FULL PAPER A Continuous Chirality Analysis of Homoleptic Hexacoordinated Complexes Santiago Alvarez,* [a] Mark Pinsky, [b,c] and David Avnir* [c] Keywords: Chirality / Stereochemistry / Coordination chemistry / Molecular symmetry / Quantitative chirality Hexacoordinated complexes are generally considered to be potentially chiral if they have either at least two bidentate ligands or at least three different monodentate ligands. Here we draw attention to a neglected general possibility, namely that homoleptic hexacoordinated complexes with molecular structures in between octahedral and trigonal prismatic, fol- lowing the Bailar twisting route, are chiral. A quantitative evaluation of the degree of chirality of such hexakis(mon- Introduction The chirality of transition metal complexes is of much current interest mainly because of their potential applica- tions as catalysts for asymmetric synthesis. [1] Following von Zelewsky (and somewhat modifying his list), [2] we note that chirality can be induced in coordination compounds by: (i) the existence of different ligands (as in [Mabcdef]); (ii) a special spatial arrangement of ligands (as in one of the ste- reoisomers of [Ma 2 b 2 c 2 ]); (iii) the removal of an improper symmetry element of a bidentate ligand through formation of chelate rings (including the mutual breaking of an im- proper rotation present in such ligands); (iv) coordination of chiral ligands, of ligands which assume chiral conforma- tions or of prochiral ligands (i.e., ligands which become chiral upon coordination because an improper symmetry is broken); or (v) rotational symmetry wrapping of the ligands around the metal. Within the rotational wrapping option, we distinguish several sub-types, namely helical wrapping, [3] the propeller-type arrangement in bis- and tris(chelate) complexes and, of relevance to this report, the Bailar-type twist, [4] which links octahedricity and trigonal prismacity in hexacoordinated complexes, as shown in 1. Perhaps the most elementary option for obtaining chiral- ity is the Bailar twist, which reduces the achiral point groups O h and D 3h to the chiral D 3 symmetry point group. The simplicity of this option originates from the fact that it [a] Departament de Quı ´mica Inorga `nica and Centre de Recerca en Quı ´mica Teo `rica, Universitat de Barcelona, Diagonal 647, 08028 Barcelona, Spain E-mail: santiago@qi.ub.es [b] Institute of Earth Sciences, The Hebrew University of Jerusalem, Jerusalem 91904, Israel [c] Institute of Chemistry and The Lise Meitner Minerva Center for Computational Quantum Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel E-mail: david@chem.ch.huji.ac.il Supporting information for this article is available on the WWW under http://www.wiley-vch.de/home/eurjic or from the authors. Eur. J. Inorg. Chem. 2001, 1499-1503  WILEY-VCH Verlag GmbH, 69451 Weinheim, 2001 1434-1948/01/0606-1499 $ 17.50+.50/0 1499 dentate) complexes shows that they reach maximum chirality when the trigonal rotation angle of the prism reaches 23°. Model calculations and analysis of experimental X-ray struc- tures are in good agreement. The most chiral of the com- plexes with monodentate ligands that have been analyzed is [Zr(SC 6 H 4 -4-OMe) 6 ] 2- . The validity of the theoretical predic- tion is also corroborated by an analysis of the chirality of the coordination sphere in twisted tris(chelate) complexes. allows homoleptic [ML 6 ] complexes to be chiral, with no special requirement for chirality or pro-chirality of the six ligands. Yet, to the best of our knowledge, no enantiomeric crystals of the two D 3 enantiomers have been reported. It is interesting to note that of all the options for obtaining chirality, the one that was highlighted since the dawn of coordination chemistry was option (iii), i.e. the use of bi- dentate ligands. Starting with the pioneering work of Alfred Werner, who resolved the two enantiomers of the cationic complexes [CoX(NH 3 )(en) 2 ] 2+ (X = Cl, Br), [5] many other octahedral metal complexes with two or three bidentate li- gands have been shown to be chiral. [2,6-12] In fact, option (iii) has overshadowed over the years all the other options for obtaining chirality in hexacoordinated complexes. Thus, it is common to find in textbooks statements such as: ‘‘Im- portant examples [of chiral molecules] are bischelate and trischelate octahedral complexes’’ (ref. [11] ); ‘‘Chiral com- plexes occur mainly when chelate rings are formed’’ (ref. [11] p. 683) ‘‘In practice, optical activity is largely confined to octahedral complexes of chelating ligands’’; [6] ‘‘The abso- lute configuration of a chiral complex is described by ima- gining a view along a threefold rotation axis of a regular octahedron and noting the handedness of the helix formed