Second-order Jahn-Teller Effect Research Articles

On the Aromaticity of Puckered Ions C4H42+ and B4H42−: Deciphering the Origin of Nonplanarity

AbstractDensity functional theory and Møller‐Plesset perturbation theory techniques have been employed to delve into the nonplanarity and aromaticity of C4H42+and B4H42−. C4H42+ is a well‐known two‐electron aromatic system with puckered four‐membered ring, while analogues of B4H42− (two‐electron aromatic system with puckered four‐membered ring) have been recently synthesized and their aromatic behavior has been argued. The present work aims at presenting a computational insight into the origin of nonplanarity of C4H42+ and B4H42−, as well as characterizing their aromatic behavior given that aromaticity in a nonplanar structure is not so common. Our results suggest an important role of the second‐order Jahn‐Teller effect (SOJTE) underlying the nonplanarity of C4H42+ and B4H42−. The aromatic behavior of the studied systems has been characterized by various parameters including the nucleus‐independent chemical shift (NICS) scan, σ‐π energy separation analysis, energy decomposition analysis, study of magnetic susceptibility, and bond‐order analysis.

Structure, Lithium-Ion Conductivity Coupled with Second-Order Jahn–Teller Effect, and Electrochemical Stability of Sr-Based Perovskite-Type Solid Electrolytes

Structure, Lithium-Ion Conductivity Coupled with Second-Order Jahn–Teller Effect, and Electrochemical Stability of Sr-Based Perovskite-Type Solid Electrolytes

Atomic Substitution to Tune ScO6 Distortion in Ba2MSc2(BO3)4 (M = Na, K, Ba) to Acquire a Large Birefringence.

Replacing alkali metals (K, Na atoms) by an alkaline-earth metal (Ba atom), α-Ba3Sc2(BO3)4 (high-temperature phase) is successfully obtained by a molten salt method, taking Ba2K1.6Na0.4Sc2(BO3)4 as the parent template. Although both of them exhibit similar layered structures composed of ScO6 and BO3 units, α-Ba3Sc2(BO3)4 shows largely distorted ScO6 octahedra (Δd = 0.56) forced by the uniform tension of a larger space effect from BaO12 polyhedrons, rather than regular ScO6 octahedra like in Ba2K1.6Na0.4Sc2(BO3)4. Experimental measurements and calculated analyses elucidate that distorted ScO6 octahedra in α-Ba3Sc2(BO3)4, displaying a second-order Jahn-Teller (SOJT) effect, enlarge the experimental birefringence up to 0.14@550 nm, while Ba2K1.6Na0.4Sc2(BO3)4 with regular ScO6 octahedra only shows Δn = 0.11 under the same condition. In addition, other optical and thermal properties of the two title compounds were characterized. The experimental results indicate that Ba2K1.6Na0.4Sc2(BO3)4 and α-Ba3Sc2(BO3)4 are promising birefringent materials.

Chemical Switching of Ferroaxial and Nonferroaxial Structures Based on Second-Order Jahn–Teller Activity in (Na,K)2Hf(BO3)2

Ferroaxial order, which is characterized by a vortex of electric dipole moments, is attracting more attention in terms of a new category of ferroic order. Here we propose that the disodium hafnium borate, Na2Hf(BO3)2, shows ferroaxial order that is stabilized by the second-order Jahn–Teller (SOJT) effect. Furthermore, the dipotassium hafnium borate, K2Hf(BO3)2, the synthesis of which has never been reported previously, is predicted to have a nonferroaxial ground state from the perspective of the SOJT effect. This prediction is demonstrated through our structural refinements on polycrystalline samples and our first-principles calculations with representation theory. This study offers a chemical perspective for developing new ferroaxial materials and controlling their ferroaxial order.

Chemical Aspect of Displacive-Type Ferroaxial Phase Transition from Perspective of Second-Order Jahn–Teller Effect: NASICON Systems as an Example

Ferroaxial order, characterized by a rotational arrangement of electric dipoles, attracts increasing attention in terms of a new family of ferroic orders. However, there has been no chemical guideline for exploring crystalline materials showing ferroaxial order, namely ferroaxial materials. Here, we present a chemical guideline grounded in staggered polyhedral connectivity, which we propose as a structural prerequisite for ferroaxial order, and the second-order Jahn-Teller (SOJT) theory extended from molecular orbitals to electronic band structures. Na-superionic conductors (NASICON) including NaM2(PO4)3 (M = early-transition or post-transition metal) are identified as potential ferroaxial materials because of their staggered structures composed of MO6 octahedra and PO4 tetrahedra. However, ferroaxial phase transitions hardly occur in some of the NASICON systems, which offers a platform to uncover a hidden factor playing an important role in driving this system into ferroaxial states. Our first-principles calculations demonstrate that a ferroaxial phase transition in NASICON systems occurs only when SOJT interaction is symmetrically allowed, that is, energy-lowering chemical bonds are formed as a consequence of the distortion. Our proposals would be not limited to NASICON systems but applicable to a variety of compounds and provide new insight into the exploration of displacive-type ferroaxial materials.

Second-order Jahn-Teller effect induced high-temperature ferroelectricity in two-dimensional NbO2X (X = I, Br).

Based on the first-principles calculations, we investigated the ferroelectric properties of two-dimensional (2D) materials NbO2X (X = I, Br). Our cleavage energy analysis shows that exfoliating one NbO2I monolayer from its existing bulk counterpart is feasible. The phonon spectrum and molecular dynamics simulations confirm the dynamic and thermal stability of the monolayer structures for both NbO2I and NbO2Br. Total energy calculations show that the ferroelectric phase is the ground state for both materials, with the calculated in-plane ferroelectric polarizations being 384.5 pC m-1 and 375.2 pC m-1 for monolayers NbO2I and NbO2Br, respectively. Moreover, the intrinsic Curie temperature TC of monolayer NbO2I (NbO2Br) is as high as 1700 K (1500 K) from Monte Carlo simulation. Furthermore, with the orbital selective external potential method, the origin of ferroelectricity in NbO2X is revealed as the second-order Jahn-Teller effect. Our findings suggest that monolayers NbO2I and NbO2Br are promising candidate materials for practical ferroelectric applications.

Growth and Characterization of a Nonlinear Optical Crystal Cd3Te2WO10 Decorated by WO4 Tetrahedra Showing a Large Band Gap

A noncentrosymmetric nonlinear optical (NLO) crystal Cd3Te2WO10 with a large band gap has been synthesized and grown using the high-temperature solution method with TeO2 as a flux. Cd3Te2WO10, crystallized in P21, contains two classes of d0 W6+ and lone-pair Te4+ cations holding asymmetric coordination environments which are associated with the second-order Jahn–Teller effect. Importantly, it has a large band gap of 4.28 eV, which is profitable for high-power application, and wide transparency region of 0.29–5.63 μm, especially in 1–5 μm possessing tremendous transmittance that exceeded 80% and fully covering the 3–5 μm range, which is one of the vital atmospheric windows, and a good Raman performance that arises from the WO4 polyhedra. In addition, Cd3Te2WO10 features phase-matching behavior owing to large birefringence and considerable second-harmonic generation response equivalent to 1.1 times that of KH2PO4, which is further elucidated by the theoretical calculation. Therefore, our experimental results demonstrate that Cd3Te2WO10 could be used as a promising functional NLO crystal.

An Overview of Basis Set Effects for Diatomic Boron Nitride Compounds (B2N(∓,0)): A Quantum Symmetry Breaking

The symmetry breaking (SB) of B2 not only exhibits an energy barrier for ionic or neutral forms dependent on various basis sets but it also exhibits a few SBs due to the asymmetry stretching and bending mode interactions. SB obeys the mechanical quantum theorem among discrete symmetries and their connection to the spin statistics in physical sciences. In this investigation, the unusual amount of energy barrier of SBs appeared upon the orbit–orbit coupling of BNB (both radical and ions) between transition states and the ground state. Our goal in this study is to understand the difference among the electromagnetic structures of the (B2N(∓,0)) variants due to effects of various basis sets and methods and also the quantum symmetry breaking phenomenon. In the D∞h point group of (B2N(∓,0)) variants, the unpaired electron is delocalized, while in the asymmetric C∞v point group, it is localized on either one of the B atoms. Structures with broken symmetry, C∞v, can be stable by interacting with the D∞h point group. In viewpoints of quantum chemistry, the second-order Jahn–Teller effect permits the unpaired electron to localize on boron atom, rather than being delocalized. In this study, we observed that the energy barrier of SB for BNB increases by post HF methods.

A sodium tantalum phosphate with a noncentrosymmetric structure: Na5Ta8P5O35

A sodium tantalum phosphate Na5Ta8P5O35 has been successfully obtained by spontaneous crystallization in high temperature solution. It belongs to the noncentrosymmetric R32 space group with a ​= ​8.895 (2) Å, c ​= ​29.992 (12) Å and Z ​= ​3. The structure resembles those of tungsten bronzes with main building blocks of the [Ta6O27] unit composed of 2 ​× ​3 corner-sharing Ta1O6 octahedra. [Ta6O27] units are joined by two P1O4 tetrahedra and two Ta2O6 octahedra forming a [Ta8P2O29]∞ layer in the bc plane. Those layers are further connected via P2O4 groups along the c direction leaving triangular and pentagonal tunnels in the 3-dimensional framework. Both sodium atoms reside in the pentagonal tunnel with Na1 (9d) site partially occupied (2/3). The Ta5+ ions show second-order Jahn-Teller effects with TaO6 distortions that are favorable to obtain large hyperpolarizabilities. Powder Kurtz-Perry test and reflectance spectroscopy studies reveal that it exhibits moderate second harmonic effect of about 0.5 ​× ​KH2PO4 and an optical band gap of 3.93 ​eV.

Organic-Inorganic Hybrid Noncentrosymmetric (Morpholinium)2Cd2Cl6 Single Crystals: Synthesis, Nonlinear Optical Properties, and Stability.

To design nonlinear optical (NLO) materials, we focused on combinations of d10 metal cation (Cd2+)-based chloride and morpholine molecules to form organic-inorganic hybrids. The O of morpholine containing lone-pair electrons can be integrated with Cd2+ by a ligand-to-metal charge transfer (LMCT) strategy to build acentric structures benefiting from the second-order Jahn-Teller effect. Introduction of the high-electronegativity chlorine can make polyhedrons of acentric crystals more distorted and conducive to a strong second harmonic generation (SHG) response. Therefore, (Morpholinium)2Cd2Cl6 crystals were constructed and synthesized by a solvent evaporation method. (Morpholinium)2Cd2Cl6 belongs to the orthorhombic P212121 space group and shows a one-dimensional (1D) structure with distorted [CdCl6] and [CdCl4O2] octahedrons. The short cutoff edge of (Morpholinium)2Cd2Cl6 was determined to be about 230 nm. The SHG response of (Morpholinium)2Cd2Cl6 exhibited an intensity of approximately 0.73 × KDP as estimated by the powder second harmonic generation technique. Furthermore, related theoretical calculations were performed to study the relationship of the band structure, refractive anisotropy, electronic state, and nonlinear optical response. Besides, (Morpholinium)2Cd2Cl6 showed relatively good thermal stability. This work can serve as a guide for the design and synthesis of new large NLO hybrid crystals with d10 transition metals.

Regulating Pseudo-Jahn–Teller Effect and Superstructure in Layered Cathode Materials for Reversible Alkali-Ion Intercalation

The Jahn-Teller effect (JTE) is one of the most important determinators of how much stress layered cathode materials undergo during charge and discharge; however, many reports have shown that traces of superstructure exist in pristine layered materials and irreversible phase transitions occur even after eliminating the JTE. A careful consideration of the energy of cationic distortion using a Taylor expansion indicated that second-order JTE (pseudo-JTE) is more widespread than the aforementioned JTE because of the various bonding states that occur between bonding and antibonding molecular orbitals in transition-metal octahedra. As a model case, a P2-type Mn-rich cathode (Na3/4MnO2) was investigated in detail. MnO6 octahedra are well known to undergo either elongation or contraction in a specific direction due to JTE. Here, the substitution of Li for Mn (Na3/4(Li1/4Mn3/4)O2) helped to oxidize Mn3+ to Mn4+ suppressing JTE; however, the MnO6 octahedra remained asymmetric with a clear trace of the superstructure. With various advanced analyses, we disclose the pseudo-JTE as a general reason for the asymmetric distortions of the MnO6 octahedra. These distortions lead to the significant electrochemical degradation of Na3/4Li1/4Mn3/4O2. The suppression of the pseudo-JTE modulates phase transition behaviors during Na intercalation/deintercalation and thereby improves all of the electrochemical properties. The insight obtained by coupling a theoretical background for the pseudo-JTE with verified layered cathode material lattice changes implies that many previous approaches can be rationalized by regulating pseudo-JTE. This suggests that the pseudo-JTE should be thought more important than the well-known JTE for layered cathode materials.

The inversion of tetrahedral p-block element compounds: general trends and the relation to the second-order Jahn-Teller effect.

The tetrahedron is the primary structural motif among the p-block elements and determines the architecture of our bio- and geosphere. However, a broad understanding of the configurational inversion of tetrahedral compounds is missing. Here, we report over 250 energies (DLPNO-CCSD(T)) for square planar inversion of third- and fourth-period element species of groups 13, 14, and 15. Surprisingly low inversion barriers are identified for compounds of industrial relevance (e.g., ≈100 kJ mol−1 for Al(OH)4−). More fundamentally, the second-order Jahn–Teller theorem is disclosed as suitable to rationalize substituent and central element effects. Bond analysis tools give further insights into the preference of eight valence electron systems with four substituents to be tetrahedral. Hence, this study develops a model to understand, memorize, and predict the angular flexibility of tetrahedral species. Perceiving the tetrahedron not as forcingly rigid but as a dynamic structural entity might leverage new approaches and visions for adaptive matter.

Electronic Origin of Non-Zone-Center Phonon Condensation: Octahedral Rotation as a Case Study.

Unstable zone-boundary phonon modes drive atomic displacements linked to a rich array of properties. Yet, the electronic origin of the instability remains to be clearly explained. In this Letter, we propose that bonding interaction between Bloch states belonging to different wave vectors leads to such instability via the pseudo- or second-order Jahn-Teller effect. Our first-principles calculations and representation theory-based analyses show that rotations of anion coordinated octahedra, an archetypal example of zone-boundary phonon condensations, are induced by this bonding mechanism. The proposed mechanism is universal to any non-zone-center phonon condensations and could offer a general approach to understanding the origin of structural phase transitions in crystals.

Structure of silver molybdate glasses by X-ray and neutron diffraction

The structure of (Ag2O)x(MoO3)1-x glasses of 0.2 ≤ x ≤ 0.4 is studied by combining X-ray and neutron diffraction which allows separating the Mo-O and Ag-O distances up to r ≤ 0.25 nm. The total Mo-O coordination numbers decrease from 5.4 to 4.2 with increasing x. This strong decrease and the excessive formation of non-bridging oxygen (NBO) require each other. A fixed ratio NBO/Oadd = 4.6 is a good approximation. Oxygen Oadd is added with the network-modifier oxide. The distributions of Mo-O distances show a sharp peak at 0.177 nm of three oxygen neighbors that is followed of a broad distribution with one to three more oxygens. Mixtures of MoO6, MoO5, and MoO4 are used to model the distance distributions. Their strong broadening is caused by the second-order Jahn-Teller effects in the MoO6 octahedra with out-of-center displacements of the Mo sites preferably to edges.

Structural units of binary vanadate glasses by X-ray and neutron diffraction

X-ray diffraction with high-energy photons (synchrotron) and neutron diffraction are performed on binary vanadate glasses with MgO, Na2O, K2O to determine their structural units. The interpretation includes results of further binary vanadate glasses where vitreous V2O5 plays a key role. Different to the V2O5 crystal the structural model of the glass widely excludes three-fold coordinated oxygen according to Zachariasen’s rules of glass formation. Results from the literature of an extensive analysis of vanadate crystals are used. VO6 units exist in definite deformations. The corresponding out-of-center displacements of the V5+ ions are attributed to the second-order Jahn-Teller effects. The corresponding mechanisms are suggested to be effective also in glass structures. Two, three or four different V-O distances of this model are taken into account and allow a consistent modelling of the distributions of the bond lengths.

Development of Sn2+-based oxyfluoride photocatalyst with visible light response of ca. 650 nm via strengthened hybridization of Sn 5s and O 2p orbitals

The hybridization between the outmost s orbitals of metal (Bi3+, Sn2+, Pb2+, Ag+) and O 2p orbitals has been widely employed to develop innovative semiconductors with upshift valence band as well as extended visible light response, but it is still challenging to obtain photocatalyst with absorption edge of above 550 nm. Here we report a novel Sn2+-based oxyfluoride Sn2TiNbO6F (STNOF) photocatalyst with a pyrochlore structure to exhibit an extended absorption edge to 650 nm and dual functionalities of both water reduction and oxidation. Density functional theory calculations suggest that the unprecedented broad-spectrum response of STNOF is mainly ascribed to the strengthened hybridization between O 2p and Sn 5s orbitals remarkably upshifting the valence band, which is caused by the distortion and compressive strain in the SnO6F2 dodecahedron with second-order Jahn-Teller effect due to partial fluorine substitution. The structural distortion and compressive strain are experimentally confirmed by the Fourier-transformed extended X-ray absorption fine spectra. As probe tests of the photocatalytic functionalities, water reduction and oxidation half reactions were examined to see obvious H2 and O2 evolution under visible light irradiation. This work may provide an alternative strategy of developing extended visible light responsive semiconductors for promising solar energy conversion.

Potential High-Temperature Piezoelectric Ceramics with Remarkable Performances Enhanced by the Second-Order Jahn-Teller Effect.

Herein, the second-order Jahn-Teller effect was applied to the design of the bismuth ferrite-based ceramics. A large distortion of an electron structure arranged along the z axis and an asymmetric distribution of charge density were calculated in 0.80(0.725BiFeO3-0.275BaTiO3)-0.20PT (0.20 PT) based on the density functional theory, indicating good ferro/piezoelectric properties. The top experimental polarization of 36.89 μC/cm2, optimal d33 value of 258 pC/N measured at room temperature, and ultrahigh d33 value of 303 pC/N measured at 370 °C were obtained at 0.20 PT, thereby further confirming the calculations. Furthermore, a high Curie point of 488 °C, as well as outstanding temperature stability ranging from room temperature to 430 °C of the 0.20 PT ceramic was observed. The domain of the 0.20 PT exhibited greater order and smaller size, resulting in easy switching when applying voltage. The distorted electron structure, plumb grains, ordered and easily switchable domains, and coexistences of tetragonal (T) and rhombohedral (R) phases contributed to the large piezoelectric constant of the 0.2 PT ceramic. BFBT-xPT ceramics are potentially promising for high-temperature piezoelectric field applications.

Revisiting the Structural, Electronic, and Magnetic Properties of (LaO)MnAs: Effect of Hubbard Correction and Origin of Mott-Insulating Behavior.

We study the structural, electronic, and magnetic properties of the antiferromagnetic-layered oxyarsenide (LaO)MnAs system from the first-principle calculation. The increasing Hubbard energy (U) in the Mn 3d orbital induces the increasing local-symmetry distortions (LSDs) in MnAs4 and OLa4 tetrahedra. The LSD in MnAs4 tetrahedra is possibly promoted by the second-order Jahn–Teller effect in the Mn 3d orbital. Furthermore, the increasing U also escalates the bandgap (Eg) and the magnetic moment of Mn (μMn). The value of U = 1 eV is the most appropriate by considering the structural properties. This value leads to Eg and μMn of 0.834 eV and 4.31 μB, respectively. The calculated μMn is lower than the theoretical value for the high-spin state of Mn 3d (5 μB) due to the hybridization between Mn 3d and As 4p states. However, dxy states are localized and show the weakest hybridization with valence As 4p states. The Mott-insulating behavior in the system is characterized by the Eg transition between the valence and conduction dzx/dzy states. This work shows new physical insights for advanced functional device applications, such as spintronics.

A new perspective on the composition-structure-property relationships on Nb/Mo/Cr-doped O3-type layered oxide as cathode materials for sodium-ion batteries

The layered transition metal oxides are an essential class of cathode materials in sodium-ion batteries. However, the capacity decay mechanisms of many materials at a wide voltage window are still ambiguous. Therefore, research on the intrinsic structure of materials at the electronic or atomic level is of great significance to unlock the potential of more materials. In this study, a new family of layered NaNi0.45Mn0.3Ti0.2M0.05O2 (M = Nb/Mo/Cr) has been demonstrated to combine high specific capacity (NaNi0.45Mn0.3Ti0.2Cr0.05O2, 12 mA g−1, 185.7 mAh g−1, 2-4.2 V) with preferable Na+ insertion/extraction activity (1920 mA g−1, 111.2 mAh g−1). The participation of Ni2+/Ni3+ and Cr3+/Cr4+/Cr6+ in the redox reaction upon cycling significantly contributes to the superior specific capacity, and the diffusion kinetics calculation indicates that the substitution of Cr for Ni can create a more suitable path with a low energy barrier for Na+ movement, which is particularly crucial for the rate performance. Besides, the unfavorable cycling stability is affected by the distortion of the crystal structure, suggesting that the Jahn-Teller effect of Mn3+/Ni3+ and the second-order Jahn-Teller effect of Nb5+/Mo6+ (d0 transition metal) together with Cr6+ migration caused by disproportionation of Cr4+ have inescapable responsibilities. Additionally, the reversible phase transition between the O3 and P3 phases upon Na+ insertion/extraction at a wide voltage window is identified by in situ XRD measurements and verified to be the key factor of the high coulombic efficiency for NMTCr. An in-depth understanding of NMTNb and NMTMo can provide new insights for material design and exploitation. The composition-structure-property relationships behind the electrochemical performance can be comprehended profoundly by coupling the experimental verification with density functional theory calculations.

Engineering Polar Oxynitrides: Hexagonal Perovskite BaWON2.

Non-centrosymmetric polar compounds have important technological properties. Reported perovskite oxynitrides show centrosymmetric structures, and for some of them high permittivities have been observed and ascribed to local dipoles induced by partial order of nitride and oxide. Reported here is the first hexagonal perovskite oxynitride BaWON2 , which shows a polar 6H polytype. Synchrotron X-ray and neutron powder diffraction, and annular bright-field in scanning transmission electron microscopy indicate that it crystalizes in the non-centrosymmetric space group P63 mc, with a total order of nitride and oxide at two distinct coordination environments in cubic and hexagonal packed BaX3 layers. A synergetic second-order Jahn-Teller effect, supported by first principle calculations, anion order, and electrostatic repulsions between W6+ cations, induce large distortions at two inequivalent face-sharing octahedra that lead to long-range ordered dipoles and spontaneous polarization along the c axis. The new oxynitride is a semiconductor with a band gap of 1.1 eV and a large permittivity.