Electron population analysis with rigid pseudoatoms

Abstract

The one-electron density function for a group of atoms within the asymmetric region of a unit cell is represented by a finite multipole expansion of the charge density about each atomic center. Each atomic expansion is called a pseudoatom. If the pseudoatom charge density is effectively rigid with nuclear motion, then the model may be used for a static charge density analysis of X-ray diffraction data. A valence density multipole model for pseudoatoms is restricted to single exponential radial functions. The representation is rotationally invariant. The model may be used for determination of static charge physical properties as well as aspects of chemical bonding. These results can be a critical test of the X-ray diffraction experiment for the determination of electron density distributions. The pseudoatoms discussed are primarily intended for crystals comprised of first and second-row atoms. The valence scattering model demands extensive data sets (probably at low temperatures) or an independent determination of atomic positions and mean square amplitudes of vibration.

Theoretical and experimental (113 K) electron-density study of lithium bis(tetramethylammonium) hexanitrocobaltate(III)

“…The electron-density determination is known to be a powerful tool to add chemical and physical information to that obtained by other techniques. For this reason, we have studied the electrondensity distribution of Li[N(CH3)4]2[Co(NO2)6] determined both experimentally at 113 K by the multipoleexpansion method (Stewart, 1976) and theoretically by the periodic Hartree-Fock method (Pisani, Dovesi & Roetti, 1988).…”

Asphericity effects in the electron density of VF2

“…The multipole basis functions compatible with the site symmetry of the V 2+ ion in VF2, mmm, include one monopole, pO, two quadrupoles, pO and P2~ c°s(2~) and three hexadecapoles, pO, I. tsin (2~) I c°s(2~) P 4~cOs(4~b) (Stewart, 1976). Hence, P~ (sin (2~)' 4[ sin (4~) the scattering factor may be written as In this analysis, only reflection data from crystal II were used.…”

“…An independent attempt to interpret the observed asphericities in the charge-density distribution of VF2 was based on the multipole model proposed by Stewart (1973Stewart ( , 1976• The wave functions used in the multipole expansion of the charge density about each atomic centre are products of a radial function for the Ithorder multipole of atom p (Rpt) and a Tesseral .,fcos (m@). harmonic P~'(cos V)~sin (m~) ' the latter are generated by orbital products among 2s, 2p and 3d atomic orbitals on the same scattering centre.…”

“…Co is a measure of the spherical contribution of the 3d electrons to the scattering factor. The aspherical electron density associated with the multipole p0, whose amplitude is C20, shows positive lobes directed along the Z axis (Stewart, 1976). Hence, the negative value obtained for C2o evidences a deficiency of charge density along the directions V 2÷-F-.…”

The electron density distribution in calcium metaborate, Ca(BO2)2

“…In the program VALRAY (Stewart, 1976;Stewart & Spackman, 1981), the total density in the asymmetric unit is assumed to be the sum of localized pseudoatom densities pat. The density with respect to its nucleus of each pseudoatom p is given by…”