Ligand

Cobalt complex [HCo(CO)₄] with five ligands

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 metal-ligand bonding can range 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."^[1][2]

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 the number of electrons donated to the metal (denticity or hapticity). The size of a ligand is indicated by its cone angle.

History

Coordination complexes have been known of—though not understood in any sense—since the beginning of chemistry, e.g. Prussian blue and copper vitriol. The key breakthrough occurred when Alfred Werner proposed, among other things, that Co(III) bears six ligands in an octahedral geometry. 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.^[3][4]

Inner- vs out-sphere ligands

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.

Metal-EDTA complex, wherein the aminocarboxylate is a hexadentate chelating ligand.

Cobalt(III) complex containing six ammonia ligands, which are monodentate. The chloride is not a ligand.

Strong field and weak field ligands

In general, ligands are viewed as donating electrons and electrostatic molecules to the central atom. Bonding is often described using the formalisms of molecular orbital theory. In general, electron pairs occupy the HOMO (Highest Occupied Molecular Orbital) 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. 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: 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.

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 ... represented by the symbols L, X, and Z, which correspond respectively to 2-electron, 1-electron and 0-electron neutral ligands."^[5][6] X ligands form from anionic precursors and L ligands from charge-neutral precursors. 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 ligand EDTA^4- 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

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 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.

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

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.

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

A bridging ligand links two or more metal centers. Polyatomic ligands such as CO₃^2- are especially prone to bridge. The bonding is complicated because polyatomic ligands are ambidentate and thus there is the capacity for many different linkage isomers. Atoms that bridge metals are sometimes indicated with the prefix "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

Non-innocent ligand

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 which have partial contributions to the overall state.

Trans-spanning ligand

Trans-spanning ligands are bidentate ligands that can span coordination positions on opposite sides of a coordination complex.

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):

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 exchange

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.

See also

• Crystal field theory
• Ligand field theory
• Coordination chemistry
• Inorganic chemistry
• Tanabe-Sugano diagram
• Spectrochemical series

References