Accurate X-ray Diffraction Data Research Articles

Electrostatic molecular interaction from X-ray diffraction data. II. Test on theoretical pyrazine data

In a previous paper [Moss & Feil (1981). Acta Cryst. A37, 414-421] a method was reported to calculate the electrostatic potential and the electrostatic interaction energy from single-crystal X-ray diffraction data. The method was applied to experimental pyrazine data; however, owing to the relatively low quality of the data, the results were inconclusive. In the present paper the results are presented of a model study in which the method has been applied to the analysis of ideal error-free diffraction data calculated from a theoretical wavefunction. The molecular quadrupole moments and the electrostatic interaction energies of two pyrazine molecules thus obtained are in very good agreement with the corresponding results derived directly from the wavefunction. Thus the proposed method may be used to determine the long-range electrostatic component of molecular interactions from highly accurate X-ray diffraction data.

Electron density distribution in V 3Ge

The electron distribution map in V 3Ge superconducting alloy of A15 family was obtained from accurate X-ray diffraction data. This map was shown having no peaks corresponding to the covalent interaction in the chains of vanadium atoms. Maxima in the map were shown to correspond to the p-electrons of germanium in the field of octahedral symmetry.

Correlations between crystallographic data and physical properties at the 240K and 80K phase transitions in stoichiometric BaVS3

The two phase transitions (at 240K and 80K) which occur in stoichiometric BaVS3 as a function of temperature have been investigated by very accurate powder X-ray diffraction data. These data indicate that the 240K transition, where the crystal symmetry is lowered from hexagonal to orthorhombic, is a displacive transition of second-order type. The thermal variations of a0 and b0/ square root 3 show that between 240K and 80K the orthorhombic distortion increases progressively and does not reach saturation even at 80K. The electric-magnetic 80K transition is accompanied by an additional discontinuity of the lattice parameters. This discontinuity is only observed in the basal a0b0 plane, whereas the c0 parameter follows a normal Debye-expansion law. The data strongly indicate that the 80K transition is of first-order type and that the lattice is still orthorhombic below the transition.

Atoms in molecules

A set of spherical density basis functions for atoms sodium through argon have been obtained by least squares fitting of the corresponding electron density function for the ground state. These density functions, conveniently scaled, can be used in electron population analysis of molecules. To make this population analysis more flexible the density basis functions are split into two inner (K and L shell) parts and one outer (M shell) part. This technique gives populations which are relatively independent of the orbital bases used in spanning the molecular wavefunction. These density functions can be easily converted to scattering factors to be used in similar population analysis of accurate X-ray diffraction data.

Electron density distributions on C–C single, double and triple bonds. Pitfalls and prospects of the analysis of accurate X-ray diffraction data

Results obtained so far at Groningen for electron densities of compounds having single, double and triple C-C bonds are compared with each other and with densities from ab initio theoretical calculations. Suggestions for the improvement of further electron density studies and for the determination of physical properties from diffraction data are made.

The projection of molecular charge density into spherical atoms. I. Density basis functions for first-row atoms

Electron population analyses of several molecular one-electron density functions have been studied by least-squares projection methods into several atomic-density basis functions. All studies have been restricted to spherically symmetrical functions, which have been fitted to the atomic-density functions for the ground-state atoms hydrogen through neon. It is found that when the atom-density basis functions are split into inner (K shell) and outer (L shell) parts, then the atomic charges reflect polarity of the molecule reasonably well and, moreover, are relatively independent of the orbital bases used in spanning the molecular wave function. The standard density basis sets given here can be used for a similar electron population analysis of accurate X-ray diffraction data.

The electron distribution in superconducting alloys: II. Room temperature analysis of Cr 3Si and comparison with V 3Si

The charge distribution in Cr 3Si a non-superconducting alloy of the A-15 family was obtained from accurate X-ray diffraction data. The deformation density in the bond between two adjacent Cr atoms in Cr 3Si is 0.17 eA −3, about three times lower than the density observed in the isomorphous V 3Si structure. Integration of the charge around the Cr and Si atoms leads to a best estimate of 1.3–1.9 electrons for the charge transfer from the Si to three Cr atoms as compared to 1.8 – 2.4 electrons transfered from the Si to the three V atoms in V 3Si.

The electron distribution in superconducting alloys: I. Analysis of V 3Si at room temperature

Accurate X-ray diffraction data are used to obtain the charge distribution in the superconducting alloy V 3Si. The main interaction is found to be strong covalent bonding between adjacent vanadium atoms within the infinite chains. Integration of the charge around the Si and V atoms leads to a best estimate of 1.8–2.4 electrons for the charge transfer from the silicon to the vanadium atoms.

X-ray studies of covalent bonding in diamond and silicon

A discussion is given of two methods used recently for studying the features of covalent bonding in diamond and silicon which are evident in accurate X-ray diffraction data. The numerical features of the approaches adopted by Weiss and Dawson are compared, and it is shown that only the latter’s approach permits adequate interpretation of the experimental evidence.

A general structure factor formalism for interpreting accurate X-ray and neutron diffraction data

The interpretation of X-ray and neutron diffraction data in accurate studies of crystal and molecular structure requires the development of a new structure factor formalism. The formalism normally employed in structure analysis fails to recognize antisymmetric features associated with nonspherical atomic charge distributions and with anharmonic components of the atomic vibration amplitudes. Both these antisymmetric features can be incorporated readily in the analysis of diffraction data by using a general formalism involving complex atomic scattering factors and complex temperature factors. Some implications of the general formalism are discussed. Relations between atomic motions and static positions are considered in terms of equilibrium and time-averaged concepts, and the case of librational motion is cited to illustrate the relation of these concepts to the type of vibrational approximation employed in data analysis. The discussion is extended to general considerations of the atomic scattering powers, and approximations in the customary handling of these quantities are noted.

Density of the Bonding Electrons in Diamond

The electron density in diamond, for the bonding electrons only, is derived from old but accurate experimental x-ray diffraction data by subtracting the contribution of the inner shall electrons from the total. The carbon-carbon single bond appears to be very diffuse.