Showing papers in "Acta Crystallographica in 1988"

On the Use of Least-Squares Restraints for Origin Fixing in Polar Space Groups

Abstract: The theory of fixing the origin of the coordinate system in a polar space group by use of restraints (soft constraints or pseudo-observations) is developed for any space group in any setting. The coefficients of the optimal restraint equation are on the average proportional to the square of the atomic numbers. They are determined directly from the unrestrained singular normal-equations matrix. Application of the restraint results in a positive-definite matrix which is as nearly diagonal as possible for the atomic positional coordinates along the origin-free axes. Correlations between these coordinates are therefore minimized. A very compact completely general and easily implemented algorithm results which functions without user intervention.

Structure of the 4:3 Complex Between Gadolinium Nitrate and 18-Crown-6 Ether: [Gd(NO3)2(C12H24O6)]3[Gd(NO3)6]

Abstract: Le compose du titre cristallise dans C2 avec affinement jusqu'a 0,049. Le complexe est constitue d'anion [Gd(NO 3 ) 6 ] 3− de symetrie 2 et de deux types de cations [Gd(NO 3 ) 2 (18-crown-6)] + , l'un en position speciale de symetrie 2, l'autre en position generale. Ces trois ions etant dans le rapport 1:1:2

Charge Density Study of Boron Nitrilotriacetate, C6H6BNO6, at 100K: a Comparison of Polar Bonds

Abstract: The charge density in the cage molecule boron nitrilotriacetate has been determined experimentally at 100 K from X-ray (MoKct, 2 = 0.71069 A) diffraction data measured to (sin0/,;I,)max= 1\"08 ,/k -Z, and calculated theoretically using an efficient and accurate density functional approach. The structure is noncentrosymmetric, orthorhombic space group Pn2~a, a = 10.468 (2), b = 10.193 (7), c = 6.754 (3) A, Z = 4. The electron density has been refined by least squares to RF= 0.77%. The model includes aspherical rigid atoms represented by a multipole expansion truncated at the hexadecapole level, spherical H atoms, isotropic secondary extinction and the standard structural parameters. Monopolar radial functions were either exponential functions, or flee-atom valence-shell functions modified by the x formalism. The deformation density was constrained to the noncrystallographic molecular symmetry 3m; partially relaxing this symmetry did not reveal features attributable to intermolecular interactions. Static and dynamic maps with infinite and finite resolutions are presented for both types of monopolar radial functions. The theoretical charge density is in good agreement with the observations. Charge densities in the six bonding regions C C , B--N, C N , B--O, C O and C---O are discussed in terms of peak height and bond polarity: the more electron rich the atoms are, the lower are the peaks; bond peaks tend to be displaced towards the more 0108-7681/88/060636-10503.00 electronegative atom. In contradiction with chemical expectation, B--N appears to be more polar than B--O, and C N more polar than C O . This is due to the representation of the bonding density as p(observed) p(promolecule).

Study of the Modulated Phase of (C3H7NH3)2CdCl4 by Single-Crystal X-ray Diffraction

Abstract: Bis(n-propylammonium) tetrachlorocadmate shows a modulated phase stable between two orthorhombic phases on the temperature scale. The superspace group could be determined unambiguously on the basis of the selection rules. In addition to Bragg main reflections, 1137 first-order and 107 second-order satellites with an intensity larger than 3a were measured. The refinement revealed a displacive modulation of harmonic type. The CdCI 6 octahedra show modulation amplitudes larger than 0.2 A. To a first approximation, the dynamics of the octahedra can be analyzed in terms of a rotation about the a axis and a translation along the c axis. The low-temperature phase can be considered as a lock-in of the modulated one with a change of q from 0.42b* to 1 b*. In this phase the rotation of the octahedra about a is frozen and a unique hydrogen-bonding scheme is adopted between the alkylammonium ion and the C1 atoms. For the modulated phase, Mr= 374.5, superspace group PAbs-T~(O,fl, O), a = 7.585 (5), b = 7.359 (1), c = 25.053 (6) A, V= 1398 (1) A 3, Z = 2 (primitive cell), MoKa, 2=0.71069A, ~=22.5cm -~, wR(F) =0.072 for 1791 independent reflections [wR(F)= 0.088 for first-order satellites].