Geometry index


In structural chemistry and crystallography, the geometry index or structural parameter is the number in a range 0...1 that indicates what the geometry 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. There is on-line application for determining geometry indices on the basis of 3D structural files.

5-coordinate compounds



To distinguish whether the geometry of the coordination center is trigonal bipyramidal or square pyramidal, the 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 Yang 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, the Hg···π interactions were found this way.