Continuous chirality measures of tetracoordinate bis(chelate) metal complexes Santiago Alvarez * a and David Avnir* b a Departament de Química Inorgànica and Centre de Recerca en Química Teòrica, Universitat de Barcelona, Diagonal 647, 08028 Barcelona, Spain b Institute of Chemistry and The Lise Meitner Minerva Center for Computational Quantum Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel Received 12th September 2002, Accepted 3rd December 2002 First published as an Advance Article on the web 17th January 2003 The interconversion pathway between the tetrahedron and the square that is represented by the structures of a large variety of tetracoordinate complexes is the achiral spread pathway in the presence of monodentate ligands but the chiral twist pathway in bis-chelated complexes. The chirality of several families of bis-chelated metal complexes is evaluated using the Continuous Chirality Measures methodology. The specific contribution to chirality from the innermost MX 4 shell, as well as from the ligands is analyzed. The maximal expected chirality value for the tetrahedral to square planar route is at a torsion angle of 45°, which is realized in [Cu(p-C 6 H 4 {p-C 2 H 5 bipyMe} 2 )] 2+ . The chiral behavior of double-stranded helicates is compared to that of analogous mononuclear complexes. The present study shows that chirality is a rather common property of bis-chelated complexes, even in the absence of asymmetric ligands. There is an extended perception that tetracoordinate bis- (chelate) complexes are chiral only if the bidentate ligands are asymmetric. 1,2 As an example of such an extended belief, let us quote two authoritative references: “. . .optical isomerism can occur only when the dihedral angle between the two chelate rings defined by the metal and donor atoms is nonzero, and is possible only for M(L–L') 2 ” (ref. 1, p. 249). “Coordination units [M(AA)a 2 ] and [M(AA)ab] have symmetries C 2v and C s , respectively and they cannot give rise to stereoisomers. The same is true for [M(AA) 2 ] with D 2d symmetry. On the other hand, [M(AB)ab] and [M(AB) 2 ] have C 1 and C 2 symmetries, respectively and they are therefore chiral” (ref. 2, p. 98), where AA and AB represent symmetric and asymmetric bidentate ligands, a and b monodentate ligands. As a further indication of such a belief, we have been unable to find any reference to the chirality of tetracoordinate transition metal complexes in all advanced Inorganic Chemistry textbooks consulted. When ref- erence is made to chirality, one finds statements such as “Tetra- hedral complexes. . . are potentially chiral just as is tetrahedral carbon. The simple form of optical isomerism exhibited by most organic enantiomers, namely four different substituents, is rarely observed. . .”; or “A form of optical isomerism analogous to that shown by organic spirocyclic compounds has been demon- strated. . . The two enantiomers of bis(benzoyl-acetonato)- beryllium are illustrated. . . the chelating ligand must be unsymmetric”. 3 However, it is being increasingly recognized by some authors that a bis-chelate complex “can distort towards a square planar geometry, becoming therewith, a chiral species”, 4 that “chelating ligands in combination with tetrahedrally coordinated metal ions lead to mononuclear complexes which already possess a helical twist” 5 and that “square planar com- plexes that deviate significantly from planarity can be chiral”. 6 In recent years we have proposed that chirality can be treated as a continuous property and that it might be useful not only to define a given molecule as chiral, but to provide a measure of how far it is from being achiral. 7–9 In order to translate this definition into practice, we have developed the Continuous Chirality Measure (CCM) methodology and a computational tool which evaluates the distance of a chiral object to the nearest achiral symmetry. An important feature of the CCM approach is that it not only computes the chirality content, but also provides the actual shape of the nearest achiral object, a feature that helps us understand the dependence of the chirality measures on the molecular geometry. In brief, given the positions of the N atoms in the investi- gated molecule defined by vectors Q k (k = 1, 2, . . . N), one searches for the nearest achiral molecule with coordinates P k (k = 1, 2, . . . N) and the sum of the squared distance between the two sets of coordinates is the chirality measure of the molecule under study, given by eqn. 1, where the denominator provides a size normalization factor (Q 0 is the coordinate vector of the center of mass of the investigated structure) that makes the chirality measure independent of size. The quotient takes values between 0 (achiral molecule) and 1, and the factor of 100 is introduced for convenience; 10 the larger S, the more chiral the molecule is. The application of the CCM approach to hexacoordinate transition metal complexes has resulted in some interesting findings. For instance, we have shown how a variety of homoleptic ML 6 complexes with monodentate ligands present disymmetric metaprismatic structures 11 (intermediate between octahedral and trigonal prismatic), and have provided compu- tational evidence that in one such family of complexes the racemization reaction should be slow at room temperature. 12 A study of the chirality measures of tris(chelate) complexes 13 has revealed the interesting feature that the first atomic shell (i.e., the metal and donor atoms) and the second shell (compris- ing the spacers between two donor atoms of a bidentate ligand) present contributions that may be either commensurate or incommensurate to the chirality of the full complex. Further- more, it was found that the chirality measure of the first two shells provides a semiquantitative estimate of that of the full molecule and the chirality of the inner shell is either amplified or attenuated depending on the type of bidentate ligand used. A detailed analysis of how several distortions affect the symmetry measures of tetracoordinate complexes relative to the square and the tetrahedron, S(D 4h ) and S(T d ), respectively, has been carried out by us recently 14,15 without specifically considering chirality measures. On the other hand, we have focused on a small group of copper bisoxazolines and found an interesting correlation between their chirality measures and the (1) DOI: 10.1039/ b208837a 562 Dalton Trans. , 2003, 562–569 This journal is © The Royal Society of Chemistry 2003