Mirror Plane Research Articles

Dual-spherical-wave optical scanning holographic microscopy with resolution enhancement and an extended depth of field

Conventional optical scanning holographic microscopy (OSHM) is realized by using a plane wave and a spherical wave as the illumination. The resolution of the conventional OSHM is limited by the numerical aperture of the spherical wave and cannot exceed the Rayleigh limit. In this paper, the OSHM by using dual spherical waves as the illumination is studied. The model of a Gaussian wave, together with the constraints on the signal strength and the visibility, are considered in the analysis of the dual-spherical-wave (DS) OSHM. For an object located at the symmetry plane of the DS-OSHM, the resolution can slightly exceed the Rayleigh limit, and the depth of field (DoF) is extended significantly. For a transparent object, the noise in the DS-OSHM is less than that of the conventional OSHM, thanks to the highly divergent scanning beam. If the object is off the symmetry plane, the resolution is still enhanced, but the extension of the DoF is limited. In addition, a clear reconstructed image will be observed not only at the original object plane, but also at its mirror plane. To the best of our knowledge, this phenomenon is reported for the first time.

Three-dimensional alkaline earth metal-organic framework poly[[μ-aqua-aqua-bis-(μ3-carba-moyl-cyano-nitro-somethanido)barium] monohydrate] and its thermal decomposition.

In the structure of the title salt, {[Ba(μ3-C3H2N3O2)2(μ-H2O)(H2O)]·H2O} n , the barium ion and all three oxygen atoms of the water mol-ecules reside on a mirror plane. The hydrogen atoms of the bridging water and the solvate water mol-ecules are arranged across a mirror plane whereas all atoms of the monodentate aqua ligand are situated on this mirror plane. The distorted ninefold coord-ination of the Ba ions is completed with four nitroso-, two carbonyl- and three aqua-O atoms at the distances of 2.763 (3)-2.961 (4) Å and it is best described as tricapped trigonal prism. The three-dimensional framework structure is formed by face-sharing of the trigonal prisms, via μ-nitroso- and μ-aqua-O atoms, and also by the bridging coordination of the anions via carbonyl-O atoms occupying two out of the three cap positions. The solvate water mol-ecules populate the crystal channels and facilitate a set of four directional hydrogen bonds. The principal Ba-carbamoyl-cyano-nitro-somethanido linkage reveals a rare example of the inherently polar binodal six- and three-coordinated bipartite topology (three-letter notation sit). It suggests that small resonance-stabilized cyano-nitroso anions can be utilized as bridging ligands for the supra-molecular synthesis of MOF solids. Such an outcome may be anti-cipated for a broader range of hard Lewis acidic alkaline earth metal ions, which perfectly match the coordination preferences of highly nucleophilic nitroso-O atoms. Thermal analysis reveals two-stage dehydration of the title compound (383 and 473 K) followed by decomposition with release of CO2, HCN and H2O at 558 K.

Signatures of hybridization of multiple Majorana zero modes in a vortex.

Majorana zero modes (MZMs) are emergent zero-energy topological quasiparticles that are their own antiparticles1,2. Detected MZMs are spatially separated and electrically neutral, so producing hybridization between MZMs is extremely challenging in superconductors3,4. Here, we report the magnetic field response of vortex bound states in superconducting topological crystalline insulator SnTe (001) films. Several MZMs were predicted to coexist in a single vortex due to magnetic mirror symmetry. Using a scanning tunnelling microscope equipped with a three-axis vector magnet, we found that the zero-bias peak (ZBP) in a single vortex exhibits an apparent anisotropic response even though the magnetic field is weak. The ZBP can robustly extend a long distance of up to approximately 100 nm at the (001) surface when the magnetic field is parallel to the ( )-type mirror plane, otherwise it displays an asymmetric splitting. Our systematic simulations demonstrate that the anisotropic response cannot be reproduced with trivial ZBPs. Although the different MZMs cannot be directly distinguished due to the limited energy resolution in our experiments, our comparisons between experimental measurements and theoretical simulations strongly support the existence and hybridization of symmetry-protected multiple MZMs. Our work demonstrates a way to hybridize different MZMs by controlling the orientation of themagnetic field and expands the types of MZM available for tuning topological states.

Structural origin of spin-splitting anisotropy in janus dichalcogenides monolayers under pressure

Abstract Janus transition-metal dichalcogenides (TMDs) have drawn a great deal of attention because of their mirror plane symmetry breaking that allows the emergence of a built-in out-of-plane dipole which determine superior piezoelectric and spin-related properties. Furthermore, it has been shown in the recent literature that pressure application is capable of modulating spin-related phenomena in this class of materials. Generally, the spin-splitting presence in real systems is explored in terms of point group symmetry reduction using solely group theory arguments. However, we seek to associate the enhancement of spin-splitting in Janus TMDs monolayers by searching the most important local asymmetries responsible for the symmetry lowering that leads the monolayer larger spin-splitting energies. In this sense, we seek to unveil a possible structural descriptor that correlates with subbands splitting magnitude in Janus TMDs. To accomplish this, we performed a detailed first-principles investigation into WSSe Janus monolayers under biaxial in-plane strain to find that pressure induces a symmetry lowering from the C 3v to the C s point group. From these observations, we found that in-plane angle asymmetries between the chalcogens yield a distortion metric that can serve as a descriptor for enhanced spin-splitting in Janus WSSe since it strongly correlates with spin-splitting energies. Hence, our work establishes that, rather than solely global symmetry analysis, specific local distortions provide a key design principle to achieve strong spin-splitting in 2D Janus TMDs.

Tunable bandgaps of guided waves by periodic shunting circuits in multilayered piezoelectric plates

The multi-mode and dispersion characteristics of guided waves in plate bring great challenges to the manipulation of guided waves and controlling vibration and noise. In this study, the Stroh formalism is developed to establish a theoretical model for deriving the dispersion relations of guided waves in a multilayered piezoelectric plate. The dispersion characteristics under different electrical boundary conditions introduced by periodic shunting circuits are discussed to reveal the influences of external circuits on guided wave propagation. The proper shunting circuit is not only the key point to obtain the specific frequency of bandgap, but also the effective method to control the bandwidth. Furthermore, for the separation of symmetric and anti-symmetric modes of guided waves, the multilayered piezoelectric plate with a mirror plane is studied by using an equivalent model. Results indicate that the propagation behaviors of guided waves in multilayered piezoelectric plates can be interpreted by developed Stroh formalism, and their bandgaps can be effectively manipulated by periodically external circuits. The tunable bandgaps in this work could be helpful for designing smart devices of wave isolation based on multilayered piezoelectric plate.

Chiral Templating in a Hybrid Chromium Chloride Hydrate.

The synthesis and characterization of three new hybrid metal halide hydrates in which mer-[CrIIICl3(H2O)3]0 cocrystallizes alongside α-methylbenzylammonium chloride are described. The enantiomorphic crystals, ((R)-(+)-α-methylbenzylammonium)2(mer-[CrCl3(H2O)3])Cl2 ((R)-1) and ((S)-(-)-α-methylbenzylammonium)2(mer-[CrCl3(H2O)3])Cl2 ((S)-1), have C2221 space group symmetry and show mirrored circular dichroism signals. The racemate, (rac-α-methylbenzylammonium)2(mer-[CrCl3(H2O)3])Cl2 ((rac)-1), adopts a polar structure with Cm space group symmetry in which enantiomers are related by mirror planes within organic bilayers. Alongside detailed crystallography and magnetism of each compound, the optical properties of the mer-[CrIIICl3(H2O)3]0 unit are revisited. Understanding the intermolecular forces that stabilize each of these crystal structures lends insights into crystal engineering methodologies for stabilizing noncentrosymmetric hybrid metal halides.

Crystallographic Quaternions

Symmetry transformations in crystallography are traditionally represented as equations and matrices, which can be suitable both for orthonormal and crystal reference systems. Quaternion representations, easily constructed for any orientations of symmetry operations, owing to the vector structure based on the direction of the rotation axes or of the normal vectors to the mirror plane, are known to be advantageous for optimizing numerical computing. However, quaternions are described in Cartesian coordinates only. Here, we present the quaternion representations of crystallographic point-group symmetry operations for the crystallographic reference coordinates in triclinic, monoclinic, orthorhombic, tetragonal, cubic and trigonal (in rhombohedral setting) systems. For these systems, all symmetry operations have been listed and their applications exemplified. Owing to their concise form, quaternions can be used as the symbols of symmetry operations, which contain information about both the orientation and the rotation angle. The shortcomings of quaternions, including different actions for rotations and improper symmetry operations, as well as inadequate representation of the point symmetry in the hexagonal setting, have been discussed.

Legume: A free implementation of the guided-mode expansion method for photonic crystal slabs

We describe legume, a free electromagnetic solver that implements the guided-mode expansion method for patterned multilayer waveguides, or photonic crystal slabs. legume has a built-in tool for automatic differentiation, which makes it suitable for the inverse design of photonic crystal structures with desired physical properties. Compared to a previous version of the method (M. Minkov et al., 2020 [12]), here we introduce several new features of the code, we discuss additional technical aspects of the method and its numerical implementation. The novel features that are treated in this paper include: (i) the separation of modes according to their mirror symmetry with respect to a vertical symmetry plane of the photonic structure, (ii) the problem of polarization mixing in coupling to far-field radiation modes, and (iii) the description of active two-dimensional layers through a suitably formulated radiation-matter coupling Hamiltonian, allowing to describe the physics of both weakly and strongly coupled exciton-photon modes, the latter leading to photonic crystal polariton eigenmodes. Detailed and direct comparisons with rigorous coupled-wave analysis simulations are used to test the accuracy of the method and the numerical efficiency of the code. These newly added features of the legume code significantly increase the prospective applications of guided-mode expansion, making it a very practical and versatile tool enabling the design of advanced photonic structures and the description of radiation-matter interaction. Program summaryProgram Title:legumeCPC Library link to program files:https://doi.org/10.17632/kf3cwknx4d.1Developer's repository link:https://github.com/fancompute/legumeLicensing provisions: MITProgramming language: PythonNature of problem: Dispersion and radiative losses of photonic eigenmodes in patterned multilayer waveguides/photonic crystal slabs/periodic metasurfaces. Interaction of photonic modes with exciton resonances leading to exciton-polaritons. Inverse design by optimization of the parameters.Solution method: Finite-basis expansion using a basis of guided modes of an effective homogeneous waveguide, perturbation theory to describe coupling with far-field radiation. Quantum theory of excitons, photons and their interaction to describe the occurrence of exciton-polaritons. Automatic differentiation via Autograd to implement inverse design. In this upgraded version of the legume code we implement symmetrization with respect to a vertical mirror plane and light-matter interaction for exciton-polaritons. Inverse design has been described previously, here we focus on the new features and applications of the code.

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.

Mirror Plane Effect of Magnetoplumbite-Type Oxide Restraining Long-Chain Polysulfides Disproportionation for High Loading Lithium Sulfur Batteries.

A facile solid-state approach is employed to synthesize a novel magnetoplumbite-type oxide of NdMgAl11O19, which integrates spinel-stacking layers (MgAl2O4) with Nd-O6 mirror plane structures. The resulting NdMgAl11O19 exhibits remarkable catalytic activity and conversion efficiency during the sulfur reduction reaction (SRR) in lithium-sulfur batteries. By employing the 2D projection mapping technique of in situ confocal Raman spectroscopy and electrochemical technique, it is discovered that the exposed mirror plane structure of Nd-O6 can effectively suppress the undesiring disproportionation reaction (S8 2-→S6 2-+1/4 S8) of long-chain lithium polysulfides at the initial stages of sulfur reduction, thereby promoting the positive process of sulfur to lithium sulfide. This not only mitigates the issue of sulfur shuttle loss but also significantly improve the kinetics of the conversion process. Leveraging these advantages, the NdMgAl11O19/S cathode delivered an impressive initial capacity of up to 1398 mAh g-1 at an electrolyte/sulfur (E/S) ratio of 5.1µL mg-1 and a sulfur loading of 2.3mg cm-2. Even when the sulfur loading is increased to 10.02mg cm-2, the cathode retained a reversible areal capacity of 10.01 mAh cm-2 after 200 cycles. This mirror engineering strategy provides valuable and universal insights into enhancing the efficiency of cathodes in Li-S battery.

Probing the limits of tetraalkylthiuram disulfide synthesis by direct reaction of secondary amines with CS2: The structures of Cy2NC(S)SSC(S)NCy2 and Cy2NC(S)SSSSC(S)NCy2

Reaction of Cy2NH with CS2 in NaOH/H2O, followed by oxidation with I2, yields a complex mixture that includes the tetracyclohexylthiuram disulfide, Cy2NC(S)SSC(S)NCy2, in mixture with S8 and the tetrasulfide Cy2NC(S)SSSSC(S)NCy2. Direct reaction of 2 eq of Cy2NH with CS2 in EtOH, followed by I2 oxidation, does not yield isolable Cy2NC(S)SSC(S)NCy2, even though other tetraalkylthiuram disulfides are effectively produced by this protocol. Deprotonation of Cy2NH with t BuLi, followed by treatment with CS2 and then oxidative coupling with I2 yields Cy2NC(S)SSC(S)NCy2 in ∼74% yield, suggesting secondary amines that are branched at the α carbon may generally require this lattermost approach to the corresponding tetraalkylthiuram disulfide. Evaporation of an Et2O solution of the crude product mixture obtained from the CS2/NaOH/H2O reaction yielded a triclinic form of Cy2NC(S)SSC(S)NCy2, which contained two independent molecules in its asymmetric unit with opposite C 2 handedness. This same product mixture contained Cy2NC(S)SSSSC(S)NCy2, which was identified crystallographically in monoclinic C2/c and is the first such tetrasulfide to be characterized by X-ray diffraction. A second polymorph of Cy2NC(S)SSC(S)NCy2, obtained by evaporation of an acetone solution, is disordered across a mirror plane in monoclinic P21/m. This monoclinic polymorph of Cy2NC(S)SSC(S)NCy2 is the only tetraalkylthiuram disulfide found to crystallize on a mirror plane.

Synthesis, disorder and Ising anisotropy in a new spin liquid candidate PrMgAl11O19

Here we report the successful synthesis of large single crystals of triangular frustrated PrMgAl11O19 using the optical floating zone technique. Single crystal x-ray diffraction (XRD) measurements unveiled the presence of quenched disorder within the mirror plane, specifically ~7% of Pr ions deviating from the ideal 2d site towards the 6h site. Magnetic susceptibility measurements revealed an Ising anisotropy with the c-axis being the easy axis. Despite a large spin–spin interaction that develops below ~10 K and considerable site disorder, the spins do not order or freeze down to at least 50 mK. The availability of large single crystals offers a distinct opportunity to investigate the exotic magnetic state on a triangular lattice with an easy axis out of the plane.

Research on Multi-Objective Optimization of Heliostat Field Based on DELSOL3 Layout

With the intensification of global climate change, it is urgent to reduce greenhouse gas emissions and protect the environment. To address this issue, it is crucial to develop the new energy industry and increase the proportion of clean energy. Tower solar power, as an innovative and environmentally friendly technology with low carbon emissions, has great potential and broad prospects. This study determines the position of the absorption tower, heliostat size, and installation height. By utilizing the ground coordinates of the heliostats and given formulas, parameters such as average optical efficiency, cosine efficiency, shadow blocking efficiency, and cut-off efficiency are calculated. The focus is on power loss caused by shading, so a shadow blocking model is constructed by using differential methods. The heliostat plane is divided into equal sections, and it is determined whether the transformed coordinates of the mirror plane are within the grid. The effective blocked area is then calculated to obtain the shadow blocking efficiency. To improve the efficiency and reduce costs of solar thermal power plants, the standard radial staggered layout in DELSOL3 empirical layout is adopted. A multi-objective optimization model is established with heliostat size and height as variables. The optimal solution for the average output thermal power per unit mirror area is obtained through genetic algorithms. Through mathematical modeling and solution methods, this study provides theoretical basis for the application of tower solar power.

Spin polarization of photoelectrons emitted from spin-orbit coupled surface states of Pb/Ge(111).

We report that the spin vector of photoelectrons emitted from an atomic layer Pb grown on a germanium substrate [Pb/Ge(111)] can be controlled using an electric field of light. The spin polarization of photoelectrons excited by a linearly polarized light is precisely investigated by spin- and angle-resolved photoemission spectroscopy. The spin polarization of the photoelectrons observed in the mirror plane reverses between p- and s-polarized lights. Considering the dipole transition selection rule, the surface state of Pb/Ge(111) is represented by a linear combination of symmetric and asymmetric orbital components coupled with spins in mutually opposite directions. The spin direction of the photoelectrons is different from that of the initial state when the electric field vector of linearly polarized light deviates from p- or s-polarization conditions. The quantum interference in the photoexcitation process can determine the direction of the spin vector of photoelectrons.

Topological band inversion and chiral Majorana mode in hcp thallium

The chiral Majorana fermion is an exotic particle that is its own antiparticle. It can arise in a one-dimensional edge of topological materials, and especially that in a topological superconductor can be exploited in non-Abelian quantum computation. While the chiral Majorana mode (CMM) remains elusive, a promising situation is realized when superconductivity coexists with a topologically non-trivial surface state. Here, we perform fully non-empirical calculation for the CMM considering superconductivity and surface relaxation, and show that hexagonal close-packed thallium (Tl) has an ideal electronic state that harbors the CMM. The kz=0 plane of Tl is a mirror plane, realizing a full-gap band inversion corresponding to a topological crystalline insulating phase. Its surface and hinge are stable and easy to make various structures. Another notable feature is that the surface Dirac point is very close to the Fermi level, so that a small Zeeman field can induce a topological transition. Our calculation indicates that Tl will provide a new platform of the Majorana fermion.

The OH stretching region in infrared spectra of the apatite OH-Cl binary system

Abstract Polarized Fourier Transform Infrared (FTIR) microspectroscopy of the OH stretching region of hydroxylapatite-chlorapatite solid solutions presents novel problems for the assignment of peaks to specific OH-Cl pairs. Crystal structure refinements of Hughes et al. (2016) identified new positions for column anions in synthetic mixed Cl-OH apatites, with three different column anion arrangements depending on composition. These structural refinements, combined with bond valence calculations, allow for interpretation of the OH stretching region. A peak at 3574 cm-1 is identified as that from end member hydroxylapatite. A second major peak at 3548 cm-1 is only found in mixed chlorapatite-hydroxylapatite solid solutions, as is a third peak at 3592 cm-1. Both represent perturbations of the OH stretching vibration as compared to hydroxylapatite, to lower and higher frequency, respectively. Both of the new peaks are the result of a Clb-OH sequence, with adjacent anions in crystallographically similar positions, both above or both below adjacent mirror planes. One configuration has the hydrogen atom pointed towards the chlorine atom. The second has the hydrogen of the OH group pointed away from the chlorine atom. Both configurations present novel problems. The shift to lower wavenumber at 3548 cm-1 is characteristic of hydrogen bonding in fluorapatite-hydroxylapatite mixtures, yet the distance between O(H) and Clb is too great to allow it. The shift of OH stretching vibrations to lower wavenumber is produced through changes in polarization of intervening Cl-Ca2’ (or Ca2) and Ca2(’)-O3 bonds, which are affected by the presence of the large chlorine atom. Lowering the OH stretching vibration mimics the expected effect of a chlorine on a neighboring OH group in the apatite c-axis column, though without hydrogen bonding. The shift to higher wavenumbers, i.e. higher frequency at 3592 cm-1, is the opposite of that expected for hydrogen bonding between column anions in the apatite mineral group. It is ascribed to interaction between an adjacent Clb and the oxygen end of an adjacent OH dipole. This pairing places an oxygen and a chlorine atom in close proximity. Possible means of accommodation are discussed. A ubiquitous peak at 3498 cm-1 represents hydrogen bonding between an OH and the OHa site, with an interoxygen distance of about 2.9 Å. Published modeling supports the hypothesis that the OHa site is occupied by an O rather than an OH. However, no clear counterpart to this pairing is observed in crystal structure refinements for specimens lacking OHa, although the infrared absorbance is present. The existence of oxyapatite is inferred from studies of plasma-sprayed biomaterials, but the crystallographic details of the substitution have remained elusive. A minor shoulder at 3517 cm-1 does not have a clear counterpart in the structural refinements. Sequences of three columnar anions (e.g. OH-Cl-OH or Cl-OH-OH) can be ruled out, but unequivocal assignment awaits further research.

Intrinsic supercurrent non-reciprocity coupled to the crystal structure of a van der Waals Josephson barrier

Non-reciprocal electronic transport in a spatially homogeneous system arises from the simultaneous breaking of inversion and time-reversal symmetries. Superconducting and Josephson diodes, a key ingredient for future non-dissipative quantum devices, have recently been realized. Only a few examples of a vertical superconducting diode effect have been reported and its mechanism, especially whether intrinsic or extrinsic, remains elusive. Here we demonstrate a substantial supercurrent non-reciprocity in a van der Waals vertical Josephson junction formed with a Td-WTe2 barrier and NbSe2 electrodes that clearly reflects the intrinsic crystal structure of Td-WTe2. The Josephson diode efficiency increases with the Td-WTe2 thickness up to critical thickness, and all junctions, irrespective of the barrier thickness, reveal magneto-chiral characteristics with respect to a mirror plane of Td-WTe2. Our results, together with the twist-angle-tuned magneto-chirality of a Td-WTe2 double-barrier junction, show that two-dimensional materials promise vertical Josephson diodes with high efficiency and tunability.

Automated localization of mandibular landmarks in the construction of mandibular median sagittal plane

ObjectiveTo use deep learning to segment the mandible and identify three-dimensional (3D) anatomical landmarks from cone-beam computed tomography (CBCT) images, the planes constructed from the mandibular midline landmarks were compared and analyzed to find the best mandibular midsagittal plane (MMSP).MethodsA total of 400 participants were randomly divided into a training group (n = 360) and a validation group (n = 40). Normal individuals were used as the test group (n = 50). The PointRend deep learning mechanism segmented the mandible from CBCT images and accurately identified 27 anatomic landmarks via PoseNet. 3D coordinates of 5 central landmarks and 2 pairs of side landmarks were obtained for the test group. Every 35 combinations of 3 midline landmarks were screened using the template mapping technique. The asymmetry index (AI) was calculated for each of the 35 mirror planes. The template mapping technique plane was used as the reference plane; the top four planes with the smallest AIs were compared through distance, volume difference, and similarity index to find the plane with the fewest errors.ResultsThe mandible was segmented automatically in 10 ± 1.5 s with a 0.98 Dice similarity coefficient. The mean landmark localization error for the 27 landmarks was 1.04 ± 0.28 mm. MMSP should use the plane made by B (supramentale), Gn (gnathion), and F (mandibular foramen). The average AI grade was 1.6 (min–max: 0.59–3.61). There was no significant difference in distance or volume (P > 0.05); however, the similarity index was significantly different (P < 0.01).ConclusionDeep learning can automatically segment the mandible, identify anatomic landmarks, and address medicinal demands in people without mandibular deformities. The most accurate MMSP was the B-Gn-F plane.

Hypercube Stereoisograms as Efficient Graphs to Represent the Stereoisomeric Relationships of Organic Molecules Containing 1 to 4 Stereogenic Centers

The n-dimensional unit hypercubes, Qn (n = 1 to 4), are used as n-dimensional graphs (Stereoisograms) to describe the stereoisomeric (enantiomeric and/or diastereomeric) relationships of molecules containing one to four RS-stereogenic centers. To achieve this goal, the strings of 0’s and 1’s, used for labelling the vertices of unit hypercubes, are substituted by strings of R’s and S’s-descriptors coming from the CIP priority rules. The development of those ndimensional unit hypercubes along ordered axes and the application of combinatorial techniques allow to locate the enantiomeric pairs at antipodal vertices (points related by a chirality center, which satisfies the bitwise operation known as “NOT”); whereas diastereomers are related by mirror planes, whose reflection results in a partial permutation of the RS-descriptors. These facts are in good agreement with the literature and the principles of the combinatorial theory applied to such hypercubes. On the other hand, because the maximum number of stereoisomers 2n is not always held, “pseudo hypercubes” containing one or more “ghost vertices” are proposed to include the meso (achiral) stereoisomers

Pressure-induced structural and magnetic ordering transitions in the J1-J2 square lattice antiferromagnets AMoOPO4Cl (A = K, Rb).

By means of ab initio density functional theory calculations taking into account electronic correlation and van der Waals force, we conducted comprehensive studies of the electronic and magnetic properties, as well as structural and magnetic ordering evolution under pressure of the square lattice antiferromagnets AMoOPO4Cl (A = K, Rb) containing Mo5+ ions with , theoretically predicted as the potential candidates for achieving quantum phases, existing in the boundary regimes for square lattice magnets. Our results indicate that the columnar antiferromagnetic ordering, experimentally determined, is the magnetic ground state of the ambient P4/nmm phase, stabilized by the predominant antiferromagnetic next nearest neighbor interaction J2 in the diagonal directions of the square lattice, regardless of the effective Hubbard amendment values. More importantly, the P4/n phase, involving the mutual twisting of the MoO5Cl and PO4 polyhedra, satisfactorily reproduces the experimentally observed structural transition and the subsequent magnetic ordering transition from columnar antiferromagnetic ordering to Néel antiferromagnetic one, identified to be the appropriate high pressure structure. Furthermore, the mechanism underlined responsible for the magnetic ordering transition at high pressure has been disclosed in terms of density of states and spin density isosurface analysis across the transition. The loss of mirror plane symmetry in the P4/n phase activates the P 3s orbitals to participate in the magnetic interaction, giving rise to a competitive ferromagnetic superexchange interaction, in addition to antiferromagnetic direct one, and consequently initiating the magnetic ordering transition. The insights revealed here not only deepen our understanding of the electronic properties and structural and magnetic ordering transitions under high pressure of square lattice antiferromagnets AMoOPO4Cl (A = K, Rb), but also push the boundaries of knowledge by recognizing the role of nonmagnetic ions P 3s in magnetic exchange coupling.