but a small bandgap (2.91 eV).There are also similar cases to C 4 H 9 NOBiBr 7 (2.2 × urea, 2.67 eV) and (C 6 H 5 (CH 2 ) 4 NH 3 ) 4 BiI 7 $H 2 O (1.3 × AGS, 2.29 eV). 41On the other hand, many non-p-conjugated OIMHs with d 10 -TM cations, such as (C 4 H 10 NO) 2 Cd 2 Cl 6 , 42 (L/D-C 10 H 20 N 2 O 4 ) 2 Cd 5 Cl 12 , 43 L/D-C 6 H 10 N 3 O 2 ZnBr 3 , 44 [C 5 H 14 NO]CdCl 3 , 45 L/D-C 12 H 20 N 6 O 4 Cd 2 Cl 5 , 49SO 3 F,47Na 10 Cd(NO 3 ) 4 (SO 3 S) 4 ,48Ba(NH 2 SO 3 ) 2 ,49Ba(SO 3 CH 3 ) 2 , 50 and so on.Hence, furthermore, H 12 C 4 N 2 CdI 4 is regarded as the model compound, and we consider that the coordination of H 10 C 4 N 2 with a Cd 2+ cation could result in the partial substitution of I − anions in the CdI 4 tetrahedron, forming a polarizable Cd-I-N unit, which could enhance the SHG response and birefringence in new OIMHs.Additionally, we also hope that new compound involves a smaller number of I − anions in order to exhibit a wider bandgap.Therefore, a novel OIMH, namely H 11 C 4 N 2 CdI 3 , is prepared via regulating the synthetic conditions of H 12 C 4 N 2 CdI 4 (a lower concentration of I − anions in the reaction system).H 11 C 4 N 2 CdI 3 contains a distorted CdNI 3 tetrahedron and demonstrates superior NLO performance in comparison to H 12 C 4 N 2 CdI 4 .Specically, H 11 C 4 N 2 CdI 3 exhibits 4 2− unit.And in metal sulfates, one effective route to overcome this problem is to partially substitute O atoms in SO 4 2− , as seen in 12 C 4 N 3 CdI 4 and H 11 C 4 N 2 CdI 3 , we conducted multiple sets of control experiments as shown in Table S1.† Several observations were made: (1) the molar ratio of Cd to H 10 C 4 N 2 had no impact on whether H 12 C 4 N 3 CdI 4 or H 11 C 4 N 2 CdI 3 was produced as the nal product; (2) changes in temperature had minimal effects on the synthesis of H 12 C 4 N 3 CdI 4 ; (3) the ratio of HI to H 2 O was the determining factor in the preparation of H 12 C 4 N 3 CdI 4 or H 11 C 4 N 2 CdI 3 .We hypothesize that a lower HI : H 2 O ratio can reduce the concentration of iodide ions in the reaction system, thus facilitating direct coordination bonding between Cd 2+ cations and H 10 C 4 N 2 , resulting in the formation of H 11 C 4 N 2 CdI 3 ; (4) in the preparation process of H 11 C 4 N 2 CdI 3 , Y 2 O 3 is essential and cannot be omitted.However, indeed, the specic role of Y 2 O 3 in the synthesis process of H 11 C 4 N 2 CdI 3 is currently unclear due to limitations in our current technological means.Their measured powder XRD patterns are consistent with those of simulated data, conrming the phase purity (Fig. S1 †).The EDS results of the Cd : I ratios are 1.0 : 4.10 and 1.0 : 2.97 for H 12 C 4 N 2 CdI 4 and H 11 C 4 N 2 CdI 3 , respectively (Fig. S2 †).In addition, elemental analysis of C, N, and H atoms is provided in Table S6 † with weight%: C 6.77, H 1.63, and N 4.02 for H 12 C 4 N 2 CdI 4 ; C 8.30, H 1.85, and N 4.53 for H 11 C 4 N 2 CdI 3 (Table S7 †).Both of them are in good agreement with the crystal structure solution.
Table S10 †).As a result, although H 12 C 4 N 2 CdI 4 has a noncentrosymmetric structure, it is nonpolar, and its net dipole moment in a unit cell is zero.However, in H 11C 4 N 2 CdI 3 , the dipole moments of CdNI 3 tetrahedra cancel out each other only along the b axis, while they add up along the a and c axes, resulting in a large net dipole moment of about 17.09 D (Table S10 †).Therefore, H 11 C 4 N 2 CdI 3 is a noncentrosymmetric and polar compound.Thermogravimetric analysis (TGA) shows the good thermal stabilities of H 12 C 4 N 2 CdI 4 and H 11 C 4 N 2 CdI 3 , at around 300 °C (Fig. The shortest wavelengths for type-I phase matching are approximately 592 nm and 466 nm for H 12 C 4 N 2 CdI 4 and H 11 C 4 N 2 CdI that of H 12 C 4 N 2 CdI 4 (0.052 @546 nm, 0.047 @1064 nm).Since piperazine is a non-p conjugated group with negligible contribution of birefringence, the larger birefringence of H 11 C 4 N 2 CdI 3 can be attributed to the microscopic asymmetry and well-arranged structure of the CdNI 3 group, exemplied by the dipole moment calculation (Table S10 †).Consequently, from H 12 C 4 N 2 CdI 4 to H 11 C 4 N 2 CdI 3 , the polarizable CdNI 3 tetrahedron induces an enlarged birefringence, ensuring phase-matching performance of H 11 C 4 N 2 CdI 3 .We further calculate the theoretical SHG coefficients of H 12 C 4 N 2 CdI 4 and H 11 C 4 N 2 CdI 3 , as shown in Table 3, respectively.This implies that under 1064 nm laser radiation, H 11 C 4 N 2 CdI 3 can achieve type-I phase matching, while H 12 C 4 N 2 CdI 4 cannot.These ndings are consistent with our SHG measurements.These calculated birefringences have been obtained from the refractive index difference (n Xn Z ) (Fig.6c), in which H 11 C 4 N 2 CdI 3 possesses a larger birefringence of (0.090 @546 nm, 0.074 @1064 nm) than summary, we have discovered two new organic-inorganic metal halides (OIMHs), H 12 C 4 N 2 CdI 4 and H 11 C 4 N 2 CdI 3 , by combining the protonated pyrazine cation with d 10 -TM-halide tetrahedra.The NLO properties of non-p-conjugated piperazine compounds are studied for the rst time.Despite being a noncentrosymmetric compound, H 12 C 4 N 2 CdI 4 exhibits a weak and non-phase-matchable SHG effect.In contrast, H 11 C 4 N 2 CdI 3 is a polar compound with excellent NLO performance, including a strong SHG response (6 × KDP), a wide bandgap (4.10 eV), large birefringence (0.074 @1064 nm) for phasematching requirement, good thermal stability (300 °C), and a suitable crystal growth habit.The structure-property relationship analysis indicates that the highly polarizable Nhybridized CdNI 3 tetrahedron in the H 11 C 4 N 2 CdI 3 structure is the primary cause of the birefringence and SHG effect.Our work provides new insights for exploring semi-organic NLO crystals that do not contain p-conjugated organic components.Further exploration of OIMHs containing N-or O-hybridized metalhalide polyhedra is currently underway.