On the abundance of chiral crystals (An optimistic lecture for the conclusion of the conference) David Avnir Institute of Chemistry The Hebrew University of Jerusalem, Israel With Chaim Dryzun Department of Chemistry, ETH Zürich Lugano Campus, Switzerland Chirality 2012, Fort Worth, Texas June 10 - June 13, 2012
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On the abundance of chiral crystals (An optimistic lecture for the conclusion of the conference) David Avnir Institute of Chemistry The Hebrew University.
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On the abundance of chiral crystals
(An optimistic lecture for the conclusion of the conference)
David Avnir
Institute of ChemistryThe Hebrew University of Jerusalem, Israel
WithChaim Dryzun
Department of Chemistry, ETH ZürichLugano Campus, Switzerland
Chirality 2012, Fort Worth, Texas June 10 - June 13, 2012
The unrecognized high abundance of chiral crystals
* ~23% of all non-biological crystals are chiral(compared to only ~10% of all non-biological molecules )
* Only ~6% of these are labelled as chiral In numbers:there are out there ~100,000 crystals the chirality of which has been ignored
It means that:The library from which one can select enantioselective catalysts, sensing materials, and chromatographic materials is by far larger than envisaged so far.
Questions to be addressed:
# Why was it overlooked?
# Why are chiral crystals much more common than chiral molecules?
# What are the practical implications of this finding?
What is a chiral crystal?
What may be chiral in a crystal?
# The molecule
# The asymmetric unit
# The unit cell
# The space-group
# The macroscopic habit
H. D. Flack, Helv. Chim. Acta, 2003, 86, 905
Class I:
The 165 space groups which contain at least one improper operation (inversion, mirror, glide or Sn operations).
Always achiral(although the 3D asymmetric unit is always chiral)
The classes of space groups
P m
Class II:
22 chiral-helical space groups (11 enantiomeric pairs)
Contain at least one screw axis which is not the 21-screw axis.
Always chiraleven if the AU is achiral
The confusing class III:
43 space groups that contain only proper rotations and the 21-screw rotation
Examples: P 21, P 4, the abundant P 21 21 21.
Despite the fact that there are no reflections, inversions etc., these space groups are achiral
Despite the fact that these space groups are achiral, the crystals which pack by them are always chiral
How can that be?
# P21 is achiral because reflection of this mathematical entity
results in unchanged P21
# P61 is chiral because its reflection results in P65
Despite the fact that there are no reflections, inversions etc., these 43 space groups are achiral
In general, a crystal may be chiral and yet belong to one of these 43 achiral space groups
Despite the fact that these space groups are achiral, the crystals which pack by them are chiral
The reason for:
* An AU in 3D is always chiral. A chiral AU on which only proper operations are applied, must result in a chiral crystal.
* If the AU is achiral (0D, 1D, 2D) – then it will usually pack in a space group which has that achiral operation, coinciding with it.
Class II and Class III are collectively known as the 65 Sohncke groups
II: 22 of the 65 are chiral (helical)III: 43 of the 65 are achiral Bottom line:
All of the 65 Sohncke groups - and only these groups - represent chiral crystals
The Sohncke symmetry space groups
Wrong
H. D. Flack, Helv. Chim. Acta, 2003, 86, 905
To remove the confusion we suggest:
Class I: 165 improper-achiral groupsAlways an achiral crystal
Class II: 22 helical-chiral groupsAlways a chiral crystal
Class III: 43 proper-achiral groupsAlways a chiral crystal
If the space group contains only proper operations, the crystal is chiral
If the space group contains only proper operations, the crystal is chiral
Proper operations: rotations, screw-rotations and translations