Maximum Entropy Method Charge Density Research Articles

Revisit: High resolution charge density study of α-rhombohedral boron using third-generation SR data at SPring-8

Experimental charge density of α-rhombohedral boron (α-B12) by a Maximum entropy method (MEM) has been re-investigated using the high resolution powder diffraction data measured at third-generation synchrotron radiation (SR) source, SPring-8. The present MEM charge density has many discrepancies from the previous MEM charge densities reported by Fujimori et al. and Hosoi et al. The data-resolution dependence of the MEM charge density was investigated using the present data. We found that diffraction data with d > 0.4 Å resolution range were needed to reveal qualitative bonding nature of α-B12 at 100 K. The peculiar bonding natures, such as a bend B–B bond and a propeller-shaped bond, which were found in the previous studies have disappeared by using d > 0.4 Å data. The bonding nature of MEM charge density using the full data with d > 0.327 Å d-spacing range is well agreed with those of theoretical calculations. The present study suggests that resolution test is important for an accurate charge density study of boron related materials.

Direct Visualization of Energy-transferred Excited State in Eu Complex

Highly luminescent lanthanide (Ln) complexes have attracted much attention because Ln3+ions show long-lived ff-emissions with narrow band shape. Their unique photo-optical properties are promising for the design of light-emitting materials and sensing devices. Although the ff-emissions are essentially weak because of Laporte forbidden, chelate ligands is effective to strengthen the intramolecular energy transfer from photo-excited organic ligands to Ln3+ions. The direct evidence of energy transfer from ligands to Ln3+and details of excited state, however, are still veiled. Here, we report direct visualization of energy-transferred excited state in Eu complex with a hexadentate ligand (L) consisting of two bipyridine moieties bridged by an ethylendiamine unit, [Eu3+(L)(NO3)2](PF6) (Eu(L))[1] by Maximum Entropy Method (MEM) charge density[2] and electrostatic potential analysis[3] based on SR X-ray diffraction. First, we confirmed that the electron numbers of Eu and ligand L in the excited state are the same as those in the ground state, which is a direct evidence of energy transfer instead of charge transfer. Next, we observed charge re-distribution in the Eu ion and the ligand L. The electrostatic potential distributions calculated using MEM charge density give an experimental evidence for the existence of polarization of ligand L both in the ground and photo-excited states. The orientation polarization in the ground state changed during pumping at 315 nm, and the charge re-distribution are qualitatively consistent with a theoretical prediction. This characteristic luminescence behavior based on the energy relaxation process have not been detected by fundamental crystal structural analysis. We have succeeded in visualization of subtle but important change due to energy transfer in the mononuclear Europium complex with hexadentate ligand at the first time.

Element-selective charge density visualization of endohedral metallofullerenes using synchrotron X-ray multi-wavelength anomalous powder diffraction data

An algorithm for determining the element-selective charge density has been developed using the maximum entropy method (MEM), Rietveld analysis and synchrotron X-ray multi-wavelength anomalous powder diffraction data. This article describes in detail both experimental and analytical aspects of the developed method. A structural study of yttrium mono-metallofullerene, Y@C82, 1:1 co-crystallized with toluene using the present technique is reported in order to demonstrate the applicability of the method even when only medium resolution data are available (d> 1.32 Å). Element-selective MEM charge density maps, computed from synchrotron X-ray powder diffraction data collected at three distinct wavelengths around the yttriumK-absorption edge (∼0.727 A), are employed for determining three crystallographic sites of the disordered yttrium.

構造生物学研究の新展開 ２．基礎研究から応用展開に向けて（ｂ）技術開発型研究 マキシムエントロピー法のタンパク質構造解析への応用

Accurate structural refinement of a putative acylphoshatase from 1.3 A X-ray diffraction data was carried out using charge densities determined by the Maximum Entropy Method (MEM). The MEM charge density clearly revealed detailed features in the solvent region of the putative acylphosphatase crystalline structure, some of which have never been seen in conventional Fourier map. The structural model in solvent region was constructed as distributions of anisotropic water atoms. The omit-MEM maps and the difference-MEM maps were effective for revealing details of protein structure, such as multi-conformers in side-chains of amino acid residues, anisotropy of atoms, and hydrogen atoms. By model building using the MEM charge densities, the reliability factors, R1 and Rfree, in the SHELX refinements were improved to 9.6% and 10.0%, respectively.

Hindered Rotation of Methane Molecules in the One-Dimensional Nanochannel of a Porous Coordination Polymer

The crystal structure of a microporous coordination polymer with adsorbed methane gas was determined by in situ synchrotron powder diffraction of the gas adsorption and the MEM (maximum entropy method)/Rietveld method. Methane molecules were found to be adsorbed forming a one-dimensional array in the nanochannels of the polymer. The MEM charge density distribution of the adsorbed methane molecules indicated some protrusions which were not observed in that of a spherical atom of adsorbed argon. This was interpreted as a mixed distribution of two uniaxially rotating molecules with different pivotal axes. The methane molecules displayed hindered rotation depending on the shape of the nanopore surface. This result indicates the capability to control the molecular arrangement and orientation by the adsorption of gas molecules on the precisely designed nanopores of coordination polymers.

Electron charge distribution of CaAl 2−xZn x: Maximum entropy method combined with Rietveld analysis of high-resolution-synchrotron X-ray powder diffraction data

Using short wavelength X-rays from synchrotron radiation (SPring-8), high-resolution powder diffraction patterns were collected. In order to study both the structural relationship and the mechanism of stability in the CaAl 2− x Zn x system, among the Laves phases (MgCu 2 and MgNi 2 type) and KHg 2-type structures, the charge density distribution of CaAl 2− x Zn x as a function of x was obtained from the diffraction data by Rietveld analysis combined with the maximum entropy method (MEM). In the MEM charge density maps overlapping electron densities were clearly observed, especially in the Kagomé nets of the Laves phases. In order to clarify the charge redistribution in the system, the deformation charge densities from the densities formed by the constituent free atoms are discussed. In the ternary MgNi 2-type phase, partial ordering of Al and Zn atoms is observed, a finding that is supported by ab-initio total energy calculations.

Application of maximum-entropy maps in the accurate refinement of a putative acylphosphatase using 1.3 Å X-ray diffraction data

Accurate structural refinement of a putative acylphosphatase using 1.3 A X-ray diffraction data was carried out using charge densities determined by the maximum-entropy method (MEM). The MEM charge density clearly revealed detailed features of the solvent region of the putative acylphosphatase crystalline structure, some of which had never been observed in conventional Fourier maps. The structural model in the solvent region was constructed as distributions of anisotropic water atoms. The omit-difference MEM maps and the difference MEM maps were effective in revealing details of the protein structure, such as multiple conformations of the side chains of amino-acid residues, anisotropy of atoms and H atoms. By model building using the MEM charge densities, the reliability factors R1 and R free in the SHELX refinement were dramatically improved from 17.9% and 18.3% to 9.6% and 10.0%, respectively. The present results prove the usefulness of MEM in improving the accuracy of refinement of protein crystal structures.

The MEM/Rietveld method with nano-applications – accurate charge-density studies of nano-structured materials by synchrotron-radiation powder diffraction

Structural studies of materials with nano-sized spaces, called nano-structured materials, have been carried out by high-resolution powder diffraction. Our developed analytical method, which is the combination of the maximum-entropy method (MEM) and Rietveld refinement, the so-called MEM/Rietveld method, has been successfully applied to the analysis of synchrotron-radiation (SR) powder diffraction data measured at SPring-8, a third-generation SR light source. In this article, structural studies of nano-porous coordination polymers and endohedral metallofullerenes are presented with the advanced technique of SR powder experiment. The structure of the adsorbed guest molecule in the coordination polymer and encapsulated atoms in the fullerene cage are clearly revealed by the MEM charge density. The methodology of MEM/Rietveld analysis is also presented.

X-ray charge density study of chemical bonding in skutteruditeCoSb3

The experimental charge density of nondoped $\mathrm{Co}{\mathrm{Sb}}_{3}$ has been determined by the maximum entropy method (MEM) using low temperature $(10\phantom{\rule{0.3em}{0ex}}\mathrm{K})$, short wavelength $(0.42\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}})$, and high-resolution $({d}_{\mathrm{min}}=0.33\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}})$ synchrotron x-ray powder diffraction data measured at SPring-8, Japan. The MEM charge density clearly reveals three types of charge density overlap between atoms in $\mathrm{Co}{\mathrm{Sb}}_{3}$. The four Sb atoms form an ${\mathrm{Sb}}_{4}$ ring, and the MEM charge densities at two types of Sb-Sb midpoints are 0.35 and $0.50\phantom{\rule{0.3em}{0ex}}e\phantom{\rule{0.2em}{0ex}}{\mathrm{\AA{}}}^{\ensuremath{-}3}$. The charge density overlap between the Co and Sb atoms at the midpoint is $0.52\phantom{\rule{0.3em}{0ex}}e\phantom{\rule{0.2em}{0ex}}{\mathrm{\AA{}}}^{\ensuremath{-}3}$, which is larger than the values observed at the Sb-Sb midpoints. The nature of the chemical bonding observed in the present MEM charge density is consistent with a previous theoretical study by Lefebvre-Devos et al. [Phys. Rev. B 63, 125110 (2001)].

MEM Charge Density Analysis of Orbital-Ordering of Nd0.35Sr0.65MnO3

The charge density distribution of Nd 0.35 Sr 0.65 MnO 3 has been investigated by means of the maximum entropy method (MEM) using the synchrotron radiation (SR) X-ray powder diffraction data. In this compound, the anisotropic optical spectra reported by Tobe et al. [Phys. Rev. B 67 (2003) 140402(R)] suggest that the d 3 z 2 - r 2 orbital-ordering survives even at 600 K (≫ T N = 260 K). Consistently, we observed an anisotropic charge density distribution around the Mn ion at 30 K (≪ T N ), indicating the long-range ordering of the d 3 z 2 - r 2 orbital. At 300 K (≥ T N ), however, the charge density distribution becomes isotropic, suggesting the disappearance of the long-range orbital ordering.

Synchrotron Radiation for Structural Chemistry—Endohedral Natures of Metallofullerenes Found by Synchrotron Radiation Powder Method

The recent progress of the structural studies of endohedral metallofullerenes by the synchrotron radiation (SR) powder diffraction utilizing the maximum entropy method (MEM) is reviewed. Results of the endohedral metallofullerenes (Y@C82, La@C82, Sc@C82, Sc2@C84, Sc3@C82, Sc2@C66, La2@C80 and Sc2C2@C84) are given. The precise MEM charge densities of metallofullerenes presents the direct image of endohedral nature of metallofullerenes indicating the charge transfer from metal atoms to carbon cage, which governs the stability of the unique endohedral structures. The MEM/Rietveld method and SR powder method using imaging plate (IP), which are the crucial methods for data analysis and measurement in order to determine structure of fulleride, are also mentioned in some detail.

Charge density study of C 60 superconductors by MEM/Rietveld analysis

The charge density study of alkali metal doped fullerenes, Rb 2CsC 60, K 2RbC 60, Na 2RbC 60 and Li 2CsC 60, was carried out at room temperature by MEM/Rietveld analysis, which is the combination of the Maximum Entropy Method (MEM) and Rietveld analysis using synchrotron radiation powder data. The distinctly different features of charge densities of the C 60 molecules relating to the superconducting properties were revealed in the obtained MEM charge densities. For Na 2RbC 60, K 2RbC 60 and Rb 2CsC 60, the rotations of the C 60 molecules were virtually quenched while the C 60 molecule in Li 2CsC 60 was in an orientational disorder. In the interatomic region, the overlapped charge density indicating the existence of a covalent bond was not found significantly between the C 60 molecules and doped metal atoms for the four materials. However, in the MEM charge densities, the relative differences among them were found significantly for the charge deficiencies of the doped metal atoms which should be associated with charge transfer from the metal atoms to the C 60 molecule.

Charge density studies utilizing powder diffraction and MEM. Exploring of high Tc superconductors, C60 superconductors and manganites

Abstract The recent progress of the accurate charge density studies by the Maximum Entropy Method(MEM) utilizing X-ray powder diffraction is reviewed with some examples. Results for PrBCO (PrBa2Cu3O7-δ), YBCO (YBa2Cu3O7-δ), C60 superconductors (Rb2CsC60, K2RbC60, Na2RbC60) and the layered manganite, NdSr2Mn2O7, which is well known as colossal magnetoresistive (CMR)-related material, are given. For non-super conductor, PrBCO, it is found in the MEM charge density that there exist directional robes of the charge density from Pr atom toward the O atoms in the CuO2 conduction planes. On the other hand, for a very well known high Tc super conductor, YBCO, appreciable charge densities in the interatomic region around the Y atom is not recognized in the MEM charge density. The distinct difference of the charge densities between PrBCO and YBCO presents clear experimental evidence of the hybridization between Pr(4f)–O(2pπ) orbitals which supports the idea that the hole trapping by the hybridizes states suppresses the superconductivity in PrBCO. The MEM charge densities of the fullerene superconductors, Rb2CsC60, K2RbC60 and Na2RbC60, show distinct structural differences from that of non-superconductors, C60 and Li2CsC60, reflecting the superconducting properties. And the charge deficiencies of the doped metal atoms, which should be associated with charge transfer from the metal atoms to the C60 molecule seems to have strong correlation to the superconducting transition temperature, Tc. As the bigger the charge charge trnsfer, the higher the Tc. In the accurate MEM charge density of antiferromagnetic manganite, NdSr2Mn2O7,the direct imaging of spontaneous ordering of the dx 2-y 2 orbital indicating anisotropic exchange couplings between the local-spins on the Mn sites, which causes an unique layered-type spin order. The theoretical background of the MEM is also mentioned in some detail.

Giant motion of La atom inside C 82 cage

An anomalous charge density distribution of La atom encapsulated in a C 82 cage has been revealed for La@C 82 by the maximum entropy method (MEM)/Rietveld analysis using synchrotron powder diffraction data. The obtained La atom charge density shows a feature almost like a bowl or a hemisphere, suggesting that the La atom has a giant motion (large amplitude motion) inside the C 82 cage at room temperature. From the obtained MEM charge density, the main results are (1) the cage structure of La@C 82 (I) has C 2 V symmetry; (2) La atom locates at an off-centered position adjacent to a six-membered ring of the carbon cage; (3) the nearest La–C distance is 2.55(8) Å and (4) the amount of charge transfer from the La atom to the carbon cage is about 3.2 e, which corresponds to the nominal electronic structure, La 3+@C 82 3−.

A charge density study of the intermetallic compound MgCu2 by the maximum entropy method

The charge density distribution of the intermetallic compound MgCu2 is obtained by the maximum entropy method (MEM) from the synchrotron powder diffraction data. In the MEM charge density map, the overlap of electron densities was clearly observed between the neighbouring Cu atoms. This clearly shows that there is a rather strong covalent bond between Cu-Cu atoms. It is also found that the Cu-Cu bonding is along the very well known kagome net, which characterizes the Laves phase structure. At least, in the case of MgCu2, the kagomé network is the electronic network in reality rather than a geometrical concept to represent structural characteristics of Laves phase compounds.

Charge Densities and Chemical Bonding of CaSi2

The charge density distribution map of CaSi2 was obtained by the Maximum Entropy Method(MEM) using synchrotron powder diffraction data. The MEM charge density map reveals that there are two types of Si layers in a unit cell. In both layers, Si atoms form rather strong covalent bond. However, they are not identical. Electron density at bond mid point are slightly different at each layer, i.e. 0.62[e/Å3] for one layer, and 0.52[e/Å3] for the other. These values shows covalent bond of the former layer is considerably stronger than that of the latter layer. As for the bond lengths, the Si-Si bond length of the former layer is 2.32 Å and that of the latter is 2.40 Å, respectively. The present direct observation of bond electrons gives one of the examples that the longer the bond length, the weaker the covalent bond. It is not recognized that there exists covalency between Ca-Ca atoms. Since the MEM charge density shows very slight overlap of electron clouds between Ca-Si, the nature of chemical bond of Ca in CaSi2 is almost ionic.

The MEM Charge Density Study of Rb2CsC60, K2RbC60, and Li2CsC60 by Synchrotron Radiation Powder Method

A charge density study of alkali metal doped fullerenes, Rb2CsC60, K2RbC60 and Li2CsC60, was carried out at room temperature by the Maximum Entropy Method (MEM) combined with the Rietveld analysis using synchrotron powder data. The MEM charge densities of the C60 molecules show distinct differences related to the superconducting properties. For both K2RbC60 and Rb2CsC60, which are superconductors at low temperature, the C60 molecules were in a merohedral disorder. On the other hand, the C60 molecules in Li2CsC60; non-superconductor even at very low temperature, were in an orientational disorder. In the interatomic region between the C60 molecules and doped metal atoms, any significant overlapped charge densities related to covalent bond were not found for all three materials. This is the clear evidence for that superconductivity of these materials and covalency of doped metals have no correlation at all. Instead, the charge deficiencies of the doped metal atoms which should be associated with charge transfer from the metal atoms to the C60 molecule seems to have a strong correlation to the superconducting transition temperature, Tc, i.e. the higher the Tc, the more the deficiencies.

A Charge Density Study of MgCu2 and MgZn2 by the Maximum Entropy Method

The charge density distributions of the Mg-base Laves phase MgCu2 and MgZn2 were obtained from the synchrotron powder diffraction data by the Maximum Entropy Method (MEM). In the MEM charge density, the overlapped electron densities were found between Cu-Cu atoms in the case of MgCu2 and between Zn-Zn atoms. These covalent bonds form the electronic kagomé network for the both compounds. By the geometrical consideration, this characteristic feature can be interpreted as the existence of p3d3 hybridization of the Cu and Zn atoms. On the other hand, there were no such overlapped densities around Mg atoms, which denies any significant covalency between Mg and Cu or between Mg and Zn atoms. Furthermore, the peculiar distortion of the covalent bond network is found in the obtained MEM charge densities for the both compounds, that is, the covalent bonds are shifted towards the Mg atoms. This rather unusual bond nature should be due to the ionic interaction between the hybridized orbital and positively charged Mg ions. As for the MgZn2, the difference of the hybridized electron density was found related to the zigzag pattern of hexagonal stacking sequence.

Ｘ線回折法による金属内包フラーレンの構造研究

Endohedral metallofullerenes are novel forms of fullerene-related materials, which encage metal atom inside a carbon cage. The recent X-ray structural studies of metallofullerenes, Sc@C82 and Sc2@C84, by the synchrotron powder diffraction experiment are presented to illustrate the usefulness of the MEM/Rietveld analysis, which is a self-consistent iterative way in combination with the MEM (Maximum Entropy Method) and Rietveld analyses. The obtained MEM charge densities clearly reveal the distinct features of encapsulated metals inside the fullerene cages as well as endohedral cage structures for Sc@C82 and Sc2@C84.

Determination of the cage structure of Sc@C82 by synchrotron powder diffraction

The cage structure of Sc@C82 (isomer I) has been determined by a synchrotron radiation powder structural analysis using the maximum entropy method (MEM). From the MEM charge density obtained the cage structure of the endohedral Sc@C82 (I) is experimentally determined to have C2V symmetry. Inside the carbon cage, the Sc atom is located at an off-center position adjacent to a carbon six-membered ring. The nearest Sc–C distance determined from the MEM charge density is 2.53(8) Å. The charge transfer from Sc to C has been estimated to be 2.2e, which is consistent with the ultraviolet photoelectron spectra and theoretical results.