Symmetry Group Research Articles

Instantons in ϕ4 theories: Transseries, virial theorems, and numerical aspects

We discuss numerical aspects of instantons in two- and three-dimensional ϕ4 theories with an internal O(N) symmetry group, the so-called N-vector model. By combining asymptotic transseries expansions for large arguments with convergence acceleration techniques, we obtain high-precision values for certain integrals of the instanton that naturally occur in loop corrections around instanton configurations. Knowledge of these numerical properties is necessary in order to evaluate corrections to the large-order factorial growth of perturbation theory in ϕ4 theories. The results contribute to the understanding of the mathematical structures underlying the instanton configurations. Published by the American Physical Society 2024

Hyperbolic vacua in Minkowski space

Families of Lorentz, but not Poincare, invariant vacua are constructed for a massless scalar field in 4D Minkowski space. These are generalizations of the Rindler vacuum with a larger symmetry group. Explicit expressions are given as squeezed excitations of the Poincare vacuum. The effective reduced vacua on the 3D hyperbolic de Sitter slices are the well-known de Sitter α-vacua with antipodal singularities in the Wightman function. Several special interesting cases are discussed.

Stabilizing hexagonally close-packed phase in single-component block copolymers through rational symmetry breaking

Despite being predicted to be a thermodynamically equilibrium structure, the absence of direct experimental evidence of hexagonally close-packed spherical phase in single-component block copolymers raises uncomfortable concerns regarding the existing fundamental phase principles. This work presents a robust approach to regulate the phase behavior of linear block copolymers by deliberately breaking molecular symmetry, and the hexagonally close-packed lattice is captured in a rigorous single-component system. A collection of discrete A1BA2 triblock copolymers is designed and prepared through an iterative growth method. The precise chemical composition and uniform chain length eliminates inherent size distribution and other molecular defects. Simply by tuning the relative chain length of two end A blocks, a rich array of ordered nanostructures, including Frank−Kasper A15 and σ phases, are fabricated without changing the overall chemistry or composition. More interestingly, hexagonally close-packed spherical phase becomes thermodynamically stable and experimentally accessible attributed to the synergistic contribution of the two end blocks. The shorter A blocks are pulled out from the core domain into the matrix to release packing frustration, while the longer ones stabilize the ordered spherical phase against composition fluctuation that tends to disrupt the lattice. This study adds a missing puzzle piece to the block copolymer phase diagram and provides a robust approach for rational structural engineering.

Non-compact gauge groups, tensor fields and Yang-Mills-Einstein amplitudes

Scattering amplitudes in Yang-Mills-Einstein theories have been investigated mostly for compact gauge groups. While non-compact gauge groups are not physically viable in Yang-Mills theory, non-compact gaugings feature prominently in the supergravity literature, where any choice of perturbative vacuum spontaneously breaks the gauge group to a compact subgroup. In this paper, we formulate double-copy constructions for several five-dimensional N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 supergravities with non-compact gauge groups. On one side of the double copy, we employ amplitudes from a super-Yang-Mills theory with a massive hypermultiplet. On the other, we use amplitudes from particular non-supersymmetric Yang-Mills-scalar theories with massive fermions, chosen to obey constraints coming from color/kinematics duality. Supergravities with massive self-dual tensors in five dimensions are also considered, showing that tensors are straightforwardly realized as double copies of gauge-theory fermions with suitable choices of signs in the corresponding solutions of the Dirac equation. We present several examples of these constructions, noting in particular the appearance of Heisenberg groups in the supergravity gauge symmetry and, in some cases, the possibility of exotic tensor-vector matter couplings.

Density Functional Theory and Spectroscopic Analysis of Stigmasterol from Garcinia wightii: Deciphering its Inhibitory Potential against Drug-Resistant Tuberculosis via Insilico Molecular Docking and Molecular Dynamics Simulations

This study investigates the molecular structure and electronic properties of stigmasterol, isolated from Garcinia wightii, using density functional theory (DFT) alongside experimental techniques including FT-IR, FT-Raman, UV–Vis, 1H and 13C NMR spectroscopy. Theoretical predictions are compared with experimental results, facilitated by vibrational energy distribution analysis for unambiguous vibrational wavenumber assignments. Natural bond orbital analyses reveal donor-acceptor bond energies and electron densities, while Fukui functions identify reactive sites susceptible to electrophilic and nucleophilic attacks. Electronic properties are further explored through various analyses, unveiling reactive surface sites. Non-covalent interactions are examined using reduced density gradient analysis. Assessment of absorption, distribution, metabolism, and excretion attributes aids in drug discovery efforts. Molecular docking studies against 20 target proteins for antitubercular screening show a stable glide score of -9.52 kcal/mol for the protein 4FDO (Mycobacterium tuberculosis DprE1 in complex with CT319). Molecular dynamics simulations over 100 ns indicate the stability of the ligand-protein complex, suggesting its potential as an antituberculosis agent. Stigmasterol's structural, vibrational, electronic, and topological properties are thoroughly investigated, revealing its ring skeleton with a flexible isooctyl side chain, adhering to C1 point group symmetry. Steric and stereo electronic interactions play crucial roles in conformation and binding to target proteins. Theoretical and experimental analyses align, confirming the compound's bioactive properties. This comprehensive investigation underscores stigmasterol's potential as a tuberculosis treatment option, providing valuable insights into its structural characteristics and therapeutic possibilities.

Optimal systems of Lie subalgebras: A computational approach

Lie groups of symmetries of differential equations constitute a fundamental tool for constructing group-invariant solutions. The number of subgroups is potentially infinite and so the number of invariant solutions; thus, it is crucial to obtain a classification of subgroups in order to have an optimal system of inequivalent solutions from which all other solutions can be derived by action of the group itself. Since Lie groups are intimately connected to Lie algebras, a classification of inequivalent subgroups induces a classification of inequivalent Lie subalgebras, and vice versa. A general method for classifying the Lie subalgebras of a finite–dimensional Lie algebra uses inner automorphisms that are obtained by exponentiating the adjoint groups. In this paper, we present an effective algorithm able to automatically determine optimal systems of Lie subalgebras of a generic finite–dimensional Lie algebra abstractly assigned by means of its structure constants, or realized in terms of matrices or vector fields, or defined by a basis and the set of non-zero Lie brackets. The algorithm is implemented in the computer algebra system Wolfram Mathematica™; some meaningful and non-trivial examples are considered.

Connecting tribimaximal and bitrimaximal mixings

In this paper, we study the connection between the tribimaximal and bitrimaximal mixing patterns. In doing so, we are forced to work in a non-diagonal charged lepton basis. This leads to several relations that must hold between the lepton mixing angles. After a short discussion, we analyze the underlying flavor symmetry responsible for this prediction. Finally, we add CP violation to bitrimaximal mixing and study its effect on the flavor symmetry group.

Predictive Guidelines for Electrocyclization of Dithienylethenes.

Molecular photoswitches undergo a structural transformation upon photoexcitation to interconvert between two or more stable forms. In some cases, the structural rearrangement involves the transition between ring-open and ring-closed forms. In this work, we develop simple guidelines for the design of organic molecules able to undergo photochemical electrocyclization, using electronic structure calculations on dithienylethene (DTE)-based compounds. We conclude that the ability to photocyclize can be predicted from the localization and symmetry of frontier molecular orbitals. These ideas are based on the Woodward-Hoffmann rules but go beyond them, allowing us to address a more general family of chromophores. Our methodology has been experimentally validated in a novel series of quinoline-based DTEs, where the ability for photocyclization depends on specific chemical modifications. We use the DTE scaffold as the workhorse model in our study; however, these simple yet powerful guidelines are expected to be generally valid to guide the design of other diarylethenes.

Combining Complex Conjugation, Time-Reversal, and Spin-Flip Symmetry Projection of Coupled Cluster Wave Functions.

Complex conjugation symmetry breaking and restoration generates two nonorthogonal configurations at the Hartree-Fock level that can capture static correlation naturally. In conjunction with broken spin-symmetry coupled cluster theory, the symmetry-projected wave function shows good agreement with full configuration interaction in beryllium hydride insertion, lithium fluoride dissociation, and symmetric stretching of tetrahedral H4. By adding spin flip projection, we can also recover time reversal symmetry in the same coupled cluster framework. We also show results including point group symmetry projection.

Synthesis of Ce(IV) Heteroleptic Double-Decker Complex with a New Helical Naphthalocyanine as a Potential Gearing Subunit.

This paper describes the synthesis of a cerium(IV)-based molecular gear composed of a thioether functionalized phthalocyanine anchoring ligand, and a helical naphthalocyanine rotating cogwheel functionalized with four carbazoles. The naphthalocyanine ligand 9 was obtained after eleven steps (overall yield of 0.2%) as a mixture of three geometrical isomers, two of which are chiral and exhibit high levels of steric hindrance, as shown by DFT calculations. Their attributions have been made using 1H-NMR based on their different symmetry groups. The ratio of isomers was also determined and the prochiral C4h naphthalocyanine shown to be the major compound (55%). Its heteroleptic complexation with cerium (IV) and the anchoring phthalocyanine ligand 10 gave the targeted molecular gear in a 16% yield.

The First Discovery of Spherical Carborane Molecular Ferroelectric Crystals

AbstractCarborane compounds, known for their exceptional thermal stability and non‐toxic attributes, have garnered widespread utility in medicine, supramolecular design, coordination/organometallic chemistry, and others. Although there is considerable interest among chemists, the integration of suitable carborane molecules into ferroelectric materials remains a formidable challenge. In this study, we employ the quasi‐spherical design strategy to introduce functional groups at the boron vertices of the o‐carborane cage, aiming to reduce molecular symmetry. This approach led to the successful synthesis of the pioneering ferroelectric crystals composed of cage‐like carboranes: 9‐OH‐o‐carborane (1) and 9‐SH‐o‐carborane (2), which undergo above‐room ferroelectric phase transitions (Tc) at approximately 367 K and 347 K. Interestingly, 1 and 2 represent uniaxial and multiaxial ferroelectrics respectively, with 2 exhibiting six polar axes and as many as twelve equivalent polarization directions. As the pioneering instance of carborane ferroelectric crystals, this study introduces a novel structural archetype for molecular ferroelectrics, thereby providing fresh insights into the exploration of molecular ferroelectric crystals with promising applications.

The number of Hamiltonian cycles in groups of Symmetry

Groups are algebraic structures in Abstract Algebra comprised of a set of elements with a binary operation that satisfies closure, associativity, identity and invertibility. Cayley graphs serve as a visualization tool for groups, as they are capable of illustrating certain structures and properties of groups geometrically. In particular, each element in a group is assigned to a vertex in Cayley graphs. By the group action of left-multiplication, distinct elements in the generating sets can act on each element to create varied directed edges (Meier[1]). By contrast, the presence of a Hamiltonian cycles within a graph demonstrates its level of connectivity. In this research paper, utilizing directed Cayley graphs, we present a series of conjectures and theorems regarding the number and existence of Hamiltonian cycles within Dihedral groups, Symmetric groups of Platonic solids and Symmetric groups. By exploring the relationship between Abstract groups and Hamiltonian graphs, this work contributes to the broader field of research pertaining to Groups of Symmetry and Geometric Group Theory.

Anomalous U(1) extension of the Standard Model

We present a set of example models in which the Standard Model (SM) symmetry group is extended by a new abelian symmetry. This additional symmetry appears anomalous in the effective low-energy theory; however, the anomalies cancel out when massive chiral fermions not present in the effective low-energy theory are taken into account. These chiral fermions under the new abelian gauge group, are chosen to be vector-like under the SM symmetries, and reside in the same representations as quarks and leptons. This allows us to quantitatively determine the magnitude of tree-level interactions between three vector bosons induced in low-energy effective field theory by the integration of chiral heavy fermions. We also examine the perturbativity constraints of the theory and the ultraviolet cut-off. We conclude by highlighting possible extensions of our work.

Symmetry group detection of point clouds in 3D via a decomposition method

Analyzing the symmetries present in point clouds, which represent sets of 3D coordinates, is important for understanding their underlying structure and facilitating various applications. In this paper, we propose a novel decomposition-based method for detecting the entire symmetry group of 3D point clouds. Our approach decomposes the point cloud into simpler shapes whose symmetry groups are easier to find. The exact symmetry group of the original point cloud is then derived from the symmetries of these individual components. The method presented in this paper is a direct extension of the approach recently formulated in Bizzarri et al. (2022a) for discrete curves in plane. The method can be easily modified also for perturbed data. This work contributes to the advancement of symmetry analysis in point clouds, providing a foundation for further research and enhancing applications in computer vision, robotics, and augmented reality.

Two symmetric Schiff base complexes: Inhibition of cell proliferation, inducing apoptosis and suppressing migration

Two complexes [Cu4L4] (1) and [Zn2Cl4L]·2[N(CH2CH3)4] (2) are synthesized and characterized with UV–Vis, IR, PXRD and TGA using a symmetrical flexible Schiff base ligand 2,2′-(1,4-phenlenebis(nitrilomethylylidene)-bis(6- methoxyphenol) (H2L). Crystallographic analysis reveals that complex 1 is a mirror symmetric single molecule with a rhombic crossing structure linked by four Cu(II) ions and four ligands encircling each other. Complex 2 is a centrosymmetric single molecule with one ligand connecting two zinc chloride salts to form an anion framework with two tetraethylammonium cations to balance charge. Antiproliferative activity of both complexes against four cancer cells and two normal cells was investigated, and the results show that complex 2 had the strongest inhibitory effect on A549 cells with IC50 value much lower than cisplatin and lower toxicity to two normal cells. Mechanistic studies showed that complex 2 could induce apoptosis of A549 cells, and inhibit cell invasion and migration of SMMC-7721 cells and A549 cells at a low concentration effectively. This work could provide a basis for developing novel metal-based anticancer agents.

Evaluation of Point Group Symmetry in Lanthanide(III) Complexes: A New Implementation of a Continuous Symmetry Operation Measure with Autonomous Assignment of the Principal Axis.

The structure of molecular systems dictates the physical properties, and symmetry is the determining factor for all electronic properties. This makes group theory a powerful tool in quantum mechanics to compute molecular properties. For inorganic compounds, the coordination geometry has been estimated as idealized polyhedra with high symmetry, which, through ligand field theory, provides predictive capabilities. However, real samples rarely have ideal symmetry, and although continuous shape measures (CShM) can be used to evaluate deviation from an ideal reference structure σideal, this often fails for lanthanide(III) complexes with high coordination numbers, no obvious choice of principal axes, and no obvious reference structure. In lanthanide complexes, the unique electronic structures and associated properties are intricately tied to the symmetry around the lanthanide center. Therefore, robust methodologies to evaluate and estimate point group symmetry are instrumental for building structure-property relationships. Here, we have demonstrated an algorithmic approach that orients a molecular structure Q in the best possible way to the symmetry axis of any given point group G and computes a deviation from the ideal symmetry σsym(G,Q). This approach does not compute the deviation from an ideal reference system, but the intrinsic deviation in the structure induced by symmetry operations. If the structure contains the symmetry operation, there is no deviation and σsym(G,Q) = 0. The σsym deviation is generated from all of the symmetry operation ÔS in a point group G using the most correct orientation of the sample structure in each group G. The best orientation is found by an algorithm that minimizes the orientation of the structure with respect to G. To demonstrate the methodology, we have investigated the structure and symmetry of 8- and 9-coordinated lanthanide(III) aqua complexes and correlated the luminescence from 3 europium(III) crystals to their actual symmetry. To document the methodology, the approach has been tested on 26 molecules with different symmetries. It was concluded that the method is robust and fully autonomous.

Mechanisms and Site Selectivity of (Het)Ar–X Oxidative Addition to Pd(0) Are Controlled by Frontier Molecular Orbital Symmetry

Mechanisms and Site Selectivity of (Het)Ar–X Oxidative Addition to Pd(0) Are Controlled by Frontier Molecular Orbital Symmetry

Interplay between charge and spin noise in the near-surface theory of decoherence and relaxation of C3v symmetry qutrit spin-1 centers

Decoherence and relaxation of solid-state defect qutrits near a crystal surface, where they are commonly used as quantum sensors, originate from charge and magnetic field noise. A complete theory requires a formalism for decoherence and relaxation that includes all Hamiltonian terms allowed by the defect's point-group symmetry. This formalism, presented here for the C3v symmetry of a spin-1 defect in a diamond, silicon carbide, or similar host, relies on a Lindblad dynamical equation and clarifies the relative contributions of charge and spin noise to relaxation and decoherence, along with their dependence on the defect spin's depth and resonant frequencies. The calculations agree with the experimental measurements of Sangtawesin [], and corroborate the importance of charge noise. Published by the American Physical Society 2024

Van Hove annihilation and nematic instability on a kagome lattice.

A nematic phase breaks the point-group symmetry of the crystal lattice and is known to emerge in correlated materials. Here we report the observation of an intra-unit-cell nematic order and associated Fermi surface deformation in the kagome metal ScV6Sn6. Using scanning tunnelling microscopy and scanning tunnelling spectroscopy, we reveal a stripe-like nematic order breaking the crystal rotational symmetry within the kagome lattice itself. Moreover, we identify a set of Van Hove singularities adhering to the kagome-layer electrons, which appear along one direction of the Brillouin zone and are annihilated along other high-symmetry directions, revealing rotational symmetry breaking. Via detailed spectroscopic maps, we further observe an elliptical deformation of the Fermi surface, which provides direct evidence for an electronically mediated nematic order. Our work not only bridges the gap between electronic nematicity and kagome physics but also sheds light on the potential mechanism for realizing symmetry-broken phases in correlated electron systems.

3DReact: Geometric Deep Learning for Chemical Reactions.

Geometric deep learning models, which incorporate the relevant molecular symmetries within the neural network architecture, have considerably improved the accuracy and data efficiency of predictions of molecular properties. Building on this success, we introduce 3DReact, a geometric deep learning model to predict reaction properties from three-dimensional structures of reactants and products. We demonstrate that the invariant version of the model is sufficient for existing reaction data sets. We illustrate its competitive performance on the prediction of activation barriers on the GDB7-22-TS, Cyclo-23-TS, and Proparg-21-TS data sets in different atom-mapping regimes. We show that, compared to existing models for reaction property prediction, 3DReact offers a flexible framework that exploits atom-mapping information, if available, as well as geometries of reactants and products (in an invariant or equivariant fashion). Accordingly, it performs systematically well across different data sets, atom-mapping regimes, as well as both interpolation and extrapolation tasks.