Inversion Center Research Articles

Even-order optical harmonics generated from centrosymmetric-material metasurfaces

Generation of even-order optical harmonics requires noncentrosymmetric structures being conventionally observed in crystals lacking the center of inversion. In centrosymmetric systems, even-order harmonics may arise, e.g., at surfaces but such effects are usually very weak. Here we observe optical harmonics up to fourth order generated under the normal incidence from centrosymmetric dielectric metasurfaces empowered by resonances. We design silicon metasurfaces supporting optical quasibound states in the continuum and guided-mode resonances, and demonstrate the enhancement of second-harmonic signals by over three orders of magnitude compared to nonresonant thin films. Under the optimal conditions, the brightness of the second harmonic approaches that of the third harmonic, and the fourth-order harmonic becomes detectable. Published by the American Physical Society 2024

Crystal and molecular structure of 2-methyl-1,4-phenylene bis(3,5-dibromobenzoate)

The aryl diester compound, 2-methyl-1,4-phenylene bis(3,5-dibromobenzoate), C21H12Br4O4, was synthesized by esterification of methyl hydroquinone with 3,5-dibromobenzoic acid. A crystalline sample was obtained by cooling a sample of the melt (m.p. = 502 K/DSC) to room temperature. The molecular structure consists of a central benzene ring with anti-3,5-dibromobenzoate groups symmetrically attached at the 1 and 4 positions and a methyl group attached at the 2 position of the central ring. In the crystal structure (space group P\overline{1}), molecules of the title aryl diester are located on inversion centers imposing disorder of the methyl group and H atom across the central benzene ring. The crystal structure is consolidated by a network of C—H...Br hydrogen bonds in addition to weaker and offset π–π interactions involving the central benzene rings as well as the rings of the attached 3,5-dibromobenzoate groups.

Bis(ethylenediammonium) μ-ethylenediaminetetraacetato-1κ3 O,N,O′:2κ3 O′′,N′,O′′′-bis[trioxidomolybdate(VI)] tetrahydrate

The title compound, (C2H10N2)2[(C10H12N2O8)(MoO3)2]·4H2O, which crystallizes in the monoclinic C2/c space group, was obtained by mixing molybdenum oxide, ethylenediamine and ethylenediaminetetraacetic acid (H4edta) in a 2:4:1 ratio. The complex anion contains two MoO3 units bridged by an edta4− anion. The midpoint of the central C—C bond of the edta4− anion is located on a crystallographic inversion centre. The independent Mo atom is tridentately coordinated by a nitrogen atom and two carboxylate groups of the edta4− ligand, together with the three oxo ligands, producing a distorted octahedral coordination environment. In the three-dimensional supramolecular crystal structure, the dinuclear anions, the organoammonium counter-ions and the solvent water molecules are linked by N—H...Ow, N—H...Oedta and O—H...O hydrogen bonds.

Cluster Odd-Parity Multipoles by Staggered Orbital Ordering in Locally Noncentrosymmetric Crystals

Odd-parity multipoles in crystals manifest themselves not only in their peculiar electronic orderings but also in unconventional parity-violating physical phenomena. We here report the emergence of odd-parity multipoles by considering staggered orbital orderings in a locally noncentrosymmetric crystal system with the global inversion center but without the inversion center at each lattice site. We show that various odd-parity multipoles, such as the electric toroidal monopole, electric dipole, and electric toroidal quadrupole, are realized depending on the type of orbital orderings in the one-dimensional zigzag chain. Such odd-parity multipoles give rise to an antisymmetric spin splitting in the electronic band structure with the aid of the relativistic spin–orbit coupling. We also show that similar states with odd-parity multipoles are realized in other locally noncentrosymmetric crystals, such as the two-dimensional honeycomb and three-dimensional diamond structures.

Synthesis, crystal structure and thermal properties of catena-poly[[bis-(4-methyl-pyridine)-nickel(II)]-di-μ-thio-cyanato], which shows an alternating all-trans and cis-cis-trans-coordination of the NiS2Np 2Nt 2 octa-hedra (p = 4-methyl-pyridine, t = thio-cyanate).

The title compound, [Ni(NCS)2(C6H7N)2] n , was prepared by the reaction of Ni(NCS)2 with 4-methyl-pyridine in water. Its asymmetric unit consists of two crystallographically independent NiII cations, of which one is located on a twofold rotational axis whereas the second occupies a center of inversion, two independent thio-cyanate anions and two independent 4-methyl-pyridine co-ligands in general positions. Each NiII cation is octa-hedrally coordinated by two 4-methyl-pyridine coligands as well as two N- and two S-bonded thio-cyanate anions. One of the cations shows an all-trans, the other a cis-cis-trans configuration. The metal centers are linked by pairs of μ-1,3-bridging thio-cyanate anions into [101] chains. X-ray powder diffraction shows that a pure crystalline phase has been obtained and thermogravimetry coupled to differential thermoanalysis reveals that the title compound loses half of the 4-methyl-pyridine coligands and transforms into Ni(NCS)2(C6H7N). Nearly pure samples of this compound can be obtained by thermal annealing and a Rietveld refinement demonstrated that it is isotypic to its recently reported Cd analog [Neumann et al., (2020 ▸). CrystEngComm. 22, 184-194] In its crystal structure, the metal cations are linked by one μ-1,3(N,S)- and one μ-1,3,3(N,S,S)-bridging thio-cyanate anion into single chains that condense via the μ-1,3,3(N,S,S)-bridging anionic ligands into double chains.

Bis(8-hy-droxy-quinolinium) naphthalene-1,5-di-sulfonate tetra-hydrate.

The inter-action between 8-hy-droxy-quinoline (8HQ, C9H7NO) and naphthalene-1,5-di-sulfonic acid (H2NDS, C10H8O6S2) in aqueous media results in the formation of the salt hydrate bis-(8-hy-droxy-quinolinium) naphthalene-1,5-di-sulfonate tetra-hydrate, 2C9H8NO+·C10H6O6S2 2-·4H2O. The asymmetric unit comprises one protonated 8HQ+ cation, half of an NDS2- dianion symmetrically disposed around a center of inversion, and two water mol-ecules. Within the crystal structure, these components are organized into chains along the [010] and [10] directions through O-H⋯O and N-H⋯O hydrogen-bonding inter-actions, forming a di-periodic network parallel to (101). Additional stabilizing inter-actions such as C-H⋯O, C-H⋯π, and π-π inter-actions extend this arrangement into a tri-periodic network structure.

Crystal structures of four gold(I) complexes [AuL 2]+[AuX 2]- and a by-product (L·LH+)[AuBr2]- (L = substituted pyridine, X = Cl or Br).

Bis(2-methyl-pyridine)-gold(I) di-bromido-aurate(I), [Au(C6H7N)2][AuBr2], (1), crystallizes in space group C2/c with Z = 4. Both gold atoms lie on twofold axes and are connected by an aurophilic contact. A second aurophilic contact leads to infinite chains of alternating cations and anions parallel to the b axis, and the residues are further connected by a short H⋯Au contact and a borderline Br⋯Br contact. Bis(3-methyl-pyridine)-gold(I) di-bromido-aurate(I), [Au(C6H7N)2][AuBr2], (2), crystallizes in space group C2/m with Z = 2. Both gold atoms lie on special positions with symmetry 2/m and are connected by an aurophilic contact; all other atoms except for one methyl hydrogen lie in mirror planes. The extended structure is closely analogous to that of 1, although the structures are formally not isotypic. Bis(3,5-di-methyl-pyridine)-gold(I) di-chlor-ido-aurate(I), [Au(C7H9N)2][AuCl2], (3) crystallizes in space group P with Z = 2. The cation lies on a general position, and there are two independent anions in which the gold atoms lie on inversion centres. The cation and one anion associate via three short H⋯Cl contacts to form a ribbon structure parallel to the b axis; aurophilic contacts link adjacent ribbons. Bis(3,5-di-methyl-pyridine)-gold(I) di-bromido-aurate(I), [Au(C7H9N)2][AuBr2], (4) is isotypic to 3. Attempts to make similar compounds involving 2-bromo-pyridine led instead to 2-bromopyridinium di-bromido-aurate(I)-2-bromo-pyridine (1/1), (C5H5BrN)[AuBr2]·C5H4BrN, (5), which crystallizes in space group P with Z = 2; all atoms lie on general positions. The 2-bromo-pyridinium cation is linked to the 2-bromo-pyridine mol-ecule by an N-H⋯N hydrogen bond. Two formula units aggregate to form inversion-symmetric dimers involving Br⋯Br, Au⋯Br and H⋯Br contacts.

A Coordinate-Free Approach to the Design of Generalized Griffis-Duffy Platforms

Architectural singularity belongs to the Type II singularity, in which a parallel manipulator (PM) gains one or more degrees of freedom and becomes uncontrollable. PMs remaining permanently in a singularity are beneficial for linear-to-rotary motion conversion. Griffis-Duffy (GD) platform is a mobile structure admitting a Bricard motion. In this paper, we present a coordinate-free approach to the design of generalized GD platforms, which consists in determining the shape and attachment of both the moving platform and the fixed base. The generalized GD platform is treated as a combination of six coaxial single-loop mechanisms under the same constraints. Owing to the inversion, hidden in the geometric structure of these single-loop mechanisms, the mapping from a line to a circle establishes the geometric transformation between the fixed base and the moving platform based on the center of inversion, and describes the shape and attachment of the generalized GD platform. Moreover, the center of inversion not only identifies the location of rotation axis, but also affects the shape of the platform mechanism. A graphical construction of generalized GD platforms using inversion, proposed in the paper, provides geometrically feasible solutions of the manipulator design for the requirement of the location of rotation axis.

Ethyl 2-[(2-oxo-2H-chromen-6-yl)oxy]acetate

Ethyl 2-[(2-oxo-2H-chromen-6-yl)oxy]acetate, C13H12O5, a member of the pharmacologically important class of coumarins, crystallizes in the monoclinic C2/c space group in the form of sheets, within which molecules are related by inversion centers and 21 axes. Multiple C—H...O weak hydrogen-bonding interactions reinforce this pattern. The planes of these sheets are oriented in the approximate direction of the ac face diagonal. Intersheet interactions are a combination of coumarin system π–π stacking and additional C—H...O weak hydrogen bonds between ethyl acetoxy groups.

Crystal structure and Hirshfeld surface analysis of 3,3′-[ethane-1,2-diylbis(oxy)]bis(5,5-dimethylcyclohex-2-en-1-one) including an unknown solvate

The title molecule, C18H26O4, consists of two symmetrical halves related by the inversion centre at the mid-point of the central –C—C– bond. The hexene ring adopts an envelope conformation. In the crystal, the molecules are connected into dimers by C—H...O hydrogen bonds with R 2 2(8) ring motifs, forming zigzag ribbons along the b-axis direction. According to a Hirshfeld surface analysis, H...H (68.2%) and O...H/H...O (25.9%) interactions are the most significant contributors to the crystal packing. The contribution of some disordered solvent to the scattering was removed using the SQUEEZE routine [Spek (2015). Acta Cryst. C71, 9–18] in PLATON. The solvent contribution was not included in the reported molecular weight and density.

Synthesis and Optical Property Modulation of Substituted [2.2]Paracylophanes through Through‐Space Conjugation

4,16‐para‐substituted [2.2]paracylophane with naphthalene (PCP⎼NAP), anthracene (PCP⎼ANTH), and tetraphenylethylene (PCP⎼TPE), as new through‐space conjugated dimers, were prepared by the Suzuki–Miyaura cross‐coupling reaction of 4,16‐diboryl[2.2]paracyclophane and the corresponding bromo derivative using Pd(PPh3)4 as a catalyst and KOH as a base. The synthesized compounds were fully characterized by NMR and HR‐MS, and their photophysical and electrochemical properties were studied. The photoluminescence quantum yield of PCP⎼NAP, PCP⎼ANTH were determined to be 0.21, 0.50 and for PCP⎼TPE in aggregated state 0.31, respectively. PCP⎼TPE exhibited aggregation‐induced emission characteristics when the water fraction was greater than 50% in THF/water mixtures. PCP⎼ANTH and PCP⎼TPE were also characterized by X‐ray crystallography, and single crystals of PCP⎼ANTH were obtained from the centrosymmetric monoclinic space group C2/c. A single crystal of PCP⎼TPE crystallizes in the centrosymmetric triclinic space group P⎼1, with one molecule residing at the inversion center. The observed properties of these π‐stacked dimers were compared with respect to through‐space conjugation and conjugation length in the structure.

Trans-Dichloridobis(secnidazole-κN 3)copper(II)

The use of acetic acid (HOAc) in a reaction between CuCl2·2H2O and secnidazole, an active pharmaceutical ingredient useful in the treatment against a variety of anaerobic Gram-positive and Gram-negative bacteria, affords the title complex, [CuCl2(C7H11N3O3)2]. This compound was previously synthesized using ethanol as solvent, although its crystal structure was not reported [Betanzos-Lara et al. (2013). Inorg. Chim. Acta, 397, 94–100]. In the molecular complex, the Cu2+ cation is situated at an inversion centre and displays a square-planar coordination environment. There is a hydrogen-bonded framework based on intermolecular O—H...Cl interactions, characterized by H...Cl separations of 2.28 (4) Å and O—H...Cl angles of 175 (3)°. The resulting supramolecular network is based on R2 2 (18) ring motifs, forming chains in the [010] direction.

Cu(II) complexes of 5-sulfamoylbenzoic acid derivatives: Synthesis and characterization

Novel three Cu(II) complexes {[Cu2(MeOsba)4(H2O)2] (1, HMeOsba = 2-methoxy-5-sulfamoylbenzoic acid), [Cu(MeOsba)2(2a5mp)2].3H2O (2, 2a5mp = 2-amino-5-methylpyridine) and [Cu(Clsba)2(2amp)2].2H2O (3, 2amp = 2-picolylamine, HClsba = 2,4-dichloro-5-sulfamoylbenzoic acid)} were synthesized. The structure of 1–3 characterized by FT-IR, AAS, X-ray crystallographic analysis, UV, molar conductivity and magnetic moment. All complexes (1–3) formed crystals in the P-1 space group and the triclinic crystal system. The symmetric units of complexes (1–3) contains two Cu(II) cations, four MeOsba anions as bridges and two aqua ligands for 1, one Cu(II) cations, two MeOsba anions, two 2a5mp and three uncoordinated water molecules for 2 and one Cu(II) cations, two Clsba anions, two 2amp and three uncoordinated water molecules for 3. The structure of 1–3 have a crystallographic inversion centre.

Coupling between cation and anion disorder in β-K2Ca3(CO3)4

Since the development of anionic group theory, the spatial arrangement of anionic groups in optical crystals has been believed to determine their functional, such as nonlinear optical, properties. At the same time, cation substitution, resulting in either the appearance of disordered cation sites in a crystal structure or the emergence of cation-ordered superstructures, has been widely used to control material properties. This work demonstrates the coupling between positional cation disorder and orientational disorder of (CO3)2− anions in the β modification of the recently described K2Ca3(CO3)4 material. In contrast to the α modification [P212121, a = 7.39134 (18), b = 8.8153 (2), c = 16.4803 (4) Å], where the ordered cation sublattice favors the non-centrosymmetric orientationally ordered arrangement of (CO3)2− anionic groups, positional cation disorder in β-K2Ca3(CO3)4 [Pnma, a = 7.5371 (2), b = 16.1777 (5), c = 8.7793 (3) Å] within the cation sublattice of the same topology leads to orientational disorder of (CO3)2− groups and the appearance of an inversion center in the average structure.

Synthesis, crystal structure and thermal properties of the dinuclear complex bis-(μ-4-methylpyridine N-oxide-κ2O:O)bis-[(methanol-κO)(4-methylpyridine N-oxide-κO)bis-(thio-cyanato-κN)cobalt(II)

Reaction of Co(NCS)2 with 4-methyl-pyridine N-oxide in methanol leads to the formation of crystals of the title compound, [Co2(NCS)4(C6H7NO)4(CH4O)2] or Co2(NCS)4(4-methyl-pyridine N-oxide)4(methanol)2. The asymmetric unit consist of one CoII cation, two thio-cyanate anions, two 4-methyl-pyridine N-oxide coligands and one methanol mol-ecule in general positions. The H atoms of one of the methyl groups are disordered and were refined using a split model. The CoII cations octa-hedrally coordinate two terminal N-bonded thio-cyanate anions, three 4-methyl-pyridine N-oxide coligands and one methanol mol-ecule. Each two CoII cations are linked by pairs of μ-1,1(O,O)-bridging 4-methyl-pyridine N-oxide coligands into dinuclear units that are located on centers of inversion. Powder X-ray diffraction (PXRD) investigations prove that the title compound is contaminated with a small amount of Co(NCS)2(4-meth-yl-pyridine N-oxide)3. Thermogravimetric investigations reveal that the methanol mol-ecules are removed in the beginning, leading to a compound with the composition Co(NCS)2(4-methyl-pyridine N-oxide), which has been reported in the literature and which is of poor crystallinity.

Synthesis, crystal structure and Hirshfeld analysis of N-ethyl-2-{3-methyl-2-[(2Z)-pent-2-en-1-yl]cyclo-pent-2-en-1-yl-idene}hydrazinecarbo-thio-amide.

The title compound (C14H23N3S, common name: cis-jasmone 4-ethyl-thio-semicarbazone) was synthesized by the equimolar reaction of cis-jasmone and 4-ethyl-thio-semicarbazide in ethanol facilitated by acid catalysis. There is one crystallographically independent mol-ecule in the asymmetric unit, which shows disorder of the terminal ethyl group of the jasmone carbon chain [site-occupancy ratio = 0.911 (5):0.089 (5)]. The thio-semicarbazone entity [N-N-C(=S)-N] is approximately planar, with the maximum deviation of the mean plane through the N/N/C/S/N atoms being 0.0331 (8) Å, while the maximum deviation of the mean plane through the five-membered ring of the jasmone fragment amounts to -0.0337 (8) Å. The dihedral angle between the two planes is 4.98 (7)°. The mol-ecule is not planar due to this structural feature and the sp 3-hybridized atoms of the jasmone carbon chain. Additionally, one H⋯N intra-molecular inter-action is observed, with graph-set motif S(5). In the crystal, the mol-ecules are connected through pairs of H⋯S inter-actions with R 2 2(8) and R 2 1(7) graph-set motifs into centrosymmetric dimers. The dimers are further connected by H⋯N inter-actions with graph-set motif R 2 2(12), which are related by an inversion centre, forming a mono-periodic hydrogen-bonded ribbon parallel to the b-axis. The crystal structure and the supra-molecular assembly of the title compound are compared with four known cis-jasmone thio-semicarbazone derivatives (two crystalline modifications of the non-substituted form, the 4-methyl and the 4-phenyl derivatives). A Hirshfeld surface analysis indicates that the major contributions for the crystal cohesion are from H⋯H (70.7%), H⋯S/S⋯H (13.5%), H⋯C/C⋯H (8.8%), and H⋯N/N⋯H (6.6%) inter-faces (only the disordered atoms with the highest s.o.f. were considered for the evaluation).

Skyrmion lattice in centrosymmetric magnets with local Dzyaloshinsky–Moriya interaction

It is common for the local inversion symmetry to break in crystals, even though the whole crystal has global inversion symmetry. This local inversion symmetry breaking allows for a local Dzyaloshinsky–Moriya interaction (DMI) in magnetic crystals. Here we show that the local DMI can stabilize a skyrmion as a metastable excitation or as a skyrmion crystal in equilibrium. We consider the crystal structure with layered structure as an example, where local inversion is violated in each layer but a global inversion center exists in the middle of the two layers. These skyrmions come in pairs that are related by inversion symmetry. The two skyrmions with opposite helicity in a pair form a bound state. We study the properties of a skyrmion pair in the ferromagnetic background and determine the equilibrium phase diagram, where a robust lattice of skyrmion pairs is stabilized. Our results point to a new direction to search for the skyrmion lattice in centrosymmetric magnets.

Piezoelectric characteristics of doped β-Ga2O3 monolayer: a first-principles study

Two-dimensional (2D) piezoelectric materials have been widely concerned because of their important applications in nano-piezoelectric generators. Finding two-dimensional materials with large piezoelectric effects is still a great challenge. In this work, the inversion center of the β-Ga2O3 monolayer was broken by substitutional doping. Not only the in-plane piezoelectric effect but also the uncommon out-of-plane piezoelectric effect is induced in the doped β-Ga2O3 monolayer. In addition, we analyzed the cause of the piezoelectric effects from their electronic properties. The values of out-of-plane (in-plane) piezoelectric coefficient for Cu-doped and Al-doped β-Ga2O3 reach −4.04 (3.95) pm/V and −2.91 (0.37) pm/V, respectively. The results are comparable with those of the commonly used bulk piezoelectric materials such as α-quartz (d11 = 2.3 pm V−1), AlN (d33 = 5.1 pm V−1), and GaN (d33 = 3.1 pm V−1), even though they are both two-dimensional structures. Our study shows a great potential application of doped β-Ga2O3 monolayer in micro and nano-electromechanical devices such as smart wearables, sensors, energy converters, and micro energy collectors.

Synthesis, crystal structure and characterization of two new cobalt(II) metal–organic frameworks with 1,4-bis((1h-imidazol-1-yl)methyl) benzene and 1,3,5-tris[(1h-imidazol-1-yl)methyl]benzene ligands

Two novel CoII metal–organic frameworks {[Co(BIMB)2(H2O)2](SO4)·EG·3 H2O}n (I) and {[Co(TIMB)2](SiF6)}n (II) were hydrothermally synthesized by corresponding metal salt with organic ligands 1,3,5-tris[(1H-imidazol-1-yl)methyl]benzene (TIMB) or 1,4-bis((1H-imidazol-1-yl)methyl)benzene (BIMB). Crystal structural analysis reveals that they exhibit varied structures. Compound I contains two crystallographically unique CoII centers, each lying on an inversion center and having a slightly distorted octahedral environment. The BIMB ligands link the CoII cations to generate a three-dimensional porous framework with a 4-connected uninodal (65.8) topology. Compound II exhibits a two-dimensional sheeted metal-organic structure running parallel to the (0 0 1) plane, in which TIMB ligands join Co2+ centers having a six-coordinated octahedral structure. In the solid state, adjacent sheets are further bridged by guest SiF6 - anions via C–H…F hydrogen-bonding interactions, giving rise to a three-dimensional supramolecular network structure with a 2-nodal (3-c)2(6-c) net. The topological analysis suggests that the point Schläfli symbol of compound II is (43)2(46.66.83). In addition, their thermal stabilities have also been investigated.

Syntheses, characterizations and crystal structures of two Ni(II) complexes [Ni2(neoc)4(H2O)(CO3)](NO3)2·3H2O and [Ni(bapa)2](NO3)2·H2O and magnetic properties of the carbonato complex

By the reaction of nickel(II) nitrate hexahydrate with 2,9-dimethyl-1,10-phenanthroline (neoc) and bis(3-aminopropyl)amine (bapa) two novel complexes were isolated, namely [Ni2(neoc)4(H2O)(CO3)](NO3)2·3H2O (1) and [Ni(bapa)2](NO3)2·H2O (2). Both structures are ionic and comprise hexacoordinated Ni(II) central atoms. Complex 1 is built up of dinuclear [Ni2(neoc)4(H2O)(CO3)]2+ complex cation, nitrate anions and water solvate molecules. The dinuclear complex cation is centrosymmetric and the two Ni(II) atoms are linked by a μ3-bridging-chelating carbonato ligand which, due to the presence of an inversion centre, exhibits two orientations with equal probability. The coordination sphere of Ni(II) atom is heteroleptic with an N4O2 donor set formed by two chelating neoc ligands and two O-donor atoms from bridging carbonato and aqua ligands. The carbonato ligand was formed by transformation of absorbed carbon dioxide from air (single crystals) or from dry ice (bulk sample). The crystal structure of 2 is formed by [Ni(bapa)2]2+ complex cation, nitrate anions and water solvate molecule. The coordination sphere of Ni(II) atom in 2 is homoleptic with N6 donor set. Both bapa ligands act as double chelating 3 N-donor ligands and are coordinated in mer-fashion. The study of the magnetic response of 1 in the temperature range 1.8–300 K revealed that the system can be considered as a system of antiferromagnetic S = 1 spin dimers with exchange interaction J/hc = -13.86 cm−1 (J/kB = -19.96 K) and axial single-ion anisotropy D/hc = -4.94 cm−1 (D/kB = -7.12 K). The experimental magnetic results were corroborated by ab initio and DFT calculations.