Coordination geometry

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The term coordination geometry is used in a number of related fields of chemistry and solid state chemistry/physics.



The coordination geometry of an atom is the geometrical pattern formed by atoms around the central atom.

Inorganic coordination complexes

In the field of inorganic coordination complexes it is the geometrical pattern formed by the atoms in the ligands that are bonded to the central atom in a molecule or a coordination complex. The geometrical arrangement will vary according to the number and type of ligands bonded to the metal centre, and to the coordination preference of the central atom, typically a metal in a coordination complex. The number of atoms bonded, (i.e. the number of σ-bonds between central atom and ligands) is termed the coordination number. The geometrical pattern can be described as a polyhedron where the vertices of the polyhedron are the centres of the coordinating atoms in the ligands. [1]

The coordination preference of a metal often varies with its oxidation state. The number of coordination bonds (coordination number) can vary from two as high as 20 in Th(η5-C5H5)4. [2]

One of the most common coordination geometries is octahedral, where six ligands are coordinated to the metal in a symmetrical distribution, leading to the formation of an octahedron if lines were drawn between the ligands. Other common coordination geometries are tetrahedral and square planar.

Crystal field theory may be used to explain the relative stabilities of transition metal compounds of different coordination geometry, as well as the presence or absence of paramagnetism, whereas VSEPR may be used for complexes of main group element to predict geometry.

Crystallography usage

In a crystal structure the coordination geometry of an atom is the geometrical pattern of coordinating atoms where the definition of coordinating atoms depends on the bonding model used. [1] For example, in the rock salt ionic structure each sodium atom has six near neighbour chloride ions in an octahedral geometry and each chloride has similarly six near neighbour sodium ions in an octahedral geometry. In metals with the body centred cubic (bcc) structure each atom has eight nearest neighbours in a cubic geometry. In metals with the face centred cubic (fcc) structure each atom has twelve nearest neighbours in a cuboctahedral geometry.

Table of coordination geometries

A table of the coordination geometries encountered is shown below with examples of their occurrence in complexes found as discrete units in compounds and coordination spheres around atoms in crystals (where there is no discrete complex).

Coordination numberGeometryExamples of discrete (finite) complexExamples in crystals (infinite solids)
2 linear Linear-3D-balls.png Ag(CN)2 in KAg(CN)2 [3] Ag in silver cyanide,
Au in AuI [2]
3 trigonal planar Trigonal-3D-balls.png HgI3 [2] O in TiO2 rutile structure [3]
4 tetrahedral Tetrahedral-3D-balls.png CoCl42− [2] Zn and S in zinc sulfide, Si in silicon dioxide [3]
4 square planar Square-planar-3D-balls.png AgF4 [2] CuO [3]
5 trigonal bipyramidal Trigonal-bipyramidal-3D-balls.png SnCl5 [3]
5 square pyramidal Square-pyramidal-3D-balls.png InCl52− in (NEt4)2InCl5 [2]
6 octahedral Octahedral-3D-balls.png Fe(H2O)62+ [2] Na and Cl in NaCl [3]
6 trigonal prismatic Prismatic TrigonalP.png W(CH3)6 [4] As in NiAs, Mo in MoS2 [3]
7 pentagonal bipyramidal Pentagonal-bipyramidal-3D-balls.png ZrF73− in (NH4)3ZrF7 [3] Pa in PaCl5
7 capped octahedral Face-capped octahedron.png MoF7 [5] La in A-La2O3
7 capped trigonal prismatic MonocappTrigPrism.CapRightps.png TaF72− in K2TaF7 [3]
8 square antiprismatic Square-antiprismatic-3D-balls.png TaF83− in Na3TaF8 [3]
Zr(H2O)84+ aqua complex [6]
Thorium(IV) iodide [3]
8 dodecahedral
(note: whilst this is the term generally
used, the correct term is "bisdisphenoid" [3]
or "snub disphenoid" as this polyhedron is a deltahedron)
Snub disphenoid.png Mo(CN)84− in K4[Mo(CN)8].2H2O [3] Zr in K2ZrF6 [3]
8 bicapped trigonal prismatic Square face bicapped trigonal prism.png ZrF84− [7] PuBr3 [3]
8 cubic Caesium chloride, calcium fluoride
8 hexagonal bipyramidal Hexagonale bipiramide.png N in Li3N [3]
8octahedral, trans-bicappedNi in nickel arsenide, NiAs; 6 As neighbours + 2 Ni capping [8]
8trigonal prismatic, triangular face bicappedCa in CaFe2O4 [3]
9 tricapped trigonal prismatic AX9E0-3D-balls.png [ReH9]2− in potassium nonahydridorhenate [2]
Th(H2O)94+ aqua complex [6]
SrCl2.6H2O, Th in RbTh3F13 [3]
9 capped square antiprismatic Monocapped square antiprism.png [Th(tropolonate)4(H2O)] [2] La in LaTe2 [3]
10bicapped square antiprismaticTh(C2O4)42− [2]
11Th in [ThIV(NO3)4(H2O)3] (NO3 is bidentate) [2]
12 icosahedron Icosahedron.png Th in Th(NO3)62− ion in Mg[Th(NO3)6].8H2O [3]
12 cuboctahedron Cuboctahedron.png ZrIV3−(BH4)4)atoms in fcc metals e.g. Ca [3]
12anticuboctahedron (triangular orthobicupola) Triangular orthobicupola.png atoms in hcp metals e.g. Sc [3]
12bicapped hexagonal antiprismatic U(BH4)4 [2]

Naming of inorganic compounds

IUPAC have introduced the polyhedral symbol as part of their IUPAC nomenclature of inorganic chemistry 2005 recommendations to describe the geometry around an atom in a compound. [9]
IUCr have proposed a symbol which is shown as a superscript in square brackets in the chemical formula. For example, CaF2 would be Ca[8cb]F2[4t], where [8cb] means cubic coordination and [4t] means tetrahedral. The equivalent symbols in IUPAC are CU−8 and T−4 respectively. [1]
The IUPAC symbol is applicable to complexes and molecules whereas the IUCr proposal applies to crystalline solids.

See also

Related Research Articles

Coordination complex Molecule or ion containing ligands datively bonded to a central metallic atom

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 metal-containing compounds, especially those that include transition metals, are coordination complexes.

<i>Cis</i>–<i>trans</i> isomerism Pairs of molecules with same chemical formula showing different spatial orientations

Cistrans isomerism, also known as geometric isomerism or configurational isomerism, is a term used in chemistry that concerns the spatial arrangement of atoms within molecules. The prefixes "cis" and "trans" are from Latin: "this side of" and "the other side of", respectively. In the context of chemistry, cis indicates that the functional groups (substituents) are on the same side of some plane, while trans conveys that they are on opposing (transverse) sides. Cistrans isomers are stereoisomers, that is, pairs of molecules which have the same formula but whose functional groups are in different orientations in three-dimensional space. Cis-trans notation does not always correspond to EZ isomerism, which is an absolute stereochemical description. In general, cistrans stereoisomers contain double bonds that do not rotate, or they may contain ring structures, where the rotation of bonds is restricted or prevented. Cis and trans isomers occur both in organic molecules and in inorganic coordination complexes. Cis and trans descriptors are not used for cases of conformational isomerism where the two geometric forms easily interconvert, such as most open-chain single-bonded structures; instead, the terms "syn" and "anti" are used.

Inorganic chemistry deals with synthesis and behavior of inorganic and organometallic compounds. This field covers chemical compounds that are not carbon-based, which are the subjects of organic chemistry. The distinction between the two disciplines is far from absolute, as there is much overlap in the subdiscipline of organometallic chemistry. It has applications in every aspect of the chemical industry, including catalysis, materials science, pigments, surfactants, coatings, medications, fuels, and agriculture.

Ligand Chelating or binding agent

In coordination chemistry, a ligand is an ion or molecule that binds to a central atom to form a coordination complex. The bonding with the metal generally involves formal donation of one or more of the ligand's electron pairs often through Lewis Bases. 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 to involve Lewis acidic "ligands".

Stereocenter particular instance of a stereogenic element that is geometrically a point

In a molecule, stereogenic element is an atom (center), axis or plane that is focus of stereoisomerism, that is, having at least two different groups bound, interchanging any two different groups would create a stereoisomer.

VSEPR theory Theoretical model used in chemistry

Valence shell electron pair repulsion theory, or VSEPR theory, is a model used in chemistry to predict the geometry of individual molecules from the number of electron pairs surrounding their central atoms. It is also named the Gillespie-Nyholm theory after its two main developers, Ronald Gillespie and Ronald Nyholm.

Isolobal principle

The isolobal principle is a strategy used in organometallic chemistry to relate the structure of organic and inorganic molecular fragments in order to predict bonding properties of organometallic compounds. Roald Hoffmann described molecular fragments as isolobal "if the number, symmetry properties, approximate energy and shape of the frontier orbitals and the number of electrons in them are similar – not identical, but similar." One can predict the bonding and reactivity of a lesser-known species from that of a better-known species if the two molecular fragments have similar frontier orbitals, the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). Isolobal compounds are analogues to isoelectronic compounds that share the same number of valence electrons and structure. A graphic representation of isolobal structures, with the isolobal pairs connected through a double-headed arrow with half an orbital below, is found in Figure 1.

Trigonal bipyramidal molecular geometry

In chemistry, a trigonal bipyramid formation is a molecular geometry with one atom at the center and 5 more atoms at the corners of a triangular bipyramid. This is one geometry for which the bond angles surrounding the central atom are not identical (see also pentagonal bipyramid), because there is no geometrical arrangement with five terminal atoms in equivalent positions. Examples of this molecular geometry are phosphorus pentafluoride (PF5), and phosphorus pentachloride (PCl5) in the gas phase.

Octahedral molecular geometry Molecular geometry

In chemistry, octahedral molecular geometry describes the shape of compounds with six atoms or groups of atoms or ligands symmetrically arranged around a central atom, defining the vertices of an octahedron. The octahedron has eight faces, hence the prefix octa. The octahedron is one of the Platonic solids, although octahedral molecules typically have an atom in their centre and no bonds between the ligand atoms. A perfect octahedron belongs to the point group Oh. Examples of octahedral compounds are sulfur hexafluoride SF6 and molybdenum hexacarbonyl Mo(CO)6. The term "octahedral" is used somewhat loosely by chemists, focusing on the geometry of the bonds to the central atom and not considering differences among the ligands themselves. For example, [Co(NH3)6]3+, which is not octahedral in the mathematical sense due to the orientation of the N−H bonds, is referred to as octahedral.

Square planar molecular geometry

The square planar molecular geometry in chemistry describes the stereochemistry that is adopted by certain chemical compounds. As the name suggests, molecules of this geometry have their atoms positioned at the corners.

Coordination polymer Polymer consisting of repeating units of a coordination complex

A coordination polymer is an inorganic or organometallic polymer structure containing metal cation centers linked by ligands. More formally a coordination polymer is a coordination compound with repeating coordination entities extending in 1, 2, or 3 dimensions.


Hapticity is the coordination of a ligand to a metal center via an uninterrupted and contiguous series of atoms. The hapticity of a ligand is described with the Greek letter η ('eta'). For example, η2 describes a ligand that coordinates through 2 contiguous atoms. In general the η-notation only applies when multiple atoms are coordinated. In addition, if the ligand coordinates through multiple atoms that are not contiguous then this is considered denticity, and the κ-notation is used once again. When naming complexes care should be taken not to confuse η with μ ('mu'), which relates to bridging ligands.

In chemistry, crystallography, and materials science, the coordination number, also called ligancy, of a central atom in a molecule or crystal is the number of atoms, molecules or ions bonded to it. The ion/molecule/atom surrounding the central ion/molecule/atom is called a ligand. This number is determined somewhat differently for molecules than for crystals.

Pentagonal bipyramidal molecular geometry

In chemistry, a pentagonal bipyramid is a molecular geometry with one atom at the centre with seven ligands at the corners of a pentagonal bipyramid. A perfect pentagonal bipyramid belongs to the molecular point group D5h.

T-shaped molecular geometry Type of molecular geometry

In chemistry, T-shaped molecular geometry describes the structures of some molecules where a central atom has three ligands. Ordinarily, three-coordinated compounds adopt trigonal planar or pyramidal geometries. Examples of T-shaped molecules are the halogen trifluorides, such as ClF3.

Nomenclature of Inorganic Chemistry, IUPAC Recommendations 2005 is the 2005 version of Nomenclature of Inorganic Chemistry. It is a collection of rules for naming inorganic compounds, as recommended by the International Union of Pure and Applied Chemistry (IUPAC).


Denticity refers to the number of donor groups in a single ligand that bind to a central atom in a coordination complex. In many cases, only one atom in the ligand binds to the metal, so the denticity equals one, and the ligand is said to be monodentate. Ligands with more than one bonded atom are called polydentate or multidentate. The word denticity is derived from dentis, the Latin word for tooth. The ligand is thought of as biting the metal at one or more linkage points. The denticity of a ligand is described with the Greek letter κ ('kappa'). For example, κ6-EDTA describes an EDTA ligand that coordinates through 6 non-contiguous atoms.

Compounds of zinc are chemical compounds containing the element zinc which is a member of the group 12 of the periodic table. The oxidation state of most compounds is the group oxidation state of +2. Zinc may be classified as a post-transition main group element with zinc(II). Zinc compounds are noteworthy for their nondescript behavior, they are generally colorless, do not readily engage in redox reactions, and generally adopt symmetrical structures.

Capped octahedral molecular geometry

In chemistry, the capped octahedral molecular geometry describes the shape of compounds where seven atoms or groups of atoms or ligands are arranged around a central atom defining the vertices of a gyroelongated triangular pyramid. This shape has C3v symmetry and is one of the three common shapes for heptacoordinate transition metal complexes, along with the pentagonal bipyramid and the capped trigonal prism.

Capped trigonal prismatic molecular geometry

In chemistry, the capped trigonal prismatic molecular geometry describes the shape of compounds where seven atoms or groups of atoms or ligands are arranged around a central atom defining the vertices of an augmented triangular prism. This shape has C2v symmetry and is one of the three common shapes for heptacoordinate transition metal complexes, along with the pentagonal bipyramid and the capped octahedron.


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