Crystallization of a Racemate Affords a P2₁ Chiral Crystal Structure: Asymmetric Unit of Two Opposite Handed Molecules Simulates Achiral P2₁/n Packing via Pseudosymmetry

Abstract

A racemic mixture consisting of a secondary ammonium salt (()-(1RS,3SR,4RS)-1-phenyl-cis-3,4-n-butano-5,6-dihydro-1H-2, 5-benzoxazocine hydrochloride (1) crystallized as a "false conglomerate" of crystals in the monoclinic system, Sohncke space group P2 1 with two molecules of opposite handedness in the asymmetric unit and at 295(2) K: a = 10.224(2) Å, b = 13.969(2) Å, c = 12.724(2) Å, β = 98.996(2)°, V = 1794.9(5) Å 3 , Z = 4, and Z 0 = 2. The cis-3,4-nbutano-5,6-dihydro-1H-2,5-benzoxazocine fused-ring skeletons are approximately enantiotopic and exhibit pseudoinversion and pseudo-nglide relationships. These noncrystallographic symmetries enable space filling in the chiral crystal structure to resemble that of a higher order achiral P2 1 /n apparent space group (Z = 4, Z 0 = 1). The secondary ammonium salt molecules crystallize in patterns influenced by a complex blend of NÀH 3 3 3 Cl, CÀH 3 3 3 Cl, CÀH 3 3 3 O, and CÀH 3 3 3 Ar interactions that seem to be responsible for different conformational twists of the phenyl rings in the structure. Avnir's CSM method was adapted for quantification of crystallographic pseudosymmetry. RmS(G) measurements of distortion from ideal G symmetries were developed for pure translation, screw rotation, and glide reflection, as well as point group symmetries. Low rmS(i) and rmS(n-glide) values show high fidelity for the emulation of P2 1 /n space filling in crystalline 1.

Chirality determination in crystals

“…One explanation for the propensity of some chiral molecules to crystallize as kryptoracemates is that pseudosymmetric elements within the unit cell would free them from symmetry positional constraints thus optimizing their interactions and allowing a more efficient packing. 60 The number of kryptoracemates deposited in the Cambridge Structural Database has been estimated between about 200 and 400, depending on the date and methodology of the search. 58,61 The superposition of the two enantiomers, after inversion of one of them, can be a simple and efficient way to highlight their differences as illustrated in the Figure 2 of ref.…”

“…In the S C H E M E 1 Substitution scheme for glycerol followed in the study of Gubaidullin et al 53 F I G U R E 1 An example of kryptoracemates with even numbers of enantiomers. 60 Left: Z 0 = 2; right: Z 0 = 4 crystal of [Co 3 (dpa) 4 (MeCN) 2 ](BF 4 ) 2 ÁMeCNÁ0.5Et 2 O (1), the asymmetric unit contains the two EMAC enantiomers, crystallizing in the space group P2 1 2 1 2 1 . Superposition of the two enantiomers with inversion of one of them shows excellent overlap, except for slight differences in the axial acetonitrile molecule angles (177.69 /178.67 and 177.42 /179.10 ), which may account for the conformational uniqueness of the two enantiomers (Figure 2C).…”

“…When Z ′ is greater than 1 and takes an even value, the crystal is known as a kryptoracemate, 57,58 also named “false conglomerate” 59,60 . The composition of the crystal is purely racemic, but the space group is a Sohncke one.…”

Computer-Aided Identification of Symmetry Relating Groups of Molecules

“…We note, however, that Glaser and coworkers have calculated midpoints of pseudosymmetrically related atoms in kryptoracemates 25 to characterize the precision and accuracy of crystallographic pseudosymmetries. 26,27 ■ THEORETICAL BASIS The pattern formed by the centroids of symmetry-related atoms can be readily derived from the mathematical formula describing the symmetry operation. For example, a 2-fold rotation axis along z relates an atom at (x, y, z) to an atom at (−x, −y, z).…”

Stereochemistry of 2,6‐Diaminoadamantane Salts: Transannular Interactions

“…Glaser and co-workers have modified and extended the Avnir CSM for the quantification of pseudo-symmetryrelated molecules in a crystal. [19] It is not uncommon in crystals that two pairs of G pseudo-symmetry-related molecules differ in their intermolecular distances. The crystallographic pseudo-symmetry tools [denoted as rmS(G)] remove the CSM distance normalization factor, so that the same value is calculated for pseudo-symmetrical pairs of molecules irrespective of their distance from one another in the lattice.…”