Applications & Special Topics — formula sheet

Proximal histidine: the histidine residue whose imidazole nitrogen is coordinated to the haem iron, on the opposite face from the O₂ site. It is the mechanical link between the metal and the protein.Distal histidine: a second histidine on the O₂ side, not coordinated to iron. It hydrogen-bonds bound O₂ and sterically discriminates against CO.

Cooperativity: binding of a ligand at one site increases the affinity of the remaining sites on the same molecule. It is positive cooperativity that makes the haemoglobin curve sigmoid.

Bohr effect: the oxygen affinity of haemoglobin falls as pH falls and as pCO₂ rises. Physiologically: haemoglobin releases more oxygen exactly where metabolism has made the environment more acidic and more CO₂-rich — i.e. in hard-working tissue.

Type 1 (blue) copper site: a copper ion bound by two histidine nitrogens and one cysteine thiolate sulfur in a roughly trigonal arrangement, with a weak axial methionine sulfur completing a distorted tetrahedral geometry.

Entatic state (Vallee–Williams) / rack mechanism: the protein imposes on the metal a coordination geometry intermediate between those preferred by the two oxidation states, raising the ground-state energy but drastically lowering the reorganisation energy for electron transfer. The site is held in a strained, ‘poised’ condition.

Thermodynamic stability (large log K, Part 7): the position of the dissociation equilibrium. It tells you how much free Gd³⁺ would be present at equilibrium.Kinetic inertness (slow dissociation, Part 8): the rate at which the complex falls apart. It tells you how much free Gd³⁺ is present in the two hours the agent is actually in the patient.

Coordinative unsaturation: the possession of fewer than the saturation electron count, and hence of a vacant coordination site. It is a prerequisite for catalysis, not an incidental feature. A catalyst precursor that is 18-electron must lose a ligand before it can do anything.

Oxidative addition: a molecule X–Y adds to a metal centre, breaking the X–Y bond and forming M–X and M–Y. The metal is oxidised by two, gains two ligands, and gains two electrons in the valence count.

Reductive elimination: the exact reverse. Two cis ligands X and Y couple and leave as X–Y. The metal is reduced by two, loses two ligands, and loses two electrons.

Migratory insertion: a group X already bound to the metal migrates onto an adjacent (cis) unsaturated ligand L, giving a new ligand X–L still bound to the metal. The oxidation state does not change. The electron count falls by two and the coordination number by one, because two ligands have become one, leaving a vacant site.

β-hydride elimination: a metal alkyl with a hydrogen on the β carbon transfers that hydrogen to the metal, releasing an alkene which usually remains coordinated. It is the microscopic reverse of migratory insertion of an alkene into an M–H bond.

δ bond: a bond formed by the face-to-face overlap of two d orbitals lying in planes perpendicular to the internuclear axis. It has two nodal planes containing that axis (compare: σ has none, π has one). It requires an eclipsed geometry and is much weaker than σ or π.

Wade’s rules (also Wade–Mingos, or the polyhedral skeletal electron pair theory, PSEPT): count the skeletal electron pairs that hold the cage together, then read the shape from the count. For a cluster with n vertices: n + 1 pairs → closo — a closed deltahedron with all n vertices occupied n + 2 pairs → nido — the deltahedron with one vertex missing n + 3 pairs → arachno — two vertices missing n + 4 pairs → hypho — three missing

Supramolecular chemistry: the chemistry of assemblies held together by non-covalent or reversible interactions — coordinate bonds, hydrogen bonds, electrostatics, π-stacking — rather than by ordinary covalent bonds. Lehn’s phrase for it is ‘chemistry beyond the molecule’.

Podand: an acyclic (open-chain) polydentate ligand — for example a glyme, CH₃O(CH₂CH₂O)_nCH₃.Corand: a monocyclic host — a crown ether.Cryptand: a macrobicyclic host — two bridgehead nitrogens joined by three polyether chains, defining a three-dimensional cavity. Its complex is called a cryptate.

Cryptate effect: the additional stability of a complex of a macrobicyclic cryptand compared with the corresponding macrocyclic (crown) complex, over and above the macrocyclic effect. It arises from complete three-dimensional encapsulation of the guest and from the near-total pre-organisation of the donor set.

Self-assembly: the spontaneous, reversible association of components into a well-defined structure under thermodynamic control. The information specifying the product is stored in the components — in the metal’s preferred coordination geometry and the ligand’s shape — not in a sequence of synthetic steps.

Molecular recognition: the selective binding of one guest in preference to others, arising from complementarity of size, shape, charge and donor character between host and guest.