Open Problems in Chemical Topology

Self-assembly of the smallest and tightest molecular trefoil knot

Molecular knots, whose synthesis presents many challenges, can play important roles in protein structure and function as well as in useful molecular materials, whose properties depend on the size of the knotted structure. Here we report the synthesis by self-assembly of molecular trefoil metallaknot with formula [Au6{1,2-C6H4(OCH2CC)2}3{Ph2P(CH2)4PPh2}3], Au6, from three units of each of the components 1,2-C6H4(OCH2CCAu)2 and Ph2P(CH2)4PPh2. Structure determination by X-ray diffraction revealed that the chiral trefoil knot contains only 54 atoms in the backbone, so that Au6 is the smallest and tightest molecular trefoil knot known to date.

Knotting matters: orderly molecular entanglements

Entangling strands in a well-ordered manner can produce useful effects, from shoelaces and fishing nets to brown paper packages tied up with strings. At the nanoscale, non-crystalline polymer chains of sufficient length and flexibility randomly form tangled mixtures containing open knots of different sizes, shapes and complexity. However, discrete molecular knots of precise topology can also be obtained by controlling the number, sequence and stereochemistry of strand crossings: orderly molecular entanglements. During the last decade, substantial progress in the nascent field of molecular nanotopology has been made, with general synthetic strategies and new knotting motifs introduced, along with insights into the properties and functions of ordered tangle sequences. Conformational restrictions imparted by knotting can induce allostery, strong and selective anion binding, catalytic activity, lead to effective chiral expression across length scales, binding modes in conformations efficacious for drug delivery, and facilitate mechanical function at the molecular level. As complex molecular topologies become increasingly synthetically accessible they have the potential to play a significant role in molecular and materials design strategies. We highlight particular examples of molecular knots to illustrate why these are a few of our favourite things.

Amplification of weak chiral inductions for excellent control over the helical orientation of discrete topologically chiral (M3L2) n polyhedra

Superb control over the helical chirality of discrete (M₃L₂)_n polyhedra (n = 2,4,8, M = Cu^I or Ag^I) created from the self-assembly of propeller-shaped ligands (L) equipped with chiral side chains is demonstrated here. Almost perfect chiral induction (>99 : 1) of the helical orientation of the framework was achieved for the largest (M₃L₂)₈ cube with 48 small chiral side chains (diameter: ∼5 nm), while no or moderate chiral induction was observed for smaller polyhedra (n = 2, 4). Thus, amplification of the weak chiral inductions of each ligand unit is an efficient way to control the chirality of large discrete nanostructures with high structural complexity.

Superb control over the helical chirality of highly-entangled (M₃L₂)_n polyhedra (M = Cu(i), Ag(i); n = 2,4,8) was achieved via multiplication of weak chiral inductions by side chains accumulated on the huge polyhedral surfaces.

Transmembrane Ion Channels Formed by a Star of David [2]Catenane and a Molecular Pentafoil Knot

A (Fe^II)₆-coordinated triply interlocked ("Star of David") [2]catenane (6₁² link) and a (Fe^II)₅-coordinated pentafoil (5₁) knot are found to selectively transport anions across phospholipid bilayers. Allostery, topology, and building block stoichiometry all play important roles in the efficacy of the ionophoric activity. Multiple Fe^II cation coordination by the interlocked molecules is crucial: the demetalated catenane exhibits no anion binding in solution nor any transmembrane ion transport properties. However, the topologically trivial, Lehn-type cyclic hexameric Fe^II helicates-which have similar anion binding affinities to the metalated Star of David catenane in solution-also display no ion transport properties. The unanticipated difference in behavior between the open- and closed-loop structures may arise from conformational restrictions in the linking groups that likely enhances the rigidity of the channel-forming topologically complex molecules. The (Fe^II)₆-coordinated Star of David catenane, derived from a hexameric cyclic helicate, is 2 orders of magnitude more potent in terms of ion transport than the (Fe^II)₅-coordinated pentafoil knot, derived from a cyclic pentamer of the same building block. The reduced efficacy is reminiscent of multisubunit protein ion channels assembled with incorrect monomer stoichiometries.

Design and synthesis of a bis-macrocyclic host and guests as building blocks for small molecular knots

The thread–link–cut (TLC) approach has previously shown promise as a novel method to synthesize molecular knots. The modular second-generation approach to small trefoil knots described herein involves electrostatic interactions between an electron-rich bis-macrocyclic host compound and electron-deficient guests in the threading step. The bis-macrocyclic host was synthesized in eight steps and 6.6% overall yield. Ammonium and pyridinium guests were synthesized in 4–5 steps. The TLC knot-forming sequence was carried out and produced a product with the expected molecular weight, but, unfortunately, further characterization did not produce conclusive results regarding the topology of the product.

Exploring and Exploiting the Symmetry-Breaking Effect of Cyclodextrins in Mechanomolecules

Cyclodextrins (CDs) are cone-shaped molecular rings that have been widely employed in supramolecular/host–guest chemistry because of their low cost, high biocompatibility, stability, wide availability in multiple sizes, and their promiscuity for binding a range of molecular guests in water. Consequently, CD-based host–guest complexes are often employed as templates for the synthesis of mechanically bonded molecules (mechanomolecules) such as catenanes, rotaxanes, and polyrotaxanes in particular. The conical shape and cyclodirectionality of the CD “bead” gives rise to a symmetry-breaking effect when it is threaded onto a molecular “string”; even symmetrical guests are rendered asymmetric by the presence of an encircling CD host. This review focuses on the stereochemical implications of this symmetry-breaking effect in mechanomolecules, including orientational isomerism, mechanically planar chirality, and topological chirality, as well as how they support applications in regioselective and stereoselective chemical synthesis, the design of molecular machine prototypes, and the development of advanced materials.

Stereoselective Synthesis of Molecular Square and Granny Knots

We report on the stereoselective synthesis of both molecular granny and square knots through the use of lanthanide-complexed overhand knots of specific handedness as three-crossing “entanglement synthons”. The composite knots are assembled by combining two entanglement synthons (of the same chirality for a granny knot; of opposite handedness for a square knot) in three synthetic steps: first, a CuAAC reaction joins together one end of each overhand knot. Ring-closing olefin metathesis (RCM) then affords the closed-loop knot, locking the topology. This allows the lanthanide ions necessary for stabilizing the entangled conformation of the synthons to subsequently be removed. The composite knots were characterized by ¹H and ¹³C NMR spectroscopy and mass spectrometry and the chirality of the knot stereoisomers compared by circular dichroism. The synthetic strategy of combining building blocks of defined stereochemistry (here overhand knots of Λ- or Δ-handed entanglement) is reminiscent of the chiron approach of using minimalist chiral synthons in the stereoselective synthesis of molecules with multiple asymmetric centers.

Electronic Peculiarities of a Self-Assembled M12L24 Nanoball (M = Pd+2, Cr, or Mo)

We use molecular mechanics and DFT calculations to analyze the particular electronic behavior of a giant nanoball. This nanoball is a self-assembled M₁₂L₂₄ nanoball; with M equal to Pd⁺²; Cr; and Mo. These systems present an extraordinarily large cavity; similar to biological giant hollow structures. Consequently, it is possible to use these nanoballs to trap smaller species that may also become activated. Molecular orbitals, molecular hardness, and Molecular Electrostatic Potential enable us to define their potential chemical properties. Their hardness conveys that the Mo system is less reactive than the Cr system. Eigenvalues indicate that electron transfer from the system with Cr to other molecules is more favorable than from the system with Mo. Molecular Electrostatic Potential can be either positive or negative. This means that good electron donor molecules have a high possibility of reacting with positive regions of the nanoball. Each of these nanoballs can trap 12 molecules, such as CO. The nanoball that we are studying has large pores and presents electronic properties that make it an apposite target of study.

Coordination Chemistry of a Molecular Pentafoil Knot

The binding of Zn(II) cations to a pentafoil (5₁) knotted ligand allows the synthesis of otherwise inaccessible metalated molecular pentafoil knots via transmetalation, affording the corresponding “first-sphere” coordination Co(II), Ni(II), and Cu(II) pentanuclear knots in good yields (≥85%). Each of the knot complexes was characterized by mass spectrometry, the diamagnetic (zinc) knot complex was characterized by ¹H and ¹³C NMR spectroscopy, and the zinc, cobalt, and nickel pentafoil knots afforded single crystals whose structures were determined by X-ray crystallography. Lehn-type circular helicates generally only form with tris-bipy ligand strands and Fe(II) (and, in some cases, Ni(II) and Zn(II)) salts, so such architectures become accessible for other metal cations only through the use of knotted ligands. The different metalated knots all exhibit “second-sphere” coordination of a single chloride ion within the central cavity of the knot through CH···Cl^– hydrogen bonding and electrostatic interactions. The chloride binding affinities were determined in MeCN by isothermal titration calorimetry, and the strength of binding was shown to vary over 3 orders of magnitude for the different metal-ion–knotted-ligand second-sphere coordination complexes.

Effects of knot tightness at the molecular level

Three 819 knots in closed-loop strands of different lengths (∼20, 23, and 26 nm) were used to experimentally assess the consequences of knot tightness at the molecular level. Through the use of 1H NMR, diffusion-ordered spectroscopy (DOSY), circular dichroism (CD), collision-induced dissociation mass spectrometry (CID-MS) and molecular dynamics (MD) simulations on the different-sized knots, we find that the structure, dynamics, and reactivity of the molecular chains are dramatically affected by the tightness of the knotting. The tautness of entanglement causes differences in conformation, enhances the expression of topological chirality, weakens covalent bonds, inhibits decomplexation events, and changes absorption properties. Understanding the effects of tightening nanoscale knots may usefully inform the design of knotted and entangled molecular materials.

A Six-Crossing Doubly Interlocked [2]Catenane with Twisted Rings, and a Molecular Granny Knot

A molecular 6 2 3 link (a six crossing, doubly interlocked, [2]catenane with twisted rings) and a 31 #31 granny knot (a composite knot made up of two trefoil tangles of the same handedness) were constructed by ring-closing olefin metathesis of an iron(II)-coordinated 2×2 interwoven grid. The connections were directed by pendant phenyl groups to be between proximal ligand ends on the same faces of the grid. The 6 2 3 link was separated from the topoisomeric granny knot by recycling size-exclusion chromatography. The identity of each topoisomer was determined by tandem mass spectrometry and the structure of the 6 2 3 link confirmed by X-ray crystallography, which revealed two 82-membered macrocycles, each in figure-of-eight conformations, linked through both pairs of loops.

Securing a Supramolecular Architecture by Tying a Stopper Knot

We report on a rotaxane-like architecture secured by the in situ tying of an overhand knot in the tris(2,6-pyridyldicarboxamide) region of the axle through complexation with a lanthanide ion (Lu3+ ). The increase in steric bulk caused by the knotting locks a crown ether onto the thread. Removal of the lutetium ion unties the knot, and when the axle binding site for the ring is deactivated, the macrocycle spontaneously dethreads. When the binding interaction is switched on again, the crown ether rethreads over the 10 nm length of the untangled strand. The overhand knot can be retied, relocking the threaded structure, by once again adding lutetium ions.

Chirality in rotaxanes and catenanes

Although chiral mechanically interlocked molecules (MIMs) have been synthesised and studied, enantiopure examples are relatively under-represented in the pantheon of reported catenanes and rotaxanes and the underlying chirality of the system is often even overlooked. This is changing with the advent of new applications of MIMs in catalysis, sensing and materials and the appearance of new methods to access unusual stereogenic units unique to the mechanical bond. Here we discuss the different stereogenic units that have been investigated in catenanes and rotaxanes, examples of their application, methods for assigning absolute stereochemistry and provide a perspective on future developments.

Molecular Trefoil Knot from a Trimeric Circular Helicate

We report the two-step synthesis of a molecular trefoil knot in 90% overall yield through the self-assembly of a 12-component trimeric circular zinc helicate followed by ring closing metathesis of six pendant alkene chains. Both the trimeric circular helicate intermediate and the resulting trefoil knot were characterized by NMR spectroscopy, mass spectrometry, and X-ray crystallography.

Molecular Knots

The first synthetic molecular trefoil knot was prepared in the late 1980s. However, it is only in the last few years that more complex small-molecule knot topologies have been realized through chemical synthesis. The steric restrictions imposed on molecular strands by knotting can impart significant physical and chemical properties, including chirality, strong and selective ion binding, and catalytic activity. As the number and complexity of accessible molecular knot topologies increases, it will become increasingly useful for chemists to adopt the knot terminology employed by other disciplines. Here we give an overview of synthetic strategies towards molecular knots and outline the principles of knot, braid, and tangle theory appropriate to chemistry and molecular structure.

Tying a Molecular Overhand Knot of Single Handedness and Asymmetric Catalysis with the Corresponding Pseudo-D3-Symmetric Trefoil Knot

We report the stereoselective synthesis of a left-handed trefoil knot from a tris(2,6-pyridinedicarboxamide) oligomer with six chiral centers using a lanthanide(III) ion template. The oligomer folds around the lanthanide ion to form an overhand knot complex of single handedness. Subsequent joining of the overhand knot end groups by ring-closing olefin metathesis affords a single enantiomer of the trefoil knot in 90% yield. The knot topology and handedness were confirmed by NMR spectroscopy, mass spectrometry, and X-ray crystallography. The pseudo-D₃-symmetric knot was employed as an asymmetric catalyst in Mukaiyama aldol reactions, generating enantioselectivities of up to 83:17 er, which are significantly higher than those obtained with a comparable unknotted ligand complex.

Optimal Self-Assembly of Linked Constructs and Catenanes via Spatial Confinement

How to direct the self-assembly of simple templates toward constructs with complex shape and topology is still an open problem. Recent advancements have made it possible to self-assemble various types of knotted constructs, but targeting general multicomponent topologies, that is, links and catenanes, has proved much harder. Here, we study how the yield and complexity of self-assembled links depends on both intrinsic and extrinsic system properties and, particularly, template shape and spatial confinement. We show that slit confinement does not necessarily suppress linking but can rather enhance it significantly thanks to entropic effects. We also found that only a limited set of binary links are recurrent for different template shapes. These privileged topologies include all those experimentally realized so far plus a few additional ones, such as the 7₇² and 7₈² links that, hence, ought to be ideal candidates for broadening the current class of constructs with addressable topology.

Lanthanide Template Synthesis of Trefoil Knots of Single Handedness

We report on the assembly of 2,6-pyridinedicarboxamide ligands (1) with point chirality about lanthanide metal ion (Ln(3+)) templates, in which the helical chirality of the resulting entwined 3:1 ligand:metal complexes is covalently captured by ring-closing olefin metathesis to form topologically chiral molecular trefoil knots of single handedness. The ligands do not self-sort (racemic ligands form a near-statistical mixture of homoleptic and heteroleptic lanthanide complexes), but the use of only (R,R)-1 leads solely to a trefoil knot of Λ-handedness, whereas (S,S)-1 forms the Δ-trefoil knot with complete stereoselectivity. The knots and their isomeric unknot macrocycles were characterized by NMR spectroscopy, mass spectrometry, and X-ray crystallography and the expression of the chirality that results from the topology of the knots studied by circular dichroism.

From Fragmentation to Construction--from Void to Massive: Fascination with Organic Mass Spectrometry and the Synthesis of Novel Three-Dimensional Polycyclic Aromatic Hydrocarbons

Detailed insights gained from our research into the gas-phase chemistry of ionized and protonated diphenylalkanes and their congeners, obtained by extended synthesis of isotopically labeled model compounds and mass spectrometry, are presented and merged with those acquired during our development of a new family of polycyclic hydrocarbons, the centropolyindanes. Aside from a Personal Account that describes "two scientific lives in one", it is demonstrated, on the one hand, how our understanding of organic chemistry can help to shed light on the details of mass spectrometric fragmentation and to unravel, in a more fundamental way, the unimolecular reactivity of gaseous ions. On the other hand, it is shown how unexpected reactivity of related ions in solution, being subject to the very same fundamentals of organic chemistry, can lead to the construction of novel and, in part, unique three-dimensional polycyclic structures that may contribute to future research in material science. Two such apparently independent fields of organic chemistry may be seen as joint contributions of the art of science.

A Solomon link through an interwoven molecular grid

A molecular Solomon link was synthesized through the assembly of an interwoven molecular grid consisting of four bis(benzimidazolepyridyl)benzthiazolo[5,4-d]thiazole ligands and four zinc(II), iron(II), or cobalt(II) cations, followed by ring-closing olefin metathesis. NMR spectroscopy, mass spectrometry, and X-ray crystallography confirmed the doubly interlocked topology, and subsequent demetalation afforded the wholly organic Solomon link. The synthesis, in which each metal ion defines the crossing point of two ligand strands, suggests that interwoven molecular grids should be useful scaffolds for the rational construction of other topologically complex structures.

A trefoil knotted polymer produced through ring expansion

A synthetic strategy is reported for the production of a trefoil knotted polymer from a copper(I)-templated helical knot precursor through ring expansion. The expected changes in the properties of the knotted polymer compared to a linear analogue, for example, reduced hydrodynamic radius and lower intrinsic viscosity, together with an atomic force microscopy (AFM) image of individual molecular knots, confirmed the formation of the resulting trefoil knotted polymer. The strategies employed here could be utilized to enrich the variety of available polymers with new architectures.

The self-sorting behavior of circular helicates and molecular knots and links

We report on multicomponent self-sorting to form open circular helicates of different sizes from a primary monoamine, Fe(II) ions, and dialdehyde ligand strands that differ in length and structure by only two oxygen atoms. The corresponding closed circular helicates that are formed from a diamine--a molecular Solomon link and a pentafoil knot--also self-sort, but up to two of the Solomon-link-forming ligand strands can be accommodated within the pentafoil knot structure and are either incorporated or omitted depending on the stage that the components are mixed.

Design and synthesis of the first triply twisted Möbius annulene

As long as 50 years ago theoretical calculations predicted that Möbius annulenes with only one π surface and one edge would exhibit peculiar electronic properties and violate the Hückel rules. Numerous synthetic attempts notwithstanding, the first singly twisted Möbius annulene was not prepared until 2003. Here we present a general, rational strategy to synthesize triply or even more highly twisted cyclic π systems. We apply this strategy to the preparation of a triply twisted [24]dehydroannulene, the structure of which was confirmed by X-ray analysis. Our strategy is based on the topological transformation of 'twist' into 'writhe'. The advantage is twofold: the product exhibits a lower degree of strain and precursors can be designed that inherently include the writhe, which, after cyclization, ends up in the Möbius product. With our strategy, triply twisted systems are easier to prepare than their singly twisted counterparts.

Construction of rotacatenanes using rotaxane and catenane frameworks

The construction of novel mechanically interlocked structures has become a topic of great current interest due to the requirements of topology and their potential application in molecular machines and devices.