Study of the picture change error at the 2nd order Douglas Kroll Hess level of theory. Electron and spin density and structure factors of the Bis[bis(methoxycarbimido) aminato] copper (II) complex

2012 ◽  
Vol 395 ◽  
pp. 44-53 ◽  
Author(s):  
Lukáš Bučinský ◽  
Stanislav Biskupič ◽  
Dylan Jayatilaka
Keyword(s):  
Spin Density ◽  
Structure Factors ◽  
Picture Change Error

Spin density and bonding in the CoCl4 2? ion in Cs3CoCl5. Part 1. Magnetic structure factors from polarised neutron diffraction

1980 ◽  
pp. 2333 ◽  
Author(s):  
Brian N. Figgis ◽  
Philip A. Reynolds ◽  
Geoffrey A. Williams ◽  
Ronald Mason ◽  
Andrew R. P. Smith ◽  
...  
Keyword(s):  
Neutron Diffraction ◽  
Magnetic Structure ◽  
Spin Density ◽  
Structure Factors

Spin density and bonding in the CoCI 2– 4 ion in Cs 3 CoCl 5 - III. The comparison of theory and experiment

1982 ◽  
Vol 384 (1786) ◽  
pp. 31-48 ◽  
Keyword(s):  
Spin Density ◽  
Cobalt Atom ◽  
Theoretical Data ◽  
Total Spin ◽  
Cubic Symmetry ◽  
Hartree Fock ◽  
Density Distributions ◽  
Tetragonal Crystal ◽  
Structure Factors ◽  
Experimental Parameters

We report improvement in the precision of certain of the polarized neutron diffraction data for Cs 3 CoCl 5 . The improvement allows us to analyse the data using a chemically based model of the spin-density distribution that is equivalent to a conventional multipole treatment to fourth order on the cobalt, and to second order on the chlorine atoms of the CoCl 2– 4 ion. To test the completeness of the model and to understand the meaning of the parameters in terms of the wavefunction, we have used it to analyse a set of theoretical magnetic structure factors. These are obtained from the wave-function of a Hartree–Fock calculation on the CoCl 2– 4 ion. We obtain an excellent fit to the theoretical ‘data’ and a much improved fit to the experimental data when the new model is used. We confirm the main features of the spin- and charge-density distributions deduced in our previous study, and we are now also able to interpret the experimental parameters in terms of the wavefunction by analogy with the fit to the theoretical data. We find that there is ca . 3 % of the total spin delocalized onto each chlorine atom of the CoCl 2– 4 ion, dominantly via σ - rather than π -bonding. There is a well defined diffuse spin density on the cobalt atom of 4p symmetry, and strong evidence for 3d–4p mixing. The spin density, in this almost cubic ion, has distinct non-cubic symmetry, which may arise from longer-range effects due to the rest of the tetragonal crystal.

Picture change error in quasirelativistic electron/spin density, Laplacian and bond critical points

2014 ◽  
Vol 438 ◽  
pp. 37-47 ◽  
Author(s):  
Lukáš Bučinský ◽  
Lenka Kucková ◽  
Michal Malček ◽  
Jozef Kožíšek ◽  
Stanislav Biskupič ◽  
...  
Keyword(s):  
Spin Density ◽  
Electron Spin ◽  
Critical Points ◽  
Electron Spin Density ◽  
Picture Change Error

Electron densities in transition metal complexes: population analysis of polarized neutron diffraction data

1980 ◽  
Vol 372 (1748) ◽  
pp. 1-7 ◽  
Keyword(s):  
Transition Metal ◽  
Metal Complexes ◽  
Spin Density ◽  
Transition Metal Complexes ◽  
Population Analysis ◽  
Atomic Spin ◽  
Density Distributions ◽  
Structure Factors ◽  
Multipole Expansions

We describe the use of local multipole expansions to parametrize the spin-density distributions in transition metal complexes, derived from Bragg magnetic structure factors, and discuss the determination of ‘local orbital’ populations. The methods are used to derive quantitative atomic spin-density distributions in the (CrF 6 ) 3- ion.

Spin density and bonding for the CoBr 2– 4 ion in Cs 3 CoBr 5 . A polarized neutron diffraction study

1982 ◽  
Vol 384 (1786) ◽  
pp. 49-55 ◽  
Keyword(s):  
Spin Density ◽  
Field Effect ◽  
Least Squares Method ◽  
Cobalt Atom ◽  
Neutron Diffraction Study ◽  
Density Data ◽  
Cubic Symmetry ◽  
Crystal Field Effect ◽  
Structure Factors ◽  
Magnetization Density

Magnetization density data have been obtained for Cs 3 CoBr 5 . A chemically based model for the spin density in the CoBr 2– 4 ion has been fitted to 160 observed magnetic structure factors by a least-squares method ( X = 1.04). Most of the spin resides in the 3d(t 2 ) orbitals as expected (2.77 (4)) but 12 % is delocalized onto the ligand bromine atoms in a bond of mainly σ symmetry, but having a significant small π -symmetry component. On the cobalt atom, there is spin in 4p z orbitals, and substantial mixing of 4p z and 3d xy orbitals. This mixing, and other parameters, show substantial deviation from cubic symmetry. While the covalence is 17 % more than in the CoCl 2– 4 ion in the isomorphous compound Cs 3 CoCl 5 , the deviation from cubic symmetry is much less . This suggests that the non-cubic distortions arise from outside the CoX 2– 4 ions, that is a ‘crystal field’ effect on the whole CoX 2– 4 ion.

Some Applications of the U. S. Steel MVEM

1973 ◽  
Vol 31 ◽  
pp. 4-5
Author(s):  
J. S. Lally ◽  
L. E. Thomas ◽  
R. M. Fisher
Keyword(s):  
Electron Diffraction ◽  
Debye Temperature ◽  
Metals And Alloys ◽  
Critical Voltage ◽  
Dynamical Diffraction ◽  
Phase Structures ◽  
Structure Factors ◽  
Local Bonding ◽  
Diffraction Phenomenon ◽  
Multi Phase

A variety of materials containing many different microstructures have been examined with the USS MVEM. Three topics have been selected to illustrate some of the more recent studies of diffraction phenomena and defect, grain and multi-phase structures of metals and minerals.(1) Critical Voltage Effects in Metals and Alloys - This many-beam dynamical diffraction phenomenon, in which some Bragg resonances vanish at certain accelerating voltages, Vc, depends sensitively on the spacing of diffracting planes, Debye temperature θD and structure factors. Vc values can be measured to ± 0.5% in the HVEM ana used to obtain improved extinction distances and θD values appropriate to electron diffraction, as well as to probe local bonding effects and composition variations in alloys.

Isomorphous replacement in electron diffraction of wet crystals of rat hemoglobin

1983 ◽  
Vol 41 ◽  
pp. 446-447
Author(s):  
William F. Tivol ◽  
Murray Vernon King ◽  
D. F. Parsons
Keyword(s):  
Electron Diffraction ◽  
Heavy Atom ◽  
Isomorphous Substitution ◽  
X Ray Diffraction ◽  
Salt Solutions ◽  
X Ray ◽  
Isomorphous Replacement ◽  
Structure Factors ◽  
Diffraction Structure ◽  
The Mean

Feasibility of isomorphous substitution in electron diffraction is supported by a calculation of the mean alteration of the electron-diffraction structure factors for hemoglobin crystals caused by substituting two mercury atoms per molecule, following Green, Ingram & Perutz, but with allowance for the proportionality of f to Z3/4 for electron diffraction. This yields a mean net change in F of 12.5%, as contrasted with 22.8% for x-ray diffraction.Use of the hydration chamber in electron diffraction opens prospects for examining many proteins that yield only very thin crystals not suitable for x-ray diffraction. Examination in the wet state avoids treatments that could cause translocation of the heavy-atom labels or distortion of the crystal. Combined with low-fluence techniques, it enables study of the protein in a state as close to native as possible.We have undertaken a study of crystals of rat hemoglobin by electron diffraction in the wet state. Rat hemoglobin offers a certain advantage for hydration-chamber work over other hemoglobins in that it can be crystallized from distilled water instead of salt solutions.

Computer processing of high-resolution images of periodic specimens

1986 ◽  
Vol 44 ◽  
pp. 2-5
Author(s):  
W. Chiu ◽  
M.F. Schmid ◽  
T.-W. Jeng
Keyword(s):  
High Resolution ◽  
Fourier Transforms ◽  
Complex Structure ◽  
Distribution Functions ◽  
Multiple Image ◽  
Cryo Electron Microscopy ◽  
Structure Factors ◽  
Unit Cells ◽  
High Resolution Images ◽  
Phase Probability Distribution

Cryo-electron microscopy has been developed to the point where one can image thin protein crystals to 3.5 Å resolution. In our study of the crotoxin complex crystal, we can confirm this structural resolution from optical diffractograms of the low dose images. To retrieve high resolution phases from images, we have to include as many unit cells as possible in order to detect the weak signals in the Fourier transforms of the image. Hayward and Stroud proposed to superimpose multiple image areas by combining phase probability distribution functions for each reflection. The reliability of their phase determination was evaluated in terms of a crystallographic “figure of merit”. Grant and co-workers used a different procedure to enhance the signals from multiple image areas by vector summation of the complex structure factors in reciprocal space.

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