In organometallic chemistry, a metal–ligand multiple bond describes the interaction of certain

ligand In coordination chemistry, a ligand is an ion or molecule ( functional group) that binds to a central metal atom to form a coordination complex. The bonding with the metal generally involves formal donation of one or more of the ligand's ele ...

s with a

metal A metal (from Greek μέταλλον ''métallon'', "mine, quarry, metal") is a material that, when freshly prepared, polished, or fractured, shows a lustrous appearance, and conducts electricity and heat relatively well. Metals are typi ...

with a

bond order In chemistry, bond order, as introduced by Linus Pauling, is defined as the difference between the number of bonds and anti-bonds. The bond order itself is the number of electron pairs ( covalent bonds) between two atoms. For example, in diat ...

greater than one."Metal–Ligand Multiple Bonds: The Chemistry of Transition Metal Complexes Containing Oxo, Nitrido, Imido, Alkylidene, or Alkylidyne Ligands" W. A. Nugent and J. M. Mayer; Wiley-Interscience, New York, 1988. .

Coordination complex A coordination complex consists of a central atom or ion, which is usually metallic and is called the ''coordination centre'', and a surrounding array of bound molecules or ions, that are in turn known as ''ligands'' or complexing agents. Many ...

es featuring multiply bonded ligands are of both scholarly and practical interest.

Transition metal carbene complex A transition metal carbene complex is an organometallic compound featuring a divalent organic ligand. The divalent organic ligand coordinated to the metal center is called a carbene. Carbene complexes for almost all transition metals have been rep ...

es catalyze the

olefin metathesis Olefin metathesis is an organic reaction that entails the redistribution of fragments of alkenes (olefins) by the scission and regeneration of carbon-carbon double bonds. Because of the relative simplicity of olefin metathesis, it often creat ...

reaction. Metal oxo intermediates are pervasive in oxidation catalysis. : As a cautionary note, the classification of a metal ligand bond as being "multiple" bond order is ambiguous and even arbitrary because

is a formalism. Furthermore, the usage of multiple bonding is not uniform. Symmetry arguments suggest that most ligands engage metals via multiple bonds. The term 'metal ligand multiple bond" is often reserved for ligands of the type and (n = 0, 1, 2) and (n = 0, 1) where R is H or an organic substituent, or

pseudohalide Pseudohalogens are polyatomic analogues of halogens, whose chemistry, resembling that of the true halogens, allows them to substitute for halogens in several classes of chemical compounds. Pseudohalogens occur in pseudohalogen molecules, inorganic ...

. Historically, and are not included in this classification, nor are

halide In chemistry, a halide (rarely halogenide) is a binary chemical compound, of which one part is a halogen atom and the other part is an element or radical that is less electronegative (or more electropositive) than the halogen, to make a f ...

Pi-donor ligands

coordination chemistry A coordination complex consists of a central atom or ion, which is usually metallic and is called the ''coordination centre'', and a surrounding array of chemical bond, bound molecules or ions, that are in turn known as ''ligands'' or complexing ...

, a pi-donor ligand is a kind of ligand endowed with filled non-bonding orbitals that overlap with metal-based orbitals. Their interaction is complementary to the behavior of

pi-acceptor ligand In chemistry, π backbonding, also called π backdonation, is when electrons move from an atomic orbital on one atom to an appropriate symmetry antibonding orbital on a ''π-acceptor ligand''. It is especially common in the organometallic ch ...

s. The existence of terminal

oxo ligand A transition metal oxo complex is a coordination complex containing an oxo ligand. Formally O2-, an oxo ligand can be bound to one or more metal centers, i.e. it can exist as a terminal or (most commonly) as bridging ligands (Fig. 1). Oxo ligan ...

s for the early transition metals is one consequence of this kind of bonding. Classic pi-donor ligands are oxide (O²⁻), nitride (N³⁻), imide (RN²⁻), alkoxide (RO⁻), amide (R₂N⁻), and fluoride. For late transition metals, strong pi-donors form anti-bonding interactions with the filled d-levels, with consequences for spin state, redox potentials, and ligand exchange rates. Pi-donor ligands are low in the

spectrochemical series A spectrochemical series is a list of ligands ordered by ligand "strength", and a list of metal ions based on oxidation number, group and element. For a metal ion, the ligands modify the difference in energy Δ between the d orbitals, called the ...

Multiple bond stabilization

Metals bound to so-called triply bonded

carbyne In organic chemistry, a carbyne is a general term for any compound whose structure consists of an electrically neutral carbon atom connected by a single covalent bond and has three non-bonded electrons. The carbon atom has either one or three ...

imide In organic chemistry, an imide is a functional group consisting of two acyl groups bound to nitrogen. The compounds are structurally related to acid anhydrides, although imides are more resistant to hydrolysis. In terms of commercial applicati ...

nitride In chemistry, a nitride is an inorganic compound of nitrogen. The "nitride" anion, N3- ion, is very elusive but compounds of nitride are numerous, although rarely naturally occuring. Some nitrides have a find applications, such as wear-resista ...

( nitrido), and oxide ( oxo) ligands are generally assigned to high oxidation states with low d electron counts. The high

oxidation state In chemistry, the oxidation state, or oxidation number, is the hypothetical charge of an atom if all of its bonds to different atoms were fully ionic. It describes the degree of oxidation (loss of electrons) of an atom in a chemical compound. ...

stabilizes the highly reduced ligands. The low

d electron count The d electron count is a chemistry formalism used to describe the electron configuration of the valence electrons of a transition metal center in a coordination complex. The d electron count is an effective way to understand the geometry and re ...

allow for many bonds between ligands and the metal center. A d⁰ metal center can accommodate up to 9 bonds without violating the 18 electron rule, whereas a d⁶ species can only accommodate 6 bonds.

Reactivity explained through ligand hybridization

A ligand described in ionic terms can bond to a metal through however many lone pairs it has available. For example, many alkoxides use one of their three lone pairs to make a single bond to a metal center. In this situation the oxygen is sp³ hybridized according to

valence bond theory In chemistry, valence bond (VB) theory is one of the two basic theories, along with molecular orbital (MO) theory, that were developed to use the methods of quantum mechanics to explain chemical bonding. It focuses on how the atomic orbitals of ...

. Increasing the bond order to two by involving another lone pair changes the hybridization at the oxygen to an sp² center with an expected expansion in the M-O-R bond angle and contraction in the M-O bond length. If all three lone pairs are included for a bond order of three than the M-O bond distance contracts further and since the oxygen is a sp center the M-O-R bond angle is 180˚ or linear. Similarly with the imidos are commonly referred to as either bent (sp²) or linear (sp). Even the oxo can be sp² or sp hybridized. The triply bonded oxo, similar to

carbon monoxide Carbon monoxide ( chemical formula CO) is a colorless, poisonous, odorless, tasteless, flammable gas that is slightly less dense than air. Carbon monoxide consists of one carbon atom and one oxygen atom connected by a triple bond. It is the si ...

, is partially positive at the oxygen atom and unreactive towards Brønsted acids at the oxygen atom. When such a complex is reduced, the triple bond can be converted to a

double bond In chemistry, a double bond is a covalent bond between two atoms involving four bonding electrons as opposed to two in a single bond. Double bonds occur most commonly between two carbon atoms, for example in alkenes. Many double bonds exist betw ...

at which point the oxygen no longer bears a partial positive charge and is reactive towards acid.

Conventions

Bonding representations

Imido ligands, also known as imides or nitrenes, most commonly form "linear six electron bonds" with metal centers. Bent imidos are a rarity limited by complexes electron count, orbital bonding availability, or some similar phenomenon. It is common to draw only two lines of bonding for all imidos, including the most common linear imidos with a six electron bonding interaction to the metal center. Similarly amido complexes are usually drawn with a single line even though most amido bonds involve four electrons. Alkoxides are generally drawn with a single bond although both two and four electron bonds are common. Oxo can be drawn with two lines regardless of whether four electrons or six are involved in the bond, although it is not uncommon to see six electron oxo bonds represented with three lines.

Representing oxidation states

There are two motifs to indicate a metal oxidation state based around the actual charge separation of the metal center. Oxidation states up to +3 are believed to be an accurate representation of the charge separation experienced by the metal center. For oxidation states of +4 and larger, the oxidation state becomes more of a formalism with much of the positive charge distributed between the ligands. This distinction can be expressed by using a Roman numeral for the lower oxidation states in the upper right of the metal atomic symbol and an Arabic number with a plus sign for the higher oxidation states (see the example below). This formalism is not rigorously followed and the use of Roman numerals to represent higher oxidation states is common. : ^IIIL_nsup>3+ vs. =M⁵⁺L_nsup>3+