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

Abstract

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) Å3, Z = 8: four molecules in the asymmetric unit] by direct methods and refined on F 2 values in space group P1¯ to final R[F 2 > 2σ(F 2)] = 0.0457 and wR(F 2) = 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 ≃ 1\over 4 or 3\over 4, 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)1\over 8 values or in their vicinity. Such operators (termed secondary pseudosymmetries) are accompanied by their respective complementary symmetries with translation(s) of ca (2n − 1)1\over 4. 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.