Coordination geometry

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The coordination geometry of an atom is the geometrical pattern defined by the atoms around the central atom. The term is commonly applied in the field of inorganic chemistry, where diverse structures are observed. The coodination geometry depends on the number, not the type, of ligands bonded to the metal centre as well as their locations. The number of atoms bonded is 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 in K[Ag(CN)2] 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 K[Ag(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 [CoCl4]2− [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 [InCl5]2− in [N(CH2CH3)4]2[InCl5] [2]
6 octahedral Octahedral-3D-balls.png [Fe(H2O)6]2+ [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 [ZrF7]3− in [NH4]3[ZrF7] [3] Pa in PaCl5
7 capped octahedral Face-capped octahedron.png [MoF7] [5] La in A-La2O3
7 capped trigonal prismatic MonocappTrigPrism.CapRightps.png [TaF7]2− in K2[TaF7] [3]
8 square antiprismatic Square-antiprismatic-3D-balls.png [TaF8]3− in Na3[TaF8] [3]
[Zr(H2O)8]4+ 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)8]4− in K4[Mo(CN)8]·2H2O [3] Zr in K2[ZrF6] [3]
8 bicapped trigonal prismatic Square face bicapped trigonal prism.png [ZrF8]4− [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)9]4+ aqua complex [6]
SrCl2·6H2O, Th in Rb[Th3F13] [3]
9 capped square antiprismatic Monocapped square antiprism.png [Th(tropolonate)4(H2O)] [2] [ clarification needed ]La in LaTe2 [3]
10bicapped square antiprismatic[Th(C2O4)4]2− [2]
11Th in [ThIV(NO3)4(H2O)3] (NO3 is bidentate) [2]
12 icosahedron Icosahedron.png Th in [Th(NO3)6]2− ion in Mg[Th(NO3)6]·8H2O [3]
12 cuboctahedron Cuboctahedron.png ZrIV(η3-[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

<span class="mw-page-title-main">Coordination complex</span> Molecule or ion containing ligands datively bonded to a central metallic atom

A coordination complex is a chemical compound consisting 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.

<span class="mw-page-title-main">Ligand</span> Ion or molecule that binds to a central metal atom to form a coordination complex

In coordination chemistry, a ligand is an ion or molecule with a 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 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".

<span class="mw-page-title-main">VSEPR theory</span> Model for predicting molecular geometry

Valence shell electron pair repulsion (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.

In molecular physics, crystal field theory (CFT) describes the breaking of degeneracies of electron orbital states, usually d or f orbitals, due to a static electric field produced by a surrounding charge distribution. This theory has been used to describe various spectroscopies of transition metal coordination complexes, in particular optical spectra (colors). CFT successfully accounts for some magnetic properties, colors, hydration enthalpies, and spinel structures of transition metal complexes, but it does not attempt to describe bonding. CFT was developed by physicists Hans Bethe and John Hasbrouck van Vleck in the 1930s. CFT was subsequently combined with molecular orbital theory to form the more realistic and complex ligand field theory (LFT), which delivers insight into the process of chemical bonding in transition metal complexes. CFT can be complicated further by breaking assumptions made of relative metal and ligand orbital energies, requiring the use of inverted ligand field theory (ILFT) to better describe bonding.

<span class="mw-page-title-main">Isolobal principle</span> Method of predicting the bonding properties of certain organometallic compounds

In organometallic chemistry, the isolobal principle is a strategy used 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.

<span class="mw-page-title-main">Octahedral molecular geometry</span> Molecular geometry

In chemistry, octahedral molecular geometry, also called square bipyramidal, 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.

Octahedral clusters are inorganic or organometallic cluster compounds composed of six metals in an octahedral array. Many types of compounds are known, but all are synthetic.

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<span class="mw-page-title-main">Hapticity</span> Number of contiguous atoms in a ligand that bond to the central atom in a coordination complex

In coordination chemistry, 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.

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<span class="mw-page-title-main">Pentagonal bipyramidal molecular geometry</span> Molecular structure having atoms at the centre and corners of a pentagonal bipyramid

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<span class="mw-page-title-main">Denticity</span> Number of atoms in a ligand that bond to the central atom of a coordination complex

In coordination chemistry, denticity refers to the number of donor groups in a given ligand that bind to the central metal 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 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.

The d electron count or number of d electrons 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 reactivity of transition metal complexes. The formalism has been incorporated into the two major models used to describe coordination complexes; crystal field theory and ligand field theory, which is a more advanced version based on molecular orbital theory. However the d electron count of an atom in a complex is often different from the d electron count of a free atom or a free ion of the same element.

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<span class="mw-page-title-main">Square antiprismatic molecular geometry</span>

In chemistry, the square antiprismatic molecular geometry describes the shape of compounds where eight atoms, groups of atoms, or ligands are arranged around a central atom, defining the vertices of a square antiprism. This shape has D4d symmetry and is one of the three common shapes for octacoordinate transition metal complexes, along with the dodecahedron and the bicapped trigonal prism.

<span class="mw-page-title-main">Capped octahedral molecular geometry</span>

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.

<span class="mw-page-title-main">Capped trigonal prismatic molecular geometry</span>

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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