Molecular versus structural chirality

Abstract

The rigorous proof that a structure crystallizing in any of the 65 Sohncke types of space groups is necessarily chiral is presented.

Vibrational Circular Dichroism Spectroscopy of Chiral Molecular Crystals: Insights from Theory

“…[29][30][31] It should be noted, however, that regardless the chirality of the constituting molecules, Sohncke space groups always deliver chiral crystal structures, while non-Sohncke space groups always deliver achiral crystal structures (Figure 2). [24,25,[32][33][34] Chiral enantiopure compounds will always crystallise in Sohncke groups, whereas P2 1 and P2 1 2 1 2 1 are the most abundant. [25] But even achiral molecules that crystallise in achiral Sohncke space groups form chiral crystals.…”

“…Molecular crystals differ from ionic crystals in that the atoms are not uniformly connected, but can be grouped into covalently bound units [33, 71] . Hence, the forces that act on the molecular units are significantly smaller than those acting on the atoms, and, as Zhang et al.…”

“…Molecular crystals differ from ionic crystals in that the atoms are not uniformly connected, but can be grouped into covalently bound units. [33,71] Hence, the forces that act on the molecular units are significantly smaller than those acting on the atoms, and, as Zhang et al put it, the "molecules preserve their individuality in the solid phase." [71] This has an important impact on the vibrational modes of the crystal that exist in two kinds: Lattice vibrations, that is, phonon modes that are determined by the translational and rotational degrees of freedom of whole molecules, and internal vibrations of the covalently bound atoms that do not shift the molecular centre of mass.…”

Response to the comment on the article Symmetry and chirality in crystals

“…Rekis ( 2023) called for a rigorous proof that the packing of achiral molecules in a Sohncke type of space group results in a chiral crystal structure. Such a proof is now available, in the same issue of this journal (Nespolo, 2023).…”

Enantiomorph ‘conversion’ in single crystals of Weyl semimetal CoSi

“…The left-and right-handed structures can be formed by chiral and achiral molecules. If such a crystal has the symmetry of a Sohncke space group, the crystal structure is chiral [19]. Not very much is known about the enantiomorph conversion within such crystals.…”