The partial structure with errors: a probabilistic treatment.

The method of the joint probability distribution functions has been applied to the case in which observed (with errors) and calculated structure factors are available, the latter referred to a part of the structure with finite errors in the coordinates, the thermal parameters and the scattering factors. Results obtained by other authors are confirmed and generalized. A new relationship is found to estimate the parameter sigmaA, affecting the reliability of the estimates of cos(varphi-varphip).

First example of low-valence ion substitution in Ln5O(OPri)13: mixed-valence europium oxoalkoxide [EuIII4EuIIO(OPri)12(HOPri)]HOPri.

The novel mixed-valence alkoxide [Eu3+(4)Eu2+O(OPri)12(HOPri)]HOPri (1) has been prepared and structurally and spectroscopically characterized. The three synthesis routes (i) metathesis of 4EuCl3, EuI2, and 14KOPri combined with hydrolysis with 1H2O, (ii) oxidation of 5[Eu4(OPri)10(HOPri)3]2HOPri with 1.5O2, and (iii) reduction of Eu5O(OPri)13 with 0.

MAD phasing: choosing the most informative wavelength combination.

Two algorithms are described for limiting data resolution and for predicting the most informative wavelength combinations in MAD techniques. Both have been successfully tested using experimental data from a large set of test structures.

Locating heavy atoms by integrating direct methods and SIR techniques.

Direct methods have been applied to the SIR (single isomorphous replacement) case to estimate structure-factor moduli from diffraction magnitudes. The joint probability distribution function P(E(H),E(p),E(d)) has been calculated by explicitly considering, as an additional primitive random variable, the cumulative error arising from measurements and from lack of isomorphism. The specific feature of the approach is that it provides estimated values of |E(H)| which depend on the experimental diffraction data as well as on errors.