Geometry index

Template:Short description In coordination chemistry and crystallography, the geometry index or structural parameter (Template:Mvar) is a number ranging from 0 to 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.

5-coordinate compounds

To distinguish whether the geometry of the coordination center is trigonal bipyramidal or square pyramidal, the Template:Math (originally just Template:Math) parameter was proposed by Addison et al.:

${\tau }_5=\frac{\beta -\alpha }{60^{\circ }}\approx -0.01667\alpha +0.01667\beta$

where: Template:Math are the two greatest valence angles of the coordination center.

When Template:Math is close to 0 the geometry is similar to square pyramidal, while if Template:Math is close to 1 the geometry is similar to trigonal bipyramidal:

4-coordinate compounds

In 2007 Houser et al. developed the analogous Template:Math parameter to distinguish whether the geometry of the coordination center is square planar or tetrahedral. The formula is:

${\tau }_4=\frac{360^{\circ }-(\alpha +\beta )}{360^{\circ }-2\theta }\approx -0.00709\alpha -0.00709\beta +2.55$

where: Template:Math and Template:Math are the two greatest valence angles of coordination center; Template:Math is a tetrahedral angle.

When Template:Math is close to 0 the geometry is similar to square planar, while if Template:Math is close to 1 then the geometry is similar to tetrahedral. However, in contrast to the Template:Math parameter, this does not distinguish Template:Math and Template:Math angles, so structures of significantly different geometries can have similar Template:Math values. To overcome this issue, in 2015 Okuniewski et al. developed parameter Template:Math that adopts values similar to Template:Math but better differentiates the examined structures:

${{\tau }_4}^{\prime }=\frac{\beta -\alpha }{360^{\circ }-\theta }+\frac{180^{\circ }-\beta }{180^{\circ }-\theta }\approx -0.00399\alpha -0.01019\beta +2.55$

where: Template:Math are the two greatest valence angles of coordination center; Template:Math is a tetrahedral angle.

Extreme values of Template:Math and Template:Math denote exactly the same geometries, however Template:Math is always less or equal to Template:Math so the deviation from ideal tetrahedral geometry is more visible. If for tetrahedral complex the value of Template:Math 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.

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• A web application for determining molecular geometry indices on the basis of 3D structural files can be found here.