1. Chirality and Achirality in Crystal Structures H. D. Flack and G. Bernardinelli University of Geneva, Switzerland www.flack.ch/howard/cristallo/publcns.html

2. L- and D- quartz

3. Chirality in Chemistry

4. Hans Erni’s drawing

5. Kelvin’s definition of chirality

6. Lord Kelvin

7. Modern definitions of Chirality IUPAC: The geometric property of a rigid object (or spatial arrangement of point or atoms) of being non-superposable by pure rotation and translation on its image formed by inversion through a point; the symmetry group of such an object contains no symmetry operations of the second kind (  1, m,  3,  4,  6). When the object is superposable by pure rotation and translation on its inverted image, the object is described as being achiral; the symmetry group of such an object contains symmetry operations of the second kind. Barron: True chirality is exhibited by systems that exist in two distinct enantiomorphic states that are interconverted by space inversion by not by time reversal combined with any proper spatial rotation.

8.  1 2/m mmm 4/mmm  3m 6/mmm (m  3m) 4/m  3 6/m (m  3) 222 422 32 622 23 432 1 2 4 3 6 4mm 3m 6mm m mm2  4  42m  6  6m2  43m 32 geometric crystal classes

9.  1 2/m mmm 4/mmm  3m 6/mmm (m  3m) 4/m  3 6/m (m  3) 222 422 32 622 23 432 1 2 4 3 6 4mm 3m 6mm m mm2  4  42m  6  6m2  43m 32 geometric crystal classes

10.  1 2/m mmm 4/mmm  3m 6/mmm (m  3m) 4/m  3 6/m (m  3) 222 422 32 622 23 432 1 2 4 3 6 4mm 3m 6mm m mm2  4  42m  6  6m2  43m 32 geometric crystal classes

11.  1 2/m mmm 4/mmm  3m 6/mmm (m  3m) 4/m  3 6/m (m  3) 222 422 32 622 23 432 1 2 4 3 6 4mm 3m 6mm m mm2  4  42m  6  6m2  43m 32 geometric crystal classes

12.  1 2/m mmm 4/mmm  3m 6/mmm (m  3m) 4/m  3 6/m (m  3) 222 422 32 622 23 432 1 2 4 3 6 4mm 3m 6mm m mm2  4  42m  6  6m2  43m 32 geometric crystal classes

13.  1 2/m mmm 4/mmm  3m 6/mmm (m  3m) 4/m  3 6/m (m  3) 222 422 32 622 23 432 1 2 4 3 6 4mm 3m 6mm m mm2  4  42m  6  6m2  43m 32 geometric crystal classes

14.  1 2/m mmm 4/mmm  3m 6/mmm (m  3m) 4/m  3 6/m (m  3) 222 422 32 622 23 432 1 2 4 3 6 4mm 3m 6mm m mm2  4  42m  6  6m2  43m 32 geometric crystal classes CA NC NA

15.  1 2/m mmm 4/mmm  3m 6/mmm (m  3m) 4/m  3 6/m (m  3) 222 422 32 622 23 432 1 2 4 3 6 4mm 3m 6mm m mm2  4  42m  6  6m2  43m 32 geometric crystal classes

16.  1 2/m mmm 4/mmm  3m 6/mmm (m  3m) 4/m  3 6/m (m  3) 222 422 32 622 23 432 1 2 4 3 6 4mm 3m 6mm m mm2  4  42m  6  6m2  43m 32 geometric crystal classes

17.  1 2/m mmm 4/mmm  3m 6/mmm (m  3m) 4/m  3 6/m (m  3) 222 422 32 622 23 432 1 2 4 3 6 4mm 3m 6mm m mm2  4  42m  6  6m2  43m 32 geometric crystal classes

18. Optical activity in crystals and molecules Single crystal Molecules gas or liquid Achiral m, mm2,  4,  42m: Yes Other point groups: No No ChiralYes Enantiopure: Yes Racemate: No Enantiomeric mixture: Yes

19. Useful terms  Enantiomorph: One of a pair of chiral objects or models of opposite chirality sense.  Enantiomer: One of a pair of chiral molecular entities of opposite chirality sense.  Racemate: An equimolar mixture of a pair of enantiomers.  IUPAC Basic Terminology of Stereochemistry http://www.chem.qmul.ac.uk/iupac/stereo/

20. Crystal structures formed from chiral and achiral molecules Achiral crystal structure Chiral crystal structure Achiral molecules Chiral molecules enantiopure Chiral molecules racemate Chiral molecules enantiomeric mixture

21. Crystal structures formed from chiral and achiral molecules Achiral crystal structure Chiral crystal structure Achiral molecules permitted Chiral molecules enantiopure Chiral molecules racemate Chiral molecules enantiomeric mixture

22. Crystal structures formed from chiral and achiral molecules Achiral crystal structure Chiral crystal structure Achiral molecules permitted Chiral molecules enantiopure Chiral molecules racemate Chiral molecules enantiomeric mixture

23. Crystal structures formed from chiral and achiral molecules Achiral crystal structure Chiral crystal structure Achiral molecules permitted Chiral molecules enantiopure forbidden Chiral molecules racemate Chiral molecules enantiomeric mixture

24. Crystal structures formed from chiral and achiral molecules Achiral crystal structure Chiral crystal structure Achiral molecules permitted Chiral molecules enantiopure forbiddenpermitted Chiral molecules racemate Chiral molecules enantiomeric mixture

25. Crystal structures formed from chiral and achiral molecules Achiral crystal structure Chiral crystal structure Achiral molecules permitted Chiral molecules enantiopure forbiddenpermitted Chiral molecules racemate permitted Chiral molecules enantiomeric mixture

26. Crystal structures formed from chiral and achiral molecules Achiral crystal structure Chiral crystal structure Achiral molecules permitted Chiral molecules enantiopure forbiddenpermitted Chiral molecules racemate permitted Chiral molecules enantiomeric mixture

27. (  ) o-tyrosine

28. Crystal structures formed from chiral and achiral molecules Achiral crystal structure Chiral crystal structure Achiral molecules permitted Chiral molecules enantiopure forbiddenpermitted Chiral molecules racemate permitted Chiral molecules enantiomeric mixture like enantiopure?

29. Idealized binary phase diagrams for enantiomeric mixtures

30. Conglomerate - phase diagram

31. Racemic structure formation – phase diagram

32.  -(1-naphthoxy) propionic acid &  -(1-naphthyl) propionic acid

33. m-fluoromandelic acid & m-chlorophenyl hydracylic acid

34. Free energy vs temperature

35. Solid solution formation

36. Methyprylon

37. Methyprylon 3D

38. Crossing isodimorphism with two minima

39. Melting point diagram of methyprylon

40. Methyprylon cell dimensions and optical activity Einem glücklichen Zufall ist zu verdanken, dass in der Fraktion A beide Modifikationen entdeckt wurden.

41. Solid solution formation

42. Frederic Stanley Kipping 1863 - 1949

43. Prelog’s L- and D- quartz

44. Brazil twin of quartz

45. Hexahelicene From racemic solutionFrom enantiopure solution

46. Characterisation of enantiomers for absolute configuration determination  Optical activity  CD spectrum (circular dichroism)  Enantioselective (chiral) chromatography

47. E. P. Kündig, M. Kondratenko, F. Robvieux, G. Bernardinelli, (2003). Organometallics, 22, -  Space group P2 1 2 1 2 1 ; crystals grown from racemate; refinements using the above configuration:  Crystal 1: Flack parameter x = 0.36(4); ee = 28(8)%  Crystal 2: Flack parameter x = 0.90(3); ee = -80(6)%  CD spectra, from crystal 1 and crystal 2 in solution, normalised to allow for the volume of the crystal.

48. E. P. Kündig, M. Kondratenko, F. Robvieux, G. Bernardinelli, (2003). Organometallics, 22, - ee(x-ray) / ee(x-ray) = -0.35(10); CD(350) / CD(350) = -0.42

49. P. Müller, D. Riegert, G. Bernardinelli, (2003). Helv. Chim. Acta 86, -  Space group P2 1 ; Flack parameter x = -0.03(12)  CD spectrum flat; [  ] D = 0.7   Substance ee = 43%, semi-preparative separation by HPLC  Enantiomer composing the single crystal used for X-ray diffraction was unequivocally identified by HPLC.

50.  1 2/m mmm 4/mmm  3m 6/mmm (m  3m) 4/m  3 6/m (m  3) 222 422 32 622 23 432 1 2 4 3 6 4mm 3m 6mm m mm2  4  42m  6  6m2  43m 32 geometric crystal classes

51. Anti-wurtzite  Mn 1–y Fe y S, y  0.05; P6 3 mc; Flack parameter x = 0.02(4)  “... is found to crystallize in the inverse wurtzite structure, i.e. the wurtzite-type structure but with the opposite absolute configuration, which can be named anti-wurtzite.”  Point group 6mm contains symmetry operations of the second kind, e.g. m.  The crystal structure is achiral.  There is no ‘opposite absolute configuration’.  Anti-wurtzite is just wurtzite in another orientation.

52. Anti-wurtzite  Model for Flack parameter: C = (1-x) X + x  X.  The macroscopic crystal C is treated as a mixture of an oriented crystal structure X and its inverted structure  X in variable proportion.  Point group 6mm contains symmetry operations of the second kind, e.g. m. The crystal structure is achiral.  X and  X are not identical but may be brought into congruence by making a pure rotation.

53. Symmetry elements in point groups 6/mmm and 6mm International Tables for Crystallography Vol. A 6/mmm6mm

54. Point groups 6/mmm and 6mm

55. 1 6 3 2 [001] 3 2 6 5 m [100] m [210] m [110] m [120] m [010] m [  110] 2 [100] 2 [  110] 2 [010] 2 [120] 2 [110] 2 [210]  1  6 5  3 5 m [001]  3  6

56. Point groups 6/mmm and 6mm 1 6 3 2 [001] 3 2 6 5 m [100] m [210] m [110] m [120] m [010] m [  110] 6/mmm 2 [100] 2 [  110] 2 [010] 2 [120] 2 [110] 2 [210]  1  6 5  3 5 m [001]  3  6

57. Point groups 6/mmm and 6mm 1 6 3 2 [001] 3 2 6 5 m [100] m [210] m [110] m [120] m [010] m [  110] 6mm 6/mmm 2 [100] 2 [  110] 2 [010] 2 [120] 2 [110] 2 [210]  1  6 5  3 5 m [001]  3  6

58. Point groups 6/mmm and 6mm 1 6 3 2 [001] 3 2 6 5 m [100] m [210] m [110] m [120] m [010] m [  110] 6mm 6/mmm 2 [100] 2 [  110] 2 [010] 2 [120] 2 [110] 2 [210]  1  6 5  3 5 m [001]  3  6

59. Point groups 6/mmm and 6mm 2 [100] 2 [  110] 2 [010] 2 [120] 2 [110] 2 [210]  1  6 5  3 5 m [001]  3  6

60. Equivalent twin operations for 6mm in 6/mmm 2 [100] 2 [  110] 2 [010] 2 [120] 2 [110] 2 [210]  1  6 5  3 5 m [001]  3  6

61. Achiral crystal structures formed from enantiopure molecules Achiral crystal structure Chiral crystal structure Achiral molecules Chiral molecules enantiopure forbidden Chiral molecules racemate Chiral molecules enantiomeric mixture

62. La Coupe du Roi

63. The End On ne peut être trop prudent dans les conclusions à déduire de l’expérience, lorsque l’on a affaire à des substances quelquefois si semblables en apparence, et qui peuvent être au fond si différentes. Louis Pasteur (1848)