D2 Symmetry Research Articles

A Remarkably Unsymmetric Hexairon Core Embraced by Two High-Symmetry Tripodal Oligo-α-pyridylamido Ligands.

Oligo-α-pyridylamides offer an appealing route to polyiron complexes with short Fe-Fe separations and large room-temperature magnetic moments. A derivative of tris(2-aminoethyl)amine (H6tren) containing three oligo-α-pyridylamine branches and 13 nitrogen donors (H6L) reacts with [Fe2(Mes)4] to yield an organic nanocage built up by two tripodal ligands with interdigitated branches (HMes = mesitylene). The nanocage has crystallographic D3 symmetry but hosts a remarkably unsymmetric hexairon-oxo core, with a central Fe5(μ5-O) square pyramid, two oxygen donors bridging basal sites, and an additional Fe center residing in one of the two tren-like pockets. Bond valence sum (BVS) analysis, density functional theory (DFT) calculations, and electrochemical data were then used to establish the protonation state of oxygen atoms and the formal oxidation states of the metals. For this purpose, a specialized set of BVS parameters was devised for Fe2+-N3- bonds with nitrogen donors of oligo-α-pyridylamides. This allowed us to formulate the compound as [Fe6O2(OH)(H3L)L], with nominally four FeII ions and two FeIII ions. Mössbauer spectra indicate that the compound contains two unique FeII sites, identified as a pair of closely spaced hydroxo-bridged metal ions in the central Fe5(μ5-O) pyramid, and a substantially valence-delocalized FeII2FeIII2 unit. Broken-symmetry DFT calculations predict strong ferromagnetic coupling between the two iron(II) ions, leading to a local S = 4 state that persists to room temperature and explaining the large magnetic moment measured at 300 K. The compound behaves as a single-molecule magnet, with magnetization dynamics detectable in zero static field and dominated by an Orbach-like mechanism with activation parameters Ueff/kB = 49(2) K and τ0 = 4(2) × 10-10 s.

A Fused [5]Helicene Dimer with a Figure-Eight Topology: Synthesis, Chiral Resolution, and Electronic Properties.

Chiral shape-persistent molecular nanocarbons are promising chiroptical materials; their synthesis, however, remains a big challenge. Herein, we report the facile synthesis and chiral resolution of a double-stranded figure-eight carbon nanobelt 1 in which two [5]helicene units are fused together. Two synthetic routes were developed, and, in particular, a strategy involving Suzuki coupling-mediated macrocyclization followed by Bi(OTf)3 -catalyzed cyclization of vinyl ether turned out to be the most efficient. The structure of 1 was confirmed by X-ray crystallographic analysis. The isolated (P,P)- and (M,M)- enantiomers show persistent chiroptical properties with relatively large dissymmetric factors (|gabs |=5.4×10-3 and |glum |=1.0×10-2 ), which can be explained by the effective electron delocalization along the fully conjugated belt and the unique D2 symmetry. 1 exhibits local aromatic character with a dominant structure containing eight Clar's aromatic sextet rings.

A Fused [5]Helicene Dimer with a Figure‐Eight Topology: Synthesis, Chiral Resolution, and Electronic Properties

AbstractChiral shape‐persistent molecular nanocarbons are promising chiroptical materials; their synthesis, however, remains a big challenge. Herein, we report the facile synthesis and chiral resolution of a double‐stranded figure‐eight carbon nanobelt 1 in which two [5]helicene units are fused together. Two synthetic routes were developed, and, in particular, a strategy involving Suzuki coupling‐mediated macrocyclization followed by Bi(OTf)3‐catalyzed cyclization of vinyl ether turned out to be the most efficient. The structure of 1 was confirmed by X‐ray crystallographic analysis. The isolated (P,P)‐ and (M,M)‐ enantiomers show persistent chiroptical properties with relatively large dissymmetric factors (|gabs|=5.4×10−3 and |glum|=1.0×10−2), which can be explained by the effective electron delocalization along the fully conjugated belt and the unique D2 symmetry. 1 exhibits local aromatic character with a dominant structure containing eight Clar's aromatic sextet rings.

Merging a Negatively Curved Nanographene and a Carbon Nanoring

Two molecular nanocarbons result from merging a negatively curved nanographene and a carbon nanoring in two constitutional isomers of D2 and C2v symmetry, respectively. They were synthesized by attachment of C-shaped paraphenylene precursors to 2,11,18,27-tetrabromooctabenzo[8]circulene and the subsequent intramolecular Yamamoto coupling and reductive aromatization reactions. The flexible nature of octabenzo[8]circulene enabled two different ways of connection in the Yamamoto coupling reactions, leading to the two constitutional isomers. The D2 isomer is shaped like a figure eight, as revealed by X-ray crystallography, and is resolved into two enantiomers by chiral HPLC. The synthesis of the C2v isomer is regarded as a further step toward precision synthesis of carbon schwarzites through a bottom-up approach.

X-ray crystallographic and mutational analysis of the NylC precursor: catalytic mechanism of autocleavage and substrate hydrolysis of nylon hydrolase.

Nylon hydrolase (NylC), a member of the N-terminal nucleophile (Ntn) hydrolase superfamily, is responsible for the degradation of various aliphatic nylons, including nylon-6 and nylon-66. NylC is initially expressed as an inactive precursor (36 kDa), but the precursor is autocatalytically cleaved at Asn266/Thr267 to generate an active enzyme composed of 27 and 9 kDa subunits. We isolated various mutants with amino acid changes at the catalytic centre. X-ray crystallographic analysis revealed that the NylC precursor forms a doughnut-shaped quaternary structure composed of four monomers (molecules A-D) with D2 symmetry. Catalytic residues in the precursor are covered by loop regions at the A/B interface (equivalent to the C/D interface). However, the catalytic residues are exposed to the solvent environment through autocleavage followed by movements of the loop regions. T267A, D306A and D308A mutations resulted in a complete loss of autocleavage. By contrast, in the T267S mutant, autocleavage proceeded slowly at a constant reaction rate (k=2.8 × 10-5 s-1 ) until complete conversion, but the reaction was inhibited by K189A and N219A mutations. Based on the crystallographic and molecular dynamic simulation analyses, we concluded that the Asp308-Asp306-Thr267 triad, resembling the Glu-Ser-Ser triad conserved in Ntn-hydrolase family enzymes, is responsible for autocleavage and that hydrogen-bonding networks connecting Thr267 with Lys189 and Asn219 are required for increasing the nucleophilicity of Thr267-OH in both the water accessible and water inaccessible systems. Furthermore, we determined that NylC employs the Asp308-Asp306-Thr267 triad as catalytic residues for substrate hydrolysis, but the reaction requires Lys189 and Tyr146 as additional catalytic/substrate-binding residues specific for nylon hydrolysis.

Theory of Projectors and Its Application to Molecular Symmetry

Projector theory can serve as a powerful tool to perform the symmetric computation of molecular systems. The work of William Harter has long demonstrated the effectiveness of this theory in molecular spectroscopy; however, it seems its usefulness has not been realized by many in the field. We have described this methodology and have considered the D3 symmetry system and the tetrahedral symmetry of methane molecules as concrete examples where the computed rotation tensors and vibrational wavefunction were derived for some symmetry states.

DELE1 oligomers revealed by cryo-EM structure promote the integrated stress response activation.

Mitochondria are dynamic organelles that must continually adapt and respond to cellular stress, and perturbations in mitochondrial function trigger the integrated stress response (ISR). Recent studies demonstrated that mitochondrial stress can be relayed from the mitochondrial interior to the cytosol by the release of a C-terminal proteolytic fragment of DELE1 that binds to the HRI kinase to initiate integrate stress response signaling. Here, we report the cryo-electron microscopy structure of the active, C-terminal cleavage product of human DELE1 at ∼3.8 Å resolution, revealing that DELE1 assembles into a high-order oligomer. We confirmed that this C-terminal fragment of DELE1 also assembles into large oligomers in cells. Structurally, the oligomer consists of eight DELE1 monomers that assemble with D4 symmetry via two sets of distinct hydrophobic inter-subunit interactions. We identified the key residues involved in DELE1 oligomerization and confirmed their role in stabilizing the octamer in vitro and in cells using mutagenesis. Further, we show that assembly-impaired DELE1 mutants are compromised in their ability to induce ISR activation in cell culture models. Together, our findings provide molecular insights into the activity of DELE1 and how it signals to promote ISR activity following mitochondrial insult.

Tetramine Aspect Ratio and Flexibility Determine Framework Symmetry for Zn8 L6 Self-Assembled Structures.

We derive design principles for the assembly of rectangular tetramines into Zn8 L6 pseudo-cubic coordination cages. Because of the rectangular, as opposed to square, geometry of the ligand panels, and the possibility of either Δ or Λ handedness of each metal center at the eight corners of the pseudo-cube, many different cage diastereomers are possible. Each of the six tetra-aniline subcomponents investigated in this work assembled with zinc(II) and 2-formylpyridine in acetonitrile into a single Zn8 L6 pseudo-cube diastereomer, however. Each product corresponded to one of four diastereomeric configurations, with T, Th , S6 or D3 symmetry. The preferred diastereomer for a given tetra-aniline subcomponent was shown to be dependent on its aspect ratio and conformational flexibility. Analysis of computationally modeled individual faces or whole pseudo-cubes provided insight as to why the observed diastereomers were favored.

Chiral explosives: A theoretical investigation of structure and chiroptical properties of triacetone triperoxide and hexamethylene triperoxide diamine.

Triacetone triperoxide (TATP) and hexamethylene triperoxide diamine (HMTD) are cyclic peroxides that exhibit atropisomerism resulting from restricted rotation around three peroxide bonds. As a result, one pair of enantiomers with D3 symmetry and another pair of enantiomers with C2 symmetry can be identified. Previous studies, based on mass spectrometry data and computational results, have shown that conformations of TATP with D3 and C2 symmetry can be isolated. Assuming that enantiomer samples of TATP and HMTD can be obtained with sufficient enantiopurity, we investigated their chiroptical properties, namely, optical rotatory dispersion (ORD), vibrational circular dichroism (VCD), and Raman optical activity (VROA). ORD curves and VCD spectra are seen to be very similar for D3 - and C2 -symmetric atropisomers with the same overall helicity. Predicted VROA results, however, show significant differences between D3 - and C2 -symmetric atropisomers with the same overall helicity. The D3 -symmetric atropisomer is predicted to exhibit considerably larger magnitude vibrational optical activity signals than the C2 -symmetric atropisomer.

Bloch-type magnetic skyrmions in two-dimensional lattices.

Magnetic skyrmions in two-dimensional lattices are a prominent topic of condensed matter physics and materials science. Current research efforts in this field are exclusively constrained to Néel-type and antiskyrmions, while Bloch-type magnetic skyrmions are rarely explored. Here, we report the discovery of Bloch-type magnetic skyrmions in a two-dimensional lattice of MnInP2Te6, using first-principles calculations and Monte-Carlo simulations. Arising from the joint effect of broken inversion symmetry and strong spin-orbit coupling, monolayer MnInP2Te6 presents large Dzyaloshinskii-Moriya interaction. This, along with ferromagnetic exchange interaction and out-of-plane magnetic anisotropy, gives rise to skyrmion physics in monolayer MnInP2Te6, in the absence of a magnetic field. Remarkably, different from all previous works on two-dimensional lattices, the resultant magnetic skyrmions feature Bloch-type magnetism, which is protected by D3 symmetry. Furthermore, Bloch-type magnetic bimerons are also identified in monolayer MnTlP2Te6. The phase diagrams of these Bloch-type topological magnetisms under a magnetic field, temperature and strain are mapped out. Our results greatly enrich the research on magnetic skyrmions in two-dimensional lattices.

Eu3+ ions as a crystal-field probe for low-symmetry sites in doped phosphors - a case study: Eu3+ at triclinic sites in Li6RE(BO3)3 (RE = Y, Gd), YBO3 and ZnO and at trigonal sites in YAl3(BO3)4.

We present crystal-field (CF) calculations of energy levels (Ei) of Eu3+ ions doped in various hosts aimed at exploring the low-symmetry properties of CF parameters (CFPs) and reliability of CFP modelling with decreasing site symmetry. The hosts studied are: Li6Y(BO3)3, Li6Gd(BO3)3, YBO3, and ZnO with Eu3+ at triclinic sites; YAl3(BO3)4 with Eu3+ ions at trigonal D3 symmetry. Two independent CFP modelling approaches utilizing the hosts' structural data are employed: the exchange charge model (ECM) and the superposition model (SPM). We adopt the Eu3+ actual site symmetry and not the approximated one. The Ei values calculated using CFPs modelled by the ECM and SPM mutually agree with the observed ones. For triclinic symmetry, the ECM/CFPs and SPM/CFPs were numerically distinct, yet turned out to be physically equivalent yielding identical rotational invariants, Sk (k = 2, 4, 6) and Ei. For trigonal symmetry, both CFP sets agree numerically, thus Sk and Ei are identical. This disparity poses a dilemma, since the modified crystallographic axis system was used in both approaches. The standardization of the triclinic CFPs using the 3DD package was performed to solve this dilemma. It has enabled discussing standardization aspects in experimental and computed CFP sets and elucidating intricate low-symmetry aspects inherent in CFP sets. Understanding of low-symmetry aspects in CF studies may bring about a better interpretation of the spectroscopic and magnetic properties of rare-earth ion doped host crystals. Thus, our study could provide more deep insights into the importance of clear definitions of axis systems and adequate treatment of actual site symmetry in the modelling of CFPs for low-symmetry cases which is essential for technological applications and engineering of rare-earth activated phosphor materials.

Широкополосная ЭПР-спектроскопия кристалла Lu-=SUB=-3-=/SUB=-Al-=SUB=-5-=/SUB=-O-=SUB=-12-=/SUB=-:Tb-=SUP=-3+-=/SUP=-

In a single crystal of lutetium aluminum garnet (Lu3Al5O12, LuAG) in the frequency range of 37–210 GHz, at a temperature of 4.2 K, the EPR spectra of non-Kramers Tb3+ impurity ions were recorded. The measurement results indicate that Tb3+ ions replace Y3+ ions in the dodecahedral position with local D2 symmetry. The value of the g factor, the hyperfine structure constant, and the energy interval between the ground and the first excited nondegenerate sublevels of the ground multiplet are determined. Weak satellite signals were also registered, the origin of which is associated with the formation of antisite defects in the environment of paramagnetic Tb3+ centers.

Wide-band EPR spectroscopy of a Lu-=SUB=-3-=/SUB=-Al-=SUB=-5-=/SUB=-O-=SUB=-12-=/SUB=-:Tb-=SUP=-3+-=/SUP=- crystal

In a single crystal of lutetium aluminum garnet (Lu3Al5O12, LuAG) in the frequency range of 37-210 GHz, at a temperature of 4.2 K, the EPR spectra of non-Kramers Tb3+ impurity ions were recorded. The measurement results indicate that Tb3+ ions replace Y3+ ions in the dodecahedral position with local D2 symmetry. The value of the g factor, the hyperfine structure constant, and the energy interval between the ground and the first excited nondegenerate sublevels of the ground multiplet are determined. Weak satellite signals were also registered, the origin of which is associated with the formation of antisite defects in the environment of paramagnetic Tb3+ centers. Keywords: hyperfine interaction, rare earth ions, spin Hamiltonian, non-Kramers ion.

K([2.2.2]‐crypt)]K[Pt3(μ2‐CO)3(PPh3)3] ⋅ 3NH3 – A New Chini‐Type Platinum Carbonyl Complex

AbstractThe titular compound [K([2.2.2]‐crypt)]K[Pt3(μ2‐CO)3(PPh3)3] ⋅ 3NH3 (1) ([2.2.2]‐crypt=4,7,13,16,21,24‐Hexaoxa‐1,10‐diazabicyclo[8.8.8]hexacosane) contains a triangular platinum complex, the approximate D3 symmetry of which is only broken by the phenyl substituents of the PPh3 ligands.. The dianionic complex represents only the second triangular carbonyl platinate characterized via single crystal X‐ray diffraction in monomeric form. The compound crystallizes in the space group P with the unit cell parameters a=13.8826 Å, b=14.2899 Å and c=21.3254 Å. For the formation of the platinate, liquid ammonia seems to play a crucial role as a solvent for the polygermanide used for the reduction as well as for the stabilization of the dianion.

Xenon Induces Its Own Preferred Heterochiral Host from Exclusive Homochiral Assembly.

Xenon binding represents a formidable challenge, and efficient hosts remain rare. Here we report our findings that while enantiomeric bis(urea)-bis(thiourea) macrocycles form exclusive homochiral dimeric assemblies, xenon is able to overcome the narcissism and induces an otherwise-nonobservable heterochiral assembly as its preferred host. An experimental approach and fitting model were developed to obtain binding constants associated with the invisible assembly species. The determined xenon binding affinity with the heterochiral capsule reaches 1600 M-1, which is 15 times higher than that with the homochiral capsule and represents the highest record for an assembled host. The origin of the large difference in xenon affinity between the two subtle diastereotopic assemblies was revealed by single-crystal analysis. In the heterochiral capsule with S4 symmetry, the xenon atom is more tightly enclosed by van der Waals surroundings of the four thiourea groups arranged in a spherical cross-array, superior to the antiparallel array in the homochiral capsule with D2 symmetry.

Stereoselective Chiral Molecular Carbon Imides Featuring 12‐Fold [5]helicenes Around Four Cores**

AbstractDespite the great progress in research on molecular carbons containing multiple helicenes around one core, realizing the stereoselectivity of carbons containing multiple helicenes around more cores is still a great challenge. Herein, molecular carbon C204 featuring 12‐fold [5]helicenes around four cores was successfully constructed by using nine perylene diimide (PDI) units, and exhibits good solubility and stability. Despite 256 possible stereoisomers caused by the 12‐fold [5]helicenes, we only obtained one pair of enantiomers with D3 symmetry. There are four possible pairs of enantiomers with D3 symmetry, namely 7A, 7B, 7C and 7D. Theoretical and experimental results verify that the obtained structure belongs to 7C, which has the lowest energy. The enantiomers can also be separated by chiral HPLC. These results suggest that choosing PDIs as building blocks can not only improve the solubility and stability but also realize the stereoselectivity and chirality of molecular carbons.

Stereoselective Chiral Molecular Carbon Imides Featuring 12-Fold [5]helicenes Around Four Cores.

Despite the great progress in research on molecular carbons containing multiple helicenes around one core, realizing the stereoselectivity of carbons containing multiple helicenes around more cores is still a great challenge. Herein, molecular carbon C204 featuring 12-fold [5]helicenes around four cores was successfully constructed by using nine perylene diimide (PDI) units, and exhibits good solubility and stability. Despite 256 possible stereoisomers caused by the 12-fold [5]helicenes, we only obtained one pair of enantiomers with D3 symmetry. There are four possible pairs of enantiomers with D3 symmetry, namely 7A, 7B, 7C and 7D. Theoretical and experimental results verify that the obtained structure belongs to 7C, which has the lowest energy. The enantiomers can also be separated by chiral HPLC. These results suggest that choosing PDIs as building blocks can not only improve the solubility and stability but also realize the stereoselectivity and chirality of molecular carbons.

Surface modifications of eight-electron palladium silver superatomic alloys

Atomically precise thiolate-protected coinage metal nanoclusters and their alloys are far more numerous than their selenium congeners, the synthesis of which remains extremely challenging. Herein, we report the synthesis of a series of atomically defined dithiophosph(in)ate protected eight-electron superatomic palladium silver nanoalloys [PdAg20{S2PR2}12], 2a–c (where R = OiPr, a; OiBu, b; Ph, c) via ligand exchange and/or co-reduction methods. The ligand exchange reaction on [PdAg20{S2P(OnPr)2}12], 1, with [NH4{Se2PR2}12] (where R = OiPr, or OnPr) leads to the formation of [PdAg20{Se2P(OiPr)2}12] (3) and [PdAg20{Se2P(OnPr)2}12] (4), respectively. Solid state structures of 2a, 2b, 3 and 4 unravel different PdAg20 metal frameworks from their parent cluster, originating from the different distributions of the eight-capping silver(I) atoms around a Pd@Ag12 centered icosahedron with C2,D3,Th and Th symmetries, respectively. Surprisingly ambient temperature crystallization of the reaction product 3 obtained by the ligand exchange reaction on 1 has resulted in the co-crystallization of two isomers in the unit cell with overall T (3a) and C3 (3b) symmetries, respectively. To our knowledge, this is the first ever characterized isomeric pair among the selenolate-protected NCs. Density functional theory (DFT) studies further rationalize the preferred geometrical isomerism of the PdAg20 core.

Effective medium perspective on topological transitions in metamaterials

Many properties of photonic structures rely on band topology characterized by the integer invariants that can change during the topological transitions and give rise to the disorder-robust topological edge, corner, or interface states. Typically, the periods of such structures are comparable to the wavelength. However, in many cases, the unit cell becomes deeply subwavelength and hence the entire metamaterial can be described in terms of the effective material parameters. Here, focusing on subwavelength topological metamaterials, we identify the behavior of permittivity and permeability accompanying the topological transition on the example of the two structures possessing D6 symmetry.

Color coordination of emerald on CIE color space based on first-principles calculations

Be3Al2(SiO3)6 including Cr3+ known as emerald have been widely studied and utilized for solid-state laser materials. Numerous theoretical investigations on these systems have also been published in the literature since the electronic energy levels, optical properties, and structures of Cr3+ impurities in emerald systems have been thoroughly investigated using a variety of experimental approaches. In general, semi-empirical computations have been used to accomplish the majority of theoretical interpretations of experimental data. Although in the case of non-empirical calculations, the agreement between theoretical and experimental optical properties was improved by taking into account the energy corrections, quantitative evaluation of the color of emitted light was not feasible until recently. Here, the color coordinates of emerald under the standard illuminant has been calculated to perform a quantitative evaluation based on the optical spectra. The “theoretical” color was calculated and presented visually on the Commission Internationale d’Eclairage (CIE) color space based on the theoretical spectra obtained non-empirically using the so-called first-principles discrete variational multi-electron method, known as DVME. The absorption spectra of emerald were calculated using CrO69− model cluster with D3 symmetry. Several key effects in reproducing optical spectra were investigated in detail, such as lattice relaxation, energy correction, and orbital effects. The accuracy of this approach in predicting absorption spectra was analyzed thoroughly under various computational conditions. The results show that accounting for all of the above effects is important to producing the absorption spectra. Specifically, enlarging the considered orbital in the calculation improved the agreement between the computed and experimentally-observed colors. This study is crucial for validating the non-empirical calculations made using the DVME approach to assess the color of emitted light quantitatively.