X-ray analysis of wavefunctions by the least-squares method incorporating orthonormality. II. Ground state of the Cu2+ ion of bis(1,5-diazacyclooctane)copper(II) nitrate in a low-symmetry crystal field

1993 ◽  
Vol 49 (6) ◽  
pp. 1001-1010 ◽  
Author(s):  
K. Tanaka
Keyword(s):  
Least Squares ◽  
Crystal Field ◽  
Ground State ◽  
Least Squares Method ◽  
X Ray ◽  
Low Symmetry

Reactions of (η5-C9H7)Rh(η2-C2H4)2 with quinones: molecular structure of [(η5-C9H7)Rh(2,3,5,6-C6O2(CH3)4)]

1999 ◽  
Vol 77 (2) ◽  
pp. 199-204
Author(s):  
Stephen A Westcott ◽  
Nicholas J Taylor ◽  
Todd B Marder
Keyword(s):  
Molecular Structure ◽  
Least Squares ◽  
Ground State ◽  
Slip Parameter ◽  
X Ray Diffraction ◽  
X Ray ◽  
A Value ◽  
Hinge Angle

Reactions of (η5-C9H7)Rh(η2-C2H4)2 (1) with quinones were investigated. Substitution of the labile ethylene ligands was observed upon addition of either duroquinone (2,3,5,6-tetramethyl-1,4-benzoquinone) or 1,4-benzoquinone to complex 1. The molecular structure of neutral (η5-C9H7)Rh(2,3,5,6-C6O2(CH3)4) (3), determined by X-ray diffraction, shows that the duroquinone ligand lies in a plane nearly parallel to the indenyl group. The carbonyl moieties of duroquinone lie in a plane incorporating Rh, C2, and the midpoint between C3a and C7a of the indenyl ring. The slip parameter (Δ= d(average Rh-C3a,7a) -d(average Rh-C1,3)) was calculated to be 0.112(2) Å; whereas a value of ca. 0.05 Å had been obtained previously from film data. Values for the hinge angle (HA = angle between normals to the least-squares planes defined by C1, C2, C3 and C1, C7a, C3a, C3) and fold angle (FA = angle between normals to the least-squares planes defined by C1, C2, C3 and C3a, C4, C5, C7, C7a) are 7.2° and 4.0°, respectively.Key words: indenyl, rhodium, quinones, ring-slippage, ground-state distortion.

The crystal structure of kogarkoite, Na3SO4F

1980 ◽  
Vol 43 (330) ◽  
pp. 753-759 ◽  
Author(s):  
L. Fanfani ◽  
G. Giuseppetti ◽  
C. Tadini ◽  
P. F. Zanazzi
Keyword(s):  
Crystal Structure ◽  
Least Squares ◽  
Least Squares Method ◽  
Thermal Parameters ◽  
Cell Content ◽  
Space Group ◽  
X Ray ◽  
Structural Relationships ◽  
Automatic Diffractometer ◽  
Monoclinic Cell

SummaryThe crystal structure of synthetic kogarkoite has been determined from X-ray data collected on an automatic diffractometer. The refinement was performed by a least-squares method employing anisotropic thermal parameters. The 3157 reflections with I > 3σ(I) converged to a conventional R value of 0.033. The cell content is 12 Na3SO4F, the space-group P21/m, a = 18.074, b = 6.958, c = 11.443 Å, β = 107.71°.Kogarkoite presents a marked trigonal subcell with c′ corresponding to [102] of the monoclinic cell. The tridimensional framework can be considered built up by nine differently stacked layers of Na atoms approximately perpendicular to the c′ axis (five sheets are present in galeite, six in sulphohalite, and seven in schairerite). The very close structural relationships between these minerals are discussed.

Crystal and molecular structure of 3-ethyl-4-hydroxy-1,2,3(4H)-benzotriazine and 6-chloro-4-hydroxy-3-methyl-4-phenyl-1,2,3-benzotriazine

1985 ◽  
Vol 63 (3) ◽  
pp. 581-585 ◽  
Author(s):  
Kwong Khee Lai ◽  
Carl H. Schwalbe ◽  
Keith Vaughan ◽  
Ronald J. Lafrance ◽  
Clive D. Whiston
Keyword(s):  
Molecular Structure ◽  
Hydrogen Bonds ◽  
Least Squares ◽  
Least Squares Method ◽  
Crystal And Molecular Structure ◽  
Tetrahedral Geometry ◽  
Orthorhombic System ◽  
Full Matrix ◽  
X Ray ◽  
R Factor

The crystal structures of the title compounds have been determined from X-ray data collected on a four-circle diffractometer and refined by the full-matrix least-squares method. The former compound crystallizes in the orthorhombic system, space group Pbcn, with a = 14.346(8), b = 7.239(1), c = 17.276(2) Å, and has been refined to a conventional R factor of 0.043 for 890 observed reflections. Corresponding results for the latter compound are monoclinic, P21/n, a = 12.222(4), b = 7.482(2), c = 14.170(8) Å, β = 94.06(4)°, R = 0.060 for 2128 observed data. The triazine rings of both compounds exhibit short N(1)—N(2) bonds and tetrahedral geometry at C(4); however, the ring is puckered in the first compound but flat in the second. Molecules in both crystals are linked by [Formula: see text] hydrogen bonds.

5d and 4f electron configuration of CeB6 at 340 and 535 K

2008 ◽  
Vol 64 (5) ◽  
pp. 534-549 ◽  
Author(s):  
Ryoko Makita ◽  
Kiyoaki Tanaka ◽  
Yoshichika Ōnuki
Keyword(s):  
Electron Transfer ◽  
Crystal Field ◽  
Ground State ◽  
Room Temperature ◽  
Atomic Orbital ◽  
Energy Levels ◽  
Electron Configuration ◽  
Acta Cryst ◽  
X Ray ◽  
The Difference

X-ray atomic orbital (XAO) analysis revealed that at both temperatures the electrons are transferred from B 2px (= py ) to Ce 5d and 4f orbitals. At 340 K 5d(j = 5/2)Γ8 orbitals are occupied partially, but 4f(j = 5/2)Γ8 orbitals are more populated than 4f(j = 5/2)Γ7 orbitals, in contrast to our observation at 430 K [Makita et al. (2007). Acta Cryst. B63, 683–692]. At 535 K the XAO analysis revealed clearly that the order of the energy levels of 4f(j = 5/2)Γ8 and Γ7 states reversed again and is the same as that at room temperature. It also limited the possible 5d configurations to three models among the nine possible ones. However, the XAO analysis could not decide which of the three models was the best with the present accuracy of the measurement. Two of them have partially and fully occupied 5d(j = 5/2)Γ7 orbitals and the remaining one has a fully occupied 5d(j = 3/2)Γ8 orbital. Since the lobes of 5d(j = 3/2)Γ8 or 5d(j = 5/2)Γ7 orbitals do not overlap with the 4f(j = 5/2)Γ8 orbitals as well as the 5d(j = 5/2)Γ8 orbitals, the order of the energy levels of the 4f(j = 5/2) orbitals became the same as that at room temperature. These results indicate that the crystal field varies with temperature due to the electron transfer from B 2p to Ce 5d orbitals. The difference densities after the spherical-atom refinement at the three temperatures clearly revealed the different combinations of 4f and 5d orbitals which are occupied. In the present study positive peaks due to the 4f electrons appear near the Ce nucleus and those due to 5d orbitals are found in the area outside the 4f peaks. Between the two areas there is a negative area distributed spherically at 340 K. The negative area produced by the contraction of 4f(j = 5/2)Γ8 orbitals seems to reduce the electron repulsion of the 5d(j = 5/2)Γ8 orbitals and helps the 4f(j = 5/2)Γ8 orbitals to remain as the ground state.

The crystal structure of nickel(II) dimethyldithiocarbamate

1980 ◽  
Vol 45 (8) ◽  
pp. 2147-2151 ◽  
Author(s):  
Jan Lokaj ◽  
Ján Garaj ◽  
Viktor Kettmann ◽  
Viktor Vrábel
Keyword(s):  
Molecular Structure ◽  
Crystal Structure ◽  
Structural Analysis ◽  
Least Squares ◽  
Least Squares Method ◽  
Crystal And Molecular Structure ◽  
Unit Cell ◽  
Special Position ◽  
X Ray ◽  
Triclinic Unit Cell

Crystal and molecular structure of nickel(II) dimethyldithiocarbamate, Ni[S2CN(CH3)2]2 was solved by X-ray structural analysis and refined by the least squares method to R = 0.06 for 1065 reflections. The compound crystallizes in a space group P I and the triclinic unit cell has the dimensions: a = 6.521 (7), b = 6.798 (9), c = 7.633 (4), α = 67.21 (8)°, β = 67.34 (6)° γ =85.59 (9)°. The experimentally observed density is 1.75 g cm-3 and the calculated value for Z = 1 is 1.73 g cm-3. In the structure , the Ni atom occupies a special position in the centre of symmetry and is coordinated by four sulphur atoms in a plane: Ni-S 0.2218 (4) and 0.2198 nm S1-Ni-S2 angle 79.62 (8)°. The ligand S2CNC2 is nearly planar.

The crystal and molecular structure of tris-butyl-tin(IV)-(1-pyrrolidinecarbodithioato)-3-propionate

1989 ◽  
Vol 54 (3) ◽  
pp. 684-690 ◽  
Author(s):  
Jan Lokaj ◽  
Viktor Vrábel ◽  
Eleonóra Kellö ◽  
Vladimír Ratay
Keyword(s):  
Molecular Structure ◽  
Structural Analysis ◽  
Least Squares ◽  
Least Squares Method ◽  
Crystal And Molecular Structure ◽  
Analysis Method ◽  
Monoclinic System ◽  
X Ray ◽  
Cell Dimensions ◽  
Unit Cell Dimensions

The crystal and molecular structure of Bu3Sn(pyrn-dtc-prop) was solved by the X-ray structural analysis method and refined by the block diagonal least squares method to R = 0.053 for 1 930 observed reflections. The compound crystallizes in the monoclinic system with a space group of P21/c, Z = 4, F(000) = 1 056, with unit cell dimensions of a = 1.4758(5), b = 0.9970(3), c = 1.9166(6) nm; β = 113.90(2)°. The measured and calculated crystal densities were Dm = 1.32 and Dc = 1.31.103 kg m-3. The tin atom is coordinated by three carbon atoms at distances of Sn-C 0.2117(8), 0.2133(8), 0.2158(11) nm and two oxygen atoms O(1) and O(2) at distances of Sn-O 0.2210(5) and 0.2399(5) nm. The coordination polyhedron is a deformed trigonal bipyramid. The S2CN ligand is approximately planar.

SOLVING MINERALOGY PROBLEMS WITH THE HELP OF THE “ORIGIN" PACKAGE

2020 ◽  
Vol 386 (4) ◽  
pp. 6-12
Author(s):  
R. T. Abdraimov ◽  
B. E. Vintaykin ◽  
P. A. Saidakhmetov ◽  
N. K. Madiyarov ◽  
M. A. Abdualiyeva
Keyword(s):  
Spectral Analysis ◽  
Fourier Analysis ◽  
Least Squares ◽  
Phase Analysis ◽  
Least Squares Method ◽  
Spectral Lines ◽  
X Rays ◽  
Cauchy Function ◽  
X Ray ◽  
Smoothing Functions

Algorithms for solving typical mineralogical problems associated with quantitative x-ray spectral analysis and quantitative x-ray phase analysis using the program “Origin” are developed. The calculation of the areas and midpoint of spectral lines using the tabular processor of the program “Origin” is considered. Various approaches to determining the parameters of spectral lines using the least squares method using the standard functions of the program “Origin” were tested. The creation of a user function for approximation of diffraction maxima by the Cauchy function taking into account the doublet character of Ka series of x-rays is also considered. Various built-in algorithms for smoothing functions (based on averaging, polynomial approximation and Fourier analysis – synthesis) were tested to find weak diffraction maxima against strong noise; optimal schemes for the application of these algorithms were found. The considered algorithms can be applied in universities when processing the results of laboratory works on the topics "Analysis of spectra of emission of atoms", "Quantitative x-ray spectral analysis" and "Quantitative x-ray phase analysis".

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