Clathrates, Inclusion Compounds & Macrocyclic Cavities

Inclusion compounds (or adducts) represent supramolecular architectures where one chemical species (the host) forms a crystalline lattice or molecular container enclosing cavities, channels, or cages in which a second chemical species (the guest) is physically trapped without forming direct covalent bonds.

Definition of Clathrates

The term clathrate (derived from the Latin clathratus, meaning "enclosed by a lattice or grating") was introduced by H. M. Powell in 1948. In a true clathrate, guest molecules are enclosed in discrete, isolated polyhedral cages formed by the host crystal lattice:

• The guest cannot escape without dismantling or melting the host crystal framework.
• The host lattice is often thermodynamically unstable in the absence of guest molecules; guest encapsulation stabilizes the empty lattice via dispersion interactions and lattice van der Waals stabilization.

Gas Hydrates (Clathrate Hydrates)

Clathrate hydrates are non-stoichiometric crystalline water inclusion complexes where hydrogen-bonded water frameworks encage small apolar gas molecules (e.g., $\text{CH}_4$, $\text{CO}_2$, $\text{C}_2\text{H}_6$, $\text{Xe}$, $\text{N}_2$). Water molecules adopt tetrahedral, four-coordinate, ice-like hydrogen bonding ($d_{\text{O}\cdots\text{O}} \approx 2.76\text{ Å}$), but crystallize into polyhedra rather than the hexagonal ice ($ ext{I}_h$) lattice:

1. $5^{12}$ Pentagonal Dodecahedron: Composed of 12 pentagonal water faces, 20 water vertices, and 30 hydrogen bonds. Average internal cavity radius $r_{\text{cav}} \approx 3.95\text{ Å}$.

2. $5^{12}6^2$ Tetrakaidecahedron: 12 pentagonal and 2 hexagonal faces, 24 water vertices. Average cavity radius $r_{\text{cav}} \approx 4.33\text{ Å}$.

3. $5^{12}6^4$ Hexakaidecahedron: 12 pentagonal and 4 hexagonal faces, 28 water vertices. Cavity radius $r_{\text{cav}} \approx 4.73\text{ Å}$.

Crystal Structures of Hydrates

• Structure I (sI): Cubic space group $Pm\bar{3}n$, unit cell composition $2\,(5^{12}) + 6\,(5^{12}6^2) = 46\,\text{H}_2\text{O}$. Traps small guests like methane ($\text{CH}_4$), ethane, and carbon dioxide. At full cage occupancy, the ideal formula is $8\,\text{G}\cdot 46\,\text{H}_2\text{O} \approx \text{G}\cdot 5.75\,\text{H}_2\text{O}$.
• Structure II (sII): Cubic space group $Fd\bar{3}m$, unit cell composition $16\,(5^{12}) + 8\,(5^{12}6^4) = 136\,\text{H}_2\text{O}$. Traps larger gases like propane, isobutane, and tetrahydrofuran (THF).
• Structure H (sH): Hexagonal space group $P6/mmm$, accommodates both tiny molecules ($ ext{CH}_4$) and large cycloalkanes (methylcyclopentane) simultaneously in different cage types.

Unlike clathrates with zero-dimensional discrete zero-void cages, channel inclusion compounds possess continuous, one-dimensional open cylindrical tunnels traversing the host crystal lattice.

Urea Inclusion Compounds

Pure crystalline urea forms a dense, tetragonal crystal lattice ($P\bar{4}2_1m$) stabilized by planar ribbons of hydrogen bonds. However, in the presence of long-chain linear guests, urea recrystallizes into a hexagonal host lattice ($P6_122$):

• Three interpenetrating spirals of urea molecules form an open hexagonal channel with an internal diameter of approximately $5.0\text{ to }5.2\text{ Å}$.
• The channel walls are lined with dense, interlocking networks of $[\text{N-H}\cdots\text{O}=\text{C}]$ hydrogen bonds, presenting an electrostatic boundary that forces the guest space inside to be completely apolar.
• Selectivity: The channel diameter ($5.1\text{ Å}$) precisely accommodates unbranched, straight-chain $n$-alkanes, $n$-fatty acids, and $\alpha,\omega$-disubstituted alkanes in an extended all-anti conformation. Branched alkanes (e.g., 2-methylheptane) or aromatic rings are too wide ($>5.6\text{ Å}$) and are rigorously excluded.

Thiourea Inclusion Compounds

Replacing the oxygen of urea with sulfur expands the molecular framework:

• The larger covalent radius of sulfur ($r_S \approx 1.02\text{ Å}$ vs $r_O \approx 0.73\text{ Å}$) expands the hexagonal channel diameter to approximately $6.8\text{ to }7.1\text{ Å}$.
• Reversed Selectivity: Linear $n$-alkanes are too thin to establish sufficient stabilizing van der Waals contacts with the wide channel walls and fail to template the thiourea lattice. Instead, branched alkanes (e.g., 2,2,4-trimethylpentane), cycloalkanes (cyclohexane, cyclooctane), and globular molecules like adamantane, ferrocene, and carbon tetrachloride form stable inclusion adducts.

Dianin's Compound

4-(4-Hydroxyphenyl)-2,2,4-trimethylchroman (Dianin's compound) forms hexameric hydrogen-bonded rings consisting of six phenolic hydroxyl groups in a chair-like hexagon:

• Two hexamers stack face-to-face, forming an hourglass-shaped cage with a constriction of $4.2\text{ Å}$ and central cavities of $6.5\text{ Å}$.
• Dianin's compound encapsulates a wide spectrum of solvent molecules (chloroform, ethanol, benzene, sulfur dioxide).

Inorganic and coordination networks also provide robust porous lattices for solid-state molecular inclusion.

Werner Complexes

Werner clathrates possess the general formula:

where:

• $\text{M}$ is a divalent transition metal cation ($ ext{Ni}^{2+}, \text{Co}^{2+}, \text{Fe}^{2+}, \text{Cu}^{2+}, \text{Mn}^{2+}$).
• $\text{X}$ is an anionic ligand, most commonly thiocyanate ($\text{NCS}^-$) or cyanate ($\text{NCO}^-$).
• $\text{A}$ is a neutral coordinating aromatic nitrogen base, such as 4-methylpyridine (4-picoline), pyridine, or 1-phenylethylamine.
• The prototypical host is $[\text{Ni}(\text{NCS})_2(4\text{-picoline})_4]$.

The coordination complex adopts an octahedral geometry with two axial trans-thiocyanates and four equatorial picoline ligands arranged in a propeller-like conformation. In the crystalline phase, propeller packing generates interstitial cavities that display extraordinary shape-selectivity for aromatic isomers, famously separating $p$-xylene from $m$-xylene and $o$-xylene with selectivity factors exceeding $\alpha_{p/m} > 10$.

Hofmann-Type Clathrates

Hofmann clathrates are two-dimensional and three-dimensional cyanometallate coordination polymers:

• Hofmann's Classic Adduct: Formed by reacting ammoniacal nickel(II) solutions with tetracyanonickelate(II) in the presence of benzene:

• The structure consists of planar square-planar $[\text{Ni}(\text{CN})_4]^{2-}$ units linked by bridging octahedral $[\text{Ni}(\text{NH}_3)_2]^{2+}$ cations, forming infinite two-dimensional square-grid sheets $[\text{Ni}_2(\text{CN})_4]_\infty$.
• The axial ammine ligands project above and below each sheet. Intercalated benzene molecules are trapped between parallel coordination layers, held tightly by aromatic $\pi$-dipole and dispersive interactions.
• Modern analogues replace $\text{NH}_3$ with bidentate bridging diamines (e.g., 4,4'-bipyridine, pyrazine) to yield 3D porous coordination networks precursor to Metal-Organic Frameworks (MOFs).

Cyclodextrins (CDs), also termed cycloamyloses or Schardinger dextrins, are cyclic oligosaccharides composed of $\alpha$-D-glucopyranoside units linked by $\alpha$-(1,4)-glycosidic bonds. They are produced enzymatically from starch by the action of cyclodextrin glucanotransferase (CGTase).

The Three Native Cyclodextrins

The three industrially and biologically prominent native cyclodextrins are:

1. $\alpha$-Cyclodextrin ($lpha$-CD): 6 glucopyranose units ($M_w = 972.8\text{ g/mol}$).

• Internal cavity diameter: $4.7\text{ to }5.3\text{ Å}$.
• Cavity volume: $V_{\text{cav}} \approx 174\text{ Å}^3$.
• Water solubility: $145\text{ g/L}$ at $25^\circ\text{C}$.

2. $\beta$-Cyclodextrin ($eta$-CD): 7 glucopyranose units ($M_w = 1135.0\text{ g/mol}$).

• Internal cavity diameter: $6.0\text{ to }6.5\text{ Å}$.
• Cavity volume: $V_{\text{cav}} \approx 262\text{ Å}^3$.
• Water solubility: $18.5\text{ g/L}$ at $25^\circ\text{C}$ (anomalously low due to a rigid, intramolecular circular belt of secondary hydrogen bonds).

3. $\gamma$-Cyclodextrin ($\gamma$-CD): 8 glucopyranose units ($M_w = 1297.1\text{ g/mol}$).

• Internal cavity diameter: $7.5\text{ to }8.3\text{ Å}$.
• Cavity volume: $V_{\text{cav}} \approx 427\text{ Å}^3$.
• Water solubility: $232\text{ g/L}$ at $25^\circ\text{C}$.

The Toroidal Truncated-Cone Morphology

Because all $\text{C}_1$ chairs of the D-glucopyranose units adopt the $^4\text{C}_1$ conformation, the cyclodextrin ring does not form a flat cylinder; instead, it adopts a truncated cone (torus):

• Wider Rim (Secondary Rim): Lined with the secondary hydroxyl groups ($ ext{C}_2-\text{OH}$ and $ ext{C}_3-\text{OH}$).
• Narrower Rim (Primary Rim): Lined with the primary hydroxyl groups ($ ext{C}_6-\text{OH}$).
• Interior Cavity Walls: Lined exclusively by the axial hydrogens ($ ext{H}_3$ and $ ext{H}_5$) and the ether-like glycosidic oxygen bridges ($ ext{C}_1-\text{O}-\text{C}_4$).

Consequently, the cavity interior is completely hydrophobic and apolar (dielectric constant $\epsilon_r \approx 20 - 30$, resembling ethanol or octanol), while the exterior rims are hydrophilic and fully hydrated in aqueous media.

In aqueous solution, cyclodextrins encapsulate apolar organic molecules, forming non-covalent $1:1$ or $1:2$ inclusion complexes:

Thermodynamic Driving Forces: The Hydrophobic Effect & High-Energy Water

The fundamental driving force for cyclodextrin inclusion is not primarily host-guest covalent attraction, but solvent reorganization:

1. Release of Enthalpically High-Energy Water:

The apolar interior cavity cannot satisfy the tetrahedral hydrogen-bonding requirements of liquid water. Water molecules enclosed inside the uncomplexed cavity have reduced hydrogen bonds and unfavorable dipolar orientations ("high-energy water"). Encapsulation of an apolar guest expels these water molecules into the bulk solvent where they form stable hydrogen bonds ($4\,\text{H}_2\text{O}$ per $\beta$-CD), yielding a favorable enthalpy change:

2. Classical Hydrophobic Effect:

Desolvation of the apolar guest disrupts the ordered ice-like water hydration shell surrounding the guest, yielding a favorable entropy of desolvation:

3. van der Waals and Dispersion Interactions:

Close geometric contacts between the hydrophobic guest skeleton and the $\text{C}_3-\text{H}$ and $\text{C}_5-\text{H}$ cavity protons contribute negative enthalpy ($\Delta H_{\text{vdW}} < 0$).

Cavity Sizing Rules

• $lpha$-CD: Accommodates linear aliphatic chains and mono-substituted benzenes ($p$-nitrophenol, toluene).
• $eta$-CD: Perfectly encloses adamantane, naphthalene derivatives, ibuprofen, and cholesterol.
• $\gamma$-CD: Accommodates bulky polycyclics, fullerenes ($ ext{C}_{60}$), steroid dimers, and can bind two planar aromatic guests simultaneously ($1:2$ complex).

Chiral Recognition & Pharmaceutical Encapsulation

Because cyclodextrins are constructed from naturally chiral D-glucose, the interior cavity is an asymmetric, chiral microenvironment.

• Enantiomeric guests experience diastereomeric inclusion complexes with distinct free energies ($\Delta \Delta G^\circ = \Delta G_{(R)}^\circ - \Delta G_{(S)}^\circ \neq 0$), enabling chiral resolution in HPLC/capillary electrophoresis.
• Pharmaceutical formulation: Enclosing hydrophobic drugs (e.g., piroxicam, itraconazole) in $\beta$-CD or modified hydroxypropyl-$\beta$-CD ($ ext{HP}-\beta\text{-CD}$) boosts water solubility up to 10,000-fold and enhances bioavailability.

Calixarenes are macrocyclic oligomers synthesized by the base-catalyzed condensation of $p$-substituted phenols with formaldehyde, pioneered by Alois Zinke and popularized by C. David Gutsche. The name derives from the Greek calix (vase or chalice) and arene (aromatic ring).

Calix[4]arene Conformations

The archetypal member is calix[4]arene (four phenolic rings linked by methylene bridges, $-\text{CH}_2-$). In solution, restricted rotation around the methylene bridges yields four distinct conformational stereoisomers:

1. Cone ($C_{4v}$): All four phenolic hydroxyl groups point in the same direction (downward toward the lower rim). Stabilized by a cyclic circular belt of four cooperative $[\text{O-H}\cdots\text{O}]$ hydrogen bonds.

2. Partial Cone ($C_s$): Three phenolic hydroxyl groups point down, and one phenolic ring is flipped $180^\circ$ pointing up.

3. 1,2-Alternate ($C_{2h}$): Two adjacent phenolic rings point down, and two adjacent rings point up.

4. 1,3-Alternate ($D_{2d}$): Opposite pairs of phenolic rings point in opposite directions (alternating up, down, up, down).

Dynamic Inversion and Bridging Methylene $^1 ext{H}$-NMR Spectroscopy

In unmodified calix[4]arene, thermal inversion between cone conformations occurs rapidly on the NMR timescale at room temperature ($E_a \approx 63\text{ kJ/mol}$):

• In the fixed cone conformation, each $-\text{CH}_2-$ methylene proton experiences an asymmetric environment: one proton is axial (pointing into the calix cup) and the other is equatorial (pointing outward).
• This produces a characteristic pair of doublets (AB quartet) in the $^1\text{H}$-NMR spectrum with a geminal coupling constant $J_{\text{gem}} \approx 12 - 14\text{ Hz}$.
• If the calixarene adopts a 1,3-alternate conformation, both methylene protons reside in identical plane-symmetric environments, collapsing the signal into a sharp singlet.

Functionalization: Upper vs Lower Rim

• Lower Rim (Phenolic Oxygen Portal): Readily alkylated with alkyl halides, crown ethers (calix-crowns), or esters/amides. Bulky substituents (e.g., propyl or larger) permanently lock the macrocycle into a specific conformation (cone, partial cone, or alternate).
• Upper Rim (Para Position): The $tert$-butyl groups of $p$-$tert$-butylcalix[4]arene are cleanly removed by retro-Friedel-Crafts dealkylation with $\text{AlCl}_3$ in toluene, allowing introduction of electrophiles ($-\text{NO}_2$, $-\text{SO}_3\text{H}$, $-\text{CHO}$) to tailor solubility and binding.

Cucurbit[$n$]urils ($ ext{CB}[n]$) are pumpkin-shaped macrocycles composed of $n$ glycoluril units linked by $2n$ methylene bridges, popularized by Kimoon Kim and Lyle Isaacs. The name stems from their resemblance to the pumpkin family Cucurbitaceae.

Synthesis & Homologues

Synthesized by the acid-catalyzed condensation of glycoluril with formaldehyde in concentrated sulfuric acid or hydrochloric acid at $>100^\circ\text{C}$:

Common homologues include $\text{CB}[5]$, $\text{CB}[6]$, $\text{CB}[7]$, $\text{CB}[8]$, and $\text{CB}[10]$:

• $\text{CB}[6]$: Internal volume $164\text{ Å}^3$, portal diameter $3.9\text{ Å}$. Accommodates linear diamines ($n$-diaminoalkanes).
• $\text{CB}[7]$: Internal volume $279\text{ Å}^3$, portal diameter $5.4\text{ Å}$. Isomorphic in volume to $\beta$-CD. Accommodates adamantanes, ferrocene, and drugs.
• $\text{CB}[8]$: Internal volume $479\text{ Å}^3$, portal diameter $6.9\text{ Å}$. Accommodates two guest molecules simultaneously.

Architecture: Portals vs Cavity

$ ext{CB}[n]$ possesses a uniquely rigid structure with two distinct chemical zones:

1. Carbonyl Portals: Two identical portals fringed with $n$ carbonyl oxygens. The electronegative carbonyl lone pairs generate an intense negative electrostatic potential, acting as ideal Lewis basic docking sites for positively charged ammonium ($\text{R-NH}_3^+$) or metal cations.

2. Hydrophobic Interior Cavity: Lined entirely with aliphatic $-\text{CH}-$ and $-\text{CH}_2-$ protons, devoid of functional groups and completely nonpolar.

Ultra-High Affinity: The Strongest Non-Covalent Synthetics

$ ext{CB}[7]$ forms the tightest non-covalent complexes ever recorded in artificial supramolecular chemistry:

• Complexation of ferrocenylmethylammonium or diamantane diammonium cations in water yields binding constants:

rivaling the biological biotin-streptavidin pair ($K_a \approx 10^{14}\text{ M}^{-1}$).

• The driving force combines:

1. Complete expulsion of high-energy cavity water.
2. Severe electrostatic attraction between cationic ammonium ends and the negatively polarized carbonyl portals.
3. Perfect van der Waals packing fraction ($PF \approx 0.55$) of the hydrophobic core.

Beyond classical calixarenes, novel generations of macrocycles and synthetic containers provide unprecedented symmetry and binding capabilities.

Pillar[n]arenes

Introduced by Tomoki Ogoshi in 2008, pillar[$n$]arenes are macrocyclic hosts formed by the condensation of 1,4-dimethoxybenzene (hydroquinone dimethyl ether) with paraformaldehyde catalyzed by Lewis acids (e.g., $\text{BF}_3\cdot\text{OEt}_2$ or $\text{FeCl}_3$):

• Unlike the conical, tapered shape of calixarenes, pillar[$n$]arenes are linked by methylene bridges at the 2- and 5-positions of the hydroquinone rings, forming a perfect, symmetrical cylindrical pillar.
• Pillar[5]arene: Symmetrical pentagonal cylinder with an internal cavity diameter of $4.7\text{ Å}$, matching the diameter of $n$-alkanes and viologens.
• Pillar[6]arene: Hexagonal cylinder with cavity diameter $6.7\text{ Å}$.
• Symmetry and Ease of Functionalization: Both upper and lower rims are chemically equivalent and symmetrically decorated with alkoxy groups (e.g., 10 identical groups for pillar[5]arene), permitting straightforward deprotection to poly-phenols or water-soluble carboxylate/ammonium salts.

Cavitands and Carcerands

Donald J. Cram introduced rigid container molecules constructed from resorcin[4]arenes:

1. Cavitands: Resorcinarene hosts in which adjacent phenolic hydroxyls are covalently linked by short bridging units (e.g., $-\text{O}-\text{CH}_2-\text{O}-$ acetal bridges or quinoxaline walls). This rigidifies the bowl into an enforced, permanent cone shape that cannot invert.

2. Deep Cavitands: Extending the aromatic walls with benzimidazole or imide groups creates deep hydrophobic pockets capable of enveloping long linear alkanes in coiled conformations or stabilizing reactive intermediates.

3. Carcerands and Hemicarcerands:

• Carcerand: Two cavitand bowls fused face-to-face by multiple covalent linkers, permanently trapping guest molecules inside. The entrapped guest cannot escape at any temperature below the covalent thermal breakdown threshold—a state known as carceplex.
• Hemicarcerand: Possesses portals large enough that guest molecules can enter and exit at high temperatures through thermal breathing, but remain locked inside at room temperature (hemicarceplex). Used by Cram to stabilize otherwise transient species like cyclobutadiene and $o$-benzyne at room temperature.