ligand, charged or uncharged molecule with one or more unshared pairs of electrons that can attach to a central metallic atom or ion to form an aggregate known as a complex ion (see chemical bond). Some ligands that share electrons with metals form very stable complexes. Some common bases that act as ligands are water and ammonia molecules and halide, hydroxide, acetate, cyanide, thiocyanate, and nitrite anions. These ligands are monofunctional, i.e., they are attached by one unshared pair of electrons during complexing. Polyfunctional ligands, which bind to the metal ion with two or more pairs of electrons, are called chelates (see chelating agents). Ethylenediamine-tetraacetate, a commonly used chelating compound, has six pairs of electrons to bind to metal ions. Electron-donating functional groups containing nitrogen, oxygen, sulfur, phosphorous, or carbon may act as ligands in complex biological systems. For example, in enzymes that need complexed metal ions to function, mercapto (sulfur-containing) groups and amino (nitrogen-containing) groups act as chelating agents; these groups fix the metal ion in a specific position. Other biologically important molecules, such as chlorophyll, vitamin B₁₂, and heme, also have nitrogen-containing groups that donate electrons and have a chelating function.

Atom, group (see functional group), or molecule attached to a central atom, usually of a transition element, in a coordination or complex compound (see bonding). It is almost always the electron-pair donor (nucleophile) in a covalent bond. Common ligands include the neutral molecules water (H₂O), ammonia (NH₃), and carbon monoxide (CO) and the anions cyanide (CN⁻), chloride (Cl⁻), and hydroxide (OH⁻). Rarely, ligands are cations and electron-pair acceptors (electrophiles). Organic ligands include EDTA (see chelate) and nitrilotriacetic acid. Biological systems rely on ligands such as the porphyrin in hemoglobin and chlorophyll, and numerous cofactors are ligands. In chelates, the ligand attaches at more than one point, sharing more than one electron pair, and is called bidentate or polydentate—having two or many “teeth.” The ligands in a complex may be the same or different.

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In chemistry, a ligand is either an atom, ion, or molecule (see also: functional group) that bonds to a central metal, generally involving formal donation of one or more of its electrons. The metal-ligand bonding ranges from covalent to more ionic. Furthermore, the metal-ligand bond order can range from one to three. Ligands are viewed as Lewis bases, although rare cases are known involving Lewis acidic "ligands.

Metal and metalloids are bound to ligands in virtually all circumstances, although gaseous "naked" metal ions can be generated in high vacuum. Ligands in a complex dictate the reactivity of the central atom, including ligand substitution rates, the reactivity of the ligands themselves, and redox. Ligand selection is a critical consideration in many practical areas, including bioinorganic and medicinal chemistry, homogeneous catalysis, and environmental chemistry.

Ligands are classified in many ways: their charge, size (bulk), the identity of the coordinating atom(s), and their denticity. The size of a ligand is indicated by its cone angle.

Inner- vs out-sphere ligands

In coordination chemistry, the ligands that are directly bonded to the metal (that is, share electrons), are sometimes called "inner sphere" ligands. "Outer-sphere" ligands are not directly attached to the metal, but are bonded, generally weakly, to the first coordination shell, affecting the inner sphere in subtle ways. The complex of the metal with the inner sphere ligands is then called a coordination complex, which can be neutral, cationic, or anionic. The complex, along with its counter ions (if required), is called a coordination compound.

Strong field and weak field ligands

In general, ligands are viewed as donating electrons to the central atom. Bonding is often described using the formalisms of molecular orbital theory. In general, electron pairs occupy the HOMO of the ligands.

Ligands and metal ions can be ordered in many ways, one ranking system focuses on ligand 'hardness' (see also hard soft acid base theory). Metal ions preferentially bind certain ligands. In general, 'hard' metal ions prefer weak field ligands, whereas 'soft' metal ions prefer strong field ligands. From a MO point of view, the HOMO of the ligand should have an energy that overlaps with the LUMO of the metal preferential. Metal ions bound to strong-field ligands follow the Aufbau principle, whereas complexes bound to weak-field ligands follow Hund's rule.

Binding of the metal with the ligands results in a set of molecular orbitals, where the metal can be identified with a new HOMO and LUMO (the orbitals defining the properties and reactivity of the resulting complex) and a certain ordering of the 5 d-orbitals (which may be filled, or partially filled with electrons). In an octahedral environment, the 5 otherwise degenerate d-orbitals split in sets of 2 and 3 orbitals (for a more in depth explanation, see crystal field theory).

3 orbitals of low energy: d_xy, d_xz and d_yz

2 of high energy: d_z² and d_x²−y²

The energy difference between these 2 sets of d-orbitals is called the splitting parameter, Δ_o. The magnitude of Δ_o is determined by the field-strength of the ligand: strong field ligands, by definition, increase Δ_o more than weak field ligands. Ligands can now be sorted according to the magnitude of Δ_o (see the table below). This ordering of ligands is almost invariable for all metal ions and is called spectrochemical series.

For complexes with a tetrahedral surrounding, the d-orbitals again split into two sets, but this time in reverse order:

2 orbitals of low energy: d_z² and d_x²−y²

3 orbitals of high energy: d_xy, d_xz and d_yz

The energy difference between these 2 sets of d-orbitals is now called Δ_t. The magnitude of Δ_t is smaller than for Δ_o, because in a tetrahedral complex only 4 ligands influence the d-orbitals, whereas in an octahedral complex the d-orbitals are influenced by 6 ligands. When the coordination number is neither octahedral nor tetrahedral, the splitting becomes correspondingly more complex. For the purposes of ranking ligands, however, the properties of the octahedral complexes and the resulting Δ_o has been of primary interest.

The arrangement of the d-orbitals on the central atom (as determined by the 'strength' of the ligand), has a strong effect on virtually all the properties of the resulting complexes. E.g. the energy differences in the d-orbitals has a strong effect in the optical absorption spectra of metal complexes. It turns out that valence electrons occupying orbitals with significant 3d-orbital character absorb in the 400-800 nm region of the spectrum (UV-visible range). The absorption of light (what we perceive as the color) by these electrons (that is, excitation of electrons from one orbital to another orbital under influence of light) can be correlated to the ground state of the metal complex, which reflects the bonding properties of the ligands. The relative change in (relative) energy of the d-orbitals as a function of the field-strength of the ligands is described in Tanabe-Sugano diagrams.

In cases where the ligand has low energy LUMO, such orbitals also participate in the bonding. The metal-ligand bond can be further stabilised by a formal donation of electron density back to the ligand in a process known as back-bonding. In this case a filled, central-atom-based orbital donates density into the LUMO of the (coordinated) ligand. Carbon monoxide is the preeminent example a ligand that engages metals via back-donation. Complementarily, ligands with low-energy filled orbitals of pi-symmetry can serve as pi-donor.

Polydentate and polyhapto ligand motifs and nomenclature

Many ligands are capable of binding metal ions through multiple sites, usually because the ligands have lone pairs on more than one atom. Ligands that bind via more than one atom are often termed chelating. A ligand that binds through two sites is classified as bidentate, and three sites as tridentate. The bite angle refers to the angle between the two bonds of a bidentate chelate. Chelating ligands are commonly formed by linking donor groups via organic linkers. The classic bidentate ligand is ethylenediamine, which is derived by the linking of two ammonia groups with an ethylene (-CH₂CH₂-) linker. A classic example of a polydentate ligand is the hexadentate chelating agent EDTA, which is able to bond through six sites, completely surrounding some metals. The number of atoms with which a polydentate ligand bind to the metal centre is called its denticity, symbolized κⁿ, where n indicates the number non-contiguous donor sites by which a ligand attaches to a metal. EDTA⁴⁻, when it is sexidentate, binds as a κ⁶-ligand, the amines and the carboxylate oxygen atoms are not contiguous. In practice, the n value of a ligand is not indicated explicitly but rather assumed. The binding affinity of a chelating system depends on the chelating angle or bite angle.

Related to but distinct to from denticity is hapticity, symbolized η or eta. Hapticity refers to the number of contiguous atoms in a ligand that are attached to a metal. Butadiene forms both η² and η⁴ complexes depending on the number of carbon atoms are bonded to the metal. To simplify matters, ηⁿ usually refers to unsaturated hydrocarbons and κⁿ usually to describe polydentate amine and carboxylate ligands.

Complexes of polydentate ligands are called chelate complexes. They tend to be more stable than complexes derived from monodentate ligands. This enhanced stability, the chelate effect, is usually attributed to effects of entropy, which favors the displacement of many ligands by one polydentate ligand. When the chelating ligand forms a large ring that at least partially surrounds the central atom and bonds to it, leaving the central atom at the centre of a large ring. The more rigid and the higher its denticity, the more inert will be the macrocyclic complex. Heme is a good example: the iron atom is at the centre of a porphyrin macrocycle, being bound to four nitrogen atoms of the tetrapyrrole macrocycle. The very stable dimethylglyoximate complex of nickel is a synthetic macrocycle derived from the anion of dimethylglyoxime.

Single atom bonding motifs

Ambidentate ligand

Unlike polydentate ligands, ambidentate ligands can attach to the central atom in two places but not both. A good example of this is thiocyanate, SCN⁻, which can attach at either the sulfur atom or the nitrogen atom. Such compounds give rise to linkage isomerism. Polyfunctional ligands, see especially proteins, can bond to a metal center through different ligand atoms to form various isomers.

Bridging ligand

Bridging ligand link two or more metal centers. Polyatomic ligands such as CO₂^2- are especially prone to bridge. The bonding is complicated because polyatomic ligands are ambidentate and thus the capacity for many different linkage isomers. Atoms that bridge metals are sometimes indicated with prefix of "μ" (mu). Most inorganic solids, e.g. FeCl₂, are polymers by virtue of the presence of multiple bridging ligands.

Metal ligand multiple bond

Metal ligand multiple bonds some ligands can bond to a metal center through the same atom but with a different number of lone pairs. The bond order of the metal ligand bond can be in part distinguished through the metal ligand bond angle (M-X-R). This bond angle is often referred to as being linear or bent with further discussion concerning the degree to which the angle is bent. For example, an imido ligand in the ionic form has three lone pairs. One lone pair is used as a sigma X donor, the other two lone pairs are available as L type pi donors. If both lone pairs are used in pi bonds then the M-N-R geometry is linear. However, if one or both these lone pairs is non-bonding then the M-N-R bond is bent and the extent of the bend speaks to how much pi bonding there may be. η¹-Nitric oxide can coordinate to a metal center in linear or bent manner.

Specialized ligand types

Noninnocent ligand

Noninnocent ligands bond with metals in such a manner that the distribution of electron density between the metal center and ligand is unclear. Describing the bonding of noninnocent ligands often involves writing multiple resonance forms which have partial contributions to the overall state.

Trans spanning ligand

Trans spanning ligands are bidentate ligands that can span opposite sites of a complex with square-planar geometry. A wide variety of ligands that chelate in the cis fashion already exist, but very few can link opposite verices on a coordination polyhedron. Early attempts to generate trans-spanning bidentate ligands relied on polymethylene chains to link the donor functionalities, but such ligands lead to coordination polymers.

A diphosphane linked with pentamethylene was claimed to span across a square planare complex. This early attempt was followed by ligands with more rigid backbones. "TRANSPHOS" was the first trans-spanning diphosphane ligand that usually coordinates to palladium(II) and platinum(I1) in a trans manner. TRANSPHOS features benzo[c]phenanthrene substituted by diphenylphosphinomethyl (Ph₂PCH₂) groups at the 1 and 11 positions. The polycyclic framework suffers sterically clashing hydrogen centers. XANTHOS is a more reliable trans-spanning ligand.^[2] without the steric problems associated with TRANSPHOS. SPANPHOS is comparable to XANTHOS.

Subsequent to the reports on SPANPHOS and related ligands was a genuine trans-spanning ligand reported, one that would form neither bimetallic nor oligomeric complexes with certain transition metals, and strictly function as a trans-chelator This ligand, TRANSDIP, represented the first trans-spanning ligand to give exclusively chelating complexes, even when reacted with d8 metal ion halides.^[2] TRANSDIP is based on a α-cyclodextrin.

Common ligands

See nomenclature.

Virtually every molecule and every ion can serve as a ligand for (or "coordinate to") metals. Monodentate ligands include virtually all anions and all simple Lewis bases. Thus, the halides and pseudohalides are important anionic ligands whereas ammonia, carbon monoxide, and water are particularly common charge-neutral ligands. Simple organic species are also very common, be they anionic (RO⁻ and RCO₂⁻) or neutral (R₂O, R₂S, R_3−xNH_x, and R₃P). The steric properties of some ligands are evaluated in terms of their cone angles.

Beyond the classical Lewis bases and anions, all unsaturated molecules are also ligands, utilizing their π-electrons in forming the coordinate bond. Also, metals can bind to the σ bonds in for example silanes, hydrocarbons, and dihydrogen (see also: agostic interaction).

In complexes of non-innocent ligands, the ligand is bonded to metals via conventional bonds, but the ligand is also redox-active.

Examples of common ligands (by field strength)

In the following table the ligands are sorted by field strength (weak field ligands first):

Ligand	formula (bonding atom(s) in bold)	Charge	Most common denticity	Remark(s)
Iodide iodo	I−	monoanionic	monodentate
Bromide bromido	Br−	monoanionic	monodentate
Sulfide thio or bridging thiolate	S2−	dianionic	monodentate (M=S), or bidentate bridging (M-S-M')
Thiocyanate thiocyanato	S-CN−	monoanionic	monodentate	ambidentate (see also isothiocyanate, below)
Chloride chlorido	Cl−	monoanionic	monodentate	also found bridging
Nitrate	O-NO2−	monoanionic	monodentate
Azide	N-N2−	monoanionic	monodentate
Fluoride fluorido	F−	monoanionic	monodentate
Hydroxide hydroxo	O-H−	monoanionic	monodentate	often found as a bridging ligand
Oxalate	[O-C(=O)-C(=O)-O]2−	dianionic	bidentate
Water aqua	H-O-H	neutral	monodentate	monodentate
Isothiocyanate isothiocyanato	N=C=S−	monoanionic	monodentate	ambidentate (see also thiocyanate, above)
Acetonitrile	CH3CN	neutral	monodentate
Pyridine	C5H5N	neutral	monodentate
Ammonia ammine	NH3	neutral	monodentate
Ethylenediamine	en	neutral	bidentate
2,2'-Bipyridine	bipy	neutral	bidentate	easily reduced to its (radical) anion or even to its dianion
1,10-Phenanthroline	phen	neutral	bidentate
Nitrite nitro	N-O2−	monoanionic	monodentate	ambidentate (see also nitrito)
Nitrite nitrito	O-N-O−	monoanionic	monodentate	ambidentate (see also nitro)
Triphenylphosphine	PPh3	neutral	monodentate
Cyanide cyano	CN−	monoanionic	monodentate	can bridge between metals (both metals bound to C, or one to C and one to N)
Carbon monoxide carbonyl	CO	neutral	monodentate	can bridge between metals (both metals bound to C)

Note: The entries in the table are sorted by field strength, binding through the stated atom (i.e. as a terminal ligand), the 'strength' of the ligand changes when the ligand binds in an alternative binding mode (e.g. when it bridges between metals) or when the conformation of the ligand gets distorted (e.g. a linear ligand that is forced through steric interactions to bind in a non-linear fashion).

Other general encountered ligands (alphabetical)

In this table other common ligands are listed in alphabetical order.

Ligand	formula (bonding atom(s) in bold)	Charge	Most common denticity	Remark(s)
Acetonitrile	MeCN	neutral	monodentate
Acetylacetonate (Acac)	CH3-C(O)-CH-C(O)-CH3	monoanionic	bidentate	In general bidentate, bound through both oxygens, but sometimes bound through the central carbon only, see also analogous ketimine analogues
Alkenes	R2C=CR2	neutral		compounds with a C-C double bond
Benzene	C6H6	neutral		and other arenes
1,2-Bis(diphenylphosphino)ethane (dppe)	Ph2PC2H4PPh2	neutral	bidentate
1,1-Bis(diphenylphosphino)methane (dppm)	C25H22P2	neutral		Can bond to 2 metal atoms at once, forming dimers
Corroles			tetradentate
Crown ethers		neutral		primarily for alkali and alkaline earth metal cations
2,2,2-crypt			hexadentate	primarily for alkali and alkaline earth metal cations
Cryptates		neutral
Cyclopentadienyl	[C5H5]−	monoanionic
Diethylenetriamine (dien)	C4H13N3	neutral	tridentate	related to TACN, but not constrained to facial complexation
Dimethylglyoximate (dmgH−)		monoanionic
Ethylenediaminetetraacetate (EDTA)		tetra-anionic	hexadentate	actual ligand is the tetra-anion
Ethylenediaminetriacetate		trianionic	pentadentate	actual ligand is the trianion
glycinate			bidentate	other α-amino acid anions are comparable (but chiral)
Heme		dianionic	tetradentate	macrocyclic ligand
Nitrosyl	NO+	cationic		bent (1e) and linear (3e) bonding mode
Scorpionate ligand			tridentate
Sulfite		monoanionic	monodentate	ambidentate
2,2',5',2''-Terpyridine (terpy)		neutral	tridentate	meridional bonding only
Thiocyanate		monoanionic	monodentate	ambidentate, sometimes bridging
Triazacyclononane (tacn)	(C2H4)3(NR)3	neutral	tridentate	macrocyclic ligand see also the N,N',N"-trimethylated analogue
Tricyclohexylphosphine	(C6H11)3P or (PCy3)	neutral	monodentate
Triethylenetetramine (trien)		neutral	tetradentate
Trimethylphosphine	PMe3	neutral	monodentate
Tri(o-tolyl)phosphine	P(o-tolyl)3	neutral	monodentate
Tris(2-aminoethyl)amine (tren)	(NH2CH2CH2)3N	neutral	tetradentate
Tris(2-diphenylphosphineethyl)amine (np3)		neutral	tetradentate
Terpyridine	C15H11N3	neutral	tridentate

See also

• 2-Mercaptoindole
• Crystal field theory
• Ligand field theory
• Coordination chemistry
• Inorganic chemistry
• Radioligand
• Tanabe-Sugano diagram
• Spectrochemical series
• Scatchard equation

References