Английская Википедия:Geometry index
Шаблон:Short description In coordination chemistry and crystallography, the geometry index or structural parameter (Шаблон: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.[1] Later, parameters for 4-coordinate compounds were developed.[2]
5-coordinate compounds
To distinguish whether the geometry of the coordination center is trigonal bipyramidal or square pyramidal, the Шаблон:Math (originally just Шаблон:Math) parameter was proposed by Addison et al.:[1]
- <math>\tau_5 = \frac{\beta-\alpha}{60^\circ} \approx -0.01667\alpha + 0.01667\beta </math>
where: Шаблон:Math are the two greatest valence angles of the coordination center.
When Шаблон:Math is close to 0 the geometry is similar to square pyramidal, while if Шаблон:Math is close to 1 the geometry is similar to trigonal bipyramidal:
4-coordinate compounds
In 2007 Houser et al. developed the analogous Шаблон:Math parameter to distinguish whether the geometry of the coordination center is square planar or tetrahedral.[2] The formula is:
- <math>\tau_4 = \frac{360^\circ - (\alpha + \beta)}{360^\circ - 2\theta} \approx -0.00709\alpha - 0.00709\beta + 2.55</math>
where: Шаблон:Math and Шаблон:Math are the two greatest valence angles of coordination center; Шаблон:Math is a tetrahedral angle.
When Шаблон:Math is close to 0 the geometry is similar to square planar, while if Шаблон:Math is close to 1 then the geometry is similar to tetrahedral. However, in contrast to the Шаблон:Math parameter, this does not distinguish Шаблон:Math and Шаблон:Math angles, so structures of significantly different geometries can have similar Шаблон:Math values. To overcome this issue, in 2015 Okuniewski et al. developed parameter Шаблон:Math that adopts values similar to Шаблон:Math but better differentiates the examined structures:[3]
- <math>\tau_4' = \frac{\beta - \alpha}{360^\circ - \theta} + \frac{180^\circ - \beta}{180^\circ - \theta} \approx -0.00399\alpha - 0.01019\beta + 2.55</math>
where: Шаблон:Math are the two greatest valence angles of coordination center; Шаблон:Math is a tetrahedral angle.
Extreme values of Шаблон:Math and Шаблон:Math denote exactly the same geometries, however Шаблон:Math is always less or equal to Шаблон:Math so the deviation from ideal tetrahedral geometry is more visible. If for tetrahedral complex the value of Шаблон: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.[4]
References
Read More
- A web application for determining molecular geometry indices on the basis of 3D structural files can be found here.
