In
chemistry,
crystallography, and
materials science, the coordination number, also called ligancy, of a central
atom
Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons.
Every solid, liquid, gas, ...
in a
molecule
A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and bioche ...
or
crystal
A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macro ...
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
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 elec ...
. This number is determined somewhat differently for molecules than for crystals.
For molecules and polyatomic ions the coordination number of an atom is determined by simply counting the other atoms to which it is bonded (by either single or multiple bonds).
For example,
3)2Cl2Br2">r(NH3)2Cl2Br2sup>− has Cr
3+ as its central cation, which has a coordination number of 6 and is described as ''hexacoordinate''. The common coordination numbers are 4, 6 and 8.
Molecules, polyatomic ions and coordination complexes
In chemistry, coordination number, defined originally in 1893 by
Alfred Werner, is the total number of neighbors of a central atom in a molecule or ion.
The concept is most commonly applied to
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. ...
es.
Simple and commonplace cases
The most common coordination number for ''d-''block
transition metal
In chemistry, a transition metal (or transition element) is a chemical element in the d-block of the periodic table (groups 3 to 12), though the elements of group 12 (and less often group 3) are sometimes excluded. They are the elements that ca ...
complexes is 6. The coordination number does not distinguish the geometry of such complexes, i.e. octahedral vs trigonal prismatic.
For transition metal complexes, coordination numbers range from 2 (e.g., Au
I in Ph
3PAuCl) to 9 (e.g., Re
VII in
9">eH9sup>2−). Metals in the ''f''-block (the
lanthanoids
The lanthanide () or lanthanoid () series of chemical elements comprises the 15 metallic chemical elements with atomic numbers 57–71, from lanthanum through lutetium. These elements, along with the chemically similar elements scandium and yttr ...
and
actinoids) can accommodate higher coordination number due to their greater ionic radii and availability of more orbitals for bonding. Coordination numbers of 8 to 12 are commonly observed for ''f''-block elements. For example, with
bidentate nitrate ions as ligands, Ce
IV and Th
IV form the 12-coordinate ions
3)6">e(NO3)6sup>2− (
ceric ammonium nitrate
Ceric ammonium nitrate (CAN) is the inorganic compound with the formula . This orange-red, water-soluble cerium salt is a specialised oxidizing agent in organic synthesis and a standard oxidant in quantitative analysis.
Preparation, properties, ...
) and
3)6">h(NO3)6sup>2−. When the surrounding ligands are much smaller than the central atom, even higher coordination numbers may be possible. One
computational chemistry study predicted a particularly stable ion composed of a central
lead
Lead is a chemical element with the symbol Pb (from the Latin ) and atomic number 82. It is a heavy metal that is denser than most common materials. Lead is soft and malleable, and also has a relatively low melting point. When freshly cu ...
ion coordinated with no fewer than 15 helium atoms. Among the
Frank–Kasper phases
Topologically close pack (TCP) phases, also known as Frank-Kasper (FK) phases, are one of the largest groups of intermetallic compounds, known for their complex crystallographic structure and physical properties. Owing to their combination of ...
, the packing of metallic atoms can give coordination numbers of up to 16. At the opposite extreme, steric shielding can give rise to unusually low coordination numbers. An extremely rare instance of a metal adopting a coordination number of 1 occurs in the
terphenyl
Terphenyls are a group of closely related aromatic hydrocarbons. Also known as diphenylbenzenes or triphenyls, they consist of a central benzene ring substituted with two phenyl groups. There are three substitution patterns: ''ortho''-terpheny ...
-based arylthallium(I) complex 2,6-Tipp
2C
6H
3Tl, where Tipp is the 2,4,6-triisopropylphenyl group.
Polyhapto ligands
Coordination numbers become ambiguous when dealing with polyhapto ligands.
For π-electron ligands such as the
cyclopentadienide
In chemistry, the cyclopentadienyl anion or cyclopentadienide is an aromatic species with a formula of and abbreviated as Cp−. It is formed from the deprotonation of the molecule cyclopentadiene.
Properties
The cyclopentadienyl anion i ...
ion
5H5">5H5sup>−,
alkene
In organic chemistry, an alkene is a hydrocarbon containing a carbon–carbon double bond.
Alkene is often used as synonym of olefin, that is, any hydrocarbon containing one or more double bonds.H. Stephen Stoker (2015): General, Organic, an ...
s and the
cyclooctatetraenide
1,3,5,7-Cyclooctatetraene (COT) is an unsaturated derivative of cyclooctane, with the formula C8H8. It is also known as nnulene. This polyunsaturated hydrocarbon is a colorless to light yellow flammable liquid at room temperature. Because of ...
ion
8H8">8H8sup>2−, the number of adjacent atoms in the π-electron system that bind to the central atom is termed the
hapticity
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 l ...
. In
ferrocene the hapticity, ''η'', of each cyclopentadienide anion is five, Fe(''η''
5-C
5H
5)
2. Various ways exist for assigning the contribution made to the coordination number of the central iron atom by each cyclopentadienide ligand. The contribution could be assigned as one since there is one ligand, or as five since there are five neighbouring atoms, or as three since there are three electron pairs involved. Normally the count of electron pairs is taken.
Surfaces and reconstruction
The coordination numbers are well defined for atoms in the interior of a
crystal lattice: one counts the nearest neighbors in all directions. The number of neighbors of an interior atom is termed the bulk coordination number. For surfaces, the number of neighbors is more limited, so the surface coordination number is smaller than the bulk coordination number. Often the surface coordination number is unknown or variable.
The surface coordination number is also dependent on the
Miller indices
Miller indices form a notation system in crystallography for lattice planes in crystal (Bravais) lattices.
In particular, a family of lattice planes of a given (direct) Bravais lattice is determined by three integers ''h'', ''k'', and '' ...
of the surface. In a
body-centered cubic (BCC) crystal, the bulk coordination number is 8, whereas, for the (100) surface, the surface coordination number is 4.
Case studies
A common way to determine the coordination number of an atom is by
X-ray crystallography
X-ray crystallography is the experimental science determining the atomic and molecular structure of a crystal, in which the crystalline structure causes a beam of incident X-rays to diffract into many specific directions. By measuring the angles ...
. Related techniques include
neutron
The neutron is a subatomic particle, symbol or , which has a neutral (not positive or negative) charge, and a mass slightly greater than that of a proton. Protons and neutrons constitute the nuclei of atoms. Since protons and neutrons beh ...
or
electron
The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family,
and are generally thought to be elementary particles because they have no ...
diffraction. The coordination number of an atom can be determined straightforwardly by counting nearest neighbors.
α-Aluminium has a regular cubic close packed structure,
fcc
The Federal Communications Commission (FCC) is an independent agency of the United States federal government that regulates communications by radio, television, wire, satellite, and cable across the United States. The FCC maintains jurisdictio ...
, where each aluminium atom has 12 nearest neighbors, 6 in the same plane and 3 above and below and the coordination polyhedron is a
cuboctahedron
A cuboctahedron is a polyhedron with 8 triangular faces and 6 square faces. A cuboctahedron has 12 identical vertices, with 2 triangles and 2 squares meeting at each, and 24 identical edges, each separating a triangle from a square. As such, it ...
. α-Iron has a
body centered cubic structure where each iron atom has 8 nearest neighbors situated at the corners of a cube.
The two most common
allotropes
Allotropy or allotropism () is the property of some chemical elements to exist in two or more different forms, in the same physical state, known as allotropes of the elements. Allotropes are different structural modifications of an element: th ...
of carbon have different coordination numbers. In
diamond
Diamond is a solid form of the element carbon with its atoms arranged in a crystal structure called diamond cubic. Another solid form of carbon known as graphite is the chemically stable form of carbon at room temperature and pressure, ...
, each carbon atom is at the centre of a regular
tetrahedron
In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners. The tetrahedron is the simplest of all th ...
formed by four other carbon atoms, the coordination number is four, as for methane.
Graphite
Graphite () is a crystalline form of the element carbon. It consists of stacked layers of graphene. Graphite occurs naturally and is the most stable form of carbon under standard conditions. Synthetic and natural graphite are consumed on lar ...
is made of two-dimensional layers in which each carbon is covalently bonded to three other carbons; atoms in other layers are further away and are not nearest neighbours, giving a coordination number of 3.
![NaCl polyhedra](https://upload.wikimedia.org/wikipedia/commons/c/c0/NaCl_polyhedra.png)
For chemical compounds with regular lattices such as
sodium chloride and
caesium chloride, a count of the nearest neighbors gives a good picture of the environment of the ions. In sodium chloride each sodium ion has 6 chloride ions as nearest neighbours (at 276 pm) at the corners of an
octahedron
In geometry, an octahedron (plural: octahedra, octahedrons) is a polyhedron with eight faces. The term is most commonly used to refer to the regular octahedron, a Platonic solid composed of eight equilateral triangles, four of which meet at ea ...
and each chloride ion has 6 sodium atoms (also at 276 pm) at the corners of an octahedron. In caesium chloride each caesium has 8 chloride ions (at 356 pm) situated at the corners of a
cube and each chloride has eight caesium ions (also at 356 pm) at the corners of a cube.
Complications
In some compounds the metal-ligand bonds may not all be at the same distance. For example in PbCl
2, the coordination number of Pb
2+ could be said to be seven or nine, depending on which chlorides are assigned as ligands. Seven chloride ligands have Pb-Cl distances of 280–309 pm. Two chloride ligands are more distant, with a Pb-Cl distances of 370 pm.
In some cases a different definition of coordination number is used that includes atoms at a greater distance than the nearest neighbours. The very broad definition adopted by the
International Union of Crystallography
The International Union of Crystallography (IUCr) is an organisation devoted to the international promotion and coordination of the science of crystallography. The IUCr is a member of the International Council for Science (ICSU).
Objectives
T ...
, IUCR, states that the coordination number of an atom in a crystalline solid depends on the chemical bonding model and the way in which the coordination number is calculated.
Some metals have irregular structures. For example, zinc has a distorted hexagonal close packed structure. Regular hexagonal close packing of spheres would predict that each atom has 12 nearest neighbours and a
triangular orthobicupola
In geometry, the triangular orthobicupola is one of the Johnson solids (). As the name suggests, it can be constructed by attaching two triangular cupolas () along their bases. It has an equal number of squares and triangles at each vertex; howev ...
(also called an anticuboctahedron or twinned cuboctahedron) coordination polyhedron.
In zinc there are only 6 nearest neighbours at 266 pm in the same close packed plane with six other, next-nearest neighbours, equidistant, three in each of the close packed planes above and below at 291 pm. It is considered to be reasonable to describe the coordination number as 12 rather than 6.
Similar considerations can be applied to the regular body centred cube structure where in addition to the 8 nearest neighbors there 6 more, approximately 15% more distant,
and in this case the coordination number is often considered to be 14.
![Strukturformel Nickelarsenid](https://upload.wikimedia.org/wikipedia/commons/e/e8/Strukturformel_Nickelarsenid.png)
Many chemical compounds have distorted structures.
Nickel arsenide
Nickeline or niccolite is a mineral consisting primarily of nickel arsenide (NiAs). The naturally-occurring mineral contains roughly 43.9% nickel and 56.1% arsenic by mass, but composition of the mineral may vary slightly.
Small quantities of ...
, NiAs has a structure where nickel and arsenic atoms are 6-coordinate. Unlike sodium chloride where the chloride ions are cubic close packed, the arsenic anions are hexagonal close packed. The nickel ions are 6-coordinate with a distorted octahedral coordination polyhedron where columns of octahedra share opposite faces. The arsenic ions are not octahedrally coordinated but have a trigonal prismatic coordination polyhedron. A consequence of this arrangement is that the nickel atoms are rather close to each other. Other compounds that share this structure, or a closely related one are some transition metal sulfides such as
FeS
Fez or Fes (; ar, فاس, fās; zgh, ⴼⵉⵣⴰⵣ, fizaz; french: Fès) is a city in northern inland Morocco and the capital of the Fès-Meknès administrative region. It is the second largest city in Morocco, with a population of 1.11 mi ...
and
CoS, as well as some intermetallics. In
cobalt(II) telluride, CoTe, the six tellurium and two cobalt atoms are all equidistant from the central Co atom.
![Haematite-unit-cell-3D-balls](https://upload.wikimedia.org/wikipedia/commons/1/10/Haematite-unit-cell-3D-balls.png)
Two other examples of commonly-encountered chemicals are
Fe2O3 and
TiO2. Fe
2O
3 has a crystal structure that can be described as having a near close packed array of oxygen atoms with iron atoms filling two thirds of the octahedral holes. However each iron atom has 3 nearest neighbors and 3 others a little further away. The structure is quite complex, the oxygen atoms are coordinated to four iron atoms and the iron atoms in turn share vertices, edges and faces of the distorted octahedra.
TiO
2 has the
rutile
Rutile is an oxide mineral composed of titanium dioxide (TiO2), the most common natural form of TiO2. Rarer polymorphs of TiO2 are known, including anatase, akaogiite, and brookite.
Rutile has one of the highest refractive indices at visib ...
structure. The titanium atoms 6-coordinate, 2 atoms at 198.3 pm and 4 at 194.6 pm, in a slightly distorted octahedron. The octahedra around the titanium atoms share edges and vertices to form a 3-D network. The oxide ions are 3-coordinate in a
trigonal planar configuration.
Usage in quasicrystal, liquid and other disordered systems
The coordination number of systems with disorder cannot be precisely defined.
The first coordination number can be defined using the
radial distribution function
In statistical mechanics, the radial distribution function, (or pair correlation function) g(r) in a system of particles (atoms, molecules, colloids, etc.), describes how density varies as a function of distance from a reference particle.
If ...
''g''(''r''):
where ''r''
0 is the rightmost position starting from ''r'' = 0 whereon ''g''(''r'') is approximately zero, ''r''
1 is the first minimum. Therefore, it is the area under the first peak of ''g''(''r'').
The second coordination number is defined similarly:
Alternative definitions for the coordination number can be found in literature, but in essence the main idea is the same. One of those definition are as follows: Denoting the position of the first peak as ''r''
p,
The first coordination shell is the
spherical shell
In geometry, a spherical shell is a generalization of an annulus to three dimensions. It is the region of a ball between two concentric spheres of differing radii.
Volume
The volume of a spherical shell is the difference between the enclosed volum ...
with radius between ''r''
0 and ''r''
1 around the central particle under investigation.
References
External links
Meteorite Book-Glossary C
{{Authority control
Chemical bonding
Stereochemistry
Molecular geometry
Materials science
Coordination chemistry