Electron population analysis with generalized x-ray scattering factors: Higher multipoles

Generalized x-ray scattering factors have been extended to include a 3d Slater-type atomic orbital. The new scattering functions include deformations that represent octapole and hexadecapole atomic charge distributions. These terms are suitable for charge density analysis of atoms with high site symmetry. For a reasonable exponential parameter, the 3d orbital does not introduce significantly different dipole and quadrupole radial scattering factors which have previously been constructed with 2s and 2p Slater-type orbital products. A new monopole term (M-shell scattering factor) is significantly different from the L-shell scattering factor, but it may be difficult to measure the corresponding population parameter from x-ray diffraction data. The valence scattering model is extended to second row atoms by restricting deformation terms to M-shell Slater-type orbitals. Neglect of L-shell deformation in the x-ray scattering analysis of second row atoms may not be appropriate; the matter warrants further study.