Mechanically Interlocked Molecules: Catenanes, Rotaxanes & Molecular Knots

Topological chemistry explores molecules whose identity and spatial connectivity are defined not merely by covalent bonds between atomic nuclei, but by physical entanglements in three-dimensional Euclidean space that cannot be disentangled without breaking one or more covalent bonds. Such species are known as Mechanically Interlocked Molecular Architectures (MIMAs).

The Mechanical Bond

In 1961, Frisch and Wasserman coined the concept of "chemical topology," proposing that two interlocked macrocyclic rings constitute an entropic and mechanical linkage without sharing a single valence electron pair between them. This link is formally designated the mechanical bond.

• While covalent bonds possess bond energies ranging from $200\text{ to }450\text{ kJ/mol}$ and strict directional orbital overlap, the mechanical bond possesses an effective dissociation energy equal to the energy required to homolytically cleave whichever covalent bond forms the weakest link in the interlocked ring or dumbbell component ($>300\text{ kJ/mol}$).
• Unlike classical covalent bonds, components linked by mechanical bonds retain large internal degrees of freedom, including relative circumrotation (pirouetting) and long-range translation (shuttling).

Core Interlocked Taxa

1. [n]Catenanes: Compounds consisting of $n$ macrocyclic rings interlocked like links in a chain. A [2]catenane comprises two mutually threaded rings. The uncomplexed macrocyclic ligand of a catenane is termed a catenand, whereas the coordination complex with an entrapped metal cation is termed a catenate.

2. [n]Rotaxanes: Consist of a linear dumbbell-shaped shaft encircled by $n-1$ macrocyclic rings. Bulky terminal groups, known as stoppers or caps, sterically prevent the macrocycles from dethreading. The cyclic ring is usually termed the macrocycle or wheel. If the stoppers are absent or too small to prevent dissociation at room temperature, the species is a pseudorotaxane.

3. Molecular Knots (Knotanes): A single continuous, covalently closed molecular strand that is tied into an open knot in space before its ends are covalently fused. The simplest nontrivial molecular knot is the trefoil knot ($3_1$ knot in Alexander-Briggs notation).

4. Molecular Borromean Rings: A topological link consisting of three closed macrocycles entangled such that no two rings are interlocked on their own (the pairwise linking number is zero, $Lk_{ij} = 0$), yet the three together cannot be pulled apart. Cleaving any single loop causes the remaining two to fall apart immediately.

Topological Stereochemistry and Isomerism

Because components cannot traverse one another, MIMAs display forms of stereoisomerism unique to topology:

• Topological Chirality: Arises when a molecule cannot be deformed into its mirror image in 3D space by any continuous deformation (isotopy) without bond cleavage, even if each constituent ring has an achiral Euclidean point group.
• Topological Isomers: Molecules having identical covalent connectivity graphs but distinct topological embedding states in $\mathbb{R}^3$ (e.g., an unknotted macrocycle vs. a trefoil knot made from the identical molecular strand).

Prior to 1983, synthesis of catenanes relied on low-yielding statistical cyclization (such as Wasserman's $1\%$ yield cyclization of diesters in the presence of deuterated macrocycles). In 1983, Jean-Pierre Sauvage revolutionized topological chemistry by introducing passive metal-template synthesis using tetrahedral copper(I) centers.

The Cu(I)-Phenanthroline Orthogonal Motif

Sauvage exploited the stereoelectronic preference of monovalent copper ($d^{10}$, $\text{Cu}^I$) for a four-coordinate, pseudo-tetrahedral geometry with bidentate chelating ligands such as 1,10-phenanthroline (phen):

When two phenanthroline units coordinate to a single $\text{Cu}^I$ cation, their rigid heterocyclic planes are held mutually perpendicular (at an angle $\theta \approx 90^\circ$), mutually intersecting in space.

Synthetic Strategy for [2]Catenanes

1. Pre-organization of Pseudorotaxane: A macrocyclic ring containing a 1,10-phenanthroline moiety (e.g., a 30-membered crown-type diether ring) is reacted with $[\text{Cu}(\text{MeCN})_4]^+$ and an open-chain phenanthroline thread bearing terminal phenolic hydroxyl groups:

Due to the high thermodynamic stability of the bis-chelate complex ($\log \beta_2 \approx 12 - 15$), the open thread is quantitatively threaded through the interior aperture of the preformed macrocycle.

2. Ring Closure (Clipping): The two terminal hydroxyl groups of the threaded phenanthroline lie on opposite faces of the macrocycle. Reaction with an $\alpha,\omega$-diiodo polyether linker (e.g., pentaethylene glycol diiodide) in the presence of $\text{Cs}_2\text{CO}_3$ in DMF effects an intramolecular Williamson ether macrocyclization:

This template-directed clipping achieves yields of $[\text{Cu}(\text{[2]catenand})]^+$ (the catenate) exceeding $42\%$, a four-hundred-fold increase over statistical methods.

3. Demetallation: The coordinated copper(I) template ion is removed by treatment with excess potassium cyanide ($\text{KCN}$) or EDTA in aqueous acetonitrile:

The metal-free [2]catenand is liberated. In the catenand, the two interlocking rings are completely free to circumrotate through each other's interior cavity.

In 1989, J. Fraser Stoddart developed a complementary, metal-free synthetic paradigm governed by donor-acceptor (D-A) aromatic $\pi-\pi$ stacking, electrostatic interactions, and $[ ext{C-H}\cdots\text{O}]$ hydrogen bonding.

The Blue Box: Cyclobis(paraquat-p-phenylene) ($ ext{CBPQT}^{4+}$)

The cornerstone of Stoddart's methodology is the tetracationic cyclophane cyclobis(paraquat-$p$-phenylene), commonly abbreviated $\text{CBPQT}^{4+}$ or the "Blue Box":

• It consists of two electron-deficient 4,4'-bipyridinium (paraquat) units linked at each end by two $p$-xylylene spacers.
• The four positive formal charges render the bipyridinium rings strong $\pi$-electron acceptors.
• The rectangular internal cavity measures approximately $7.2\text{ Å} \times 10.3\text{ Å}$, ideally suited to intercalate flat, electron-rich aromatic guest systems.

Complementary Electron-Rich Donors

Ideal $\pi$-donors include:

1. Hydroquinone (HQ) or 1,4-dimethoxybenzene derivatives.

2. 1,5-Dioxynaphthalene (DNP): A fused bicyclic polyether derivative with an exceptionally high $\pi$-electron density, yielding association constants with $\text{CBPQT}^{4+}$ of $K_a \approx 3 \times 10^4\text{ M}^{-1}$ in acetonitrile.

3. Tetrathiafulvalene (TTF): An outstanding two-electron reversible redox donor.

Three Primary Synthetic Methodologies for Rotaxanes

1. Threading-and-Capping: A linear dumbbell precursor containing the recognition site (e.g., DNP) is mixed with the macrocycle (e.g., $\text{CBPQT}^{4+}$) to establish a dynamic equilibrium with the pseudorotaxane. Bulky stoichiometric stoppers (e.g., triisopropylsilyl or tetraarylmethane halides) are reacted with the termini to permanently trap the ring.

2. Clipping: An open-chain precursor (such as a bis-quaternary salt) is mixed with the preformed dumbbell carrying the electron-rich station. The thread acts as a template, aligning the precursors so that a bis-alkylation cyclization with $\alpha,\alpha'$-dibromo-$p$-xylene closes the ring directly around the shaft.

3. Slipping: A preformed macrocycle and preformed stoppered dumbbell with borderline steric stoppers are heated. Thermal activation allows the macrocycle to transiently stretch and slip over the bulky stopper. Upon cooling to room temperature, the system is kinetically trapped as the rotaxane.

While passive template synthesis (Sauvage, Stoddart) uses the template solely as a geometric organizing scaffold, Leigh introduced the Active Metal Template (AMT) strategy in 2006. In AMT, the metal ion acts concurrently as:

1. The geometric organizing template that holds the macrocyclic and linear components in an interlocked pseudo-rotaxane orientation.
2. The catalytic engine that directly mediates the covalent bond-forming reaction between thread fragments within the macrocyclic cavity.

The CuAAC Active Metal Template Mechanism

The classic AMT reaction utilizes copper(I)-catalyzed azide-alkyne cycloaddition (CuAAC "click" chemistry):

1. Endo-Cavity Coordination: A macrocycle bearing an internal coordination site (e.g., a pyridine-containing macrocycle or an endo-functionalized phenanthroline macrocycle) coordinates a $\text{Cu}^I$ ion inside its central aperture.

2. Assembly of Reactive Intermediates: An alkyne-bearing half-thread and an azide-bearing half-thread (each already capped at one terminus by a bulky stopper) coordinate to the internal $\text{Cu}^I$ center:

3. Intra-Cavity Cycloaddition: The 1,3-dipolar cycloaddition proceeds strictly *through* the cavity of the macrocycle, forming a 1,4-disubstituted 1,2,3-triazole ring that bridges the two stoppers.

4. Mechanical Trapping: The newly forged covalent triazole link is too large to dethread through the macrocycle, and the terminal stoppers prevent slip-off. The $\text{Cu}^I$ catalyst dissociates and is turned over into subsequent catalytic cycles:

Covalent Templating Strategies

In covalent templating, interlocked rings are formed by assembling a single temporary covalent scaffold:

• Two macrocyclic rings are joined together through temporary covalent acetal, ether, or ester bonds.
• A ring-closing metathesis (RCM) or macrocyclization yields a fused bicyclic or bicyclo-spiro framework.
• Selective chemical cleavage of the temporary bridging covalent bond releases the two interlocked rings, providing the [2]catenane. Although conceptually elegant, multi-step synthetic complexity has largely yielded primacy to coordination-driven and AMT methods.

A molecular shuttle is a rotaxane in which the macrocycle can undergo translational Brownian motion along the linear shaft between two or more discrete recognition sites, termed stations.

Degenerate Shuttling

In a degenerate [2]rotaxane, the two stations along the shaft are chemically and magnetically identical (e.g., two hydroquinone units separated by a flexible polyether linker, encircled by $\text{CBPQT}^{4+}$):

• Because both stations are identical, the free energy difference between the two positional states is zero: $\Delta G^\circ = 0$, giving an equilibrium constant $K_{\text{eq}} = 1$.
• Shuttling occurs as thermal Brownian motion across the intervening barrier $\Delta G^\ddagger$.
• The rate of degenerate shuttling $k_{\text{shuttle}}$ can be directly quantified by variable-temperature dynamic nuclear magnetic resonance ($^1\text{H}$ VT-NMR). At the coalescence temperature $T_c$:

where $\Delta \nu$ is the peak separation in Hertz between the free and occupied station resonances in the slow-exchange limit.

• Typical activation barriers for polyether shafts range from $\Delta G^\ddagger = 50\text{ to }70\text{ kJ/mol}$, corresponding to hopping frequencies of $100\text{ to }100{,}000\text{ s}^{-1}$ at $298\text{ K}$.

Non-Degenerate Translational Isomers (Co-Conformers)

In a non-degenerate [2]rotaxane, the two stations have differing chemical structures (e.g., Station 1 = TTF, Station 2 = DNP).

• The state where the ring resides on Station 1 has free energy $G_1$, while Station 2 has $G_2$.
• The equilibrium distribution is governed by the Boltzmann distribution:

• The fraction occupied at Station 1 is:

If the affinity of Station 1 exceeds that of Station 2 by $15\text{ kJ/mol}$ at $298\text{ K}$, $f_1 > 99.7\%$, locking the ring almost exclusively at Station 1 under ambient conditions.

A bistable molecular switch is a non-degenerate rotaxane or catenane whose ground-state co-conformation can be reversibly toggled between two distinct stations by the application of external stimuli.

Redox-Switchable Rotaxanes

Consider a rotaxane with an electron-rich tetrathiafulvalene ($ ext{TTF}$) station and a 1,5-dioxynaphthalene ($ ext{DNP}$) station, encircled by $\text{CBPQT}^{4+}$:

1. Neutral State: TTF is a significantly stronger $\pi$-donor than DNP ($\Delta G^\circ \approx -12\text{ kJ/mol}$). The ring resides $>99\%$ on the TTF station.

2. One-Electron Oxidation: Applying an electrochemical potential ($E_{1/2}^{(1)} \approx +0.35\text{ V}$ vs SCE) oxidizes TTF to its radical cation $\text{TTF}^{+\bullet}$. Strong electrostatic repulsion between $\text{TTF}^{+\bullet}$ and the tetracationic $\text{CBPQT}^{4+}$ ring drives the ring to shuttle to the neutral DNP station:

3. Chemical/Electrochemical Reduction: Reducing $\text{TTF}^{+\bullet}$ back to neutral TTF restores the initial thermodynamic landscape, and the macrocycle shuttles back to TTF.

Photochemically Gated Switches

Incorporating a photoisomerizable azobenzene unit into the shaft creates light-gated shuttles:

• Trans-Azobenzene: Planar, apolar, easily slips through or interacts with cyclodextrin ($lpha$-CD) rings ($K_a \approx 10^4\text{ M}^{-1}$).
• Cis-Azobenzene: Formed upon UV irradiation ($\lambda = 365\text{ nm}$). Non-planar, bulky, with a high dipole moment. The $\alpha$-CD ring is sterically ejected or compelled to migrate to an adjacent alkyl or oligoethylene glycol station.
• Visible light ($\lambda = 450\text{ nm}$) or thermal relaxation restores the trans isomer, causing the ring to return.

pH-Switched Ammonium/Amine and Cryptand Systems

Stoddart and Leigh developed ammonium/triazolium or ammonium/crown shuttles:

• In the protonated state, secondary dialkylammonium $-\text{CH}_2\text{NH}_2^+\text{CH}_2-$ forms strong hydrogen bonds to dibenzo-24-crown-8 (DB24C8) ($K_a > 10^5\text{ M}^{-1}$).
• Addition of base ($ ext{Et}_3 ext{N}$ or phosphazene) deprotonates the ammonium to neutral amine ($-\text{CH}_2\text{NHCH}_2-$), abolishing the charge-assisted hydrogen bonds ($K_a < 10\text{ M}^{-1}$). The DB24C8 ring immediately shuttles to a secondary station (e.g., a bipyridinium or triazolium unit).
• Re-addition of acid ($\text{CF}_3\text{COOH}$) reprotonates the amine, pulling the crown ether back.

Molecular topology reaches its zenith in molecular knots and Borromean rings, where multi-component self-assembly and topology intertwine.

Molecular Knots (Knotanes)

In knot theory, a knot is an embedding of a single circle $S^1$ in three-dimensional space $\mathbb{R}^3$.

• The Trefoil Knot ($3_1$): The simplest non-trivial knot, possessing three alternating crossings in its minimal planar projection. It exists as two non-superimposable topological enantiomers: right-handed (plus) and left-handed (minus).
• Sauvage Double-Stranded Metallo-Helicate Precursor:

Sauvage synthesized the first molecular trefoil knot in 1989 using a double-helical dinuclear copper(I) complex:

The two linear strands cross over one another twice at the copper centers. By designing an appropriate length for the terminal linkers, cross-connection of the terminal hydroxyl groups across opposite sides of the helix forces a third topological crossing. Subsequent demetallation with cyanide yields the stable, single-strand trefoil knotane.

Leigh's Pentafoil Knot ($5_1$) and Composite Knots

In 2012, David Leigh synthesized a pentafoil knot ($5_1$ knot, 5 crossings) using a circular helicate of five iron(II) or zinc(II) ions coordinated to five bis-bidentate pyridyl-imine ligands. Ring-closing olefin metathesis (RCM) joined the 10 strand ends, creating a single closed loop of 160 atoms with five alternating mechanical crossings.

Molecular Borromean Rings

In 2004, Stoddart and co-workers accomplished the rational self-assembly of molecular Borromean rings:

• Utilizing a dynamic covalent template, 6 equivalents of 2,6-diformylpyridine, 6 equivalents of 4,4'-diaminobiphenyl, and 6 zinc(II) cations undergo clean self-assembly in a 24-component single-pot reaction:

• The structure contains three interlocked macrocyclic rings formed by 12 imine bonds.
• Removal of the zinc ions with cyanide yields the pure organic Borromean link. Cleaving any single ring breaks the mechanical entanglement of the other two.

The 2016 Nobel Prize in Chemistry was awarded jointly to Jean-Pierre Sauvage, Sir J. Fraser Stoddart, and Ben L. Feringa "for the design and synthesis of molecular machines." A molecular machine is defined as an assembly of molecular components capable of performing directional mechanical motion in response to specific energy inputs (chemical fuel, photons, or electrons).

Physics of the Nanoworld: The Low Reynolds Number Regime

Molecular machines operate in a regime drastically distinct from macroscopic engines:

• Zero Inertia: At the nanoscale, the Reynolds number is extremely small ($Re = \rho v L / \eta \ll 10^{-4}$), meaning inertial forces are utterly negligible compared to viscous drag. Movement stops the instant driving forces cease ($v \propto F$).
• Thermal Brownian Noise: Molecular components are subject to continuous, chaotic thermal fluctuations ($k_B T \approx 4.1 \times 10^{-21}\text{ J}$ at $300\text{ K}$).
• Brownian Ratchets: Directional motion cannot be achieved simply by "pushing"; rather, it requires rectifying random thermal Brownian fluctuations via kinetic or energy ratchets (Feynman-Smoluchowski ratchet principle).

Molecular Muscles, Lifts, and Rotary Motors

1. Sauvage's Contractile Molecular Muscle:

A daisy-chain dimer of [2]rotaxanes that switches reversibly between an extended state (length $8.5\text{ nm}$) when coordinated to $\text{Zn}^{2+}$ (five-coordinate terpy/phen) and a contracted state (length $6.5\text{ nm}$) when coordinated to $\text{Cu}^I$ (four-coordinate bis-phen), producing a $24\%$ macroscopic length change.

2. Stoddart's Molecular Elevator:

A platform consisting of a tripod host with three macrocyclic crown rings threaded on a three-legged rig. Reversible acid-base titration lowers and raises the platform between two distinct height levels with an operating force of $\approx 200\text{ pN}$.

3. Feringa's Light-Driven Rotary Motor:

Sterically overcrowded alkenes featuring a rotor and stator connected by a central $\text{C}=\text{C}$ double bond. A four-step cycle combines photochemical cis-trans isomerizations with thermal helix inversions, enforcing strict $360^\circ$ unidirectional continuous rotation at frequencies up to $10^7\text{ Hz}$.

Chemical Fuel-Driven Autonomous Pumps

Modern synthetic nanomachines (Leigh, Stoddart) consume chemical fuels (such as carbodiimides or activated esters) in out-of-equilibrium dissipative cycles, pumping macrocycles from solution onto high-energy storage stations against thermodynamic gradients.