Coordination number

In solid-state physics and chemistry, the coordination number of an atom in a chemical compound is the number of atoms directly attached to it. For example, in methane the coordination number of the carbon atom is 4.

In organic chemistry, the coordination number, which is represented by the Greek letters sigma (σ) or delta (δ) with a superscript, and is applied to the case of organometallic compounds, is the number of atoms to which the central atom is directly bonded, or the number of σ bonds in the central atom,

In materials science and solid-state chemistry, the coordination number (NC) is the number of neighbors that are in direct contact with a particular atom or ion in a lattice or structure crystalline.

In inorganic chemistry the coordination number is the number of atoms, ions or molecules that a central atom or ion maintains as its nearest neighbors in a coordination complex or a crystal. It can range from 2 to 12, with 6 being the most common. We can also define the coordination number as the number of electron pairs that a Lewis acid accepts (usually a metal center), that is, if a coordination compound has two species that are donating pairs of electrons, then it will have a number coordination number 2. The coordination number of a complex is influenced by the relative sizes of the metal ion and the ligands, as well as electronic factors, which will change depending on the electronic configuration of the metal ion.

Depending on the ratio of radius it can be observed that the higher the charge of the metal ion, the more attraction there will be towards negatively charged ligands, however at the same time, the higher the charge the smaller the ion becomes, which then it limits the number of groups with which it can coordinate. It is important to recognize that each geometry has a specific coordination number, but each complex with a certain coordination number will have different geometric options to choose from.

The factors that determine the coordination number are:

• The size of the atom or central ion
• The aesthetic (size) interactions between the ligands
• Electronic interactions (cargo density transferred from metal ligands)

Low coordination numbers

They are those compounds whose metal center is attached to one, two or three ligands.

Coordination number 1

They are just organometallic compounds with highly hindered ligands. They are found in the gas phase at high temperatures, but are rare under ordinary circumstances. Two elements that make organometallic compounds with coordination number 1 are Cu(I) and Ag(I).

Coordination number 2

They are elements of groups 11 and 12 with configuration d¹⁰ such as Cu(I), Ag (I), Au(I), Hg(I). Elements with this coordination number are rare, although at high temperatures they are in the gas phase. Some examples include [CuCl₂]^-, [Ag(NH ₃)₂]⁺, [Au(CN)₂]^-, (R₃P)AuCl (where R is an alkyl or aryl group), in each of which the metal center is in a linear neighborhood.

Coordination number 3

3 coordination complexes are not very common. Trigonal-planar structures are commonly seen and examples with d¹⁰ metal centers include:

• [Fe(N(SiMe)₃)₂)₃]
• [Cu(CN)₃]^2-
• [AgTe₇]^3-
• [HgI₃]^-
• [Pt(PPh)₃)₃]

Coordination number 4

The most common structures with compounds with this coordination number are tetrahedral and square-planar, with the tetrahedron being the most frequently observed structure.

Tetrahedron

The tetrahedron is sometimes “flattened” and the distortions are attributed to steric or crystal packing effects, in some cases to electronic effects. Simple tetrahedral species include

• [MnO]₄]^-
• [NiCl₄]^2-
• [FeCl₄]^2-
• [ZnCl₄]^2-
• [Cu(CN)₄]^3-

Square-flat

These complexes are rarer than tetrahedral complexes and are often associated with d8 configurations in which electronic factors strongly favor a square-planar arrangement. As an example we can mention

• [PdCl₄]^2-
• [PtCl₄]^2-
• [AuCl₄]^-
• [AuBr₄]^2-
• [RhCl(PPh)₃)₃]

Coordination number 5

The limiting structures for coordination number 5 are the trigonal dipyramid and the square-based pyramid. The energy difference between both structures is very low. In fact many molecules with five ligands either have one of these two structures or can switch from one to the other very easily. Among the simple complexes with 5-coordination and bipyramidal-trigonal structure are:

• [CdCl₅]^3-
• [CuCl₅]^3-
• [HgCl₅]³-

Some complexes with a square-based pyramid structure are:

• [NbCl₄(O)]^-
• [V(acac)₂O]
• [WCl₄(O)]^-

Coordination number 6

Six is the most common coordination number. The most common structure is the octahedral, however trigonal prisms are also known. Compounds with this coordination number arise from transition metals with d⁸ and d¹⁰ configurations.

Octahedrons

If a metal ion is large enough to allow six ligands around it and the d-shell electrons are ignored, it turns out this type of geometry is the most common for first row transition metals, including aqua ions. In some cases some tetragonal distortions are observed for d⁴ and d⁹ metal ions, which can be explained in terms of the Jahn Teller effect.

Some examples of this type of geometries are:

• [Co(en)₃)]³⁺

• [Co(NO)₂) ₆]^3-

Trigonal prism

Most compounds with this structure have three bidentate ligands. This geometry occurs when two triangular faces are eclipsed, such as:

• [ReMe₆]

• [TaMe₆]^-

• [ZrMe₆]^2-

Coordination number 7

Not a very common number for first row transition metal complexes. The energy difference between the structures is small so distortions can occur to stabilize them. Distortions can make it difficult to determine the geometry of compounds. Coordination numbers equal to and greater than 7 are more frequently observed in ions of the first metals of the second and third rows of the d block and for the lanthanides and actinides.

In capped forms, the seventh ligand is simply added to the face of the structure, with appropriate adjustments to the rest of the angles so that they all fit. Although not a very common coordination number, three geometric shapes have been found, with differences apparently resulting from the different counterions and the steric requirements of the ligands. The three possible geometric shapes are: pentagonal dipyramid, covered trigonal prism, covered octahedron.

Coordination number 8

As the number of vertices of a polyhedron increases, so does the number of possible structures. Possibly the best known polyhedron with eight vertices is the cube, but it is hardly observed as an arrangement of the donor atoms in a complex. The few examples that exist include the anions of the actinide complexes Na₃[PaF₈], Na₃[UF₈]. The steric hindrance between ligands can be reduced by converting a cubic arrangement to a square antiprismatic one, that is, going from eclipsed squares to rotated squares. They are mainly composed of heavy metals from groups 4 to 6 in the +4 or +5 oxidation state. It can have geometric shapes of square antiprism, dodecahedron and hexagonal dipyramid.

Large coordination numbers

Coordination numbers up to 16 are known, however those greater than 8 are very rare to find. Currently available data indicate that higher coordination is limited to f block metal ions.

Coordination number 9

Most compounds with this coordination number have a trigonal tripoint geometry, e.g. [ReH₉]^2-, [TcH₉]^2-. This coordination number is associated with more often yttrium, lanthanum, and f block elements.

Coordination number 10

Its most stable geometry is: square bilayer antiprism.10 This coordination number requires both a large central atom and a very compact ligand, which is why it only occurs in lanthanide cation complexes and actinides in combination with small unidentate donor atoms. An example of this type is [Th(C₂O₄)₄]^2-.

Coordination and packing number

Taking for example in a crystal the central atom of a body centered cubic cell (BCC), it is clearly in contact with 4 neighboring atoms on the upper face and 4 atoms below, therefore:

• The coordination number for the BCC structure is 8.

Recalling that a HCP (Hexagonal Compact) crystal is formed by compact hexagonal planes in ABC order, then it can be seen that taking any atom of the crystal, it has 6 neighbors in the same plane, 3 neighbors above and 3 below.

• The coordination number for the HCP structure is 6 + 3 + 3 = 12.

And for the same reason above:

• The coordination number for the structural structure of the so-called FCC is 12 compact because it serves to compact or unite puzzle pieces.
• If you take the atom from the center of one of the faces you can see that it surrounds 4 atoms and, that below and above is also touched by 4 atoms on each side