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 (m3m)

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 (m3m)

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 (m3m)

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 (m3m)

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 (m3m)

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 (m3m)

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 (m3m)

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 (m3m)

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 (m3m)

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 (m3m)

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 crystalMolecules

gas or liquid

Achiralm, mm2,4,42m: Yes

Other point groups: NoNo

Chiral Yes

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 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 permitted

Chiral molecules

enantiopureforbidden

Chiral molecules

racemate

Chiral molecules

enantiomeric mixture

Crystal structures formed from chiral and achiral molecules

Achiral

crystal structure

Chiral

crystal structure

Achiral molecules permitted permitted

Chiral molecules

enantiopureforbidden permitted

Chiral molecules

racemate

Chiral molecules

enantiomeric mixture

Crystal structures formed from chiral and achiral molecules

Achiral

crystal structure

Chiral

crystal structure

Achiral molecules permitted permitted

Chiral molecules

enantiopureforbidden permitted

Chiral molecules

racematepermitted

Chiral molecules

enantiomeric mixture

Crystal structures formed from chiral and achiral molecules

Achiral

crystal structure

Chiral

crystal structure

Achiral molecules permitted permitted

Chiral molecules

enantiopureforbidden permitted

Chiral molecules

racematepermitted permitted

Chiral molecules

enantiomeric mixture

() o-tyrosine

Crystal structures formed from chiral and achiral molecules

Achiral

crystal structure

Chiral

crystal structure

Achiral molecules permitted permitted

Chiral molecules

enantiopureforbidden permitted

Chiral molecules

racematepermitted permitted

Chiral molecules

enantiomeric mixturelike enantiopure? 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 solution From 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, -

CrOC

OCO

O

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. Acta 86, -

NH

SO2

CH3

H

13

6

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.

1 2/m mmm

4/mmm 3m

6/mmm (m3m)

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

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 + xX .

The macroscopic crystal C is treated as a mixture of an

oriented crystal structure X and its inverted structureX in

variable proportion.

Point group 6mm contains symmetry operations of the

second kind, e.g. m. The crystal structure is achiral.

X andX 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

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 35 m[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]

6/mmm

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

1 65 35 m[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]

6mm

6/mmm

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

1 65 35 m[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]

6mm

6/mmm

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

1 65 35 m[001] 3 6

Point groups 6/mmm and 6mm

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

1 65 35 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 65 35 m[001] 3 6

Achiral crystal structures formed from enantiopure molecules

Achiral

crystal structure

Chiral

crystal structure

Achiral molecules

Chiral molecules

enantiopureforbidden

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)