Incoordination chemistryandcrystallography,thegeometry indexorstructural parameter(τ) is a number ranging from 0 to 1 that indicates what thegeometryof 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
editTo distinguish whether the geometry of the coordination center is trigonal bipyramidal or square pyramidal, theτ5(originally justτ) parameter was proposed by Addisonet al.:[1]
where:β>αare the two greatest valence angles of the coordination center.
Whenτ5is close to 0 the geometry is similar to square pyramidal, while ifτ5is close to 1 the geometry is similar to trigonal bipyramidal:
4-coordinate compounds
editIn 2007 Houseret al.developed the analogousτ4parameter to distinguish whether the geometry of the coordination center is square planar or tetrahedral.[2]The formula is:
where:αandβare the two greatest valence angles of coordination center;θ= cos−1(−1⁄3) ≈ 109.5°is a tetrahedral angle.
Whenτ4is close to 0 the geometry is similar to square planar, while ifτ4is close to 1 then the geometry is similar to tetrahedral. However, in contrast to theτ5parameter, this does not distinguishαandβangles, so structures of significantly different geometries can have similarτ4values. To overcome this issue, in 2015 Okuniewskiet al.developed parameterτ4′that adopts values similar toτ4but better differentiates the examined structures:[3]
where:β>αare the two greatest valence angles of coordination center;θ= cos−1(−1⁄3) ≈ 109.5°is a tetrahedral angle.
Extreme values ofτ4andτ4′denote exactly the same geometries, howeverτ4′is always less or equal toτ4so the deviation from ideal tetrahedral geometry is more visible. If for tetrahedral complex the value ofτ4′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···πinteractions were found this way.[4]
References
edit- ^abAddison, A. W.; Rao, N. T.; Reedijk, J.; van Rijn, J.; Verschoor, G. C. (1984). "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 ".J. Chem. Soc., Dalton Trans.(7): 1349–1356.doi:10.1039/dt9840001349.
- ^abYang, L.; Powell, D. R.; Houser, R. P. (2007). "Structural variation in copper(I) complexes with pyridylmethylamide ligands: structural analysis with a new four-coordinate geometry index,τ4".Dalton Trans.(9): 955–64.doi:10.1039/b617136b.PMID17308676.
- ^Okuniewski, A.; Rosiak, D.; Chojnacki, J.; Becker, B. (2015). "Coordination polymers and molecular structures among complexes of mercury(II) halides with selected 1-benzoylthioureas".Polyhedron.90:47–57.doi:10.1016/j.poly.2015.01.035.
- ^Rosiak, D.; Okuniewski, A.; Chojnacki, J. (2018). "Novel complexes possessing Hg‒(Cl, Br, I)···O=C halogen bonding and unusual Hg2S2(Br/I)4kernel. The usefulness ofτ4′structural parameter ".Polyhedron.146:35–41.doi:10.1016/j.poly.2018.02.016.
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edit- A web application for determining molecular geometry indices on the basis of 3D structural files can be foundhere.