Helmuth Zimmermann

Chemie polyfunktioneller moleküle: C. synthese und Röntgenstrukturanalyse von dicarbonyl-nitrosyl-(5-diphenylphosphino-uracil) cobalt(—I) ·Methanol(12)☆

Abstract The compound dicarbonylnitrosyl-(5-diphenylphosphino-uracil)cobalt(−I)· methanol( 1 2 ) was prepared by the reaction of Co(NO)(CO)3 with 5-(diphenylphosphino)uracil in tetrahydrofuran and recrystallized from methanol. The complex was identified from its 1H NMR, IR, and mass spectra, and studied by X-ray crystallography. It crystallizes in the monoclinic space group P21/n with a 8.755(1), b 16.549(8), c 16.319(3) A, β 91.97(2)° and Z = 4. The struture was refined on the basis of 3504 reflectios to R = 0.059. The Co atom is four-coordinated in a slightly distorted tetrahedral geometry. The 5-(diphenylphosphino)uracil ligand coordinates through the P atom. One NO and two CO groups occupy the other three sites. The CoP, CoNO and two CoCo distances are 2.231(1), 1.641(3), 1.755(3) and 1.774(3) A, respectively. In the crystal, methanol molecules connect the uracil moieties by hydrogen bonds in a one-dimensional arrangement along the a axis.

Structure determination without Fourier inversion. Part I. Unique results for centrosymmetric examples

Abstract A concept is presented for determining a one-dimensional structure of m independent point scatterers by mapping into an m-dimensional space Pm at least m observations as (m – 1)-dimensional so-called “isosurfaces” defined by s(h) · g(h) or g(h) alone, where s(h) and g(h) are sign and modulus, respectively, of the geometrical structure factor. Values of g(h) are derived from the observed |F(h)|. The “solution vector(s)”, (x1, …, xm), representing the coordinates xj of the point scatterers is (are) found from the “common” intersection(s) of n ≥ m different isosurfaces. Homometric and quasi-homometric structures can thus safely be detected from multiple solutions, the latter mainly arising from the experimental uncertainties of the g(h). Spatial resolution is by far higher than that offered by a corresponding Fourier transform. Computer time can be drastically reduced upon consideration of both the symmetry of Pm and the anti-symmetry and self-similarity properties of the isosurfaces, which allow for tayloring of the intersection search routines and/or applying linear approximations. The basic principles of the method are illustrated by various two- and three-atom structure examples and discussed in view of the application potential to real structure problems.

Structure determination without Fourier inversion. Part II: The use of intensity ratios and inequalities

Abstract Using for a one-dimensional centrosymmetric structure of m equal point scatterers an m-dimensional coordinate parameter space Pm and the (n – 1) independent ratios q(h, k) = [I′(h)/I′(k)]1/2 = g′(h)/g′(k) of n > 1 structure amplitudes observed on relative scale it is shown that the determination of the structure or possibly homometric structures is equivalent to finding the common intersection(s) of (n – 1) ≥ m independent isosurfaces Q[h, k; q] of dimension (m – 1).A fast and efficient reduction of the parameter space to the fraction(s) of Pm that contain(s) the solution(s) can already be achieved on the basis of the qualitative inequalities between the observations. Therefore, emphasis is put on showing that each q(h, k) < 1, i.e.g′(h) < g′(k) (or vice versa) rules out all the regions in Pm that contain point scatterer arrangements incompatible with q(h, k). For small structures, solution strategies are discussed and an estimate is given on the number of data necessary for solving even ‘tough’ problems.

On symmetry classes of crystal structures.

An open-ended classification scheme for crystal structures based on Wyckoff sets and affine normalizer groups is proposed. It is free of metrical and geometrical considerations. All structures of one structure type belong to the same symmetry class. An application is given for the Inorganic Crystal Structure Database (version 2, 2007).

On the symmetry of the symmetry minimum function

The symmetry groups for the symmetry minimum functions often coincide with the Euclidean normalizer (Cheshire group) of the space group of the related crystal structures — but sometimes they do not, as the table in this paper shows.