Ligand

In chemistry, a ligand is an atom, ion, or molecule (see also: functional group) that generally donates one or more of its electrons through a coordinate covalent bond to, or shares its electrons through a covalent bond with one or more central atoms or ions (these ligands act as a Lewis base. Fewer examples exist where a molecule can be described as a ligand that accepts electrons from a Lewis base (hence, the ligand acts as a Lewis acid).

Most commonly the central atom is a metal or metalloid in inorganic chemistry, but also in organic chemistry ligands are used, e.g. to protect functional groups (e.g. BH₃ as ligand for the protection of phosphines), or to stabilise reactive compounds (THF as a ligand for BH₃ to make BH₃ easier to handle). The molecule resulting from the coordination of a ligand (or an array of ligands) to a central atom is termed a complex.

Factors that characterise the ligands are their charge, size (bulk), and of course the nature of the constitutent atoms.

The ligands in a complex:

stabilise the central atom, and
dictate the reactivity of the central atom.

Ligands in metal complexes

The constitution of metal complexes has been described by Alfred Werner. Werner developed the basis for modern coordination chemistry. The ligands that are directly bonded to the metal (that is, share electrons), are called "inner sphere" ligands. If the inner-sphere ligands do not balance the charge of the central atom (the oxidation number), this may be done by simple ionic bonding with another set of counter ions (the "outer-sphere" ligands). The complex of the metal with the inner sphere ligands is then called a complex ion (which can be either cationic or anionic). The complex, along with its counter ions, is called a coordination compound.

Donation and back-donation

In general, ligands donate electron density to the (electron deficient) central atom (that is, overlap between the highest occupied molecular orbital (HOMO) of the ligand with the lowest unoccupied molecular orbital (LUMO) of the central atom). The ligand thus acts as a Lewis base by donating electron density (in general electron pairs) to the central atom, acting as a Lewis acid. In some cases ligands donate only one electron from a singly occupied orbital (the donating atom in these ligands is a radical).

Some metal centers in combination with certain ligands (e.g. carbon monoxide) can be further stabilised by donating 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.

Strong field vs. weak field ligands

Ligands and metal ions can be ordered by their 'hardness' (see also hard soft acid base theory). Certain metal ions have a preference for 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 makes overlap 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 (see crystal field theory).

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.

Denticity

Denticity (symbol κ) is the property of a ligand defining the number of coordination sites to which it binds. Ligands that only bind through one site are termed monodentate or unidentate. Some ligand molecules are able to bind to the metal ion through multiple sites because they have free lone pairs on more than one atom. Ligands that bind to more than one site are termed chelating (from the Greek for claw). For example, a ligand binding through two sites is bidentate and three sites is tridentate. The bite angle refers to the angle between the two bonds of a bidentate chelate. A classic example of a polydentate ligand is EDTA. It is able to bond through six sites, completely surrounding some metals. Polydentate ligands are commonly formed by joining organic molecules together. The number of atoms with which a polydentate ligand bind to the metal centre is called its denticity (symbol κ). Hapticity and denticity should not be confused. An η⁵ ligand may be κ¹ if all five bonding atoms of the ligand bond to one coordination site (as in cyclopentadienyl). Similarly, when EDTA^4- binds through all six of its donor atoms, it binds in an κ⁶ mode.

Complexes of polydentate ligands are called chelate complexes. They tend to be more stable than monodentate complexes, as it is necessary to break all of the bonds to the central atom for the ligand to be displaced. This increased stability or inertness is called the chelate effect. Entropy favors the displacement of many ligands by one polydentate ligand. The increase in the total number of molecules in solution is favorable.

Related to the chelate effect is the macrocyclic effect. A macrocyclic ligand is any large cyclic ligand which 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. Haem 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.

Unlike polydentate ligands, ambidentate ligands can attach to the central atom in two places but not both. A good example of this is thiocyanide, SCN^-, which can attach at either the sulfur atom or the nitrogen atom. Such compounds give rise to linkage isomerism.

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 important charge-neutral ligands. Simple organic compounds are also very important, be they anionic (RO^- and RCO₂^-) or neutral (R₂O, R₂S, R_3-xNH_x, and R₃P). 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).

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	I^-	monoanionic	monodentate
Bromide	Br^-	monoanionic	monodentate
Sulphide	S^2-	dianionic	monodentate (M=S), or bidentate bridging (M-S-M')
Thiocyanate	S-CN^-	monoanionic	monodentate	ambidentate (see also isothiocyanate, vide infra
Chloride	Cl^-	monoanionic	monodentate	also found bridging
Nitrate	O-NO₂^-	monoanionic	monodentate
Azide	N-N₂^-	monoanionic	monodentate
Fluoride	F^-	monoanionic	monodentate
Hydroxide	O-H^-	monoanionic	monodentate	often found as a bridging ligand
Oxalate	^*^2-	dianionic	bidentate
Water	H-O-H	neutral	monodentate	monodentate
Isothiocyanate	N=C=S^-	monoanionic	monodentate	ambidentate (see also thiocyanate, vide supra)
Acetonitrile	CH₃CN	neutral	monodentate
Pyridine	C₅H₅N	neutral	monodentate
Ammonia	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	O-N-O^-	monoanionic	monodentate	ambidentate
Triphenylphosphine	PPh₃	neutral	monodentate
Cyanide	CN^-	monoanionic	monodentate	can bridge between metals (both metals bound to C, or one to C and one to N)
Carbon monoxide	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)
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
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	^*^-	monoanionic
Diethylenetriamine (dien)		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)
Haem		dianionic	tetradentate	macrocyclic ligand
Nitrosyl		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
Triethylenetetramine (trien)		neutral	tetradentate
Tris(2-aminoethyl)amine (tren)		neutral	tetradentate
Tris(2-diphenylphosphineethyl)amine (np₃)		neutral	tetradentate
Terpyridine		neutral	tridentate

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