Residual Electron Density Research Articles

Electron density distribution in crystals of potassium trifluorocobaltate(II)

The electron density distribution in crystals of KCoF 3 was investigated on the basis of X-ray intensity data collected by diffractometry at 293 K. The characteristic residual electron density around the Co 2+ ion in the octahedral crystal field was observed on the difference Fourier maps when spherical scattering factors were used for the Co 2+ ion. With aspherical scattering factors for the 3d electrons of the Co 2+ ion, structure amplitudes were calculated for two electron configurations, i.e. high spin 4Tg(t2g)5(eg) 2 and low spin 2Eg(t2g)6(eg ). Refinement on the assumption of high spin decreased the R value significantly (0.0077) from that (0.0088) obtained with the spherical refinement, while assumption of low spin increased the value (0.0120). The difference density maps obtained after these refinements also showed that the high-spin (tEg)5(eg) 2 electron configuration is a good approximation of the electronic state for the Co 2+ ion in cubic KCoF 3 crystals at room temperature. [Crystal data: cubic, Pm3m, a = 4.0688 (7)A, V = 67.36 (3)/~3, Z = 1, D x = 3.821 Mg m -3, 2(MoKa) = 0.7107A, /~(Mo Ka) = 7.943 mm -~, T = 293 K; 743 reflections with IFI > 3trlFI.] crystal fields were observed in crystals of y-Co2SiO 4 (Marumo, Isobe & Akimoto, 1977) and CoA120 4 (Toriumi, Ozima, Akaogi & Saito, 1978) respectively. On the deformation density maps of y-C02SiO 4 eight positive peaks were observed around the Co 2+ ion on the lines along the (111 ) directions of the cubic lattice, and six negative peaks on the Co-O bonds. These peaks indicate that the electron density of the t2g orbitals is higher than that of the eg orbitals as a result of splitting of the d orbitals in a quasi-octahedral field. The deformation density around the Co 2÷ ion in CoA120 4 clearly shows that the density on the t2g orbitals is lower than that on the eg, giving an arrangement of negative and positive peaks reversed to that in an octahedral field. The present study was undertaken to increase knowledge on electron density distributions around the transition-metal ions in an octahedral field. In the octahedral crystal field, the ground state of a Co 2+ ion can be either high spin (t2g)5(eg) 2 or low spin (12g)6(eg) depending upon the strength of the crystal field. The refinements were performed for both configurations with aspherical scattering factors and the residual densities after these refinements were compared.

Chemistry of the metal carbonyls. Part 76. Platinum–osmium carbonyl complexes derived from decacarbonyldi-µ-hydrido-triosmium; X-ray crystal structure of [Os3Pt(µ-H)2(CO)10{P(cyclo-C6H11)3}

Reactions between [OS3(µ-H)2(CO)10] and the compounds [Pt(C2H4)2(PR3)][PR3= P(cyclo-C6H11)3, PPh3, or PBut2Me] afford tetranculear metal complexes [Os3Pt(µ-H)2(CO)10(PR3)]. Examination of the variable-temperature 1H n.m.r. spectra of these ‘58-electron’ clusters reveals dynamic behaviour with site exchange of the two hydrido-ligands, the energy barrier for this process for the PBut2Me derivative being ca. 58 kJ mol–1. In order to establish the molecular structure of these complexes a single-crystal X-ray diffraction study was made on the compound containing the P(cyclo-C6H11)3 ligand. Crystals are monoclinic, space group P21/c, Z= 4, in a unit cell of dimensions a= 11.822(4), b= 16.584(5), c= 17.763(9)A, and β= 108.10(4)°. The structure has been refined to R 0.035 (R′ 0.038) for 5 737 reflections to 2θ < 60°(Mo-Kα, X-radiation) collected at 200 K. The metal atoms adopt a slightly asymmetric tetrahedral structure [Os–Os 2.777(1), 2.741(1), and 2.789(1)A; Os–Pt 2.791(1), 2.832(1), and 2.863(1)A]. The platinum atom is bonded to a CO group and to the P(cyclo-C6H11)3 ligand, and each osmium is attached to three CO groups. The hydrido-ligands bridge the longer of the Os–Os and Os–Pt bonds, as deduced from observation of residual electron densities, from widening of certain Pt–Os–CO and Os–Os–CO angles, from staggered conformations of two of the Os(CO)3 groups with respect to the two longer edges of the tetrahedron, and from calculation of potential energy minima.

On the estimation of atomic charges by the X-ray method for some oxides and silicates

Based on accurate X-ray diffraction intensity data collected from spherically shaped single crystals, net atomic charges and electron density distributions have been studied for MnO, Mn2SiO4, Mg2Si2O6, LiAlSi2O6 and CaMgSi2O6. Examination of various procedures for determining atomic charges in a given structure has led to the conclusion that the following approach appears to be most reliable. (1) For cations: the number of electrons in the sphere of radius ER, effective distribution radius, which is defined according to the characteristics of radial distribution functions or difference-Fourier maps, is calculated. (2) For oxygen atoms: with the cation charges fixed at the values obtained from the above procedure and the total charge of the crystal constrained to be neutral, oxygen charges are estimated from least-squares refinements using atomic scattering factors. The final charges of atoms examined are less ionic than the corresponding formal ones: those of Li, O, Mg, Al, Si, Ca and Mn are respectively + 0.7 (1), -1.1 to -1.5, + 1.4 (1) to + 1.8, + 2.4(1), + 2.2 (1) to + 2.6, + 1.4 (2) and + 1.2 (1) to + 1.6 e. Residual electron densities between Si and O have been clearly observed in difference-Fourier maps after charge refinements for crystals of LiAlSi2O6, CaMgSi2O6 and Mg2Si2O6.

MO and vibrational normal coordinate calculations of 1,1,4,4,-tetramethyl-1,4-diazonia-2,5-diboratacyclohexane

All-valence-electron IEHT and CNDO/2 molecular orbital calculations and an infrared vibrational normal coordinate analysis were carried out for the study of the bonding in the title compound with its six-membered ring, repeating, all-four-coordinated NBC sequence. Results of these calculations agree qualitatively with one another as well as with the residual electron density map calculated from the observed and calculated structure factors in an X-ray structure determination, which showed that the BC bond is relatively stronger than the BN bond in this molecule. The results of MO calculations also indicate that partial electron transfer from the nitrogen to the boron atom has occurred in the formation of the boronnitrogen bond. The stretching force constants for the BN and BC bonds are 2.19 and 3.33 mdyn Å −1, respectively.

Cation ordering in the tetrahedral sites of the thiospinel FeIn 2S 4 (indite)

Recent X-ray and electron diffraction studies have substantiated earlier indications, based on dielectric behavior, e.s.r. studies, elastic constants, magnetic measurements, specific heat and spectral data, that in many cases the cubic spinel structure exhibits a small deviation from Fd3 m symmetry. This discrepancy has been associated with a small displacement (less than 0.10Å) of the octahedrally coordinated metal atom along [111] in space group F4̄3 m but has not hitherto been tested using precise single crystal X-ray diffraction data. Although more than thirty hk0 reflections of the type h + k = 4 n + 2, structurally forbidden for the space group Fd3 m, are clearly visible in diffraction patterns from the thiospinel indite ( FeIn 2S 4; a = 10.618(3) A ̊ ), a refinement in space group Fd3 m using 412 unique X-ray data ( u = 0.25907(7); inversion parameter = 0.947(7); R = 0.048) indicates that the structure may be satisfactorily described in terms of the conventional symmetry. A refinement of the data in space group F4̄3 m shows that the displacement, if present, is not detectable within experimental error but allows a rationalization of the observed diffraction symmetry in terms of an unequal distribution of In atoms over the two nonequivalent tetrahedral sites in F4̄3 m (100 and 83 ± 1% In, respectively) and the presence of a nonspherical distribution of residual electron density about the octahedral site.

Ｘ線の異常散乱 強度測定と精度

Accuracy of the structural parameters determined by the least-squares refinements and the features of residual electron densities are affected by the errors both in the observed and calculated X-ray structure factors, as well as by the refinement procedures. These errors are summarized and discussed. Anomalous dispersion effect could be one of these error sources if it is not treated properly. Some successful examples are given, in which the absolute configuration of molecules composed of light atoms is determined by means of X-ray anomalous scattering.

Density matrix in the open shell theory

AbstractAll the second‐order density matrix spin components for the spin‐projected Slater determinant are presented as expansions in direct products of powers of unprojected spin‐ and residual electron density matrices. Spin components of the second‐order transition density matrices between spin‐projected Slater determinants built of orthogonal orbitals are also obtained.

Matrix formulation of the generalized Hartree‐Fock methods

AbstractSpin‐projected one‐particle density and spin density matrices are presented as polynomials of suitable unprojected quantities with generalized Sasaki‐Ohno coefficients. Thus an explicit form of Harriman's theorems is given. For the two‐particle spatial density matrix an expansion in direct products of powers of unprojected residual electron and spin density matrices is given. For these basic matrices of the scheme the variational spin‐extended equations are formulated.

Residual ionization in the polar lower ionosphere

S>Turbulent scattering of 2.3 Mc/s radio waves is found to persist throughout the polar night between altitudes of 80 and 100 km at a geomagnetic latitude of 79 deg S. Residual electron densities are estimated to increase from 5/cm/sup 2/ at 80 km to 1 or 2 x 10/sup 2/ between 90 and 100 km. Transport processes are unable to maintain these concentrations, though tarbulent transport may assist. Present estimates of electron loss rates require ionization rates in excess of cosmic-ray production. An equivalent vertical flux of protons of 0.2 < E < 4 Mev energy and density up to 170/cm/sup 2/ sec, or, alternatively, of electrons with 10 kev < E < 100 kev and denstty about 70/cm/sup 2/ sec, is called for. Time variations associated with solar protons and Forbush decreases of cosmic radiation suggest that protons are responsible. (auth)

Improved Keep-Alive Design for TR Tubes

The conditions leading to crystal deterioration and burnout in tr tubes, which exhibit apparent satisfactory leakage characteristics, are investigated experimentally. The characteristics of coaxial keep-alive structures are evaluated by monitoring with probes and light intensity measurements the residual electron density in the interaction gap spacing. The prime factor leading to crystal deterioration is random fluctuations in the electron density which are attributed to a wandering of the keep-alive discharge along the cone wall. During the period of fluctuation the spike energy can become excessive. An improved keep-alive design, in which the cone wall is insulated and the cathode is fabricated from stainless steel, eliminates this effect. TR tubes with the improved keep-alive structure have successfully operated in excess of 1000 hours without any apparent crystal deterioration.