Editing Coordination complex (section)

===Geometry===
In coordination chemistry, a structure is first described by its [[coordination number]], the number of ligands attached to the metal (more specifically, the number of donor atoms). Usually one can count the ligands attached, but sometimes even the counting can become ambiguous. Coordination numbers are normally between two and nine, but large numbers of ligands are not uncommon for the lanthanides and actinides. The number of bonds depends on the size, charge, and [[electron configuration]] of the metal ion and the ligands. Metal ions may have more than one coordination number.

Typically the chemistry of transition metal complexes is dominated by interactions between s and p [[molecular orbital]]s of the donor-atoms in the ligands and the d orbitals of the metal ions.  The s, p, and d orbitals of the metal can accommodate 18 electrons (see [[18-Electron rule]]). The maximum coordination number for a certain metal is thus related to the electronic configuration of the metal ion (to be more specific, the number of empty orbitals) and to the ratio of the size of the ligands and the metal ion. Large metals and small ligands lead to high coordination numbers, e.g. {{chem2|[Mo(CN)8](4-)}}. Small metals with large ligands lead to low coordination numbers, e.g. {{chem2|Pt[P(CMe3)]2}}. Due to their large size, [[lanthanide]]s, [[actinide]]s, and early transition metals tend to have high coordination numbers.

Most structures follow the points-on-a-sphere pattern (or, as if the central atom were in the middle of a [[polyhedron]] where the corners of that shape are the locations of the ligands), where orbital overlap (between ligand and metal orbitals) and ligand-ligand repulsions tend to lead to certain regular geometries. The most observed geometries are listed below, but there are many cases that deviate from a regular geometry, e.g. due to the use of ligands of diverse types (which results in irregular bond lengths; the coordination atoms do not follow a points-on-a-sphere pattern), due to the size of ligands, or due to [[electronic effect]]s (see, e.g., [[Jahn–Teller distortion]]):

*[[Linear molecular geometry|Linear]] for two-coordination
*[[Trigonal planar molecular geometry|Trigonal planar]] for three-coordination
*[[Tetrahedral molecular geometry|Tetrahedral]] or [[square planar molecular geometry|square planar]] for four-coordination
*[[Trigonal bipyramid molecular geometry|Trigonal bipyramidal]] for five-coordination
*[[Octahedral molecular geometry|Octahedral]] for six-coordination
*[[Pentagonal bipyramidal molecular geometry|Pentagonal bipyramidal]] for seven-coordination
*[[Square antiprismatic molecular geometry|Square antiprismatic]] for eight-coordination
*[[Tricapped trigonal prismatic molecular geometry|Tricapped trigonal prismatic]] for nine-coordination

The idealized descriptions of 5-, 7-, 8-, and 9- coordination are often indistinct geometrically from alternative structures with slightly differing L-M-L (ligand-metal-ligand) angles, e.g. the difference between square pyramidal and trigonal bipyramidal structures.<ref>Wells A.F. (1984) ''Structural Inorganic Chemistry'' 5th edition Oxford Science Publications {{ISBN|0-19-855370-6}}</ref>

*[[Square pyramidal molecular geometry|Square pyramidal]] for five-coordination<ref>{{cite journal
| title = Transition metal pentacoordination
|author1=Angelo R. Rossi |author2=Roald. Hoffmann | journal = [[Inorganic Chemistry (journal)|Inorganic Chemistry]]
| year = 1975
| volume = 14
| issue = 2
| pages = 365–374
| doi = 10.1021/ic50144a032
}}</ref>
* [[Capped octahedral molecular geometry|Capped octahedral]] or [[Capped trigonal prismatic molecular geometry|capped trigonal prismatic]] for seven-coordination<ref>{{cite journal
| title = Seven-coordination. A molecular orbital exploration of structure, stereochemistry, and reaction dynamics
|author1=Roald. Hoffmann |author2=Barbara F. Beier |author3=Earl L. Muetterties |author4=Angelo R. Rossi | journal = [[Inorganic Chemistry (journal)|Inorganic Chemistry]]
| year = 1977
| volume = 16
| issue = 3
| pages = 511–522
| doi = 10.1021/ic50169a002
}}</ref>
* [[Dodecahedral molecular geometry|Dodecahedral]] or [[Bicapped trigonal prismatic molecular geometry|bicapped trigonal prismatic]] for eight-coordination<ref>{{cite journal
| title   = Eight-Coordination
| author1 = Jeremy K. Burdett
| author2 =  Roald Hoffmann
| author3 =  Robert C. Fay
| journal = [[Inorganic Chemistry (journal)|Inorganic Chemistry]]
| year    = 1978
| volume  = 17
| issue   = 9
| pages   = 2553–2568
| doi     = 10.1021/ic50187a041
}}</ref>
*[[Capped square antiprismatic molecular geometry|Capped square antiprismatic]] for nine-coordination

To distinguish between the alternative coordinations for five-coordinated complexes, the [[Geometry index|τ geometry index]] was invented by Addison et al.<ref>{{cite journal |last1 = Addison |first1 = A. W. |last2 = Rao |first2 = N. T. |last3 = Reedijk |first3 = J. |last4 = van Rijn |first4 = J. |last5 = Verschoor |first5 = G. C. |year = 1984 |title = Synthesis, structure, and spectroscopic properties of copper(II) compounds containing nitrogen–sulphur donor ligands; the crystal and molecular structure of aqua[1,7-bis(''N''-methylbenzimidazol-2′-yl)-2,6-dithiaheptane]copper(II) perchlorate |journal = J. Chem. Soc., Dalton Trans. |issue = 7 |pages = 1349–1356 |doi = 10.1039/dt9840001349}}</ref> This index depends on angles by the coordination center and changes between 0 for the square pyramidal to 1 for trigonal bipyramidal structures, allowing to classify the cases in between. This system was later extended to four-coordinated complexes by Houser et al.<ref>{{cite journal |last1 = Yang |first1 = L. |last2 = Powell |first2 = D. R. |last3 = Houser |first3 = R. P. |year = 2007 |title = Structural variation in copper(I) complexes with pyridylmethylamide ligands: structural analysis with a new four-coordinate geometry index, {{math|''τ''{{sub|4}}}} |journal = Dalton Trans. |issue = 9 |pages = 955–64 |doi = 10.1039/b617136b|pmid = 17308676 }}</ref> and also Okuniewski et al.<ref>{{cite journal |last1 = Okuniewski |first1 = A. |last2 = Rosiak |first2 = D. |last3 = Chojnacki |first3 = J. |last4 = Becker |first4 = B. |year = 2015 |title = Coordination polymers and molecular structures among complexes of mercury(II) halides with selected 1-benzoylthioureas |journal = Polyhedron |volume = 90 |pages = 47–57 |doi = 10.1016/j.poly.2015.01.035}}</ref>

In systems with low [[d electron count]], due to special electronic effects such as (second-order) [[Jahn–Teller effect|Jahn–Teller]] stabilization,<ref>{{cite journal | title = "Non-VSEPR" Structures and Bonding in d<sup>0</sup> Systems | first = Martin | last = Kaupp | journal = [[Angewandte Chemie|Angew. Chem. Int. Ed. Engl.]] | year = 2001 | volume = 40 | issue = 1 | pages = 3534–3565 | doi =  10.1002/1521-3773(20011001)40:19<3534::AID-ANIE3534>3.0.CO;2-#| pmid = 11592184 }}</ref> certain geometries (in which the coordination atoms do not follow a points-on-a-sphere pattern) are stabilized relative to the other possibilities, e.g. for some compounds the trigonal prismatic geometry is stabilized relative to octahedral structures for six-coordination.

*[[Bent molecular geometry|Bent]] for two-coordination
*[[Trigonal pyramidal molecular geometry|Trigonal pyramidal]] for three-coordination
*[[Trigonal prismatic molecular geometry|Trigonal prismatic]] for six-coordination