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

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

L- and D- quartz

Chirality in Chemistry

Hans Erni’s drawing

Kelvin’s definition of chirality

Lord Kelvin

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.

 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

 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

 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

 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

 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

 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

 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

 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

 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

 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

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

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/

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

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

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

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

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

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

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

(  ) o-tyrosine

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?

Idealized binary phase diagrams for enantiomeric mixtures

Conglomerate - phase diagram

Racemic structure formation – phase diagram

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

m-fluoromandelic acid & m-chlorophenyl hydracylic acid

Free energy vs temperature

Solid solution formation

Methyprylon

Methyprylon 3D

Crossing isodimorphism with two minima

Melting point diagram of methyprylon

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

Solid solution formation

Frederic Stanley Kipping 1863 - 1949

Prelog’s L- and D- quartz

Brazil twin of quartz

Hexahelicene From racemic solutionFrom enantiopure solution

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

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.

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

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.

 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

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.

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.

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

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

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

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

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

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

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

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

La Coupe du Roi

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)

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