Symmetry Group Research Articles

Developing single ligand strategy for engineering a high-performance photocatalyst with the pore space partition and open-metal sites

Realizing the precise structure design and functional customization of photocatalysts is essential for achieving high conversion and selectivity. Herein, we propose an innovative pore space partition strategy for constructing a high-performance photocatalyst from a single ligand by regulating the group modification and symmetry of the ligand, which solves the problem of open-metal sites occupation. A novel polyoxometalate-based metal-organic framework, CoW–BTIz, was synthesized successfully from a new donor-acceptor-donor type photosensitizer 4, 7-bis (imidazolyl) benzothiazole, Co cations and electron sponge [BW12O40]5– anions. The push−pull effect of the D–A–D units in the confined spatial ensures the charge rapid transport processes. Incorporating POM into photoactive MOF is beneficial to produce single •O2– via type I pathway primarily in air atmosphere by photogenerated electron transfer. CoW–BTIz gave a high yield in the aerobic synthesis of 2-arylbenzothiazole and the cyclization of thioamide to 1,2, 4-thiadiazole by the synergetic effect of each component in mild conditions.

Symmetry adaptation for self-consistent many-body calculations

The exploitation of space group symmetries in numerical calculations of periodic crystalline solids accelerates calculations and provides physical insight. We present results for a space-group symmetry adaptation of electronic structure calculations within the finite-temperature self-consistent GW method along with an efficient parallelization scheme on accelerators. Our implementation employs the simultaneous diagonalization of the Dirac characters of the orbital representation. Results show that symmetry adaptation in self-consistent many-body codes results in substantial improvements of the runtime, and that block diagonalization on top of a restriction to the irreducible wedge results in additional speedup.

Electronic and Optical Properties of 2D Heterostructure Bilayers of Graphene, Borophene and 2D Boron Carbides from First Principles.

In the present work the atomic, electronic and optical properties of two-dimensional graphene, borophene, and boron carbide heterojunction bilayer systems (Graphene-BC3, Graphene-Borophene and Graphene-B4C3) as well as their constituent monolayers are investigated on the basis of first-principles calculations using the HSE06 hybrid functional. Our calculations show that while borophene is metallic, both monolayer BC3 and B4C3 are indirect semiconductors, with band-gaps of 1.822 eV and 2.381 eV as obtained using HSE06. The Graphene-BC3 and Graphene-B4C3 bilayer heterojunction systems maintain the Dirac point-like character of graphene at the K-point with the opening of a very small gap (20-50 meV) and are essentially semi-metals, while Graphene-Borophene is metallic. All bilayer heterostructure systems possess absorbance in the visible region where the resonance frequency and resonance absorption peak intensity vary between structures. Remarkably, all heterojunctions support plasmons within the range 16.5-18.5 eV, while Graphene-B4C3 and Graphene-Borophene exhibit a π-type plasmon within the region 4-6 eV, with the latter possessing an additional plasmon at the lower energy of 1.5-3 eV. The dielectric tensor for Graphene-B4C3 exhibits complex off-diagonal elements due to the lower P3 space group symmetry indicating it has anisotropic dielectric properties and could exhibit optically active (chiral) effects. Our study shows that the two-dimensional heterostructures have desirable optical properties broadening the potential applications of the constituent monolayers.

Entwining tetrahedron maps

We present three non-equivalent procedures to obtain entwining (non-constant) tetrahedron maps. Given a tetrahedron map, the first procedure incorporates its underlying symmetry group. With the second procedure we obtain several classes of entwining tetrahedron maps by considering certain compositions of pentagon with reverse-pentagon maps which satisfy certain compatibility relations the so-called ten-term relations. Using the third procedure, provided that a given tetrahedron map admits at least one companion map (partial inverse), we obtain entwining set theoretical solutions of the tetrahedron equation.

Insights into the gas-phase structure and internal dynamics of diphenylsilane: A broadband rotational spectroscopy study.

The rotational spectrum of diphenylsilane was investigated using chirped-pulse Fourier transform microwave spectroscopy in the frequency range of 2-8 GHz. The lowest energy structure of diphenylsilane has C2 point group symmetry with the C2 symmetry axis coinciding with the binertial axis of the molecule. Through the assignment of the main isotopologue as well as singly substituted heavy-atom isotopologues, including 13C, 29Si, and 30Si, we were able to obtain a comprehensive gas-phase structure of diphenylsilane. The structure of diphenylsilane was compared with its oxygen analogue, diphenylether, including a discussion of the barrier height to the large-amplitude motion of the phenyl rings. Furthermore, the structural comparison was extended to include a range of C-Si bond lengths and bond angles from other organosilicon molecules where the silicon atom is bonded to aliphatic and/or aromatic moieties.

Quaternion and Biquaternion Representations of Proper and Improper Transformations in Non-Cartesian Reference Systems

Quaternion and biquaternion symmetry transformations have been applied to non-Cartesian reference systems of direct and reciprocal crystal lattices. The transformations performed directly in the sets of crystal reference axes simplify the calculations, eliminate the need for orthogonalization, permit the use of crystallographic vectors for defining the directions of rotations and perform the computations directly in the crystal coordinates. The applications of the general quaternion transformations are envisioned for physical, chemical, crystallographic and engineering applications. The general quaternion multiplication rules for any symmetry-unrestricted lattices have been derived for the triclinic crystallographic system and have been applied to the biquaternion representations of all point-group symmetry elements, including the crystallographic hexagonal system. Cayley multiplication matrices for point-groups, based on the biquaternion symbols of proper and improper symmetry elements, have been exemplified.

Study of dielectric relaxation and electrical conduction mechanism in the double perovskite La2MnRuO6

We have prepared the La2MnRuO6 sample via the sol–gel self-combustion technique and studied the electrical modulus as well as the other dielectric properties using impedance spectroscopy. The Rietveld refinement of the powder XRD profile at ambient temperature revealed that only one phase is constituted in the elaborated sample. It crystallizes in the orthorhombic structure with Pbnm space group symmetry. The complex impedance spectroscopy was used to study the mechanism of electrical transport and dielectric relaxation. Jonscher’s universal power law controls accurately how the alternating current conductivity (AC) spectra behave. While the dielectric constant showed the effects of Maxwell-Wagner interfacial polarisation, the dielectric loss factor exhibited a frequency dependency at all the investigated values of the temperature. Two peaks can be seen in the imaginary component of the impedance Z″ spectra. The first peak is located in the low-frequencies region whereas the second peak is in the high-frequency range. A peak shift into the high-frequency region is observed when the temperature increases, which comes from the gathering at the interface of free charges with increasing temperature. Moreover, the activation energy values obtained from the conductivity were in good agreement with those obtained by the modulus.

Comments on Global Symmetries and Anomalies of 5d SCFTs

We study various aspects of global symmetries in five-dimensional superconformal field theories. Whenever a supersymmetry-preserving relevant deformation is available, the infrared gauge theory description might exhibit a finite order mixed ’t Hooft anomaly between a 1-form symmetry and the instantonic symmetry. This anomaly constrains the flavor symmetry group acting faithfully on the SCFT and the consistency of certain RG flows. As an additional example, we consider the instructive case of three-dimensional N=4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {N}=4$$\\end{document} SQED. Finally, we discuss the compatibility between conformal invariance and the presence of 1-form and 2-group global symmetries.

Enhanced photodegradation of organic dyes using copper and zinc aluminate nanophotocatalysts

This study aims to enhance the photocatalytic efficiency of CuxZn1-xAl2O4 (x = 0.0, 0.2, 0.4, 0.6, and 0.8) nanophotocatalysts synthesized via a sol-gel self-combustion method. Rietveld analysis confirmed the formation of single-phase spinels with a face-centered cubic structure and Fd-3m space group symmetry, while electron density distribution analysis supported the ionic character of bonding within the material. Subsequent UV–visible spectroscopy revealed that the addition of Cu(II) reduced the band gap from 4.66 eV to 2.54 eV, facilitating enhanced light absorption. Consequently, the catalyst with x = 0.8 deteriorated 95 % of methyl orange (MO) and 93 % of rhodamine-B (RhB) in 120 min of visible light irradiation, following a pseudo-first-order kinetic model. The Cu0.8Zn0.2Al2O4 sample demonstrated significant reusability and stability, with degradation rates of 93–79 % for RhB and 95–81 % for MO after four cycles. Scavenging studies indicated that photoexcited holes (h), hydroxyl radicals (OH•), and superoxide radicals (O₂•⁻) were key factors in the degradation process. This study presents an improved approach for enhancing the photodegradation performance of the Cu0.8Zn0.2Al2O4 catalyst for pharmaceutical and wastewater treatment applications.

Finding discrete symmetry groups via machine learning

Finding discrete symmetry groups via machine learning

Synthesis and Optical Properties of Organic-Inorganic Hybrid[(18-Crown-6)K][MoOCl4(H2O)

Crown ether anchored organic-inorganic hybrid halides have been recently reported as interesting luminescent materials in the visible region of electromagnetic spectrum. Is it possible to develop such crown ether anchored hybrid materials for near infrared emission? Motivated by this question, we designed a new hybrid material, namely, [(18-Crown-6)K][MoOCl4(H2O)]. 18-Crown-6 ether bound with K+ form the cationic part [(18-Crown-6)K]+. The K+ of [(18-Crown-6)K]+ electrostatically interacts with Cl- of the anionic part [MoOCl4(H2O)]-, forming the hybrid crystal [(18-Crown-6)K][MoOCl4(H2O)]. It crystallizes in orthorhombic crystal system with Pnma space group. The Mo(V) possesses one d-electron (d1) in C4v point group symmetry in the [MoOCl4(H2O)]- polyhedra. This electronic configuration leads to multiple spin-allowed d-d transitions along with a ligand to metal charge transfer (LMCT) resulting into multiple optical absorption bands in the near UV-visible-near infrared (NIR) region. The lowest energyd-dtransition via 2E to2B2 leads to NIR PL with peak at 952 nm, but with a poor intensity at room temperature.

DMRG-Tailored Coupled Cluster Method in the 4c-Relativistic Domain: General Implementation and Application to the NUHFI and NUF3 Molecules.

Heavy atom compounds represent a challenge for computational chemistry due to the need for simultaneous treatment of relativistic and correlation effects. Often such systems also exhibit strong correlation, which hampers the application of perturbation theory or single-reference coupled cluster (CC) methods. As a viable alternative, we have proposed externally correcting the CC method using the density matrix renormalization group (DMRG) wave functions, yielding the DMRG-tailored CC method. In a previous paper [J. Chem. Phys. 2020, 152, 174107], we reported a first implementation of this method in the relativistic context, which was restricted to molecules with real double group symmetry. In this work, we present a fully general implementation of the method, covering complex and quaternion double groups as well. The 4c-TCC method thus becomes applicable to polyatomic molecules, including heavy atoms. For the assessment of the method, we performed calculations of the chiral uranium compound NUHFI, which was previously studied in the context of the enhancement of parity violation effects. In particular, we performed calculations of a cut of the potential energy surface of this molecule along the stretching of the N-U bond, where the system exhibits strong multireference character. Since there are no experimental data for NUHFI, we have performed also an analogous study of the (more symmetric) NUF3 molecule, where the vibrational frequency of the N-U bond can be compared with spectroscopic data.

Study of the Torquoselectivity of a Set of Unusual Ring‐Opening Electrocyclic Reactions: Determination of the Electronic Bonding Structure Through the Methodologies of Natural Bond Orbital Analysis and Quantum Theory of Atoms in Molecules, and Analysis of the Electronic Reaction Mechanism Through Bond Reactivity Descriptors

ABSTRACTIn this work, we have studied the torquoselectivity of a set of unusual ring‐opening electrocyclic reactions that have not been successfully rationalized using models based on orbital symmetry nor have they been explained by steric hindrance. Firstly, the corresponding transition states have been obtained, and it has been verified that the intrinsic reaction coordinates associated with these transition states are consistent with the reactants and products of the reactions studied. This has allowed us to theoretically calculate the reaction barriers (with their corresponding thermal corrections) and compare them with the corresponding experimental values. In a second step, we have analyzed the electronic bonding structure using the methodologies of Natural Bond Orbital Analysis and Quantum Theory of Atoms in Molecules, searching for interactions that may significantly stabilize the transition states. Finally, we have analyzed the reactivity using a recent model that has allowed us to calculate the corresponding bond reactivity descriptors.

Quantum Equation-of-Motion Method with Single, Double, and Triple Excitations.

The quantum equation-of-motion (qEOM) method with single and double excitations (qEOM-SD) has been proposed to study electronically excited states, but it fails to handle states dominated by double excitations. In this work, we reformulate the qEOM method within the effective Hamiltonian framework that satisfies the killer condition, and then present an efficient implementation incorporating single, double, and triple excitations. To reduce computational complexity, we employ point-group symmetry and perturbation theory to screen triple excitations, effectively reducing the scaling from No6Nv6 to No5Nv5, where No and Nv are the numbers of occupied and virtual spin orbitals, respectively. Furthermore, we account for the effect of neglected triple excitations by introducing a perturbative correction to the excitation energy. We apply this method to challenging cases where the qEOM-SD method exhibits significant errors, such as the 2 1Δ state of CH+ and the 2 1Σ state of HF. Our new method achieves energy errors below 0.18 eV while incorporating less than 8.2% of triple excitations. Additionally, we extend the operator screening technique to the quantum subspace expansion method for the efficient inclusion of selected triple excitations.

Boundary crossing problems and functional transformations for Ornstein–Uhlenbeck processes

ABSTRACT We are interested in the law of the first passage time of an Ornstein–Uhlenbeck process to time-varying thresholds. We show that this problem is connected to the laws of the first passage time of the process to members of a two-parameter family of functional transformations of a time-varying boundary. For specific values of the parameters, these transformations appear in a realisation of a standard Ornstein–Uhlenbeck bridge. We provide three different proofs of this connection. The first is based on a similar result for Brownian motion, the second uses a generalisation of the so-called Gauss–Markov processes, and the third relies on the Lie group symmetry method. We investigate the properties of these transformations and study the algebraic and analytical properties of an involution operator which is used in constructing them. We also show that these transformations map the space of solutions of Sturm–Liouville equations into the space of solutions of the associated nonlinear ordinary differential equations. Lastly, we interpret our results through the method of images and give new examples of curves with explicit first passage time densities.

Study of Two-Photon induced excited state absorption of Three-Branched triphenylamine Derivatives: Cooperative and Anti-Cooperative effect of electron transition in the excited state

For multi-branched molecules, intramolecular cooperative effect can significantly enhance the molecular nonlinear optical absorption. Three triphenylamine-cored compounds (N1, N2 and N3) with three branches are synthesized to study the cooperative and anti-cooperative effect of electron transition in the excited state on two-photon absorption (TPA) and excited state absorption (ESA). Molecular polarization of these multi-branched triphenylamine derivatives is regulated by changing the molecular symmetry and the planarity of peripheral branches, to regulate their charge distribution and electron transition characteristics in the excited state. Here, we show that due to electronic coupling and interaction between certain branches, the asymmetric distribution of electron clouds in the excited states of these multi-branched molecules will lead to an enhancement of their TPA and ESA cross-sections, which is known as the cooperative effect of electron transitions. On the contrary, electronic coupling and interaction among all branches will lead to a highly symmetric distribution of electron clouds in the excited states of these multi-branched molecules, which will cause anti-cooperative effects and result in significant attenuation of TPA and ESA cross-sections.

Orbit symmetry breaking in MXene implements enhanced soft bioelectronic implants.

Bioelectronic implants featuring soft mechanics, excellent biocompatibility, and outstanding electrical performance hold promising potential to revolutionize implantable technology. These biomedical implants can record electrophysiological signals and execute direct therapeutic interventions within internal organs, offering transformative potential in the diagnosis, monitoring, and treatment of various pathological conditions. However, challenges remain in improving excessive impedance at the bioelectronic-tissue interface and thus the efficacy of electrophysiological signaling and intervention. Here, we devise orbit symmetry breaking in MXene (a low-cost scalability, biocompatible, and conductive two dimensionally layered material, which we refer to as OBXene), which exhibits low bioelectronic-tissue impedance, originating from the out-of-plane charge transfer. Furthermore, the Schottky-induced piezoelectricity stemming from the asymmetric orbital configuration of OBXene facilitates interlayered charge transport in the device. We report an OBXene-based cardiac patch applied on the left ventricular epicardium of both rodent and porcine models to enable spatiotemporal epicardium mapping and pacing while coupling the wireless and battery-free operation for long-term real-time recording and closed-loop stimulation.

Black flowers and real forms of higher spin symmetries

Using Chern-Simons formulation, we investigate higher spin (HS) black holes in AdS3 with soft Heisenberg hair and establish linkage with the real forms of the underlying complexified gauge symmetries taken here as SL(N, ℂ)L × SL(N, ℂ)R. We study the various conserved currents characterizing the HS black flowers (HS-BF) and show that they can be formed of layers indexed by the elements of the centre of the gauge symmetry. This feature follows from requiring the holonomy of the asymptotic gauge connection around the thermal cycle to sit in the centre ℤN of the symmetry group. With regard to the compact subgroups of the real forms of the complexified gauge symmetry, we calculate the entropies of the HS-BF and verify that, unless we are considering trivial holonomies, there are no continuous paths joining the HS-BF to the core spin 2 black holes. As explicit illustrations, we give quantum field realisations of the soft Heisenberg hair in terms of bosonic and fermionic primary conformal fields and compute the HS-BF entropy as a function of the number of fermions occupying the ground state of the Heisenberg soft hair.

Duality and stacking of bosonic and fermionic SPT phases

We study the interplay of duality and stacking of bosonic and fermionic symmetry-protected topological phases in one spatial dimension. In general the classifications of bosonic and fermionic phases have different group structures under the operation of stacking, but we argue that they are often isomorphic and give an explicit isomorphism when it exists. This occurs for all unitary symmetry groups and many groups with antiunitary symmetries, which we characterize. We find that this isomorphism is typically not implemented by the Jordan-Wigner transformation, nor is it a consequence of any other duality transformation that falls within the framework of topological holography. Along the way to this conclusion, we recover the fermionic stacking rule in terms of G\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{G} $$\\end{document}-pin partition functions, give a gauge-invariant characterization of the twisted group cohomology invariant, and state a procedure for stacking gapped phases in the formalism of symmetry topological field theory.

Exact dynamics of the Tomonaga-Luttinger liquid and shortcuts to adiabaticity

Controlling many-body quantum systems is a highly challenging task required to advance quantum technologies. Here, we report progress in controlling gapless many-body quantum systems described by the Tomonaga-Luttinger liquid (TLL). To do so, we investigate the exact dynamics of the TLL induced by an arbitrary interaction quench, making use of the SU(1,1) dynamical symmetry group and the Schrödinger picture. First, we demonstrate that this approach is useful to perform a shortcut to adiabaticity, which cancels the final nonadiabatic residual energy of the driven TLL and is experimentally implementable in the semiclassical limit of the sine-Gordon model. Second, we apply this framework to analyze various driving schemes in finite time, including linear ramps and smooth protocols. Published by the American Physical Society 2024