In coordination chemistry, a ligand is an ion or molecule (see also: functional group) that binds to a central metal atom to form a coordination complex. The bonding between metal and ligand generally involves formal donation of one or more of the ligand's electron pairs. The nature of metal-ligand bonding can range from covalent to 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, their size (bulk), the identity of the coordinating atom(s), and the number of electrons donated to the metal (denticity or hapticity). The size of a ligand is indicated by its cone angle.
The composition of coordination complexes have been known since the early 1800s, e.g. Prussian blue and copper vitriol. The key breakthrough occurred when Alfred Werner reconciled formulas and isomers. He showed, among other things, that the formulas of many cobalt(III) and chromium(III) compounds can be understood if the metal has six ligands in an octahedral geometry. The first to use the term "ligand" were Alfred Stock and Carl Somiesky, in relation to silicon chemistry. The theory allows one to understand the difference between coordinated and ionic chloride in the cobalt ammine chlorides and to explain many of the previously inexplicable isomers. He resolved the first coordination complex called hexol into optical isomers, overthrowing the theory that chirality was necessarily associated with carbon compounds.
Strong field and weak field ligands
In general, ligands are viewed as electron donors and the metals as electron acceptors. Bonding is often described using the formalisms of molecular orbital theory. The HOMO (Highest Occupied Molecular Orbital) can be mainly of ligands or metal character.
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, 'soft' metal ions prefer weak field ligands, whereas 'hard' metal ions prefer strong field ligands. According to the molecular orbital theory, the HOMO of the ligand should have an energy that overlaps with the LUMO (Lowest Unoccupied Molecular Orbital) 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: dxy, dxz and dyz
- 2 of high energy: dz2 and dx2−y2
The energy difference between these 2 sets of d-orbitals is called the splitting parameter, Δo. The magnitude of Δo is determined by the field-strength of the ligand: strong field ligands, by definition, increase Δo more than weak field ligands. Ligands can now be sorted according to the magnitude of Δo (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: dz2 and dx2−y2
- 3 orbitals of high energy: dxy, dxz and dyz
The energy difference between these 2 sets of d-orbitals is now called Δt. The magnitude of Δt is smaller than for Δo, 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 Δo 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.
Classification of ligands as L and X
Especially in the area of organometallic chemistry, ligands are classified as L and X (or combinations of the two). The classification scheme - the "CBC Method" for covalent bond classification - was popularized by M.L.H. Green and "is based on the notion that there are three basic types [of ligands]... represented by the symbols L, X, and Z, which correspond respectively to 2-electron, 1-electron and 0-electron neutral ligands." L ligands from charge-neutral precursors and are represented by amines, phosphines, CO, N2, and alkenes. X ligands typically are derived from anionic precursors such as chloride but includes ligands where salts of anion do not really exist such as hydride and alkyl. Thus, the complex IrCl(CO)(PPh3)2 is classified as an MXL3 complex, since CO and the two PPh3 ligands are classified as L's. The oxidative addition of H2 to IrCl(CO)(PPh3)2 gives an 18e- ML3X3 product, IrClH2(CO)(PPh3)2. EDTA4- is classified as an L2X4 ligand, as it features four anions and two neutral donor sites. Cp is classified as an L2X ligand.
Polydentate and polyhapto ligand motifs and nomenclature
Denticity (represented by κ) refers to the number of times a ligand bonds to a metal through non-contiguous donor sites. 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. A 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 times a polydentate ligand bind to a metal centre is symbolized with "κn", where "n" indicates the number sites by which a ligand attaches to a metal. EDTA4−, when it is hexidentate, 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.
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.
Hapticity (represented by η) refers to the number of contiguous atoms that comprise a donor site and attach to a metal center. Butadiene forms both η2 and η4 complexes depending on the number of carbon atoms that are bonded to the metal.
In coordination chemistry, the ligands that are directly bonded to the metal (that is, share electrons), form part of the first coordination sphere and 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.
Trans-spanning ligands are bidentate ligands that can span coordination positions on opposite sides of a coordination complex.
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.
A bridging ligand links two or more metal center. Virtually all inorganic solids with simple formulas are coordination polymers, consisting of metal centres linked by bridging ligands. This group of materials includes all anhydrous binary metal halides and pseudohalides. Bridging ligands also persist in solution. Polyatomic ligands such as carbonate are ambidentate and thus are found to often bind to two or three metals simultaneously. Atoms that bridge metals are sometimes indicated with the prefix "μ" (mu). Most inorganic solids, 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
Non-innocent 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 that have partial contributions to the overall state.
Bulky ligands are used to control the steric properties of a metal center. They are used for many reasons, both practical and academic. On the practical side, they influence the selectivity of metal catalysts, e.g. in hydroformylation. Of academic interest, bulky ligands stabilize unusual coordination sites, e.g. reactive coligands or low coordination numbers. Often bulky ligands are employed to simulate the steric protection afforded by proteins to metal-containing active sites. Of course excessive steric bulk can prevent the coordination of certain ligands.
Chiral ligands are useful for inducing asymmetry within the coordination sphere. Often the ligand is employed as an optically pure group. In some cases, e.g. secondary amines, the asymmetry arises upon coordination. Chiral ligands are essential components of asymmetric homogeneous catalysis.
- 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, R3−xNHx, 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 (bromo) Br− monoanionic monodentate Sulfide (thio or less commonly "bridging thiolate") S2− dianionic monodentate (M=S), or bidentate bridging (M-S-M') Thiocyanate (S-thiocyanato) S-CN− monoanionic monodentate ambidentate (see also isothiocyanate, below) Chloride (chloro) Cl− monoanionic monodentate also found bridging Nitrate (nitrato) O-NO2− monoanionic monodentate Azide (azido) N-N2− monoanionic monodentate Fluoride (fluorido) F− monoanionic monodentate Hydroxide (hydroxo) O-H− monoanionic monodentate often found as a bridging ligand Oxalate (oxalato) [O-C(=O)-C(=O)-O]2− dianionic bidentate Water (aqua) H-O-H neutral monodentate monodentate Nitrite (nitrito) O-N-O− monoanionic monodentate ambidentate (see also nitro) Isothiocyanate (isothiocyanato) N=C=S− monoanionic monodentate ambidentate (see also thiocyanate, above) Acetonitrile (acetonitrilo) CH3CN neutral monodentate Pyridine C5H5N neutral monodentate Ammonia (ammine or less commonly "ammino") 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) 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) Acetylacetonate (Acac) CH3-C(O)-CH2-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 (Cp) [C5H5]− monoanionic Although monoanionic, by the nature of its occupied MO's, it is capable of acting as a tridentate ligand. 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 (Glycinato) monoanionic 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 Oxo O dianion monodentate sometimes bridging Pyrazine N2C4H4 neutral ditopic sometimes bridging Scorpionate ligand tridentate Sulfite monoanionic monodentate ambidentate 2,2',5',2-Terpyridine (terpy) neutral tridentate meridional bonding only 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 Tropylium C7H7+ cationic Carbon dioxide CO2 see transition metal carbon dioxide complex
Ligand exchange (also ligand substitution) is a type of chemical reaction in which one ligand in a chemical compound is replaced by another ligand. In organometallic chemistry this can take place by associative substitution or by dissociative substitution.
Pronounced ˈlɪgənd with the first syllable sounding like the word "lithium" or 'laɪgənd with the first syllable sounding like the word "lie". 
- Crystal field theory
- Ligand dependent pathway
- Ligand field theory
- Coordination chemistry
- Inorganic chemistry
- Tanabe-Sugano diagram
- Spectrochemical series
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