Electron population analysis of accurate diffraction data. I. Formalisms and restrictions

Abstract

A two-dimensional polynomial method is described which allows rapid evaluation of bond-scattering factors in a structure factor least-squares program. Correlation effects between electron population parameters are analyzed. It is concluded that simultaneous refinement of 2s2 and three 2p2 one-center populations is not possible. Similarly, for the y axis being along a bond AB, the distributions px(A)pz(B) and pz(A)px(B) are identical and only the sum of the corresponding population parameters can be refined. A variety of models is discussed, in which the number of parameters is reduced by selective elimination. In the two-center model all terms but those describing 'long' bonds are included. In the symmetry-restricted two-center model all bonds are required to have mm symmetry, while in the one-center model all two-center terms are neglected. Finally, a full table of symmetry restrictions on population parameters and a brief discussion of thermal motion treatment are given.