Zur Strukturbestimmung mit Hilfe von Superpositionsmethoden

Abstract

By means of two superpositions of P atterson diagrams, it is possible to obtain a model of the structure – at least, theoretically. Further superpositions, if possible m of them, where m is the number of atoms, lead to the electron density function ϱ ( xyz ). The relations of the electron density function to the individual product functions are derived, considering both vector differences and weights. The B uerger formula for these relations is corrected for those maxima which are used as displacement vectors. For Π m , the equation given in this paper is valid. The sum function is unfavorable compared to product function and minimum function. For centrosymmetrical structures one superposition of P atterson diagrams is sufficient, if a ± 2 r i vector is used. The relation of this function ( Π 2 ) to the electron density is easily understood. Generally one can say that the method of superposition of P atterson diagrams is able to yield the relative positions of the atoms of a structure – and, therefore, the electron density ϱ ( xyz ). The refinement can be carried out with the help of the customary procedures.