Cryocrystallography of 3-isopropylmalate dehydrogenases at 100 and 150 K

Tanaka, N.; Nagata, Chisato; Moriyama, Hiroshi; Oshima, T.; Nakasako, Masayoshi; Yamamoto, Masanobu; Ueki, Tatzuo

doi:10.1107/s0108767396098595

Cited by 4 publications

(13 citation statements)

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“…where ! is the multiplicity of the th atom, and T ðkÞ is the temperature factor of the th atom translated by the th symmetry operation which includes anharmonic vibration (Tanaka & Marumo, 1982 Table 5 Allowed coefficients a ik of the ith AO based on real functions.…”

Section: Electron Density and Structure Factorsmentioning

confidence: 99%

“…In this method, the AHV potential defined on the Cartesian coordinates (u 1 , u 2 , u 3 ) parallel to the main axes of the harmonic thermal ellipsoid is expanded by the power series of the u i 's and the expansion coefficients are determined by the least-squares method. Since the physical meaning of the AHV parameters is specified, the separation of the two aspherical EDD's due to electron configuration and thermal vibration seems to be done better than by other statistical methods such as the Edgeworth expansion and the Gram-Charlier expansion (Tanaka & Marumo, 1982;Tanaka, 1993;Tanaka & O " nuki, 2002;Makita et al, 2007). However, complete separation is not possible although thermal vibration affects the higher-order reflections more while the bonding outer-shell electrons contribute more to lower-order reflections.…”

Section: Temperature Factorsmentioning

confidence: 99%

“…Its application to EDD investigations at different temperatures has been fruitful. Electron transfer from Ce to B 6 was found when the temperature was lowered from room temperature to 100 K, accompanied by enhanced anharmonic vibration (AHV) at 165 and 100 K (Tanaka & O " nuki, 2002). It was concluded that electron transfer continued because it enhances the AHV which corresponds to an increase in entropy.…”

Section: Introductionmentioning

confidence: 98%

“…When the symmetry of the crystal field is lower than that of the cubic and hexagonal point groups, the coefficients of the linear combination of the five real d orbitals become adjustable variables in the least-squares refinement and the orthonormal relationships between AO's need to be introduced in the refinement (Tanaka, 1988). The method was applied to the determination of d-orbital functions of the Cu 2+ ion of bis-(1,5-diazacyclooctane)copper(II) nitrate (Tanaka, 1993) and the 3d-orbital functions in the C i crystal field were determined.…”

Section: Introductionmentioning

confidence: 99%

“…The extension of the analysis to treat all the atomic orbitals in crystals including s, p, d and f orbitals is what we call XAO analysis. It was applied to CeB 6 crystals (Tanaka et al, 1997;Tanaka & O " nuki, 2002) with the program QNTAO (KT), 1 keeping the orthonormal condition and electroneutrality of the crystal. In the XAO analysis, each atom is divided into subshell electrons, which makes it possible to keep the crystal electrically neutral and to analyse the electron transfer among AO's in the unit cell.…”

Section: Introductionmentioning

confidence: 99%

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X-ray atomic orbital analysis. I. Quantum-mechanical and crystallographic framework of the method

et al. 2008

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The scattering unit of X-ray crystal structure analysis is changed from atoms to the subshell electrons by X-ray atomic orbital analysis (XAO). All the atoms in the unit cell are divided into groups of subshell electrons in the XAO analysis. Each subshell is treated as an independent pseudo-atom, which enables the atomic orbitals (AO's) and the electron population of each AO expressed as a linear combination of s/p/d/f orbitals in each subshell to be determined. When the environmental condition of the sample is varied, the electron transfer among the AO's in the crystal can be traced with XAO. It is applicable mainly to analyses of the electron-density distribution in ionic solids including those with a nonstoichiometric structure. The expansion coefficients of each AO are calculated with the perturbation theory putting a point charge on each atom in the unit cell. This automatically makes the perturbation potential have the point-group symmetry of the atom in the crystal field. Then the coefficients of each AO are refined to fit to the observed structure factors keeping the orthonormal relationships among the AO's. Complex basis functions with alpha or beta spin as well as real ones are employed for heavy atoms and the relationships among the coefficients for the AO's of an electron in the crystal fields of the 32 point-group symmetries are derived for p, d and f orbitals. The AO's thus derived can be applicable to an anti-symmetrized multi-electron system, although X-ray diffraction cannot specify the atomic terms occupied when the crystal symmetry permits the atom to have many terms.

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Section: Electron Density and Structure Factorsmentioning

confidence: 99%

Section: Temperature Factorsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

X-ray atomic orbital analysis. I. Quantum-mechanical and crystallographic framework of the method

et al. 2008

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4f-Electron Density Distribution in Crystals of CeB₆ at 165 K and its Analysis Based on the Crystal Field Theory

Tanaka¹,

Kato²,

Ōnuki³

1997

Acta Crystallogr Sect B

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Abstract4f-Electron density in single crystals of CeB 6, cerium hexaboride, was measured at 165 K by X-ray diffractometry. Significant peaks 2.0eA -3 high were found along the (100) directions at 0.41A from Ce on the deformation density map. Analysis based on the crystal field theory removed the peaks, confirming that they were due to the Ce 4f-electrons on the tlu-orbital. The deformation density in the B 6 octahedron was also markedly improved by the analysis and coincides qualitatively with a theoretical molecular orbital (MO) calculation. It also coincides with the model deformation density map of CaB 6 composed of only light atoms. These facts guarantee the accuracy of the intensity measurement for the present study. Since Ce 3+ has only one 4f-electron, a highly accurate intensity measurement is necessary to detect its 4f-electron density distribution. A ~-scan technique was therefore employed to avoid multiple diffraction (MD) and to measure the intensities at w and X angles with minimum fluctuation of temperature at the sample position. Relativistic radial functions for orbitals of Ce 3+ and the corresponding scattering factors, which take the aspherical electron density distribution of 4f-electrons into account, were used for the analysis. CeB 6 is a typical dense Kondo material. The Kondo effect occurs in CeB 6 from low temperature to above room temperature. X-ray analysis of the f-electron density based on atomic orbitals (AO) revealed that 1.5(2) electrons are donated from B 6 to Ce and a total of 2.5 (2) electrons localize on the 4f-orbital. x values are consistent with the 4f-orbitals being highly contracted and thus stabilized. These may be related to the Kondo effect.

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X-ray molecular orbital analysis. I. Quantum mechanical and crystallographic framework

Tanaka

2018

Acta Cryst Sect A

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Molecular orbitals were obtained by X-ray molecular orbital analysis (XMO). The initial molecular orbitals (MOs) of the refinement were calculated by the ab initio self-consistent field (SCF) MO method. Well tempered basis functions were selected since they do not produce cusps at the atomic positions on the residual density maps. X-ray structure factors calculated from the MOs were fitted to observed structure factors by the least-squares method, keeping the orthonormal relationship between MOs. However, the MO coefficients correlate severely with each other, since basis functions are composed of similar Gaussian-type orbitals. Therefore, a method of selecting variables which do not correlate severely with each other in the least-squares refinement was devised. MOs were refined together with the other crystallographic parameters, although the refinement with the atomic positional parameters requires a lot of calculation time. The XMO method was applied to diformohydrazide, (NHCHO), without using polarization functions, and the electron-density distributions, including the maxima on the covalent bonds, were represented well. Therefore, from the viewpoint of X-ray diffraction, it is concluded that the MOs averaged by thermal vibrations of the atoms were obtained successfully by XMO analysis. The method of XMO analysis, combined with X-ray atomic orbital (AO) analysis, in principle enables one to obtain MOs or AOs without phase factors from X-ray diffraction experiments on most compounds from organic to rare earth compounds.

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Cryocrystallography of 3-isopropylmalate dehydrogenases at 100 and 150 K

Cited by 4 publications

References 0 publications

X-ray atomic orbital analysis. I. Quantum-mechanical and crystallographic framework of the method

X-ray atomic orbital analysis. I. Quantum-mechanical and crystallographic framework of the method

4f-Electron Density Distribution in Crystals of CeB₆ at 165 K and its Analysis Based on the Crystal Field Theory

X-ray molecular orbital analysis. I. Quantum mechanical and crystallographic framework

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Cryocrystallography of 3-isopropylmalate dehydrogenases at 100 and 150 K

Cited by 4 publications

References 0 publications

X-ray atomic orbital analysis. I. Quantum-mechanical and crystallographic framework of the method

X-ray atomic orbital analysis. I. Quantum-mechanical and crystallographic framework of the method

4f-Electron Density Distribution in Crystals of CeB6 at 165 K and its Analysis Based on the Crystal Field Theory

X-ray molecular orbital analysis. I. Quantum mechanical and crystallographic framework

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Product

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4f-Electron Density Distribution in Crystals of CeB₆ at 165 K and its Analysis Based on the Crystal Field Theory