In
coordination chemistry
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 ...
and
crystallography
Crystallography is the experimental science of determining the arrangement of atoms in crystalline solids. Crystallography is a fundamental subject in the fields of materials science and solid-state physics (condensed matter physics). The wor ...
, the geometry index or structural parameter () is a number ranging from 0 to 1 that indicates what the
geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...
of the coordination center is. The first such parameter for 5-coordinate compounds was developed in 1984.
Later, parameters for 4-coordinate compounds were developed.
5-coordinate compounds
To distinguish whether the geometry of the coordination center is trigonal bipyramidal or square pyramidal, the (originally just ) parameter was proposed by Addison ''et al.'':
:
where: are the two greatest valence angles of the coordination center.
When is close to 0 the geometry is similar to square pyramidal, while if is close to 1 the geometry is similar to trigonal bipyramidal:
4-coordinate compounds
In 2007 Houser ''et al.'' developed the analogous parameter to distinguish whether the geometry of the coordination center is square planar or tetrahedral.
The formula is:
:
where: and are the two greatest valence angles of coordination center; is a tetrahedral angle.
When is close to 0 the geometry is similar to square planar, while if is close to 1 then the geometry is similar to tetrahedral. However, in contrast to the parameter, this does not distinguish and angles, so structures of significantly different geometries can have similar values. To overcome this issue, in 2015 Okuniewski ''et al.'' developed parameter that adopts values similar to but better differentiates the examined structures:
:
where: are the two greatest valence angles of coordination center; is a tetrahedral angle.
Extreme values of and denote exactly the same geometries, however is always less or equal to so the deviation from ideal tetrahedral geometry is more visible. If for tetrahedral complex the value of parameter is low, then one should check if there are some additional interactions within coordination sphere. For example, in complexes of mercury(II), the Hg···''π'' interactions were found this way.
References
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Crystallography
Chemistry
Chemical structures
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*A web application for determining molecular geometry indices on the basis of 3D structural files can be foun
here