Multi-fidelity machine learning for predicting bandgaps of nonlinear optical crystals

Nonlinear optical (NLO) materials are of great importance in modern optics and industry because of their intrinsic capability of wavelength conversion. Bandgap is a key property of NLO crystals. In recent years, machine learning (ML) has become a powerful tool to predict the bandgaps of compounds before synthesis. However, the shortage of available experimental data of NLO crystals poses a significant challenge for the exploration of new NLO materials using ML. In this work, we proposed a new multi-fidelity ML approach based on the multilevel descriptors developed by us (Z.-Y. Zhang, X. Liu, L. Shen, L. Chen and W.-H. Fang, J. Phys. Chem. C, 2021, 125, 25175-25188) and the gradient boosting regression tree algorithm. The calculated and experimental bandgaps of NLO crystals were collected as the low- and high-fidelity labels, respectively. The experimental values were predicted based on chemical compositions of crystals without prior knowledge about crystal structures. The multi-fidelity ML model overcame the performance of single-fidelity predictor. Furthermore, it was observed that less accurate predictions on the low-fidelity label may result in more accurate prediction on the high-fidelity label, at least in the present case. Using the multi-fidelity ML model with the best performance in this work, the mean absolute error on the test set of experimental bandgaps was 0.293 eV, which is smaller than that using the single-fidelity model (0.355 eV). It is far from perfect but accurate enough as an effective computational tool in the first step to discover novel NLO materials.

AIB3 IIC2 IIIQ6 VIXVII: A Thioborate Halide Family for Developing Wide Bandgap Infrared Nonlinear Materials by Coupling Planar [BS3] and Polycations

Developing high-performance infrared (IR) nonlinear optical (NLO) materials is urgent but challenging due to the competition between NLO coefficient and bandgap in one compound. Herein, by coupling NLO-active [BS3] planar units and halide-centered polycations, six new metal thioborate halides ABa3B2S6X (A = Rb, Cs; X = Cl, Br, I) composed of zero-dimensional [XBamRbn/Csn] polycations and [BS3] units, belonging to a newA I B 3 II C 2 III Q 6 VI X VII ${\mathrm{A}}^{\mathrm{I}}{\mathrm{B}}_{3}^{\mathrm{II}}{\mathrm{C}}_{2}^{\mathrm{III}}{\mathrm{Q}}_{6}^{\mathrm{VI}}{\mathrm{X}}^{\mathrm{VII}}$ family, are rationally designed and fabricated. The compounds show an interesting structural transition from Pbcn (ABa3B2S6Cl) to Cmc21 (ABa3B2S6Br and ABa3B2S6I) driven by the clamping effect of polycationic frameworks. ABa3B2S6Br and ABa3B2S6I are the first series metal thioborate halide IR NLO materials, and the introduction of [BS3] unit effectively widens the bandgap of planar unit-constructed chalcogenides. ABa3B2S6Br and ABa3B2S6I, exhibiting wide bandgaps (3.55-3.60 eV), high laser-induced damage thresholds (≈ 6 × AgGaS2), and strong SHG effects (0.5-0.6 × AgGaS2) with phase-matching behaviors, are the promising IR NLO candidates for high-power laser applications. The results enrich the chemical and structural diversity of boron chemistry and give some insights into the design of new IR NLO materials with planar units.

Ca2 Ln(BS3 )(SiS4 ) (Ln = La, Ce, and Gd): Mixed Metal Thioborate-Thiosilicates as Well-Performed Infrared Nonlinear Optical Materials

The first examples of thioborate-thiosilicates, namely Ca2 Ln(BS3 )(SiS4 ) (Ln = La, Ce, and Gd), are synthesized by rationally designed high-temperature solid-state reactions. They crystalize in the polar space group P63 mc and feature a novel three-dimensional crystal structure in which the discrete [BS3 ]3- and [SiS4 ]4- anionic groups are linked by Ca2+ and Ln3+ cations occupying the same atomic site. Remarkably, all three compounds show comprehensive properties required as promising infrared nonlinear optical materials, including phase-matchable strong second harmonic generation (SHG) responses at 2.05 µm (1.1-1.2 times that of AgGaS2 ), high laser-induced damage thresholds (7-10 times that of AgGaS2 ), wide light transmission range (0.45-11 µm), high thermal stabilities (>800 °C), and large calculated birefringence (0.126-0.149 @1064 nm), which justify the material design strategy of combining [BS3 ]3- and [SiS4 ]4- active units. Theoretical calculations suggest that their large SHG effects originate mainly from the synergy effects of the LnS6 , BS3 , and SiS4 groups. This work not only broadens the scope of research on metal chalcogenides but also provides a new synthetic route for mixed anionic thioborates.

[RbSr3X][(BS3)2] (X = Cl, Br): two salt-inclusion thioborates with large birefringence and structure transformation from centrosymmetric to asymmetric

[RbSr3X][(BS3)2] (X = Cl, Br), two salt-inclusion chalcogenides with planar [BS3] as anionic units, were obtained. Structure analysis indicates that the size effect of halogens may adjust the arrangement between the [BS3] units and further lead to the CS-to-NCS structure transformation. Experimental characterizations reveal that they have wide bandgaps (3.64-3.70 eV), large birefringence (0.136-0.144) and high LIDT (12-14 × AgGaS2). This work indicates that the thioborate family is a rich source to explore structure chemistry and promising infrared functional materials.

Ag4SnGe2S7: A Noncentrosymmetric Chalcogenide in I4-II-IV2-VI7 System with Non-Diamond-Like Structure Featuring 1D ∞[SnGe2S8]6- Infinite Chain

The I₄-II-IV₂-VI₇ metal chalcogenide system has become an attractive research system because of its excellent physical and chemical properties. Here, we report the discovery of a new Sn^II-based quaternary chalcogenide in the I₄-II-IV₂-VI₇ system, Ag₄SnGe₂S₇, with a non-diamond-like structure and crystallizing in the Cc space group. The compound is characterized by isolated pyramid-like [SnS₃] units and one-dimensional _∞[SnGe₂S₈]^6- infinite chains with two orientations formed by the corner-sharing connected [SnGe₂S₈]^6- units. It has a band gap of 2.40 eV and is insensitive to air and moisture.

Quaternary Noncentrosymmetric Rare-Earth Sulfides Ba4RE2Cd3S10 (RE = Sm, Gd, or Tb): A Joint Experimental and Theoretical Investigation

Multinary rare-earth chalcogenides with d-block transition metals have attracted considerable attention owing to their intriguing structural architectures and promising practical applications. In this work, three quaternary rare-earth sulfides, Ba₄RE₂Cd₃S₁₀ (RE = Sm, Gd, or Tb), have been obtained by the high-temperature solid-state method. These compounds are isostructural and belong to the noncentrosymmetric orthorhombic space group Cmc2₁ (No. 36). The basic structural unit contains unique two-dimensional anionic [RE₂Cd₃S₁₀]^8- layers, which are separated by Ba²⁺ cations. Remarkably, Ba₄Sm₂Cd₃S₁₀ exhibits a high second-harmonic-generation intensity (1.8 times that of AgGaS₂) and a significantly higher laser-induced damage threshold (14.3 times that of AgGaS₂), which is the first case possessing an infrared (IR) nonlinear optical (NLO) property in the quaternary AE/RE/TM/Q (AE = alkaline-earth metals; RE = rare-earth metals; TM = d-block transition metals; and Q = chalcogen) systems. Moreover, theoretical investigations of the structure-property relationship indicate that the combined action of various types of NLO-active units makes the main contribution to the SHG activity. This discovery may shed light on broadening the frontiers of IR-NLO materials.

Lanthanide thioborates, an emerging class of nonlinear optical materials, efficiently synthesized using the boron–chalcogen mixture method

Single crystals of LnBS3 (Ln = La–Nd) were synthesized by the combined boron–chalcogen mixture and molten flux growth methods. SHG measurements confirmed the expectation that LaBS3 would exhibit a strong SHG response, measured at 1.5 × KDP.

A Series of Pentanary Salt-Inclusion Chalcogenoborates Containing a B12Q12 (Q = S, Se) Cluster Exhibiting a Kleinman-Forbidden Frequency-Doubling Effect

A series of pentanary chalcogenoborates (A₃X)[InB₁₂(InQ₄)₃] (A = K, Rb, Cs; X = Cl, Br, I; Q = S, Se) were obtained by high-temperature solid-state reactions. These salt-inclusion chalcogenides crystallize in the hexagonal space group P6₃22, a type of Kleinman-forbidden noncentrosymmetric structure. Their structures feature a [InB₁₂(InQ₄)₃] open framework built by InQ₆ octahedra and InQ₄ tetrahedra consolidated B₁₂ cluster, which accomodates octahedral cavities for XA₆ units. They are second-harmonic generation active, and their optical properties were studied experimentally and theoretically. This work can evoke more interest in chalcogenoborate-based second-order nonlinear optical materials.

Ba2BS3Cl and Ba5B2S8Cl2: first alkaline-earth metal thioborate halides with [BS3] units

Ba2BS3Cl and Ba5B2S8Cl2 have been synthesized by using PbCl2 as the flux and source of halogen. The two compounds show 3D network structures built by isolated [BS3] units with different Ba-S-Cl groups. This work enriches the structural diversity of boron chemistry and provides an insight into the synthesis of thioborates.

Ultraviolet nonlinear optical crystals A3SrBi(P2O7)2 (A = K, Rb) with large second harmonic generation responses

Two non-centrosymmetric pyro-phosphates of K₃SrBi(P₂O₇)₂ and Rb₃SrBi(P₂O₇)₂ have short UV cut-off edges (∼240 nm) and large SHG responses.

Synthesis, characterization and theoretical investigation of a new chalcohalide, Ba4GaS4F3

A new fluorine-containing chalcohalide, Ba4GaS4F3, has been synthesized by conventional high-temperature solid-state reaction. The compound crystallizes in the centrosymmetric space group I41/a with a = b = 16.628 (5) Å, c = 17.139 (10) Å, Z = 16. Experimental and theoretical results confirm that Ba4GaS4F3 is a direct band gap compound with an experimental band gap of about 3.13 eV, and the band gap is mainly determined by the Ba-5p, F-2p and S-3p orbitals. What's more, different from the many newly discovered chalcohalides in the Ba3AM4Q (A = Ga, In; M = S, Se; Q = Cl, Br, I) family, Ba4GaS4F3 is the first reported compound in the Ba4AM4D3 (A = Ga, In; M = chalcogen; D = halogen) family. The results enrich the structural diversity of metal chalcohalides.

Coordinated regulation on critical physiochemical performances activated from mixed tetrahedral anionic ligands in new series of Sr6A4M4S16 (A = Ag, Cu; M = Ge, Sn) nonlinear optical materials

Coordinated regulation on physiochemical performances activated from mixed anionic ligands in a new series of IR NLO materials was systematically investigated.

Ba4(BS3S)2S4: a new thioborate with unprecedented [BS3-S] and [S4] fundamental building blocks

The first BS-S group, BS₃S, with π-conjugation composed of planar BS₃ and a non-polar covalent S–S bond.

Na3Ca4(TeO3)(PO4)3: a new noncentrosymmetric tellurite phosphate with fascinating multimember-ring architectures and intriguing nonlinear optical performance

A new functional compound Na₃Ca₄(TeO₃)(PO₄)₃ exhibits a fascinating multimember-ring configuration and intriguing nonlinear optical performance.

Na6Zn3MIII2Q9 (MIII = Ga, In; Q = S, Se): four new supertetrahedron-layered chalcogenides with unprecedented vertex-sharing T3-clusters and desirable photoluminescence performances

Four new supertetrahedron-layered chalcogenides as the first example of exhibiting vertex-sharing T₃-clusters in the known quaternary chalcogenides were discovered.

A series of pentanary inorganic supramolecular sulfides (A3X)[MB12(MS4)3] (A = K, Cs; X = Cl, Br, I; M = Ga, In, Gd) featuring B12S12 clusters

A series of multinary thiogallate- or thioindate-closo-dodecaborates synthesized by solid state reactions demonstrate second-harmonic generation behaviors.