Topological Description of Pseudosymmetries in trans-2,3,4,5,5a,6,7,8,9,9a-Decahydro-2-methyl-4-phenylaminocarbonylbenzo[f][1,4]oxazepin-3-one and Other Structures which Crystallize in Space Group P-1 with Z = 8

The pseudosymmetries of the title compound resemble a monoclinic unit cell with space group P112₁/a. However, the structure of C₁₇H₂₂N₂O₃ was determined in a triclinic unit cell [a = 10.500 (4), b = 11.617 (3), c = 28.622 (3) Å, α = 83.15 (2), β = 83.41 (4), γ = 68.48 (2)°; V = 3215 (2) ų, Z = 8: four molecules in the asymmetric unit] by direct methods and refined on F² values in space group P1 to final R[F² > 2σ(F²)] = 0.0457 and wR(F²) = 0.114. The conformation of molecule M1 basically agrees with that of M4, whereas molecules M2 and M3 form a second group of conformers. M1–M2 and M4–M3 dimers are related by a pseudoscrew axis along the c axis and complemented by a pseudoglide plane located at z ≃ or , respectively. The analysis of pseudosymmetries in the title crystal was then extended to other structures selected from 66 Cambridge Structural Database entries with P1 and Z = 8. A topological survey of the pseudosymmetries reveals a rich variety of the *2₁/*c pair. In the unit cells of several crystals one or two coordinates of these types of pseudosymmetries are bound to (2n − 1) values or in their vicinity. Such operators (termed secondary pseudosymmetries) are accompanied by their respective complementary symmetries with translation(s) of ca (2n − 1). Their cooperation with primary pseudosymmetries (possessing standard position and translation) and with themselves seems to shed light on the origin of symmetries in crystals. These observations are also valid for a few monoclinic crystals.

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