Ligand

A ligand is an atom, ion, or molecule bound to an entity regarded as central. In coordination chemistry, ligands are the atoms or groups attached to a central atom, usually a metal, within a coordination complex. In biochemistry, the term has a broader meaning: the central entity may be a protein or another multiatomic structure rather than a single atom. These usages share the idea of binding, but describe different kinds of interaction and should not be treated as interchangeable. (goldbook.iupac.org)

Ligands in coordination chemistry

Many coordination ligands bind through a donor atom that supplies an electron pair to form a covalent bond with the central atom. This description emphasizes how the bond forms; it does not make the resulting bond fundamentally different from a covalent bond formed by another route. Metal–ligand bonding may require a more detailed electronic description than a simple electron-pair donation model. (goldbook.iupac.org)

Ligands may be neutral or charged. Familiar neutral examples include water and ammonia, which commonly coordinate through oxygen and nitrogen respectively. Chloride is a common anionic ligand. A complex therefore contains distinguishable central atoms and ligands, while its overall charge depends on the charges assigned to all its components. Coordination nomenclature identifies both the ligands and their attachment to the central atom. (publications.iupac.org)

The coordination number of a central atom must be distinguished from the number of ligand molecules. One ligand can attach through several donor atoms. For example, three ethylenediamine molecules, each attached through two nitrogen atoms, supply six donor atoms to one metal center. Counting ligand molecules alone would therefore not give the coordination number. (publications.iupac.org)

Denticity, chelation, and bridging

Denticity describes the number of donor groups from one ligand attached to the same central atom. A monodentate ligand binds through one donor group; bidentate and tridentate ligands bind through two and three, respectively. When two or more separate binding sites within one ligand attach to a single center, the interaction is called chelation. Ethylenediamine is a standard example of a ligand capable of bidentate chelation through its two nitrogen atoms. The actual attachment pattern matters: possessing several possible donor groups does not mean that all are coordinated in every complex. (old.goldbook.iupac.org)

A bridging ligand binds to more than one central atom, linking the centers into a larger coordination entity. Bridging is indicated in names and formulas by the Greek letter μ. It differs from chelation: chelation involves multiple separate sites binding one center, whereas bridging involves attachment to multiple centers. A sufficiently complex ligand can exhibit both behaviors. (iupac.qmul.ac.uk)

Hapticity describes another attachment pattern: the number of contiguous ligand atoms bonded to a metal center. It is written as a superscript after η. In ferrocene, each cyclopentadienyl ligand is described as η⁵ because five contiguous carbon atoms participate in its attachment to iron. This is not normally classified as five separate chelating donor sites; denticity and hapticity describe different structural features. (goldbook.iupac.org)

Electronic description

Ligand field theory provides an electronic description of metal–ligand interactions that allows for their covalent character. It develops beyond crystal field theory, whose simpler treatment emphasizes the field associated with the surrounding ligands. Thus, describing a ligand requires more than identifying its composition: the identity of its binding atoms and the character of its interaction with the metal are also relevant. (old.goldbook.iupac.org)

The word ligand does not itself specify a particular charge, attachment geometry, or bond strength. Those properties belong to the particular ligand–center combination and coordination arrangement. Nomenclature consequently distinguishes ligand identity from information about donor atoms, bridging, and attachment mode. (publications.iupac.org)

Biological ligands

In biological usage, a ligand binds to a molecular target, often at a particular binding site. Ligands need not be small organic molecules: ions and other proteins can also serve as ligands. The designation is relational. Calcium ions, for example, can be called ligands of calmodulin when the protein is regarded as central; when calcium is regarded as central, the coordinating groups of the protein are its ligands. (goldbook.iupac.org)

Protein–ligand association involves molecular recognition, with binding determined by the spatial and chemical compatibility of interacting surfaces. Noncovalent interactions include hydrogen bonds, electrostatic attractions, and van der Waals interactions. A ligand may be a substrate bound to an enzyme, a transported molecule, or a signaling molecule bound to a receptor. Binding and biological response are distinct: attachment does not by itself establish what functional effect follows. (ncbi.nlm.nih.gov)

In pharmacology, an agonist promotes receptor activation, whereas an antagonist opposes agonist-mediated activation. Affinity describes binding, while efficacy describes the ability of a bound ligand to produce a response. These properties must be assessed separately, although receptor-state changes can complicate their experimental separation. (ncbi.nlm.nih.gov)

Binding affinity and measurement

For a simple reversible, one-site interaction between target $P$ and ligand $L$,

Here the dissociation constant $K_d$ uses equilibrium concentrations of free target, free ligand, and complex. A lower $K_d$ indicates stronger affinity under the specified conditions. In this model, half the binding sites are occupied when the free ligand concentration equals $K_d$. These relationships require the assumed binding model and equilibrium conditions to hold. (ncbi.nlm.nih.gov)

Binding also has a kinetic dimension. For a single-step interaction, $K_d=k_{\mathrm{off}}/k_{\mathrm{on}}$, relating dissociation and association rate constants. Equal equilibrium affinities can therefore coexist with different binding and unbinding rates. Experiments using radiolabeled or fluorescent ligands can measure association, dissociation, saturation, or competition. More complicated systems, including multistep binding and interacting binding sites, require models beyond the simple one-site equation. (ncbi.nlm.nih.gov)