Inversion Center Research Articles

Measuring linear electric quadrupole susceptibility of non-centrosymmetric crystals with reflectivity difference.

I report experimental methods for measuring real and imaginary parts of the linear electric quadrupole susceptibility tensor of nonlinear optical crystals that lack inversion centers. The third-ranked tensor is related to the corresponding second-order nonlinear susceptibility tensor. For opaque materials such as GaAs, the methods involve normal-incidence reflectivity difference detection schemes. For transparent materials, quadrupole susceptibility tensor elements may be measured with similarly construed transmission difference detection schemes.

Topological crystalline phases in a disordered inversion-symmetric chain

When translational symmetry is broken by bulk disorder, the topological nature of states in topological crystalline systems may change depending on the type of disorder that is applied. In this work, we characterize the phases of a one-dimensional (1D) chain with inversion and chiral symmetries, where every disorder configuration is inversion-symmetric. By using a basis-independent formulation for the inversion topological invariant, chiral winding number, and bulk polarization, we are able to construct phase diagrams for these quantities when disorder is present. We show that unlike the chiral winding number and bulk polarization, the inversion topological invariant can fluctuate when the bulk spectral gap closes at strong disorder. Using the position-space renormalization group, we are able to compare how the inversion topological invariant, chiral winding number and bulk polarization behave at low energies in the strong disorder limit. We show that with inversion symmetry-preserving disorder, the value of the inversion topological invariant is determined by the inversion eigenvalues of the states at the inversion centers, while quantities such as the chiral winding number and the bulk polarization still have contributions from every state throughout the chain. We also show that it is possible to alter the value of the inversion topological invariant in a clean system by occupying additional states at the inversion centers while keeping the bulk polarization fixed. We discuss the implications of our results for topological crystalline phases in higher-dimensional electronic systems, and in ultra-cold atomic systems.

Di-μ2-chlorido-bis-{chlorido-[2,4,6-tris-(pyridin-2-yl)-1,3,5-triazine-κ3 N 2,N 1,N 6]nickel(II)}.

In the title compound, [Ni2Cl4(C18H12N6)2], the NiII ions are hexa-coordinated in a distorted octa-hedral coordination environment defined by three N atoms of the tridentate 2,4,6-tri-2-pyridyl-1,3,5-triazine ligand and three Cl- anions in a meridional geometry. The two NiII ions are bridged by two Cl anionic ligands, thereby forming a dinuclear complex. A crystallographic centre of inversion is located at the centroid of the Ni2Cl2 ring.

Prior Likelihoods and Space-Group Preferences of Solvates

For a range of organic solvents, the likelihood of the solvent forming solvates has been estimated using the recrystallization solvent (RS) data in the Cambridge Structural Database (CSD). Although RS data are viewed with caution by some crystallographers, most of the likelihood estimates are shown to have good precision. Strong trends are apparent in the results. For example, high likelihoods are found for aromatic solvents with electron-withdrawing substituents and low likelihoods for acyclic aliphatic hydrocarbons. Results for different CSD subsets, such as organic and metalloorganic, are highly correlated. The likelihood that a solvent will form solvates is almost always higher when the solvent is part of a mixture than when it is pure. The likelihood of two solvents forming a heterosolvate (i.e., both solvents in the structure) can be well estimated by the product of the likelihoods of the solvents forming normal solvates (i.e., only one solvent in the structure). The space-group preferences of solvates vary significantly with the nature of the cocrystallized solvent. Those of nonsolvates vary significantly with the solvent(s) from which they were crystallized. Solvents with inversion centers favor solvate crystallization in centrosymmetric space groups, and solvents with 2-fold rotational symmetry promote crystallization in space groups with 2-fold proper rotational axes. The inclusion of cyclohexane and carbon tetrachloride in a lattice can facilitate crystallization in trigonal and tetragonal space groups, respectively. Our results can: (a) guide solvent selection when solvates are undesired; (b) assist in predicting solvate formation, e.g., using Bayesian algorithms; (c) assist in the choice of space groups for solvate crystal structure prediction; and (d) suggest ways in which solvent incorporation can be used to influence space groups.

Spectroscopic study of the Eu3+ local symmetry in EuF3 crystal

We employed the simple overlap model (SOM) with the method of equivalent nearest neighbours (MENN) to indicate the local symmetry of the Eu3+ in the europium trifluoride (EuF3) compound through two analyses based on the emission spectra. In first situation, three lines were observed at the 5D0 → 7F1 (0-1) transition. Therefore, based on the amount of non-null crystal field parameters, we indicate that the Eu ion occupies a site with distorted inversion centre as a combination of C2 and C2h symmetries, with the following charge factors: g1 = 0.438, g2 = 0.292, g3 = 0.411, g4 = 0.201, g5 = 0.396 and g6 = 0.293. In second situation, with two lines at the 0-1 transition, we suggested the luminescent site as a combination of the D3d and D3h symmetries with g1 = 0.279 and g2 = 0.495. The 7F1 manifold splitting was obtained through Auzel-Malta equation. All theoretical calculations reproduced satisfactorily the 7F1, 7F2 and 5D1 energy sublevels in good agreement with experimentals data.

Structure and NMR properties of the dinuclear complex di-μ-azido-κ4 N 1:N 1-bis-[(azido-κN)(pyridine-2-carboxamide-κ2 N 1,O)zinc(II)

The new diamagnetic complex, [Zn2(N3)4(C6H6N2O)2] or [Zn2(pca)2(μ1,1-N3)2(N3)2] was synthesized using pyridine-2-carboxamide (pca) and azido ligands, and characterized using various techniques: IR spectroscopy and single-crystal X-ray diffraction in the solid state, and nuclear magnetic resonance (NMR) in solution. The mol-ecule is placed on an inversion centre in space group P . The pca ligand chelates the metal centre via the pyridine N atom and the carbonyl O atom. One azido ligand bridges the two symmetry-related Zn2+ cations in the end-on coordination mode, while the other independent azido anion occupies the fifth coordination site, as a terminal ligand. The resulting five-coordinate Zn centres have a coordination geometry inter-mediate between trigonal bipyramidal and square pyramidal. The behaviour of the title complex in DMSO solution suggests that it is a suitable NMR probe for similar or isostructural complexes including other transition-metal ions. The diamagnetic nature of the complex is reflected in similar 1H and 13C NMR chemical shifts for the free ligand pca as for the Zn complex.

Synthesis, structure and photophysical properties of two tetranuclear copper(I) iodide complexes based on acetylpyridine and diphosphine mixed ligands.

Two copper(I) iodide tetramers, namely, [μ2-1,3-bis(diphenylphosphanyl)propane-κ2P:P']di-μ3-iodido-di-μ2-iodido-[1-(pyridin-3-yl)ethan-1-one-κN]tetracopper(I) dichloromethane disolvate, [Cu4I4(C6H7NO)2(C27H26P2)2]·2CH2Cl2 (CuL3), and [μ2-1,3-bis(diphenylphosphanyl)propane-κ2P:P']di-μ3-iodido-di-μ2-iodido-[1-(pyridin-4-yl)ethan-1-one-κN]tetracopper(I), [Cu4I4(C6H7NO)2(C27H26P2)2] (CuL4), have been synthesized from reactions of CuI, 1,3-bis(diphenylphosphanyl)propane (dppp) and 3- or 4-acetylpyridine (3/4-acepy). The complexes were characterized by elemental analysis, IR spectroscopy, single-crystal X-ray diffraction (XRD), powder XRD and photoluminescence spectroscopy. Both complexes possess a stair-step [Cu4I4] cluster structure with a crystallographic inversion centre located in the middle of a Cu2I2 ring (Z' = 1/2). The dppp ligands each adopt a bidentate coordination mode that bridges two CuI centres on one side of the [Cu4I4] cluster and the acepy ligands act as terminal ligands. The solid-state samples of similar complexes show highly efficiency thermally activated delayed fluorescence (TADF) at room temperature. At ambient temperature, both CuL3 and CuL4 exhibit photoluminescence, with a maximum emission in the region 560-580 nm and with short emissive decay times, but only phosphorescence was observed at 77 K. The narrow gaps between the higher lying singlet state and the triplet state, ΔE(S1 - T1), also confirm the presence of TADF. Structure analysis and consideration of photoluminescence indicates that the position of the acetyl group on the heterocyclic ligand has an obvious influence on the structural arrangement, on intermolecular interactions and on the observed photophysical properties.

The crystal structure of the deca-aluminum alkoxide cluster Al10O4(OH)8 L 14 (L = 1,1,1,3,3,3-hexa-fluoro-propan-2-olate).

In the title centrosymmetric cluster compound, hexa-kis-(μ2-1,1,1,3,3,3-hexa-fluoro-propan-2-olato)octa-kis-(1,1,1,3,3,3-hexa-fluoro-propan-2-olato)octa-μ2-hydroxido-di-μ4-oxido-di-μ3-oxido-deca-aluminium, [Al10(C3HF6O)14(OH)8O4] (C42H22Al10F84O26), there is a central μ4-OAl4 moiety, which has six edges of which three contain μ(O)-1,1,1,3,3,3-hexa-fluoro-propan-2-olate (L) ligands and two contain μ-OH groups each bridging two Al atoms along an edge. The sixth edge is occupied by a group containing a fifth aluminium atom [bis-μ(OH)-, μ3(O)-AlL]. This last μ3(O) group generates a centrosymmetric Al2O2 dimer, thus the μ3(O) atom is linked to two Al atoms in the asymmetric unit as well as a third Al atom through a center of inversion. Three of the hexa-fluoro-propyl groups of the C3HF6O- ligands are disordered and each was refined with two conformations with occupancies of 0.770 (3)/0.230 (3), 0.772 (3)/0.228 (3) and 0.775 (3)/0.225 (3). The five unique Al centers have coordination numbers varying from four to six with bond angles that show considerable distortions from regular geometry: for the four-coordinate atom, τ4' = 0.886, while three Al atoms are five-coordinate (τ5 values = 0.098, 1.028, and 0.338) and one is distorted six-coordinate with O-Al-O bond angles ranging from 74.22 (9) to 171.59 (12)°. The geometry about the central O atom in the OAl4 block is significantly distorted tetra-hedral (τ4' = 0.630) with Al-O-Al angles ranging from 95.50 (9) to 147.74 (13)°. The extended structure features numerous O-H⋯O, O-H⋯F, C-H⋯O and C-H⋯F hydrogen bonds and short F⋯F contacts.

Evidence for a higher-order topological insulator in a three-dimensional material built from van der Waals stacking of bismuth-halide chains.

Low-dimensional van der Waals materials have been extensively studied as a platform with which to generate quantum effects. Advancing this research, topological quantum materials with van der Waals structures are currently receiving a great deal of attention. Here, we use the concept of designing topological materials by the van der Waals stacking of quantum spin Hall insulators. Most interestingly, we find that a slight shift of inversion centre in the unit cell caused by a modification of stacking induces a transition from a trivial insulator to a higher-order topological insulator. Based on this, we present angle-resolved photoemission spectroscopy results showing that the real three-dimensional material Bi4Br4 is a higher-order topological insulator. Our demonstration that various topological states can be selected by stacking chains differently, combined with the advantages of van der Waals materials, offers a playground for engineering topologically non-trivial edge states towards future spintronics applications.

Synthesis, structure, and theoretical studies of a calcium complex of a unique dianion derived from 1-methyl-pyrrolidin-2-one.

The title compound, catena-poly[[tetra-kis-(1-methyl-pyrrolidin-2-one-κO)calcium(II)]-μ-(E)-1,1'-dimethyl-2,2'-dioxo-1,1',2,2'-tetra-hydro-[3,3'-bipyrrolyl-idene]-5,5'-bis-(thiol-ato)-κ2 O:O'], [Ca(C10H8N2O2S2)(C5H9NO)4] n , 1, crystallizes in the triclinic space group P . The crystal studied was twinned by non-merohedry via two different twofold operations, about the normals to (001) and (10), giving four twin domains with refined occupancies of 0.412 (4), 0.366 (4), 0.055 (1), 0.167 (4). The Ca atoms are located on centers of inversion. Each Ca is surrounded by four 1-methyl-pyrrolidin-2-one (NMP) ligands and coordinated through one of the two O atoms to two (E)-1,1'-dimethyl-2,2'-dioxo-1,1',2,2'-tetra-hydro-[3,3'-bipyrrolyl-idene]-5,5'-bis-(thiol-ate), [C10H8N2O2S2]2-, dianions (abbreviation: DMTBT). This dianion thus facilitates the formation of a 1-D polymer, which propagates in the [011] direction. These ribbons are linked by inter-molecular C-H⋯S inter-actions. Each Ca atom is in an octa-hedral CaO6 six-coordinate environment with Ca-O bond lengths ranging from 2.308 (6) to 2.341 (6) Å, cis bond angles ranging from 88.2 (2) to 91.8 (2)° and the trans angles all 180° due to the Ca atoms being located on centers of inversion. Theoretical calculations were carried out using density functional theory (DFT) and the results showed that although the central DMTBT dianion is planar there is likely some resonance across the central bond between both aza-pentyl rings, but this is not sufficient to establish a ring current. The calculated UV-vis spectrum shows a peak at 625 nm, which accounts for the deep blue-purple color of solutions of the complex.

Noncentrosymmetric Weyl phase and topological phase transition in bulk MoTe.

Ideal topological materials are those stable materials with less nontrivial band crossing near the Fermi surface and a long Fermi arc. By means of first-principles calculations, here we present that the 3D monochalcogenide molybdenum telluride (Pm-MoTe) without an inversion center shows a type-II Weyl semimetal (WSM) phase which cannot checked by symmetry index method. A total of eight Weyl points (WPs) are found in different quadrants of the Brillouin zone (BZ) of Pm-MoTe, which guarantee a long Fermi arc. The WSM phase is robust against the spin-orbit coupling (SOC) effect because of mirror symmetry and time reversal symmetry. It is also found that a topological phase transition can be tuned by strain. For different types of strain, the number of WPs can be effectively modulated to a minimum number, and their energies could be closer to Fermi level. These findings propose a promising material candidate that partly satisfies the ideal WSM criteria and extends the potential applications of the tunable topological phase.

Направленные поверхностные акустические волны в нецентросимметричных решетках

Spatial distribution of surface Rayleigh acoustic wave propagating along the surface of GaAs semiconductor covered by a periodic grating of gold stripes is calculated. We demonstrated that when the lattice has no center of spatial inversion the distribution of deformation for the surface wave with the Bloch wave vector kx = 0 is asymmetric and characterized by nonzero mean momentum in the interface plane and nonzero degree of transverse polarization in the plane perpendicular to the surface. The work has been supported by the Russian Science Foundation Grant No. 20-12-00194.

In vitro and in silico assessment of antitumor properties and biomolecular binding studies for two new complexes based on NiII bearing k2N,S-donor ligands

This work deals with two new molecule-based materials, namely NiII-complexes of general formulae [Ni(L1)2] (Ni1) and [Ni(L2)2] (Ni2), where L1 = trans-cinnamaldehyde-N(4)-methyl thiosemicarbazone and L2 = trans-cinnamaldehyde-N(4)-ethyl thiosemicarbazone, as potential antitumor agents. Both compounds were characterized by elemental analysis, molar conductivity and spectroscopic techniques (FTIR and NMR). Their molecular structures were obtained by single-crystal X-ray diffraction analysis. Each one crystallizes in a monoclinic space group P 21/c, also the asymmetric unit comprises of one NiII ion located on an inversion centre and one anionic ligand, which acts as a κ2N,S-donor affording a five-membered metallaring. The compounds were screened against two selected tumour cell lines (MCF-7 and A549) and non-tumour fibroblasts cell line (MRC-5) via MTT assays. In both tumour cells, all compounds exhibited higher cytotoxicity than the control drug (cisplatin). The IC50 values ranges of 3.70 – 41.37 μM and 1.06 – 14.91 μM were found for MCF-7 and A549, respectively. Importantly, all of them were less toxicity than cisplatin in MRC-5 with SI values ranged at 11.80 – 86.60. The red blood cell (RBC) assay revealed Ni2 as non-toxic due to its reduced haemolytic effect (0‐–9% at 1‐–10 μM). The DNA binding was investigated through a combination of spectrophotometric absorption and emission titrations, electrophoresis, and circular dichroism experiments. As a result, these metal complexes were not able to strongly binding to DNA (Kb values ~104 mol L‐−1) but suggesting groove-binding interactions. The scavenging ability of them towards 2,2-diphenyl-1-picrylhydrazyl (DPPH) free-radical was also evaluated in this work, but no important antioxidant behaviour was detected. Further, the interaction of Ni1 and Ni2 to human serum albumin (HSA) was explored by quenching of tryptophan emission, warfarin competitive assay, and molecular docking protocols. The HSA binding analyses indicated good affinity of both complexes to Sudlow site I (Kb values ⁓103 mol L−1).

Crystal structure of the coordination polymer catena-poly[[bis-[hy-droxy(phen-yl)acetato-κ2 O 1,O 2]zinc(II)]-μ2-1,2-bis-(pyridin-4-yl)ethane-κ2 N:N'

In the title polymeric ZnII compound, [Zn(C8H7O3)2(C12H12N2)] n , the Zn cation is coordinated by two N atoms from 1,2-bis-(pyridin-4-yl)ethane unit and four O atoms from two mandelate [or hy-droxy(phen-yl)acetate] anions in a slightly distorted octa-hedral coordination geometry. The 1,2-bis-(pyridin-4-yl)ethane unit bridges two ZnII cations, related by an inversion centre, to form a polymeric chain along [110]. The crystal structure features extensive O-H⋯O and weak C-H ⋯O hydrogen bonds, with C-H ⋯ π inter-actions and π-π inter-actions also being present. The centroid-centroid distance between the phenyl ring of the mandelate group and the 1,2-bis-(pyridine-4-yl)ethane moiety is 4.951 (2) Å. The 1,2-bis-(pyridin-4-yl)ethane ligand is disordered over two positions, with a refined occupancy of 0.578 (14) for the major component.

Removing the C-terminal protecting group enlarges the crystal size: Z-(Gly-Aib)2-OH·H2O.

The achiral tetrapeptide monohydrate N-(benzyloxycarbonyl)glycyl-α-aminoisobutyrylglycyl-α-aminoisobutyric acid monohydrate, Z-Gly-Aib-Gly-Aib-OH·H2O (Z is benzyloxycarbonyl, Aib is α-aminoisobutyric acid and Gly is glycine) or C20H28N4O7·H2O, exhibits two conformations related by the symmetry operation of an inversion centre. It adopts only one of two possible intramolecular hydrogen bonds in a type I (and I') β-turn and forms a maximum of intermolecular hydrogen bonds partly mediated by water. The space group, the molecular structure and the crystal packing differ from two already described (Gly-Aib)2 peptides which vary only in the protecting groups. This structure confirms the high structural flexibility of Gly-Aib peptides and points to a strong relationship between intermolecular hydrogen bonding and crystal quality and size.

Computational simulation and crystal field analysis of the Eu3+-doped LiF

The local symmetry of the Eu3+ was obtained through atomistic simulation and crystal field models applied to lanthanides. Structural properties such as lattice parameters and unit cell volume were reproduced using a set of empirical interatomic potentials with good accuracy. The LiF Anti-Schottky intrinsic defect was most favourable energetically. The solution energy obtained by bound extrinsic defects showed that the Eu3+ prefers the Li+ site compensated by lithium vacancy. Spectroscopic calculations revealed that the europium occupies a luminescent site with distorted inversion centre. A slightly distorted D4h symmetry is most favourable with the charge factors: g1 = 0.629, g2 = 0.738, g3 = 0.627 and g4 = 0.625, which reproduced satisfactorily the 7F1 manifold splitting and the 7F1, 7F2 and 5D1 energy sublevels.

Crystal structure of the unusual coordination polymer catena-poly[[gold(I)-μ-1,2-bis-(di-phenyl-phosphino-thio-yl)ethane-κ2 S:S'] di-bromido-aurate(I)

In the title compound, {[Au(C26H24P2S2)][AuBr2]} n , the gold(I) centres of the cation are coordinated by the P=S groups of the di-sulfide ligands to form a chain polymer parallel to the c axis. Both independent gold atoms lie on the same twofold axis, and the midpoint of the H2C-CH2 bond lies on an inversion centre. The anions flank the polymeric chain; they are connected to it by short aurophilic inter-actions and C-H⋯Br contacts, and to each other by Br⋯Br contacts.

Morphological Studies, Photocatalytic Activity, and Electrochemistry of Platinum Disulfide Nanoparticles from Bis(morpholinyl-4-carbodithioato)-platinum(II).

Bis(morpholinyl-4-carbodithioato)-platinum(II) was synthesized and characterized using spectroscopic techniques and single-crystal X-ray crystallography. The Pt(II) complex crystallized in a monoclinic space group P21/n with a Pt(II) ion located on an inversion center coordinated two morpholinyl dithiocarbamate ligands that are coplanar to form a slightly distorted square planar geometry around the Pt(II) ion. The complex was thermolyzed at 120, 180, and 240 °C to prepare PtS2 nanoparticles. Powder X-ray diffraction patterns confirmed the hexagonal crystalline phase for the as-prepared PtS2 nanoparticles irrespective of thermolysis temperature. Bead-like shaped PtS2-120 nanoparticles with a particle size in the range of 12.46–64.97 nm were formed at 120 °C, while PtS2-180 prepared at 180 °C is quasi-spherical in shape with particles in the range of 24.30–46.87 nm. The PtS2-240 obtained at 240 °C is spherical with particles in the range of 11.45–46.85 nm. The broad emission maxima of the as-prepared PtS2 nanoparticles are ascribed to the particles’ broad size distributions. The photocatalytic degradation of methylene blue by the PtS2 nanoparticles shows a maximum efficiency of 87% for PtS2-240 after 360 min. The effects of photocatalytic dosage, irradiation time, pH medium, and scavengers were also evaluated. Cyclic voltammetry of the PtS2 nanoparticles showed a reversible redox reaction, while the electrochemistry of the as-prepared PtS2 indicates that the electron transfer process is diffusion-controlled.

Synthesis and crystal structure of a heterobimetallic nickel-manganese 12-metallacrown-4 methanol disolvate monohydrate compound.

The synthesis and crystal structure of the title compound [systematic name: di-μ-acetato-tetra-kis-(μ4-N,2-dioxido-benzene-1-carboximidato)hexa-methano-ltetra-manganese(III)nickel(II) methanol disolvate monohydrate], [Mn4Ni(C7H4NO3)4(C2H3O2)2(CH4O)6]·2CH4O·H2O or Ni(OAc)2[12-MCMn(III)N(shi)-4](CH3OH)6·2CH3OH·H2O, where MC is metallacrown, -OAc is acetate, and shi3- is salicyl-hydroximate, are reported. The macrocyclic metallacrown is positioned on an inversion center located on the NiII ion that resides in the central MC cavity. The macrocycle consists of an MnIII-N-O repeat unit that recurs four times to generate an overall square-shaped mol-ecule. Both the NiII and MnIII ions are six-coordinate with an octa-hedral geometry. In addition, the MnIII ions possess an elongated Jahn-Teller distortion along the z-axis of the coordination environment. The inter-stitial water mol-ecule is slightly offset from and disordered about an inversion center.

Crystal structure of bis-[μ-N-(η2-prop-2-en-1-yl)piperidine-1-carbo-thio-amide-κ2 S:S]bis-[(thio-cyanato-κN)copper(I)

The title crystalline compound, [Cu2(NCS)2(C9H16N2)2], was obtained from the reaction of copper(I) thio-cyanate (CuSCN) with (N-prop-2-en-1-yl)piperidine-1-carbo-thio-amide as a chelating and bridging thio-urea ligand in chloro-benzene. The Cu2S2 core of the dimeric mol-ecule is situated on a crystallographic inversion centre. The copper atom is coordinated by a thio-cyanate nitro-gen atom, each sulfur atom of the two thio-urea ligands, and the C=C double bond of the ligand in a distorted tetra-hedral geometry. The dimers are linked by N-H⋯S hydrogen bonds, forming a network extending in two dimensions parallel to (100).