Symmetry Group Research Articles

QSPR-based prediction model for the melting point of polycyclic aromatic hydrocarbons using MLR and ANN methods

The melting point is an important property that helps generate specific compounds with desired thermos-physical properties. Much work has been done applying quantitative structure-property relationships to improve the melting-point correlations, but they are unreliable. This gap might come from the melting point's sensitivity for small molecular variations and descriptors, which currently do not fully consider all factors determining melting behavior. In this work, we provide a QSPR model for predicting the melting point of a heterogeneous polycyclic aromatic hydrocarbons dataset. The model was generated using a robust hybrid linear approach (Genetic Algorithm-Multiple Linear Regression) and a nonlinear approach named Artificial Neural Network (ANN). Three descriptors were chosen to explain the influence of molecular weight and symmetry on melting point. The resulting QSPR model can model melting-point behavior with an RMSE of 34.88K, a coefficient correlation value of R²=0.887, and a prediction coefficient of Q²LOO= 0.863. This study reveals that the results produced by MLR were appropriate and served to predict melting points. However, compared to the results obtained by the ANN model, we conclude that the latter is more effective and better than the MLR model. Based on the results, our suggested model may be effective in predicting melting points, and the selected descriptors play essential roles in determining melting points.

Photoionization of aziridine: Nonadiabatic dynamics of the first six low-lying electronic states of the aziridine radical cation.

In this article, the theoretical photoionization spectroscopy of the aziridine (C2H5N) molecule is investigated. To start with, we have optimized the geometry of this molecule at the neutral electronic ground state at the density functional theory/augmented correlation-consistent polarized valence triple zeta level of theory using the G09 program. The electronic structure calculations were restricted to the first six low-lying electronic states in order to account for the experimental photoelectron spectrum of the C2H5N molecule. The first six low-lying electronic states (X̃2A', Ã2A', B̃2A″, C̃2A″, D̃2A', and Ẽ2A') of the potential energy surfaces (PESs) are calculated by both equation of motion-ionization potential-coupled cluster singles and doubles and multi-configuration quasi-degenerate perturbation theory abinitio quantum chemistry methods along the dimensionless normal displacement coordinates in which multiple conical intersections were established among the considered electronic states. A (6 × 6) model vibronic Hamiltonian is constructed on a diabatic electronic basis, using the symmetry selection rules and Taylor series expansion. The Cs symmetry point group of the aziridine molecule leads to electronic states symmetry of either A' or A″, and these states are close in energy, due to which the same symmetry electronic states avoid each other. To get a smooth diabatic PES, a fourfold diabatization scheme is used, which is implemented in the General Atomic and Molecular Electronic Structure Systems suite of programs. All the parameters used in the diabatic vibronic coupling model Hamiltonian are calculated in terms of the normal modes of vibrational coordinates. Finally, the vibronic model Hamiltonian constructed for the coupled six electronic states is used to solve both time-independent and time-dependent Schrödinger equations using the multi-configuration time-dependent Hartree program module to obtain the dynamical observables. The theoretical vibronic band structure is found to be in good accord with the available experimental results.

Peierls Transition in Gross-Neveu Model from Bethe Ansatz

The two-dimensional Gross-Neveu model is anticipated to undergo a crystalline phase transition at high baryon charge densities. This conclusion is drawn from the mean-field approximation, which closely resembles models of Peierls instability. We demonstrate that this transition indeed occurs when both the rank of the symmetry group and the dimension of the particle representation contributing to the baryon density are large (the large N limit). We derive this result through the exact solution of the model, developing the large N limit of the Bethe ansatz. Our analytical construction of the large-N solution of the Bethe ansatz equations aligns perfectly with the periodic (finite-gap) solution of the Korteweg–de Vries (KdV) of the mean-field analysis. Published by the American Physical Society 2024

Non-relativistic torque and Edelstein effect in non-collinear magnets

The Edelstein effect is the origin of the spin-orbit torque: a current-induced torque that is used for the electrical control of ferromagnetic and antiferromagnetic materials. This effect originates from the relativistic spin-orbit coupling, which necessitates utilizing materials with heavy elements. Here, we show that in magnetic materials with non-collinear magnetic order, the Edelstein effect and, consequently, a current-induced torque can exist even in the absence of the spin-orbit coupling. Using group symmetry analysis, model calculations, and realistic simulations on selected compounds, we identify large classes of non-collinear magnet candidates and demonstrate that the current-driven torque is of similar magnitude as the celebrated spin-orbit torque in conventional transition metal structures. We also show that this torque can exist in an insulating material, which could allow for highly efficient electrical control of magnetic order.

Three-dimensional topological crystalline insulator without spin–orbit coupling in nonsymmorphic photonic metacrystal

Abstract By including certain point group symmetry in the classification of band topology, Fu proposed a class of three-dimensional topological crystalline insulators (TCIs) without spin–orbit coupling in 2011. In Fu’s model, surface states (if present) doubly degenerate at Γ ¯ and M ¯ when time-reversal and C 4 symmetries are preserved. The analogs of Fu’s model with surface states quadratically degenerate at M ¯ are widely studied, while surface states with quadratic degeneracy at Γ ¯ are rarely reported. In this study, we propose a three-dimensional TCI without spin–orbit coupling in a judiciously designed nonsymmorphic photonic metacrystal. The surface states of photonic TCIs exhibit quadratic band degeneracy in the (001) surface Brillouin zone (BZ) center ( Γ ¯ point). The gapless surface states and their quadratic dispersion are protected by C 4 and time-reversal symmetries, which correspond to the nontrivial band topology characterized by Z 2 topological invariant. Moreover, the surface states along lines from Γ ¯ to the (001) surface BZ boundary exhibit zigzag feature, which is interpreted from symmetry perspective by building composite operators constructed by the product of glide symmetries with time-reversal symmetry. The metacrystal array surrounded with air possesses high order hinge states with electric fields highly localized at the hinge that may apply to optical sensors. The gapless surface states and hinge states reside in a clean frequency bandgap. The topological surface states emerge at the boundary of the metacrystal and perfect electric conductor (PEC), which provide a pathway for topologically manipulating light propagation in photonic devices.

Symmetries in Riemann-Cartan Geometries

Riemann-Cartan geometries are geometries that admit non-zero curvature and torsion tensors. These geometries have been investigated as geometric frameworks for potential theories in physics including quantum gravity theories and have many important differences when compared to Riemannian geometries. One notable difference, is the number of symmetries for a Riemann-Cartan geometry is potentially smaller than the number of Killing vector fields for the metric. In this paper, we will review the investigation of symmetries in Riemann-Cartan geometries and the mathematical tools used to determine geometries that admit a given group of symmetries. As an illustration, we present new results by determining all static spherically symmetric and all stationary spherically symmetric Riemann-Cartan geometries. Furthermore, we have determined the subclasses of spherically symmetric Riemann-Cartan geometries that admit a seven-dimensional group of symmetries.

Modeling of textile composite using analytical network-averaging and gradient damage approach

In this contribution, we present a gradient damage model for anisotropic textile reinforcements including fiber inextensibility and fiber sliding. In contrast to previous works, the gradient damage formulation stems not from a numerical regularization basis but from the thermodynamics of internal variables. It results in a nonlocal term as the internal energy of fiber bending with measurable nonlocal parameter. Furthermore, to guarantee a priori that rotations and reflections determined by orthogonal tensors among the symmetry group do not affect the response function of the anisotropic constitutive law, a novel mesoscopic kinematic measure for the representative volume element of the fabric is defined on the basis of the analytical network-averaging concept. Such kinematic measure is of crucial importance for material modeling of damage-elastoplasticity in anisotropic textile reinforcements, and allows for analytical descriptions of inter- and intra-ply sliding of fibers. A mixed finite element formulation is then presented for textile reinforcements taking into account fiber inextensibility. The predictive capability of the computational model is demonstrated by comparing with multiple experimental datasets of dry textile fabrics.

Non-magnetic layers with a single symmetry-protected Dirac cone: Which additional dispersions must appear?

In two-dimensional (2D), non-magnetic materials, a single Dirac cone at high-symmetry point (HSP) of the Brillouin zone (BZ), akin to the one in graphenes’ band structure, cannot appear as the only quasiparticle at the Fermi level. Here we found two layer groups with time-reversal symmetry, among all possible both without and with spin-orbit coupling, that host one Dirac cone at HSP and we show which additional dispersions appear: a pair of Dirac lines on opposite BZ edges and a pair of Dirac cones that can be moved but not removed by symmetry preserving perturbations, on the other two BZ edges. We illustrate our theory by a tight-binding band structure and discuss real 2D materials that belong to one of the two symmetry groups. Finally, we single out smaller or bigger discrepancies among the published papers on the same or related topic.

Symmetry relationships between hybrid lead halide perovskite-derived phases: vacancy ordering as a key classification factor

For the first time, based on symmetry group–subgroup relation-ships, an approach is presented to create a clear classification of hybrid lead halides with low-dimensional vacancy-ordered perovskite-related crystal structures to facilitate the identification and prediction of hybrid lead-halide materials that have desired properties.

K0.72Na1.71Ca5.79Si6O19 - the first oligosilicate based on [Si6O19]-hexamers and its stability compared to cyclosilicates.

Synthesis experiments were conducted in the quaternary system K2O-Na2O-CaO-SiO2, resulting in the formation of a previously unknown compound with the composition K0.72Na1.71Ca5.79Si6O19. Single crystals of sufficient size and quality were recovered from a starting mixture with a K2O:Na2O:CaO:SiO2 molar ratio of 1.5:0.5:2:3. The mixture was confined in a closed platinum tube and slowly cooled from 1150°C at a rate of 0.1°C min-1 to 700°C before being finally quenched in air. The structure has tetragonal symmetry and belongs to space group P4122 (No. 91), with a = 7.3659 (2), c = 32.2318 (18) Å, V = 1748.78 (12) Å3, and Z = 4. The silicate anion consists of highly puckered, unbranched six-membered oligomers with the composition [Si6O19] and point group symmetry 2 (C2). Although several thousands of natural and synthetic oxosilicates have been structurally characterized, this compound is the first representative of a catena-hexasilicate anion, to the best of our knowledge. Structural investigations were completed using Raman spectroscopy. The spectroscopic data was interpreted and the bands were assigned to certain vibrational species with the support of density functional theory at the HSEsol level of theory. To determine the stability properties of the novel oligosilicate compared to those of the chemically and structurally similar cyclosilicate combeite, we calculated the electronegativity of the respective structures using the electronegativity equalization method. The results showed that the molecular electronegativity of the cyclosilicate was significantly higher than that of the oligostructure due to the different connectivities of the oxygen atoms within the molecular units.

(α+2)-Dimensional fractional evolution equation: group classification, symmetries, reduction and conservation laws

ABSTRACT A preliminary group classification based on symmetry operators is applied to study invariance properties of the time-fractional ( α + 2 ) -dimensional fractional evolution equation. The concepts of Riemann–Liouville and Caputo fractional derivatives are used in this study. The similarity variables obtained from symmetries and one-dimensional optimal systems of constructed Lie algebras are used in order to find the group-invariant solutions of the equation. Finally conservation laws of the equation are derived via a modified version of Noether’s theorem.

Variational Vibrational States of Methanol (12D).

Full-dimensional (12D) vibrational states of the methanol molecule (CH3OH) have been computed using the GENIUSH-Smolyak approach and the potential energy surface from Qu and Bowman (2013). All vibrational energies are converged better than 0.5 cm-1 with respect to the basis and grid size up to the first overtone of the CO stretch, ca. 2000 cm-1 beyond the zero-point vibrational energy. About 70 torsion-vibration states are reported and assigned. The computed vibrational energies agree with the available experimental data within less than a few cm-1 in most cases, which confirms the good accuracy of the potential energy surface. The computations are carried out using curvilinear normal coordinates with the option of path-following coefficients, which minimize the coupling of the small- and large-amplitude motions. It is important to ensure tight numerical fulfillment of the C3v(M) molecular symmetry for every geometry and coefficient set used to define the curvilinear normal coordinates along the torsional coordinate to obtain a faithful description of degeneracy in this floppy system. The reported values may provide a computational reference for fundamental spectroscopy, astrochemistry, and for the search of the proton-to-electron mass ratio variation using the methanol molecule.

Anisotropic excitonic magnetism from discrete C4 symmetry in CeRhIn5

Anisotropy in strongly correlated materials is a central parameter in determining the electronic ground state and is tuned through the local crystalline electric field. This is notably the case in the CeCoxRh1−xIn5 system where the ground-state wave function can provide the basis for antiferromagnetism and/or unconventional superconductivity. We develop a methodology to understand the local magnetic anisotropy and experimentally investigate with neutron spectroscopy applied to antiferromagnetic (TN=3.8K) CeRhIn5, which is isostructural to d-wave superconducting (Tc=2.3K) CeCoIn5. Through diagonalizing the local crystal field Hamiltonian with discrete tetragonal C4 point group symmetry and coupling these states with the random phase approximation, we find two distinct modes polarized along the crystallographic c and a−b planes, agreeing with experiment. The anisotropy and bandwidth, underlying the energy scale of these modes, are tuneable with a magnetic field which we use experimentally to separate in energy single and multiparticle excitations thereby demonstrating the instability of excitations polarized within the crystallographic a−b plane in CeRhIn5. We compare this approach to a Seff=12 parametrizations and argue for the need to extend conventional SU(2) theories of magnetic excitations to utilize the multilevel nature of the underlying crystal-field basis states constrained by the local point-group C4 symmetry. Published by the American Physical Society 2024

SPORT: A Subgraph Perspective on Graph Classification with Label Noise

Graph neural networks (GNNs) have achieved great success recently on graph classification tasks using supervised end-to-end training. Unfortunately, extensive noisy graph labels could exist in the real world because of the complicated processes of manual graph data annotations, which may significantly degrade the performance of GNNs. Therefore, we investigate the problem of graph classification with label noise, which is demanding because of the complex graph representation learning issue and serious memorization of noisy samples. In this work, we present a novel approach called S ubgra p h Set Netw or k with Sample Selection and Consis t ency Learning (SPORT) for this problem. To release the overfitting of GNNs, SPORT proposes to characterize each graph as a set of subgraphs generated by certain predefined stratagems, which can be viewed as samples from its underlying semantic distribution in graph space. Then we develop an equivariant network to encode the subgraph set with the consideration of the symmetry group. To further release the influences of noisy examples, we leverage the predictions of subgraphs to measure the likelihood of a sample being clean or noisy, followed by effective label updating. In addition, we propose a joint loss to advance the model generalizability by introducing consistency regularization. Comprehensive experiments on a wide range of graph classification datasets demonstrate the effectiveness of our SPORT. Specifically, SPORT outperforms the most competing baseline by up to 6.4%.

Spin Space Groups: Full Classification and Applications

In this work, we exhaust all the spin space symmetries, which fully characterize collinear, noncollinear, and commensurate spiral as well as incommensurate spiral magnetism, etc., and investigate enriched features of electronic bands that respect these symmetries. We achieve this by systematically classifying the so-called spin space groups (SSGs)—joint symmetry groups of spatial and spin operations that leave the magnetic structure unchanged. Generally speaking, they are accurate (approximate) symmetries in systems where spin-orbit coupling (SOC) is negligible (finite but weaker than the energy scale of interest), but we also show that specific SSGs could remain valid even in the presence of strong SOC. In recent years, SSGs have played increasingly pivotal roles in various fields such as altermagnetism, topological electronic states, and topological magnon, etc. However, due to its complexity, a complete SSG classification has not been completed up to now. By representing the SSGs as O(N) representations, we—for the first time—obtain the complete classifications of 1421, 9542, and 56 512 distinct SSGs for collinear (N=1), coplanar (N=2), and noncoplanar (N=3) magnetism, respectively. SSG not only fully characterizes the symmetry of spin degrees of freedom, but also gives rise to exotic electronic states, which, in general, form projective representations of magnetic space groups (MSGs). Surprisingly, electronic bands in SSGs exhibit features never seen in MSGs, such as (i) nonsymmorphic SSG Brillouin zone, where SSG operations behave as a glide or screw when acting on momentum, (ii) effective π flux, where translation operators anticommute with each other and yield duplicate bands, (iii) higher-dimensional representations unexplained by MSGs, and (iv) unconventional spin texture on a Fermi surface, which is completely determined by SSGs, independent of Hamiltonian details. To apply our theory, we identify the SSG for each of the 1595 published magnetic structures in the MAGNDATA database on the Bilbao Crystallographic Server. Material examples exhibiting the novel features (i)–(iv) are discussed with emphasis. We also investigate new types of SSG-protected topological electronic states that are unprecedented in MSGs. In particular, we propose a 3D Z2 topological insulator state with a fourfold degenerate Dirac point on the surface and a new scenario of anomalous Z2 helical states that appear on magnetic domain walls. Published by the American Physical Society 2024

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.

Symmetries for the 4HDM. II. Extensions by rephasing groups

Abstract We continue classification of finite groups which can be used as symmetry group 
of the scalar sector of the four-Higgs-doublet model (4HDM). 
Our objective is to systematically construct non-abelian groups via the group extension procedure,
starting from the abelian groups $A$ and their automorphism groups $\Aut(A)$.
Previously, we considered all cyclic groups $A$ available for the 4HDM scalar sector.
Here, we further develop the method and apply it to extensions 
by the remaining rephasing groups $A$, namely $A = \Z_2\times\Z_2$, $\Z_4\times \Z_2$, and $\Z_2\times \Z_2\times \Z_2$.
As $\Aut(A)$ grows, the procedure becomes more laborious, but we prove an isomorphism theorem which 
helps classify all the options.
We also comment on what remains to be done to complete the classification of all finite 
non-abelian groups realizable in the 4HDM scalar sector without accidental continuous symmetries.

On self-dual Carrollian conformal nonlinear electrodynamics

In this work, we study the duality symmetry group of Carrollian (nonlinear) electrodynamics and propose a family of Carrollian ModMax theories, which are invariant under Carrollian SO(2) electromagnetic (EM) duality transformations and conformal transformation. We define the Carrollian SO(2) EM transformations, with the help of Hodge duality in Carrollian geometry, then we rederive the Gaillard-Zumino consistency condition for EM duality of Carrollian nonlinear electrodynamics. Together with the traceless condition for the energy-momentum tensor, we are able to determine the Lagrangian of the Carrollian ModMax theories among pure electrodynamics. We furthermore study their behaviors under the TT¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{T\\overline{T}} $$\\end{document} deformation flow, and show that these theories deform to each other and may reach two endpoints under the flow, with one of the endpoint being the Carrollian Maxwell theory. As a byproduct, we construct a family of two-dimensional Carrollian ModMax-like multiple scalar theories, which are closed under the TT¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{T\\overline{T}} $$\\end{document} flow and may flow to a BMS free multi-scalar model.

Symmetry analysis, optimal system, conservation laws and exact solutions of time-fractional diffusion-type equation

In Liu et al. [On the generalized time fractional diffusion equation: Symmetry analysis, conservation laws, optimal system and exact solutions, Int. J. Geom. Methods Mod. Phys. 17(01) (2020) 2050013], the generalized time-fractional diffusion equation [Formula: see text] is studied by the symmetry analysis method. Liu et al. obtained two group generators [Formula: see text] [Formula: see text] and only one trivial solution [Formula: see text] for the equation. In this paper, we classify the Lie symmetry group admitted by the equation, and for the case [Formula: see text], we obtain a richer set of group generators and some nontrivial solutions, including unprecedented exact solutions and power series solutions. In addition, we construct the one-dimensional optimal system of the Lie symmetry group admitted by the time-fractional diffusion-type equation by Olver’s method, and obtain the conservation laws for all the obtained Lie symmetries using the general method developed by Ibragimov. For the novel exact solutions and power series solutions, we analyze their dynamic behavior graphically.

The Symmetry Group of the Grand Antiprism

The grand antiprism A is an outlier among the uniform 4-polytopes, since it is not obtainable from Wythoff’s construction. Its symmetry group G(A) has been incorrectly described as [[10,2+,10]] or even as an ‘ionic diminished Coxeter group’. In fact, G(A) is another group of order 400, namely the group ±[D10×D10]·2, in the notation of Conway and Smith. We explain all this and so correct a persistent error in the literature. This fresh look at the beautiful geometry of the polytope A is also a fine opportunity to introduce the reader to the elegance of Wythoff’s construction and to the less familiar use of quaternions to classify the finite 4-dimensional isometry groups.