Aspherical atomic scattering factors in crystal structure refinement. I. Coordinate and thermal motion effects in a model centrosymmetric system

The consequences of ]-refinement procedures on atoms whose charge distributions are intrinsically non-centrosymmetric are examined in terms of a simple hypothetical structure consisting of two sp a hybrid valence 'prepared' state nitrogen atoms which are centrosymmetrically disposed in a unit cell and asstuned to be vibrating isotropically. The 'observed' F(hkl) data based on the threef curves appropriate to the non-centrosymmetric atomic shape assumed differ considerably from the 'calculated' F(hIcl) derived with the ] curve which corresponds to the spherically averaged form of the atomic shape : in one instance, the R index reflecting the intrinsic shape is ca. 8 %. The differences AF between F and T, for data in the full Cu range and in the restricted range 0 < sin 0/~t < 0.5 A -1, are used to display the magnitude of shape effects A o in Fourier line and plane sections through the atomic centre and along its symmetry axis. A~ is shown to consist of two parts, Ao~c which arises from the difference between the centrosymmetric component of the non-centrosymmetric atom and the spherically averaged treatment, and Oa which represents the antisymmetric atomic component which is ignored in the spherical approximation. The features of A~ and its components are given for the thermal conditions corresponding to ]~ = l, 2 or 3 A 2.