Coordination chemistry

Coordination chemistry studies coordination complexes, including their ligands in coordination chemistry, structures and reactions.

Formation of a coordination complex through association of a central chemical atom or ion with donor groups. Different oxidation states can have different complex stabilities, coupling complexation to redox equilibrium.

The spatial arrangement of donor atoms around a central atom. coordination number counts neighbours but does not by itself distinguish geometries with the same number of donors.

A five-coordinate geometry with two axial and three equatorial positions. The ideal geometry has a threefold axis and an equatorial mirror plane.

A discrete molecular assembly in which metal–ligand connections surround a cavity. coordination number, preferred binding angles and ligand connectivity restrict possible cage stoichiometries.

A coordination complex that retains donor sites capable of binding additional metal ions. Distinguishable internal and external coordination sites permit hierarchical construction of heterometallic assemblies.

Transfer of an organic group from one element to a metal centre. A rhodium hydroxide and an arylboronic acid can exchange Rh-OH and B-Ar connectivity to form Rh-Ar and boric acid.

An orbital that contains an unpaired electron and dominates a center’s exchange interactions.

A complex in which a metal is bound between two cyclopentadienyl-type rings, commonly with hapticity ${\eta }^5$ at each ring. In ionic electron counting, each unsubstituted cyclopentadienyl anion donates six electrons.

The sandwich complex $\mathrm{Cr}({\eta }^5\text{-}{\mathrm{C}}_5{\mathrm{H}}_5{)}_2$, with a conventional 16-electron count.

A ferrocene analogue with a pyrrolyl ring replacing one cyclopentadienyl ring, $\mathrm{Fe}({\eta }^5-{\mathrm{C}}_5{\mathrm{H}}_5)({\eta }^5-{\mathrm{C}}_4{\mathrm{H}}_4\mathrm{N})$. Both anionic rings are six-electron donors.

The sandwich compound $\mathrm{Ni}({\eta }^5-{\mathrm{C}}_5{\mathrm{H}}_5{)}_2$, conventionally Ni(II), $d^8$, and 20-electron. The extra electrons relative to ferrocene occupy metal–ring antibonding orbitals.

The cation $[\mathrm{Co}({\eta }^5-{\mathrm{C}}_5{\mathrm{H}}_5{)}_2{]}^{+}$, conventionally Co(III), $d^6$, and 18-electron.

The neutral sandwich compound $\mathrm{Co}({\eta }^5-{\mathrm{C}}_5{\mathrm{H}}_5{)}_2$, conventionally Co(II), $d^7$, with 19 valence electrons. One-electron oxidation gives the 18-electron cobaltocenium cation.

The sandwich compound $\mathrm{Fe}({\eta }^5-{\mathrm{C}}_5{\mathrm{H}}_5{)}_2$, conventionally Fe(II), $d^6$, with 18 valence electrons.

A repeating structure in which metal centres are connected by bridging ligands. Its coordination connectivity can extend along one, two or three independent directions.

Interconversion between electronic forms that differ in the formal distribution of oxidation among metal and ligands, without changing overall composition. A cobalt dioxolene example exchanges low-spin Co(III)–catecholate–semiquinonate and high-spin Co(II)–bis(semiquinonate) forms. This differs from changing only the spin state at fixed metal and ligand charges.

The set of ligands directly associated with a metal centre in the stated structural model. Distinguish primary donor bonds from secondary contacts and outer-sphere ions or lattice solvent.

A ligand for which assigning an integer oxidation state separately from the metal can obscure substantial electron delocalization or accessible ligand-centred redox states.

Replacement of one coordinated ligand by another. Formal metal oxidation state need not change, even though local electron count can change while association or dissociation occurs.

A donor tethered to a complex captures a vacant coordination site created by coordination ligand loss. Its effective proximity can compete favourably with weakly coordinating bulk solvent, provided its geometry allows it to reach the metal.

Photoexcitation can dissociate a carbonyl ligand, creating a coordinatively unsaturated metal fragment. Capture by solvent or a tethered donor competes with CO recombination; net substitution therefore depends on both the photochemical step and subsequent trapping.

Substitution promoted by prior deprotonation of a coordinated ligand. In cobalt(III) ammine complexes, an amido donor can assist departure of another ligand; solvent capture and reprotonation complete the substitution.

Different distributions of water between the metal coordination sphere and lattice for the same overall composition. Geometrical isomers can occur within one hydration class.

The presence of distinguishable formal oxidation states of the same element in a compound. Formal localization need not imply complete physical localization of charge.

An octahedral platinum(IV) complex containing two chloride, two acetate and two neutral amine donors; its $d^6$ metal configuration is low spin. This article concerns its coordination chemistry.

The square-planar coordination compound cis-diamminedichloroplatinum(II), with Pt(II), a $d^8$ metal configuration and a 16-electron local valence count. This article concerns its coordination chemistry.

The Dewar-Chatt-Duncanson model describes an alkene–metal bond through donation from the filled alkene $\pi$ orbital to the metal and pi backbonding from the metal into alkene ${\pi }^{\ast }$. Backbonding weakens and lengthens the alkene double bond. A $d^0$ early-metal ion has little conventional $d$-electron backbonding.

A metal cluster contains several connected metal centers. A triangular three-metal cluster can support three edge metal-metal bonds; early-metal clusters often have stable counts below the 18-electron rule.

Chelation binds multiple donor sites of one ligand to the same central atom, forming a chelate ring. It can retain a donor near a metal even when one attachment temporarily opens.

A coordination ligand that coordinates one metal through three donor atoms. A facial tridentate donor set occupies the vertices of one face of an octahedron.

Enhanced complex stability associated with donor sites being held in a macrocycle, relative to comparable open-chain ligands. The comparison depends on donor geometry, solvation and strain.

The donor–metal–donor angle imposed by a chelating ligand. Tether length, ring conformation, donor distances and substituent crowding all influence it.

The chelate effect is the enhanced stability often associated with binding several donor sites from one ligand compared with comparable independent donors. Solvent release, effective local concentration and enthalpic contributions all matter; it is not simply a consequence of satisfying an electron-count rule.

A chelate ring is a closed bonded path containing the central atom and a ligand with multiple attachments to it. A tethered Cp–pyridyl ligand can close such a path when the pyridyl N coordinates.

The trans effect is a kinetic influence whereby a ligand accelerates substitution opposite itself, classically in square-planar complexes. It must be distinguished from ground-state bond weakening and from the carbonyl cis effect.

Electron counting records metal valence electrons plus ligand donations using a declared convention. In ionic counting, subtract metal oxidation state from its group number, then add donor electrons; in neutral counting, combine neutral metal and ligand fragments consistently. An Fe–Fe single bond contributes one electron to the count at each metal.

The 18-electron rule is a useful closed-shell guideline for many low-valent transition-metal complexes, filling nine valence orbitals. It is not universal: many early-metal $d^0$ complexes have fewer electrons, while stable square-planar $d^8$ complexes are often 16-electron.

A ligand field describes how ligands split and mix the central metal orbitals. Sigma donation, pi donation and pi backbonding explain trends that a purely electrostatic picture misses.

A parameter in a compact description of intra-atomic electron repulsion within a configuration. $B$ and $C$ control relative d-shell multiplet energies; $B$ is not the octahedral splitting or a rotational constant.

A plot of many-electron ligand-field term energies relative to the ground state against a normalized ligand-field strength. Axes commonly use $E/B$ and ${\Delta }_o/B$, with the ratio of other interelectronic parameters stipulated. A change of ground-state term can create a break in the plotted reference.

A model in which six donor orbitals of an octahedral complex form $a_{1g}+e_g+t_{1u}$ symmetry-adapted combinations. metal s, p and two d orbitals supply matching symmetry partners; the other three d orbitals remain nonbonding $t_{2g}$ orbitals. The model neglects ligand pi donation, backbonding and departures from octahedral symmetry.

The degeneracy-weighted mean energy of a specified group of orbitals, $\overline{\epsilon }={\sum }_i{g}_i{\epsilon }_i/{\sum }_i{g}_i$. Keeping it fixed separates level splitting from a common energy shift.

A qualitative d-orbital splitting in a square-planar environment, with the strongly in-plane antibonding $d_{x^2-y^2}$ orbital highest. Ordering among the remaining orbitals can depend on the ligand set.

The energetic cost assigned to pairing electrons in an orbital rather than placing them in distinct orbitals within a specified ligand-field model.

Spin crossover interconverts electronic states with different total spin, often in response to temperature. For octahedral iron(II), $t_{2g}^4{e}_g^2$ and $t_{2g}^6$ correspond to $S=2$ and $S=0$. Removing electrons from metal–ligand antibonding $e_g$ orbitals shortens bonds in the low-spin state. Crystal packing and hydrogen bonds can affect transition temperatures.

The electron pairing energy represents the energetic penalty for putting electrons into already occupied orbitals rather than suitable separate orbitals. A simple comparison with octahedral splitting explains high-spin and low-spin alternatives.

A high-spin complex retains more unpaired electrons when the energy required for pairing exceeds the relevant orbital splitting. An octahedral high-spin $d^6$ center has $t_{2g}^4{e}_g^2$ and $S=2$.

The Jahn-Teller effect is an instability of a nonlinear molecular arrangement with an orbitally degenerate electronic ground state toward a symmetry-lowering distortion. An octahedral high-spin $d^4$ ion has unequal occupation of its $e_g$ orbitals and often undergoes tetragonal elongation.

For a real nonmagnetic electronic multiplet, a vibrational coordinate can couple linearly through a real symmetric electronic operator only if its representation occurs in the symmetric square. Remove the fully symmetric component when asking about symmetry-lowering distortion. In $T_d$, both ${\mathrm{Sym}}^2{T}_1$ and ${\mathrm{Sym}}^2{T}_2$ equal $A_1+E+T_2$, so $E$ and $T_2$ modes are symmetry-eligible for either triplet; coupling strengths are not determined by this decomposition.

A symmetry-lowering change separating two axial metal–ligand distances from four equatorial ones. Occupancy of the split orbitals determines the electronic energy gain, while elastic cost and pre-existing ligand asymmetry affect the observed structure.

Crystal field theory models the effect of surrounding ligand charges or dipoles on metal atomic orbitals. Directional repulsion splits the $d$ levels. Unlike molecular orbital theory, the simplest model does not explicitly construct covalent metal–ligand bonds.

Separation of metal d-orbital energies by the electrostatic field of surrounding coordination ligands. An octahedral field puts the three $t_{2g}$ orbitals below the two $e_g$ orbitals.

In the ideal tetrahedral point-charge model, the five metal d orbitals split into a lower twofold $e$ set and an upper threefold $t_2$ set. Relative to their weighted barycentre their energies are $-3{\Delta }_t/5$ and $+2{\Delta }_t/5$, where ${\Delta }_t>0$ is the separation. For occupancies $e^{n_e}{t}_2^{n_t}$, the crystal field stabilization energy is $(-0.6n_e+0.4n_t){\Delta }_t$. Under weak-field high-spin filling it is $-0.6{\Delta }_t$, $-1.2{\Delta }_t$, $-0.8{\Delta }_t$ and zero for $d^6,d^7,d^8,d^{10}$ respectively. Shorter metal–ligand distances generally increase the splitting, so orbital filling can superimpose nonmonotonic bond-length changes on an ionic-size trend. The model alone does not determine an absolute bond length.

The change in d-electron energy relative to the unsplit barycentre in a crystal-field model, before separately accounting for pairing and other bonding contributions.

A low-spin complex has the smaller-spin occupancy favored when ligand-field splitting outweighs the cost of pairing electrons in the lower orbitals. An octahedral low-spin $d^6$ center has $t_{2g}^6{e}_g^0$ and total spin zero.

The spectrochemical series orders ligands empirically by the splitting they produce in comparable complexes. Pi-donor ligands tend toward smaller splittings and pi-acceptor ligands toward larger ones. Metal, geometry and oxidation state still matter; a sigma-basicity scale is not an interchangeable substitute.

In an ideal octahedral molecular geometry, the metal $d$ orbitals divide into lower $t_{2g}$ and higher $e_g$ sets. Their separation is ${\Delta }_o$. Whether electrons pair in the lower set depends on that separation relative to pairing costs; observed many-electron transition energies need not equal ${\Delta }_o$ exactly.

Linkage isomerism occurs when complexes have the same composition but an ambidentate ligand attaches through different atoms. N-bound and O-bound nitrite provide the classical example. This is a difference in attachment connectivity, rather than the different spatial arrangements of unchanged connectivity in stereoisomers.

Linkage isomerization changes which atom of an ambidentate ligand is bound to a central atom. Its rate depends on a reaction barrier, whereas the final equilibrium depends on relative free energies.

A linkage isomer is one member of a set exhibiting linkage isomerism, such as the N-bound or O-bound form of a coordinated nitrite.

A ligand in coordination chemistry is an atom, ion or molecule attached to a central atom through one or more donor sites. This use is distinct from a protein-binding ligand. A neutral CO ligand and an anionic chloride ligand can both donate two electrons in ionic electron counting.

Two linked pyrimidine rings; the 2,2′-linked isomer has two N,N donor pockets. It can bind one metal as a bidentate ligand, or bridge two metals by using one pocket at each end. In the latter mode it is a bis-bidentate bridging ligand.

A coordination ligand assigned a negative formal charge in ionic electron counting. Distinguish the assigned charge from its electron donation and from the actual distributed charge in the complex.

An axially chiral binaphthyl diphosphine ligand used in asymmetric transition-metal catalysis.

A commonly anionic N–C–N ligand with delocalized bonding. Substituents and denticity influence both steric protection and the geometry of supported metal centres.

The ligand $[\mathrm{ArNCHNAr}{]}^{-}$ in a common diaryl form. Three such bridges can support a lantern-type dimetal unit.

A bound $\mathrm{C}{\mathrm{N}}^{-}$ ligand, usually C-bound in the strongly pi-accepting coordination mode used in elementary spectrochemical comparisons. It is an anionic two-electron donor in ionic electron counting.

A silicon-bound $\mathrm{Si}{\mathrm{R}}_3^{-}$ group, normally a two-electron X-type donor in ionic electron counting.

A carbon-bound group $-\mathrm{C}(\mathrm{O})\mathrm{R}$, formally anionic and normally a two-electron donor in ionic electron counting. It differs from a neutral carbonyl ligand $\mathrm{CO}$.

A ligand with three donor sites arranged to bind one metal in a meridional pattern. The framework may impose a preferred geometry and may itself undergo redox or proton-transfer changes.

An intact ${\mathrm{N}}_2$ group coordinated to a metal. End-on neutral dinitrogen normally counts as a two-electron L-type donor; metal-to-ligand pi backbonding can weaken its N–N bond without making it a fully cleaved nitride.

The anion formed by N–H deprotonation of pyrrole. It can bind through nitrogen as a two-electron ${\eta }^1$ donor, or through its aromatic ring as a six-electron ${\eta }^5$ donor. Specifying hapticity is essential for electron counting.

A coordinated oxide, formally ${\mathrm{O}}^{2-}$. A terminal $\mathrm{M}=\mathrm{O}$ unit is conventionally counted as an $X_2$ ligand giving four electrons in ionic electron counting. Additional oxygen-to-metal pi donation is an orbital-bonding issue and must not be silently mixed with another counting convention.

A carboxylate bound through one or both oxygen atoms. It can be monodentate, chelating or bridging; its charge is $-1$ regardless of whether one or two oxygen donors bind.

An ortho-dioxygen aromatic framework that can bind through both oxygen atoms in several redox states. The semiquinonate monoanion has a ligand-centred unpaired electron, whereas the catecholate dianion has a filled-shell configuration. non-innocent ligand behaviour means metal oxidation state cannot be inferred from an overall complex charge without specifying the ligand redox state.

A free radical monoanion intermediate in redox state between a quinone and a catecholate; an isolated ligand has spin $S=1/2$. Its spin may couple to a metal spin in a complex.

The dianionic, closed-shell O,O donor obtained by two deprotonations of catechol.

A bidentate ligand binds a metal through two donor atoms. Simultaneous attachment can produce a chelate ring; the two donor atoms need not be the same element.

The number of donor atoms from one ligand in coordination chemistry bonded to a particular metal centre. Unlike hapticity, it counts distinct donor sites rather than a contiguous bonded fragment.

A metal-bound methyl group, formally CH3-minus in ionic electron counting; it is commonly an X-type ligand.

The anion ${\mathrm{C}}_3{\mathrm{H}}_3{\mathrm{N}}_2^{-}$ formed from pyrazole. Bridging through both nitrogen atoms supplies four ligand electrons overall in ionic counting, or three in neutral counting.

Coordinated NO is non-innocent. Conventional neutral counting assigns three electrons to a terminal linear NO, one to a terminal bent NO, and three in total to a simple doubly bridging NO.

A bent M–N–O mode conventionally represented as $\mathrm{N}{\mathrm{O}}^{-}$, a two-electron ionic donor and a one-electron neutral donor. These are formal bookkeeping limits rather than measured atomic charges.

A near-linear M–N–O coordination mode conventionally represented as $\mathrm{N}{\mathrm{O}}^{+}$, a two-electron donor in ionic counting and a three-electron donor in neutral counting.

A nitrosyl shared between metal centres. In the simple mu2 counting model it contributes three electrons overall in the neutral method, or can be represented as an $\mathrm{N}{\mathrm{O}}^{-}$ donor of four electrons overall in ionic counting.

An oxygen-bound anionic ligand derived formally by removing a proton from an alcohol; it is normally X-type in electron counting.

An alkyne bound through its pi system. The neutral two-electron donor picture and a reduced metallacyclic picture emphasize different limits of the same bonding interaction.

A coordinated aryne. Strong metal-to-aryne electron transfer can make a dianionic metallacyclopropene description more useful than an unreduced neutral alkyne description.

A ligand attached through an alkene carbon, commonly an X-type ligand in electron counting.

A ligand attached to a metal through an aromatic carbon, commonly counted as an X-type ligand with charge minus one in ionic bookkeeping.

A bromide ligand is coordinated $\mathrm{B}{\mathrm{r}}^{-}$, conventionally an anionic two-electron donor in ionic electron counting.

A boryl ligand attaches through boron as an X-type ligand. In ionic electron counting it is formally anionic and contributes two electrons. It is distinct from a neutral borylene and from attachment to an entire borazine pi face.

An alkene ligand commonly binds through both double-bond carbons, ${\eta }^2$. The balance of donation and backbonding is described by the Dewar-Chatt-Duncanson model.

A phosphite ligand such as $\mathrm{P}(\mathrm{OR}{)}_3$ binds through a phosphorus lone pair and can accept pi backbonding. Its donation and acceptance differ from those of both phosphine ligands and carbonyl ligands.

Hapticity, written ${\eta }^n$, specifies the number of contiguous ligand atoms involved in attachment to a metal. It differs from denticity, which counts donor sites in a chelate.

A change in the number of adjacent ring atoms coordinating a metal, such as ${\eta }^5\to {\eta }^3$. It changes the coordination ligand donation and can open a site without loss of the entire ring coordination ligand.

An allyl ligand can bind as ${\eta }^3$ ${\mathrm{C}}_3{\mathrm{H}}_5^{-}$, donating four electrons in ionic electron counting. Protonation can release an alkene and make coordination sites available.

The cyclopentadienyl ligand is based on ${\mathrm{C}}_5{\mathrm{H}}_5^{-}$. In its common ${\eta }^5$ mode it binds through five ring carbons and donates six electrons in ionic electron counting. Ring substitution can create distinct NMR environments.

The five ring p orbitals form one nondegenerate and two doubly degenerate symmetry-adapted sets. About the ring normal, these match metal $d_{z^2}$, $(d_{xz},d_{yz})$, and $(d_{xy},d_{x^2-y^2})$ by sigma, pi and delta symmetry respectively. Matching symmetry permits interaction, but spatial overlap and energy separation determine its strength.