Borromean Ring Research Articles

Pyrene-Functionalized Ru-Catenated Metallacycles: Conversion of Catenated System to Monorectangle through Aging.

Molecular transformation behavior within a mechanically interlocked system is often assisted by chemical manipulation, such as the inclusion of guest molecules, variation in the solution concentration, or swapping of solvents. We present in this report the synthesis of ruthenium metal and π-conjugated pyrene-based (2 + 2)2 catenated rectangles. Additionally, we discuss the structural conversion of these catenated rectangles into monorectangles through adjustments in concentration and solvent composition. In the presence of a methanol solution, a transformation into monorectangles was observed as the concentration declined. However, interestingly, in the presence of a nitromethane solution, an alteration in conformation to monorectangles was noted by just standing at room temperature for a few hours without any chemical manipulation. Furthermore, theoretical calculations were studied to provide insights into the formation of catenated structures over other potential ring-in-ring or Borromean-ring-type structures. The computational study with the GFN2-xTB method combined with density functional theory (DFT) calculations showed that the lower binding energy within the rectangles favors a catenated structure over other potential ring-in-ring or Borromean-ring-type structures. This work represents a new example of an intertwined structure that self-assembles into a catenated ring rather than a ring-in-ring or Borromean ring and transforms into a monorectangle in nitromethane without the use of any template, alteration in solution concentration, or exchange of solvents, but simply by standing at room temperature.

The codriven assembly of molecular metalla-links (613, 623) and metalla-knots (41, 31) via coordination and noncovalent interactions

Although mechanically interlocked molecules (MIMs) display unique properties and functions associated with their intricate connectivity, limited assembly strategies are available for their synthesis. Herein, we presented a synergistic assembly strategy based on coordination and noncovalent interactions (π-π stacking and CH⋯π interactions) to selectively synthesize molecular closed three-link chains ([Formula: see text] links), highly entangled figure-eight knots ([Formula: see text] knots), trefoil knot ([Formula: see text] knot), and Borromean ring ([Formula: see text] link). [Formula: see text] links can be created by the strategic assembly of nonlinear multicurved ligands incorporating a furan or phenyl group with the long binuclear half-sandwich organometallic Cp*RhIII (Cp* = η5-pentamethylcyclopentadienyl) clip. However, utilizing much shorter binuclear Cp*RhIII units for union with the 2,6-naphthyl-containing ligand led to a [Formula: see text] knot because of the increased π-π stacking interactions between four consecutive stacked layers and CH⋯π interactions. Weakening such π-π stacking interactions resulted in a [Formula: see text] knot. The universality of this synergistic assembly strategy for building [Formula: see text] knots was verified by utilizing a 1,5-naphthyl-containing ligand. Quantitative conversion between the [Formula: see text] knot and the simple macrocycle species was accomplished by adjusting the concentrations monitored by NMR spectroscopy and electrospray ionization mass spectrometry (ESI-MS). Furthermore, increasing the stiff π-conjugated area of the binuclear unit afforded molecular Borromean ring, and this topology is a topological isomer of the [Formula: see text] link. These artificial metalla-links and metalla-knots were confirmed by single-crystal X-ray diffraction, NMR and ESI-MS. The results offer a potent strategy for building higher-order MIMs and emphasize the critical role that noncovalent interactions play in creating sophisticated topologies.

Alpha clustering in nuclear astrophysics and topology

When we think of clustering in nuclear physics, the astrophysical importance within light nuclei and structural manifestations with classical analogs immediately come to mind. 4He, also known as the alpha particle, is the most abundant nucleus in the Universe, being quite tightly bound for its mass, with a first excited state of over 20 MeV. The nature of the alpha particle places it in a unique position within nuclear astrophysics and structure (including geometry). The plurality of energy release from stellar hydrogen fusion—whether quiescent or explosive—comes from the conversion of hydrogen to helium. Within more complex nuclei, the alpha particles are continuously arranged, leading to fascinating phenomena such as excited rotational bands, Borromean ring ground states, and linear structures. Nuclei with an equal and even number of protons and neutrons are colloquially referred to as “alpha conjugate nuclei,” where such special properties are the most pronounced and easiest to spot. However, when a single nucleon or a pair of nucleons is added to the system, alpha clustering not only remains evident but it may also be enhanced. Excited states with large alpha partial widths are a signature of clustering behavior, and these states can have a profound effect on the reaction rates in astrophysical systems when the excitation energy aligns with the so-called Gamow energy—the preferential thermal energy to statistically overcome the Coulomb barrier. In this article, we will consider in detail the specific ramifications of alpha clustering in selected scenarios for both nuclear astrophysics and topology. In particular, we discussed the astrophysical reactions of 7Li (α, γ), 7Be+α, 11C (α, p), and 30S (α, p), where α-clusters may increase the reaction rates from 10% to an order of magnitude; large α resonances make the astrophysical rate of 18F (p, α) quite uncertain. We also focused on the α rotational bands of both positive and negative parities of 11B and 11C, and finally on the strongest evidence for the linear-chain cluster state observed in 14C.

Highly selective synthesis and near-infrared photothermal conversion of metalla-Borromean ring and [2]catenane assemblies.

Although the selective synthesis of complicated supramolecular architectures has seen significant progress in recent years, the exploration of the properties of these complexes remains a fascinating challenge. Herein, a series of new supramolecular topologies, metalla[2]catenanes and Borromean ring assemblies, were constructed based on appropriate Cp*Rh building blocks and two rigid alkynyl pyridine ligands (L1, L2) via coordination-driven self-assembly. Interestingly, minor differences between the two rigid alkynyl pyridine ligands with/without organic substituents led to products with dramatically different topologies. Careful structural analysis showed that π–π stacking interactions play a crucial role in stabilizing these [2]catenanes and Borromean ring assemblies, while also promoting nonradiative transitions and triggering photothermal conversion in both the solution and the solid states. These results were showcased through comparative studies of the NIR photothermal conversion efficiencies of the Borromean ring assemblies, [2]catenanes and metallarectangles, which exhibited a wide range of photothermal conversion efficiencies (12.64–72.21%). The influence of the different Cp*Rh building blocks on the NIR photothermal conversion efficiencies of their assemblies was investigated. Good photothermal conversion properties of the assemblies were also found in the solid state. This study provides a new strategy to construct valuable half-sandwich-based NIR photothermal conversion materials while also providing promising candidates for the further development of materials science.

Stimuli-Responsive Topological Transformation of a Molecular Borromean Ring via Controlled Oxidation of Thioether Moieties.

A Cp*-Rh based D-shaped binuclear metallacycle and a template-free molecular Borromean ring (BR) were obtained in high yield using the semi-rigid thioether dipyridyl ligand 1,4-bis[(pyridin-4-ylthio)methyl]benzene (Bptmb). The topological transformation from a binuclear metallacycle and a BR to tetranuclear metallacycles was realized via the controlled oxidation of thioethers. The strategy used in this work can be regarded as a new form of stimuli-responsive post-synthesis modification (PSM).

Stimuli‐Responsive Topological Transformation of a Molecular Borromean Ring via Controlled Oxidation of Thioether Moieties

AbstractA Cp*‐Rh based D‐shaped binuclear metallacycle and a template‐free molecular Borromean ring (BR) were obtained in high yield using the semi‐rigid thioether dipyridyl ligand 1,4‐bis[(pyridin‐4‐ylthio)methyl]benzene (Bptmb). The topological transformation from a binuclear metallacycle and a BR to tetranuclear metallacycles was realized via the controlled oxidation of thioethers. The strategy used in this work can be regarded as a new form of stimuli‐responsive post‐synthesis modification (PSM).

Selective Construction of Trefoil knots and a Molecular Borromean Ring Induced by Steric Hindrance of Thioether Ligands.

Two Cp*-RhIII based trefoil knots were obtained in high yield under ambient conditions via the coordination-driven self-assembly of semi-rigid thioether dipyridyl ligand 1,4-bis[(pyridin-4-ylthio)methyl]benzene (L1 ), ligand chloranilic acid (H2 -CA) and 6,11-dihydroxytetracene-5,12-dione (H2 -TtDo) with Cp*RhIII metal corner units, respectively. Furthermore, using the bulkier 4,4'-{[(2,5-dimethyl-1,4-phenylene)bis(methylene)]bis(sulfanediyl)}dipyridine (L2 ) in the place of ligand L1 in the construction process resulted in the formation of a teranuclear metallacycle and a template-free Borromean ring in high yields thanks to significantly altered intermolecular forces between the constituent ligands induced by the sterically-hindering methyl groups of L2 , as demonstrated via a detailed X-ray crystallographic analysis and NMR spectroscopy.

Innenrücktitelbild: Stimuli‐Responsive Topological Transformation of a Molecular Borromean Ring via Controlled Oxidation of Thioether Moieties (Angew. Chem. 28/2021)

Innenrücktitelbild: Stimuli‐Responsive Topological Transformation of a Molecular Borromean Ring via Controlled Oxidation of Thioether Moieties (Angew. Chem. 28/2021)

Inside Back Cover: Stimuli‐Responsive Topological Transformation of a Molecular Borromean Ring via Controlled Oxidation of Thioether Moieties (Angew. Chem. Int. Ed. 28/2021)

A crystal-like molecular Borromean ring topology is illustrated in the picture by blinking stars with wavering meteors as background. Guo-Xin Jin and co-workers outline in their Research Article on page 15466 that the exploration of structural transformations and applications of complex topologies is a hot topic in the field of supramolecular chemistry.

An efficient lattice-based linkable ring signature scheme with scalability to multiple layer

In this paper, we propose a novel lattice-based linkable ring signature scheme based on the Borromean ring signature. In our scheme, to avoid the extra overhead caused by reject sampling that used in the existing schemes, we use an exact indistinguishable distribution to replace it. Using our method, signature will be successfully generated without repeating, so the size of the signature can be reduced. Furthermore, our scheme can be extended to multiple layers easily. We also propose a lattice-based multilayer linkable ring signature scheme which can be use for transactions with multiple inputs. Then, we prove that our scheme has unforgeability, anonymity, linkability and non-slanderability that a linkable ring signature scheme should have. Efficiency analysis shows that our scheme has a smaller signature size under the same security conditions.

Selective Construction of Very Large Stacking-Interaction-Induced Molecular 818 Metalla-knots and Borromean Ring Using Curved Dipyridyl Ligands.

Two molecular metalla-knots containing over 500 non-hydrogen atoms (especially 16 RhIII ions) and one molecular Borromean ring were obtained in high yields facilitated by multiple intermolecular interactions between their components. The syntheses rely on the strategic selection of the nonlinear dipyridyl ligand 2,7-di(pyridin-4-yl)-9H-fluorene (L1) as precursor, and the structures of the assemblies were confirmed by detailed X-ray crystallographic analysis. Subsequently, replacing L1 with the bulkier ligand 4,4'-(9,9-dimethyl-9H-fluorene-2,7-diyl)dipyridine (L2) led to the formation of three tetranuclear metallocycles in high yields on account of the weakened π-π stacking interactions between the naphthacene/anthracene and fluorene moieties, which in turn confirmed the significance of stacking interactions in the construction of the molecular 818 metalla-knots and the molecular Borromean ring.

One Ball Tips the Balance toward Three-Component Borromean Ring Systems

In this issue of <i>Chem</i>, Metrangolo and colleagues describe the selective mechanochemical formation of three-component halogen-bonded ionic co-crystals that adopt a Borromean ring topology. Intriguingly, a seemingly minor adjustment of the milling conditions results in profound changes to the supramolecular reaction trajectory and final product, as monitored by <i>in situ</i> synchrotron diffraction.

Open versus Interpenetrated: Switchable Supramolecular Trajectories in Mechanosynthesis of a Halogen-Bonded Borromean Network

Summary Precise control over topologically intricate molecular architectures remains an open challenge for chemists due to their inherent structural complexity. We report a simple solvent-free strategy to selectively prepare two multi-component supramolecular crystalline systems based on the halogen bond, endowed with either an unknot topology or a Borromean-type entanglement. Real-time in situ monitoring of the solvent-free mechanochemical synthesis of these three-component halogen-bonded ionic co-crystals reveals that the choice of milling conditions leads to a switch in the supramolecular reaction trajectory, resulting in the selective formation of an open halogen-bonded network or a halogen-bonded Borromean-type assembly.

On Design of Single-Layer and Multilayer Code-Based Linkable Ring Signatures

In this paper, we present an effective code-based linkable ring signature scheme based on Borromean ring signature. The security of the scheme is based on the hardness of Syndrome Decoding problem, General Syndrome Decoding problem and Codeword Finding problem. We prove that our scheme has all the properties that a linkable ring signature scheme should have: unforgeability, anonymity, linkability and non-slanderability. Efficiency analysis shows that our scheme has a smaller signature size than the existing scheme under the same security conditions. Furthermore, this signature scheme can be easily extended to multiple layers. That is, code-based multilayer linkable ring signature scheme can be obtained and used for transactions with multiple inputs.

Covalent Post-assembly Modification Triggers Structural Transformations of Borromean Rings.

A series of supramolecular transformation cascades are presented here, employing ligand exchange reactions, concentration-dependent Borromean ring (BR) linking and unlinking, and inverse electron-demand Diels-Alder (IEDDA) reactions. The new family of template-free, tetrazine-edged BRs are constructed by using ligand exchange reactions, and their concentration-dependent linking and unlinking reactions have been observed. Moreover, Borromean precursors have been demonstrated to further undergo supramolecular structural transformations induced by rapid and efficient IEDDA reactions to afford corresponding post-assembly modified architectures. Remarkably, subtle steric increases of the pyridazine fragments obtained by IEDDA reactions is regarded to induce controlled topological transformations in the cascade, unlinking the Borromean structures by using electron-rich dienophiles as triggering signals.

Ordered Entanglement in Actinide-Organic Coordination Polymers

Abstract Entangled structures in actinide-organic hybrid materials featured by intertwining between isolated motifs show promising potential in the application of different fields, such as radionuclide separation, radiation detection, photocatalysis and smart materials. Since how the individual motifs are entangled in combination of molecular structures of the structural units and topology of the individual motifs contributes most to the properties of actinide entangled materials, it is of significance to summarize and analyze these entanglements with diverse topologies. For this contribution, we will summarize all the entanglements in the reported actinide-organic entangled structures by classifying them according to the diverse catalogues of individual motifs and entangled patterns between them, among which are included all these intriguing types of entanglement in different seperate sections: 1) polyrotaxanes; 2) parallel interpenetration (INT) and polycatenation (P-CAT and I-CAT); and 3) Borromean ring (BR). This work is aimed at figuring out some clues on design principles of actinide-organic entangled structures, the underlying rules of ordered entanglement and driving forces behind from our perspective so as to provide some valuable principles guiding the assembly process of entangled structures for reference and help to achieve the controlled syntheses of actinide compounds of interest in the future.

Interparticle Reactions: An Emerging Direction in Nanomaterials Chemistry

Nanoparticles exhibit a rich variety in terms of structure, composition, and properties. However, reactions between them remain largely unexplored. In this Account, we discuss an emerging aspect of nanomaterials chemistry, namely, interparticle reactions in solution phase, similar to reactions between molecules, involving atomically precise noble metal clusters. A brief historical account of the developments, starting from the bare, gas phase clusters, which led to the synthesis of atomically precise monolayer protected clusters in solution, is presented first. Then a reaction between two thiolate-protected, atomically precise noble metal clusters, [Au25(PET)18]- and [Ag44(FTP)30]4- (PET = 2-phenylethanethiol, FTP = 4-fluorothiophenol), is presented wherein these clusters spontaneously exchange metal atoms, ligands, and metal-ligand fragments between them under ambient conditions. The number of exchanged species could be controlled by varying the initial compositions of the reactant clusters. Next, a reaction of [Au25(PET)18]- with its structural analogue [Ag25(DMBT)18]- (DMBT = 2,4-dimethylbenzenethiol) is presented, which shows that atom-exchange reactions happen with structures conserved. We detected a transient dianionic adduct, [Ag25Au25(DMBT)18(PET)18]2-, formed between the two clusters indicating that this adduct could be a possible intermediate of the reaction. A reaction involving a dithiolate-protected cluster, [Ag29(BDT)12]3- (BDT = 1,3-benzenedithiol), is also presented wherein metal atom exchange alone occurs, but with no ligand and fragment exchanges. These examples demonstrate that the nature of the metal-thiolate interface, that is, its bonding network and dynamics, play crucial roles in dictating the type of exchange processes and overall rates. We also discuss a recently proposed structural model of these clusters, namely, the Borromean ring model, to understand the dynamics of the metal-ligand interfaces and to address the site specificity and selectivity in these reactions. In the subsequent sections, reactions involving atomically precise noble metal clusters and one- and two-dimensional nanosystems are presented. We show that highly protected, stable clusters such as [Au25(PET)18]- undergo chemical transformation on graphenic surfaces to form a bigger cluster, Au135(PET)57. Finally, we present the transformation of tellurium nanowires (Te NWs) to Ag-Te-Ag dumbbell nanostructures through a reaction with an atomically precise silver cluster, Ag32(SG)19 (SG = glutathione thiolate). The starting materials and the products were characterized using high resolution electrospray ionization mass spectrometry, matrix assisted laser desorption ionization mass spectrometry, UV/vis absorption, luminescence spectroscopies, etc. We have analyzed principally mass spectrometric data to understand these reactions. In summary, we present the emergence of a new branch of chemistry involving the reactions of atomically precise cluster systems, which are prototypical nanoparticles. We demonstrate that such interparticle chemistry is not limited to metal clusters; it occurs across zero-, one-, and two-dimensional nanosystems leading to specific transformations. We conclude this Account with a discussion of the limitations in understanding of these reactions and future directions in this area of nanomaterials chemistry.

Wilson operator algebras and ground states of coupled BF theories

The multi-flavor $BF$ theories in (3+1) dimensions with cubic or quartic coupling are the simplest topological quantum field theories that can describe fractional braiding statistics between loop-like topological excitations (three-loop or four-loop braiding statistics). In this paper, by canonically quantizing these theories, we study the algebra of Wilson loop and Wilson surface operators, and multiplets of ground states on three torus. In particular, by quantizing these coupled $BF$ theories on the three-torus, we explicitly calculate the $\mathcal{S}$- and $\mathcal{T}$-matrices, which encode fractional braiding statistics and topological spin of loop-like excitations, respectively. In the coupled $BF$ theories with cubic and quartic coupling, the Hopf link and Borromean ring of loop excitations, together with point-like excitations, form composite particles.

Mechanism of enhanced rectification in unimolecular Borromean ring devices

We have studied charge transport through individual Borromean Ring complexes, both with and without anchor groups, in gated double barrier tunneling junctions (DBTJs) formed using the electrical breakjunction technique on gold nanowires. While common single molecule device characteristics can be observed with either form of the Borromean Rings, the complexes with anchor groups show strong rectification of conduction in a relatively high percentage of samples. We present our data along with a simple model underlining the mechanism by which the arrangement and composition of the weakly bonding anchor groups attached to the electroactive element may promote a device configuration resulting in rectification.

Nanoscale Borromeates

[Structure: See text] In addition to a parent zinc(II) Borromean ring (BR) complex, the preparation and characterization of two hexasubstituted BR complexes with either 4-acetoxymethylphenyl or 4-methylthiophenyl substituents associated in turn with all six pyridyl rings has been achieved convergently in good yields by appealing to the dynamic features of the reactions between primary amino groups in a preformed acyclic ligand and 2,6-diformylpyridine. Two molecules of the acyclic ligands react with two molecules of 2,6-diformylpyridine to form a cyclic [2 + 2] tetraimine in the presence of Zn(II) ions as templates in 2-propanol at 70 degrees C. The successful preparation of the two derivatives by convergent template-directed syntheses opens up opportunities to self-assemble, under equilibrium control, numerous nanoscale metallo-organic particles with potentially useful properties.