Chirality and Achirality in Crystal Structures

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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.

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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

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.
32 geometric crystal classes

222 422 32 622 23 432

1 2/mmmm 4/mmm3m 6/mmm (m3m)

1 2 4 3 6

4/m3 6/m (m 3)

4mm 3m 6mm m mm2

4 42m

6 6m2 43m

32 geometric crystal classes

222 422 32 622 23 432

1 2/mmmm 4/mmm3m 6/mmm (m3m)

1 2 4 3 6

4/m3 6/m (m 3)

4mm 3m 6mm m mm2

4 42m

6 6m2 43m

32 geometric crystal classes

222 422 32 622 23 432

1 2/mmmm 4/mmm3m 6/mmm (m3m)

1 2 4 3 6

4/m3 6/m (m 3)

4mm 3m 6mm m mm2

4 42m

6 6m2 43m

32 geometric crystal classes

222 422 32 622 23 432

1 2/mmmm 4/mmm3m 6/mmm (m3m)

1 2 4 3 6

4/m3 6/m (m 3)

4mm 3m 6mm m mm2

4 42m

6 6m2 43m

32 geometric crystal classes

222 422 32 622 23 432

1 2/mmmm 4/mmm3m 6/mmm (m3m)

1 2 4 3 6

4/m3 6/m (m 3)

4mm 3m 6mm m mm2

4 42m

6 6m2 43m

32 geometric crystal classes

222 422 32 622 23 432

1 2/mmmm 4/mmm3m 6/mmm (m3m)

1 2 4 3 6

4/m3 6/m (m 3)

4mm 3m 6mm m mm2

4 42m

6 6m2 43m

32 geometric crystal classes

222 422 32 622 23 432

1 2/mmmm 4/mmm3m 6/mmm (m3m)

NC

1 2 4 3 6

CA

4/m3 6/m (m 3)

4mm 3m 6mm m mm2

NA

4 42m

6 6m2 43m

32 geometric crystal classes

222 422 32 622 23 432

1 2/mmmm 4/mmm3m 6/mmm (m3m)

1 2 4 3 6

4/m3 6/m (m 3)

4mm 3m 6mm m mm2

4 42m

6 6m2 43m

32 geometric crystal classes

222 422 32 622 23 432

1 2/mmmm 4/mmm3m 6/mmm (m3m)

1 2 4 3 6

4/m3 6/m (m 3)

4mm 3m 6mm m mm2

4 42m

6 6m2 43m

32 geometric crystal classes

222 422 32 622 23 432

1 2/mmmm 4/mmm3m 6/mmm (m3m)

1 2 4 3 6

4/m3 6/m (m 3)

4mm 3m 6mm m mm2

4 42m

6 6m2 43m

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/
Methyprylon cell dimensions and optical activity

Einem glücklichen Zufall ist zu verdanken, dass in der Fraktion A beide Modifikationen entdeckt wurden.

Hexahelicene

From racemic solution

From enantiopure solution

• Optical activity
• CD spectrum (circular dichroism)
• Enantioselective (chiral) chromatography
E. P. Kündig, M. Kondratenko, F. Robvieux, G. Bernardinelli, (2003). Organometallics, 22, -
• Space group P212121; 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. Acta86, -
• Space group P21; 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.
32 geometric crystal classes

222 422 32 622 23 432

1 2/mmmm 4/mmm3m 6/mmm (m3m)

1 2 4 3 6

4/m3 6/m (m 3)

4mm 3m 6mm m mm2

4 42m

6 6m2 43m

Anti-wurtzite
• Mn1–y FeyS, y 0.05; P63mc; 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 6mmInternational Tables for Crystallography Vol. A

6/mmm

6mm

Point groups 6/mmm and 6mm

1 6 3 2[001] 32 65

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 6535m[001]3 6

Point groups 6/mmm and 6mm

1 6 3 2[001] 32 65

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 6535m[001]3 6

6/mmm

Point groups 6/mmm and 6mm

1 6 3 2[001] 32 65

m[100]m[210]m[110] m[120]m[010]m[110]

6mm

2[100] 2[110] 2[010] 2[120] 2[110] 2[210]

1 6535m[001]3 6

6/mmm

Point groups 6/mmm and 6mm

1 6 3 2[001] 32 65

m[100]m[210]m[110] m[120]m[010]m[110]

6mm

2[100] 2[110] 2[010] 2[120] 2[110] 2[210]

1 6535m[001]3 6

6/mmm

Point groups 6/mmm and 6mm

2[100] 2[110] 2[010] 2[120] 2[110] 2[210]

1 6535m[001]3 6

Equivalent twin operations for 6mm in 6/mmm

2[100] 2[110] 2[010] 2[120] 2[110] 2[210]

1 6535m[001]3 6

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)