S4 Symmetry Research Articles

Heterofullerene C48B12-impregnated MOF-5 and IRMOF-10 for hydrogen storage: A combined DFT and GCMC simulations study

The H2 storage properties of isoreticular metal-organic framework materials (IRMOFs), MOF-5 and IRMOF-10, impregnated with different numbers and types of heterogeneous C48B12 molecules were investigated using density functional theory and grand canonical Monte Carlo (GCMC) calculations. The excess hydrogen adsorption isotherms of IRMOFs at 77 K within 20 bar indicate that suitable number and type of C48B12 molecules play a crucial role in improving the H2 storage properties of IRMOFs. Among the studied pure and nC48B12 (n = 1, 2, 4, 8) in Ci symmetry impregnating into MOF-5, at 77 K under 6 bar, MOF-5-4C48B12 with a 3.5 wt% and 29.9 g/L hydrogen storage density, and at 77 K under 12 bar, the pure MOF-5 with a 4.9 wt% and 31.0 g/L hydrogen storage density has the best hydrogen storage properties. Whereas, among the studied pure and nC48B12 (n = 1, 2, 4, 8) in S6 symmetry impregnating into IRMOF-10, IRMOF-10-8C48B12 always shows the best hydrogen storage properties among the pure and C48B12-impregnated IRMOF-10 at 77 K within 20 bar. IRMOF-10-8C48B12 has a 6.0 wt% and 34.6 g/L hydrogen storage density at 77 K under 6 bar, and has a 7.1 wt% and 41.4 g/L hydrogen storage density at 77 K under 12 bar. The confinement effect of IRMOFs on C48B12 molecules, and steric hindrance effect of C48B12 molecules on IRMOFs mainly affects the H2 uptake capacity by comparing the absolute H2 molecules in individual IRMOFs units, C48B12 molecules, and IRMOFs-nC48B12 compounds. The absolute hydrogen adsorption profiles show that eight C48B12 molecules impregnating into MOF-5 can exert obvious steric effects for H2 adsorption. The saturated gravimetric and volumetric H2 densities of IRMOF-10-8C48B12 higher than those of MOF-5-8C48B12 due to with larger free volume.

Lanthanide-doped niobium oxide nanoparticles on nanoarchitectured silica spheres as potential probe for NIR luminescent markers

We have prepared Nb2O5:Eu3+ and Nb2O5:Nd3+ nanostructured materials and SiO2@Nb2O5:Eu3+ core@shell nanoparticles by the sol–gel route to evaluate how the annealing temperature influences their structural and luminescent features, aiming at their potential application as optical markers. An intense red emission under excitation at the blue region was detected from the Nb2O5:Eu3+ solids. Inhomogeneous broadening on the photoluminescence spectra was observed for the sample annealed at 600 °C, while the allocation of the Eu3+ ions on S4 symmetry sites was attributed for higher annealing temperature (1100 °C). A discrete formation of the H-phase (monoclinic) of niobium oxide for the sample annealed at an intermediate temperature of 900 °C was observed, with its photoluminescence spectra revealing the preferential occupation of the Eu3+ ions on sites in this crystalline phase. Photoluminescence decay curves recorded for the 5D0 excited state revealed average lifetime values in the order of milliseconds. The Nb2O5:Nd3+ solids displayed analogous behavior: Nd3+ preferentially occupied the monoclinic phase symmetry sites. In water dispersion and under low-power laser excitation (808 nm), the Nb2O5:Nd3+ systems emitted in biological windows. The sample annealed at 600 °C provided the most promising luminescence intensity and colloidal stability. The surface of the SiO2 nanoparticles was successfully decorated with Nb2O5:Eu3+ nanoparticles in the T-phase. The SiO2@Nb2O5:Eu3+ core@shell nanoparticles presented color tunability due to red light emission from Eu3+ and blue light emission from defect centers in the SiO2 template. The possibility of functionalizing SiO2 nanoparticles with red-emitting Nb2O5:Eu3+ nanoparticles combined with blue excitation and lifetime values in the order of milliseconds renders the prepared SiO2@Nb2O5:Eu3+ core@shell nanoparticles promising biomarkers that can be explored by time-gated luminescence techniques.

Renormalizable standard model extension with S4 symmetry for neutrino mass and mixing

We suggest a renormalizable standard model extension based on S4 symmetry that accommodates the recent observed neutrino oscillation pattern. Through the type-I seesaw mechanism, the smallness of the active neutrino mass and its hierarchy are produced. The model generates the updated data on neutrino parameters in which the reactor neutrino mixing angle θ13, the atmospheric neutrino mixing θ23, and the Dirac phase δ for both NH and IH belong to 1σ range, while the solar mixing angle θ12 = 35.70° belongs to 2σ range. The effective masses are found to be 〈 mee〉 = 5.74 meV for NH and 〈 mee〉 = 48.1 meV for IH within their allowed constraints.

High-temperature non-centrosymmetric magnets for skyrmionics

Such topological spin textures as magnetic skyrmions and antiskyrmions have attracted significant interest in recent years owing to their rich variety of underlying physics and potential applications in next-generation magnetic devices. In the domain of applications, it is essential to stabilize the topological spin textures over a wide range of temperatures, including room temperature, and manipulate them with various external stimuli. Significant developments have been made in room-temperature skyrmions and antiskyrmions arising from the Dzyaloshinskii–Moriya interaction (DMI) in several magnetic materials with broken inversion symmetry. In this Perspective, we review recent progress in non-centrosymmetric magnets with bulk DMI, which host skyrmions and antiskyrmions above room temperature. We first provide an overview of room-temperature Bloch-type skyrmions and the robustness of their metastability, the variety of their forms, and their dynamics in Co–Zn–Mn alloys with a β-Mn-type chiral structure. We then focus on room-temperature antiskyrmions as well as their topological transformations in Heusler alloys with D2d symmetry and Pd-doped (Fe,Ni)3P with S4 symmetry. The robust skyrmions and antiskyrmions, with versatile tunability in these non-centrosymmetric materials at room temperature, represent a step toward the long-sought milestone of “skyrmionics.”

Two Zirconium Metal–Organic Cages with S4 and D2d Symmetry: Construction and Detection of Antibiotics

The construction of robust zirconium metal–organic cages (Zr-MOCs) with specific geometric structures and properties is of great significance but is challenging. Herein, two Zr-MOCs (Zr-MOC-1 and Zr-MOC-2), which respectively comprise triphenylamine and carbazole functional groups, are synthesized and structurally characterized. Compared with the perfect tetrahedral geometry with S4 symmetry in Zr-MOC-1, the presence of carbazole structural units leads the tetrahedral structure of Zr-MOC-2 to be distorted, and then assumes it a trigonal pyramid geometry with D2d symmetry. Furthermore, these two Zr-MOCs could be used as soluble chemical sensors for probing nitrofuran antibiotics, and the detection sensitivity of Zr-MOC-2 is higher than that of Zr-MOC-1. These results demonstrate that the introduction of appropriate structural units into Zr-MOCs may significantly impact their architectures and properties.

Doping Control of Magnetic Anisotropy for Stable Antiskyrmion Formation in Schreibersite (Fe,Ni)3 P with S4 symmetry.

Magnetic skyrmions, vortex-like topological spin textures, have attracted much interest in a wide range of research fields from fundamental physics to spintronics applications. Recently, growing attention is also paid to antiskyrmions emerging with opposite topological charge in non-centrosymmetric magnets with D2d or S4 symmetry. In these magnets, complex interplay among anisotropic Dzyaloshinskii-Moriya interaction, uniaxial magnetic anisotropy, and magnetic dipolar interactions generates various magnetic textures. However, the precise role of these magnetic interactions in stabilizing antiskyrmions remains to be elucidated. In this work, the uniaxial magnetic anisotropy of schreibersite (Fe,Ni)3 P with S4 symmetry is controlled by doping and its impact on the stability of antiskyrmions is investigated. The authors' magnetometry study, supported by ferromagnetic resonance spectroscopy, shows that the variation of the Ni content and slight doping with 4d transition metals considerably change the magnetic anisotropy. In particular, doping with Pd induces easy-axis anisotropy, giving rise to formation of antiskyrmions, while a temperature-induced spin reorientation is observed in an Rh-doped compound. In combination with Lorentz transmission electron microscopy and micromagnetic simulations, the stability of antiskyrmion as functions of uniaxial anisotropy and demagnetization energy is quantitatively analyzed, and demonstrated that subtle balance between them is necessary to stabilize the antiskyrmions.

Luminescence properties of Yb3+ and Er3+ co-doped into Gd2O3:Bi3+ phosphor powder

Yb3+ and Er3+ co-doped Gd2O3:Bi3+ phosphor were prepared via a combustion method. The structural properties and surface morphology of the phosphors were studied with X-ray diffraction and a scanning electron microscope. UV–visible absorption, photoluminescence and cathodoluminescence (CL) spectra were also investigated. The optical bandgap of Gd2O3 increased with additional doping. The visible emission confirmed that the Gd2O3:Bi3+ co-doped with Yb3+ is located in the blue and green band regions related to the Bi3+ in the S6 and C2 symmetry sites. The near-infrared (NIR) down-conversion (DC) emission intensity increased upon increasing the Yb3+ concentration. The visible Bi3+ emission was reduced when adding a higher Yb3+ ion concentration while the NIR emission increased due to the energy transfer from the Bi3+ to the Yb3+ ions. UV-Vis energy excitation photons were successfully converted into NIR photons. The up-conversion (UC) visible emission spectra of Gd2O3:Bi3+ co-doped Er3+ consisted of two strong green, weak red and NIR emission bands. The 980 nm infrared excitation was successfully converted into UV-Vis emission. The CL emission spectra confirmed blue emission bands assigned to the 3P1 → 1S0 transitions of the Bi3+ ions and the green-yellow emission bands corresponded to an overlap between the 3P1 → 1S0 transitions of the Bi3+ ions and the 2H11/2, 4S3/2 → 4I15/2 transitions of the Er3+ ions. A significant enhancement of the emission intensities of Yb3+ and Er3+ ions was observed after Bi3+ doping. The results indicated that Gd2O3 materials based on the Bi3+–Yb3+ and Bi3+–Er3+ couples may be possible phosphors for improving photovoltaic conversion efficiency via spectral modification utilizing the DC and UC processes.

4-dimensional lattice models for the quantum range

Some finite subspace models L are presented for quantum structures which replace the use of countable infinite Hilbert space H dimensions. A maximal Boolean sublattice, called block, is 24, where its four atoms directly above 0εL, base vectors of H in 24 are drawn as four points on an interval. Blocks can overlap in one or two atoms. Different kinds of operators can map one block onto another and interpretations are given such that subspaces can carry on their base vector tuple real, complex or quaternionic numbers, energies, symmetries and generate coordinate lines. Describing states of physical systems is done using L and its applications for dynamical modelling. They don‘t need the infinte dimensional vectors of H. L has in the first model 11 blocks and 24 atoms (figure 1). They correspond to the 24 elements of the tetrahedral S4 symmetry. S4 arises from a spin-line rgb-graviton whirl operator with center at the tip of a tetrahedron and a nucleon triangle base with three quarks as vertices. The triangles factor group D3 of S4 is due to the CPT Klein normal subgroup Z2 x Z2 of S4 . It has a strong interaction SI rotor for the nucleons inner dynamics which is used for integrating functions, exchanging energies of nucleon with its environment and setting barycentrical coordinates in the triangle. At their intersection B as barycenter sets a Higgs boson or field the rescaled quark mass of a nucleon. Each factor class of one element from D3 assigns to it a color charge, a coordinate, an energy vector and a symmetry. Symmetries attached can be different according to interactions involved. Every atom of L has then a specific character with different properties.Three characters are added to octonian base vectors, listed by their indices as n = 0,1,…,7, and named for the atoms of L as na, nb, nc. The structure and element attributes of the finite subspace lattices L are desribed in many examples and models which technical constructed run macroscopically. Several models are described below. Example, the color charge whirl as rgb-graviton projection operator maps the block 2c3b5a6a to 0a1a2a3a. The symmetries change dimension from 3x3- to 2x2-matrices. From SU(3) are λ1 on 3b mapped to the SU(2) x-coordinate Pauli matrix σ1, from λ2 on 5a to σ2 y-coordinate and from λ3 on 6a to σ3 z-coordinate of real Euclidean space R³. The SU(3) matrices have complex w3 = z +ict, w2 = (iy,f), w1 = (x,m) coordinates. In figure 3 is shown how a rotation of two proton tetrahedrons for fusion changes the two linearly independent wj vectors to the 1-dimensional x,y,z base vectors. In deuteron then on one coordinate line sit with Cooper paire u-d-quarks at the ends the Heisenberg coupled energy or space vector rays 15 (x,m), m mass measured in kg, x in meter, 23 (iy,E(rot)), E(rot) rotational energy measured in Joule J, y in meter, 46 (ict,f), t time measured in seconds, f = 1/∆t frequency s inverse time interval measured in Hz. The six color charges are red r on +x as octonian coordinate 1, green g on +y as 2 , blue b on -z as 6, turquoise on -x as 5, magenta on -y as 3, yellow on +z as 4..

Racemic and Meso Crystal Structures of an Axial-Chiral Spirobi-(dinaphthoazepin)ium Salt: Emergence of an S4-Symmetric Molecule

To date, only a few instances of S4-symmetric organic molecules exist. In principle, spirobi-(dinaphthoazepin)ium cations can achieve this highly symmetric point group. Heating racemic 2,2′-bis(bromomethyl)-1,1′binaphthyl with aqueous ammonia afforded a mixture of rac- and meso-3,3′,5,5′-tetrahydro-4,4′-spirobi[dinaphtho[2,1-c:1′,2′-e]azepin]-4-ium bromide which was separated by fractional crystallisation. Both stereoisomers were characterised spectroscopically, and their crystal structures were determined and compared. The rac crystal structure differs significantly from the known enantiopure one. The meso molecules display a near-perfect S4 symmetry. Upon treatment with KOtBu, both isomers undergo Stevens rearrangement.

Theoretical and computational investigation of the Eu3+ ion local symmetry in fluorides compounds

We employed the computational modelling technique with crystal field models to indicate the local symmetry of the Eu3+ ion in AF2 (A = Ca, Sr and Ba) crystals. Using a set of Buckingham potential parameters, the lattice parameters and the unit cell volume for all these crystals were reproduced satisfactorily with good fit in comparison with experimental data. Bound extrinsic defects calculations through low solution energy revealed that the Eu3+ occupies the A2+ site compensated by cationic vacancies. The spectroscopic study using the SOM with the MENN showed that the Eu3+ occupies a distorted inversion centre being a distorted S6 symmetry. In this indication, we used a set of phenomenological charge factors that reproduced the 7F1 level splitting and the 7F1, 7F2 and 5D1 energy sublevels.

Room-temperature antiskyrmions and sawtooth surface textures in a non-centrosymmetric magnet with S4 symmetry.

Topological spin textures have attracted much attention both for fundamental physics and spintronics applications. Among them, antiskyrmions possess a unique spin configuration with Bloch-type and Néel-type domain walls owing to anisotropic Dzyaloshinskii-Moriya interaction in the non-centrosymmetric crystal structure. However, antiskyrmions have thus far only been observed in a few Heusler compounds with D2d symmetry. Here we report a new material, Fe1.9Ni0.9Pd0.2P, in a different symmetry class (S4), in which antiskyrmions exist over a wide temperature range that includes room temperature, and transform into skyrmions on changing magnetic field and lamella thickness. The periodicity of magnetic textures greatly depends on the crystal thickness, and domains with anisotropic sawtooth fractals were observed at the surface of thick crystals and attributed to the interplay between the dipolar interaction and the Dzyaloshinskii-Moriya interaction as governed by crystal symmetry. Our findings provide an arena in which to study antiskyrmions, and should stimulate further research on topological spin textures and their applications.

High-throughput screening for Weyl semimetals with [formula omitted] symmetry

Based on irreducible representations (or symmetry eigenvalues) and compatibility relations (CR), a material can be predicted to be a topological/trivial insulator (satisfying CR) or a topological semimetal (violating CR). However, Weyl semimetals (WSMs) usually go beyond this symmetry-based strategy. In other words, Weyl nodes could emerge in a material, no matter if its occupied bands satisfy CR, or if the symmetry indicators are zero. In this work, we propose a new topological invariant χ for the systems with S4 symmetry (i.e., the improper rotation S4(≡IC4z) is a proper fourfold rotation (C4z) followed by inversion (I)), which can be used to diagnose the WSM phase. Moreover, χ can be easily computed through the one-dimensional Wilson-loop technique. By applying this method to the high-throughput screening in our first-principles calculations, we predict a lot of WSMs in both nonmagnetic and magnetic compounds. Various interesting properties (e.g., magnetic frustration effects, superconductivity and spin-glass order, etc.) are found in predicted WSMs, which provide realistic platforms for future experimental study of the interplay between Weyl fermions and other exotic states.

Dirac neutrino mass models with a modular S4 symmetry

In this paper, we investigate lepton mass spectra, flavor mixing and CP violation with a modular S4 symmetry under the assumption that neutrinos are Dirac fermions. We find that the Majorana mass term can be forbidden by adjusting the weight of the right-handed neutrino superfields. We study the scenarios where modular forms in the neutrino sector take the lowest non-trivial weight two, while those in the charged-lepton sector vary from two to six. The corrections from renormalization-group running effects to our model have also been discussed in detail. We totally obtain twelve different classes of models and find that ten of them can accommodate current neutrino oscillation data.

Nonrigid water octamer: Computations with the 8-cube.

A 8-cube model of the fully nonrigid water octamer is considered within the 8-dimensional hyperoctahedral wreath product group with 10,321,920 operations and 185 irreducible representations by employing computational and mathematical techniques. For the two lowest-lying isomers of (H2 O)8 with D2d and S4 symmetries of a rigid (H2 O)8 , correlation tables and nuclear spin statistics are constructed for the tunneling splittings of the rotational levels are computed by a computational matrix polynomial generating function technique combined with Möbius inversion, and the relationship to the 8-cube multinomials are pointed out. Multinomial generating functions combined with the induced representation techniques are employed to compute and construct the nuclear spin species, nuclear spin statistical weights and tunneling splittings of rovibronic levels. We have also computed the spin statistical weights and tunneling splittings of the rotational levels for a semirigid water octamer within the wreath product Oh [S2 ] consisting of 12,288 operations.

Polyhydrido Copper Nanoclusters with a Hollow Icosahedral Core: [Cu30 H18 {E2 P(OR)2 }12 ] (E=S or Se; R=nPr, iPr or iBu).

Although atomically precise polyhydrido copper nanoclusters are of prime interest for a variety of applications, they have so far remained scarce. Herein, this work describes the synthesis of a dithiophosphate-protected copper(I) hydride-rich nanocluster (NC), [Cu30 H18 {S2 P(OnPr)2 }12 ] (1H ), fully characterized by various spectroscopic methods and single-crystal X-ray diffraction. The X-ray structure of 1H reveals an unprecedented central Cu12 hollow icosahedron. Six faces of this icosahedron are capped by Cu3 triangles, the whole Cu30 core being wrapped by twelve dithiophosphate ligands and the whole cluster has ideal S6 symmetry. The locations of the 18 hydrides in 1H were ascertained by a single-crystal neutron diffraction study. They are composed of three types: capping μ3 -H, interstitial μ4 -H (seesaw) and μ5 -H ligands (square pyramidal), in good agreement with the DFT simulations. The numbers of hydrides and ligand resonances in the 1 H NMR spectrum of 1H are in line with their coordination environment in the solid state, retaining the S6 symmetry in solution. Furthermore, two new Se-protected polyhydrido copper nanoclusters, [Cu30 H18 {Se2 P(OR)2 }12 ] (2H : R=iPr 3H : R=iBu) were synthesized from their sulfur relative 1H via ligand displacement reaction and their X-ray structures feature the exceptional case where both the NC shape and size are fully conserved during the course of ligand exchange. DFT and TD-DFT calculations allow understanding the bonding and optical properties of clusters 1H -3H . In addition, the reaction of 1H with [Pd(PPh3 )2 Cl2 ] in the presence of terminal alkynes led to the formation of new bimetallic Cu-Pd alloy clusters [PdCu14 H2 {S2 P(OnPr)2 }6 (C≡CR)6 ] (4: R=Ph; 5: R=C6 H4 F).

The minimal seesaw model with a modular S4 symmetry

In this paper, we incorporate the modular S4 flavor symmetry into the supersymmetric version of the minimal type-I seesaw model, in which only two right-handed neutrino singlets are introduced to account for tiny Majorana neutrino masses, and explore its implications for the lepton mass spectra, flavor mixing and CP violation. The basic idea is to assign two right-handed neutrino singlets into the unique two-dimensional irreducible representation of the modular S4 symmetry group. Moreover, we show that the matter-antimatter asymmetry in our Universe can be successfully explained via the resonant leptogenesis mechanism working at a relatively-low seesaw scale ΛSS≈ 107 GeV, with which the potential problem of the gravitino overproduction can be avoided. In this connection, we emphasize that the observed matter-antimatter asymmetry may lead to a stringent constraint on the parameter space and testable predictions for low-energy observables.

Additivity and non-additivity of dissociation energies in intermolecular interactions. Theoretical studies on (H2)n, n = 2-8, (CO2)n, n = 2-6 and (HF)n, n = 2-8

CCSD(T) and MP2 results using the aug-cc-pV5Z basis set are reported for chain, cyclic and other structures of the clusters (H2)n, n = 2-8, (CO2)n, n = 2-6 and (HF)n, n = 2-8. In chain-like structures of (H2)n and (CO2)n, with the bonding type of the dimer maintained, the dissociation energy De of the dimer doubles for the trimer, triples for the tetramer, and so on. Due to these systems being dominated by short-range forces, interactions are essentially restricted to neighbouring monomers. For other types of (H2)n and (CO2)n structures, the multipliers relative to the dimerisation energy can be much higher. Dissociation energies for the hexamers in S6 symmetry of both H2 (379 cm−1) and CO2 (4925 cm−1) are over ten times the respective dimerisation energies. For the chain-like trimer of HF, however, De is in excess of double the dimer value. Mainly due to longer-range dipolar forces, the interactions reach beyond the neighbouring monomers. The interaction energy between HF monomers in chains follows an approximate R−2 (R being the F–F distance) relationship, The calculated dissociation energies of the HF octamer are 15,985 cm−1 (factor of 10.4) for the chain, and 21,003 cm−1 (factor of 13.7) for the C6h cyclic structure.

A new Littlest Seesaw model

We propose and discuss a new Littlest Seesaw model, realized in the tri-direct CP approach, in which the couplings of the two right-handed neutrinos to the lepton doublets are proportional to (0, −1, 1) and (1,5/2, −1/2) respectively with the relative phase η = −π/2. This model can give an excellent description of lepton flavour mixing, including an atmospheric neutrino mixing angle in the second octant, in terms of only two input parameters. We show that the observed baryon asymmetry can be generated for the lightest right-handed neutrino mass M1 = 1.176 × 1011 GeV in SM and M1 = 3.992 × 1010 GeV in MSSM with . We construct an explicit Littlest Seesaw model based on the flavour symmetry S4 × Z5 × Z8 in which the desired alignments and the phase η = −π/2 are achieved.

New A4 lepton flavor model from S4 modular symmetry

We study a flavor model with A4 symmetry which originates from S4 modular group. In S4 symmetry, Z2 subgroup can be anomalous, and then S4 can be violated to A4. Starting with a S4 symmetric Lagrangian at the tree level, the Lagrangian at the quantum level has only A4 symmetry when Z2 in S4 is anomalous. We obtain modular forms of two singlets and a triplet representations of A4 by decomposing S4 modular forms into A4 representations. We propose a new A4 flavor model of leptons by using those A4 modular forms. We succeed in constructing a viable neutrino mass matrix through the Weinberg operator for both normal hierarchy (NH) and inverted hierarchy (IH) of neutrino masses. Our predictions of the CP violating Dirac phase δCP and the mixing sin2θ23 depend on the sum of neutrino masses for NH.

Fourfold symmetric MCR's via the tetraisocyanide 1,3-diisocyano-2,2-bis(isocyanomethyl)propane.

Oligoisocyanides are attractive synthetic targets, however, only a few are known. Here, we describe the smallest stable tetraisocyanide possible, the 1,3-diisocyano-2,2-bis(isocyano-methyl)propane (1) with S4 symmetry. Its four-step synthesis, structure, and reactivity in unprecedented symmetric fourfold Ugi 4CR and fourfold Passerini 3CR are described. Exhibiting high functional group tolerance and moderate to high yields, we foresee multiple applications of 1,3-diisocyano-2,2-bis(isocyanomethyl)propane, for example in MOFs, COFs, dendrimers, or artificial organs.