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)over-bar with Z=8

The pseudosymmetries of the title compound resemble a monoclinic unit cell with space group P112(1)/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) Angstrom, alpha = 83.15 (2), beta = 83.41 (4), gamma = 68.48 (2)degrees; V = 3215 (2) Angstrom(3), Z = 8: four molecules in the asymmetric unit] by direct methods and refined on F-2 values in space group (1) over bar T to final R[F-2 > 2 sigma(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 similar or equal to 1/4 or 3/4, respectively. The analysis of pseudosymmetries in the title crystal was then extended to other structures selected from 66 Cambridge Structural Database entries with PI and Z = 8. A topological survey of the pseudosymmetries reveals a rich variety of the *2(1)/*c pair. In the unit cells of several crystals one or two coordinates of these types of pseudosymmetries are bound to (2n - 1)1/8 values or in their vicinity. Such operators (termed secondary pseudosymmetries) are accompanied by their respective complementary symmetries with translation(s) of ca (2n - 1)1/4. 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.