Experimental Structure Factors Research Articles

Refinement of the experimental dynamic structure factor for liquid para-hydrogen and ortho-deuterium using semi-classical quantum simulation.

The dynamic structure factor of liquid para-hydrogen and ortho-deuterium in corresponding thermodynamic states (T = 20.0 K, n = 21.24 nm(-3)) and (T = 23.0 K, n = 24.61 nm(-3)), respectively, has been computed by both the Feynman-Kleinert linearized path-integral (FK-LPI) and Ring-Polymer Molecular Dynamics (RPMD) methods and compared with Inelastic X Ray Scattering spectra. The combined use of computational and experimental methods enabled us to reduce experimental uncertainties in the determination of the true sample spectrum. Furthermore, the refined experimental spectrum of para-hydrogen and ortho-deuterium is consistently reproduced by both FK-LPI and RPMD results at momentum transfers lower than 12.8 nm(-1). At larger momentum transfers the FK-LPI results agree with experiment much better for ortho-deuterium than for para-hydrogen. More specifically we found that for k ∼ 20.0 nm(-1) para-hydrogen provides a test case for improved approximations to quantum dynamics.

Structure formation in binary Al-TM (TM = Mn, Co, Ni, Cu) melts

The structures of binary Al-TM (transition metal TM = Mn, Co, Ni, Cu) melts at near-liquidus temperatures are studied by X-ray diffraction and simulation using the reverse Monte Carlo method. The melts are found to have chemical local atomic ordering, and this ordering depends on the nature and content of TM. Chemical local atomic ordering leads to a medium-range order as a result of TM atom localization at distances of 0.4–0.5 nm in the composition of polytetrahedral clusters having icosahedral symmetry. A medium-range order in the melts is identified due to the presence of an additional maximum (prepeak) in the left slope of the first peak in experimental structure factor curves. The local atomic orders in the melts and the corresponding crystalline and quasicrystalline phases are found to correlate with each other.

NATURAL ORBITALS IN RELATION TO QUANTUM INFORMATION THEORY: FROM MODEL LIGHT ATOMS THROUGH TO EMERGENT METALLIC PROPERTIES

The review begins with a consideration of three forms of quantum information entropy associated with Shannon and Jaynes. For model two-electron spin compensated systems, some analytic progress is first reported. The Jaynes entropy is clearly related to correlation kinetic energy. A way of testing the usefulness of a known uncertainty principle inequality is proposed for a whole class of model two-electron atoms with harmonic confinement but variable electron-electron interaction. Emerging properties are then studied by reference to bcc Na at ambient pressure and its modeling by "jellium". Jellium itself has collective behavior with changes of the density, especially noteworthy being the discontinuity of the momentum distribution at the Fermi surface. This has almost reduced to zero at rs = 100 a.u., the neighborhood in which the quantal Wigner electron solid transition is known to occur. However, various workers have studied crystalline Na under pressure and their results are compared and contrasted. Work by DFT on K, Rb and Cs is discussed, but now with reduced density from the ambient pressure value. The crystalline results for the cohesive energy of these metals as a function of lattice parameters and local coordination number are shown to be closely reproduced by means of ground and excited states for dimer potential energy curves. Then, pair potentials for liquid Na and Be are reviewed, and compared with the results of computer simulations from the experimental structure factor for Na . Finally, magnetic field effects are discussed. First a phenomenological model of the metal-to-insulator transition is presented with an order parameter which is the discontinuity in the Fermi momentum distribution. Lastly, experiments on a two-dimensional electron assembly in a GaAs / AlGaAs heterojunction in a perpendicular magnetic field are briefly reviewed and then interpreted.

Comparative study of X-ray charge-density data on CoSb3

CoSb3 is an example of a highly challenging case for experimental charge-density analysis due to the heavy elements (suitability factor of ~0.01), the perfect crystallinity and the high symmetry of the compound. It is part of a family of host-guest structures that are potential candidates for use as high-performance thermoelectric materials. Obtaining and analysing accurate charge densities of the undoped host structure potentially can improve the understanding of the thermoelectric properties of this family of materials. In a previous study, analysis of the electron density gave a picture of covalent Co-Sb and Sb-Sb interactions together with relatively low atomic charges based on state-of-the-art experimental and theoretical data. In the current study, several experimental X-ray diffraction data sets collected on the empty CoSb3 framework are compared in order to probe the experimental requirements for obtaining data of high enough quality for charge-density analysis even in the case of very unsuitable crystals. Furthermore, the quality of the experimental structure factors is tested by comparison with theoretical structure factors obtained from periodic DFT calculations. The results clearly show that, in the current study, the data collected on high-intensity, high-energy synchrotron sources and very small crystals are superior to data collected at conventional sources, and in fact necessary for a meaningful charge-density study, primarily due to greatly diminished effects of extinction and absorption which are difficult to correct for with sufficient accuracy.

Static structure and dynamic properties in liquid Sn96.2 Ag3.8 lead free solder: Structure factor, diffusion coefficients and viscosity

Abstract Starting from the pseudopotential formalism, we developed a new pseudopotential able to describe accurately both heavy metals like tin and noble metals like copper and silver which are the basic elements of the new lead free solders. The pseudopotential describes the interaction between electrons and ions. To describe the atomic structure it is necessary to use an effective pair potential describing the interaction between ions taking into account the electron screening cloud. This pair potential is deduced from our new pseudopotential. It enters into a simulation program using molecular dynamics. First we calculate the atomic structure factor that has been compared to that measured experimentally by neutron or X ray scattering. In the case of a binary alloy, we determined three partial structure factors describing the system. These can be calculated but in general cannot be obtained experimentally. To do a comparison we must combine adequately the calculated partial structure factors and compare it to the experimental total structure factor. By molecular dynamics we can follow the individual movement of particles to obtain the different diffusion coefficients which, as partial structure factors, are very difficult to measure accurately. We followed the collective movement of all particles and got the shear viscosity by Green–Kubo formalism. We compared our results to the existing experimental viscosity which is a little easier to measure. However, in the bibliography, we observe high discrepancies between the different authors. It is thus important to be able to calculate accurately these properties as functions of temperature and composition.

X-ray Constrained Extremely Localized Molecular Orbitals: Theory and Critical Assessment of the New Technique.

Following the X-ray constrained wave function approach proposed by Jayatilaka, we have devised a new technique that allows to extract molecular orbitals strictly localized on small molecular fragments from sets of experimental X-ray structure factors amplitudes. Since the novel strategy enables to obtain electron distributions that have quantum mechanical features and that can be easily interpreted in terms of traditional chemical concepts, the method can be also considered as a new useful tool for the determination and the analysis of charge densities from high-resolution X-ray experiments. In this paper, we describe in detail the theory of the new technique, which, in comparison to our preliminary work, has been improved both treating the effects of isotropic secondary extinctions and introducing a new protocol to halt the fitting procedure against the experimental X-ray scattering data. The performances of the novel strategy have been studied both in function of the basis-sets flexibility and in function of the quality of the considered crystallographic data. The tests performed on four different systems (α-glycine, l-cysteine, (aminomethyl)phosphonic acid and N-(trifluoromethyl)formamide) have shown that the achievement of good statistical agreements with the experimental measures mainly depends on the quality of the crystal structures (i.e., geometry positions and thermal parameters) used in the X-ray constrained calculations. Finally, given the reliable transferability of the obtained Extremely Localized Molecular Orbitals (ELMOs), we envisage to exploit the novel approach to construct new ELMOs databases suited to the development of linear-scaling methods for the refinement of macromolecular crystal structures.

Peptide Crystal Simulations Reveal Hidden Dynamics

Molecular dynamics simulations of biomolecular crystals at atomic resolution have the potential to recover information on dynamics and heterogeneity hidden in X-ray diffraction data. We present here 9.6 μs of dynamics in a small helical peptide crystal with 36 independent copies of the unit cell. The average simulation structure agrees with experiment to within 0.28 Å backbone and 0.42 Å all-atom RMSD; a model refined against the average simulation density agrees with the experimental structure to within 0.20 Å backbone and 0.33 Å all-atom RMSD. The R-factor between the experimental structure factors and those derived from this unrestrained simulation is 23% to 1.0 Å resolution. The B-factors for most heavy atoms agree well with experiment (Pearson correlation of 0.90), but B-factors obtained by refinement against the average simulation density underestimate the coordinate fluctuations in the underlying simulation where the simulation samples alternate conformations. A dynamic flow of water molecules through channels within the crystal lattice is observed, yet the average water density is in remarkable agreement with experiment. A minor population of unit cells is characterized by reduced water content, 310 helical propensity and a gauche(-) side-chain rotamer for one of the valine residues. Careful examination of the experimental data suggests that transitions of the helices are a simulation artifact, although there is indeed evidence for alternate valine conformers and variable water content. This study highlights the potential for crystal simulations to detect dynamics and heterogeneity in experimental diffraction data as well as to validate computational chemistry methods.

Bulk-solvent and overall scaling revisited: faster calculations, improved results.

A fast and robust method for determining the parameters for a flat (mask-based) bulk-solvent model and overall scaling in macromolecular crystallographic structure refinement and other related calculations is described. This method uses analytical expressions for the determination of optimal values for various scale factors. The new approach was tested using nearly all entries in the PDB for which experimental structure factors are available. In general, the resulting R factors are improved compared with previously implemented approaches. In addition, the new procedure is two orders of magnitude faster, which has a significant impact on the overall runtime of refinement and other applications. An alternative function is also proposed for scaling the bulk-solvent model and it is shown that it outperforms the conventional exponential function. Similarly, alternative methods are presented for anisotropic scaling and their performance is analyzed. All methods are implemented in the Computational Crystallography Toolbox (cctbx) and are used in PHENIX programs.

Formation of the short-range order in Al-based liquid alloys

The short-range order in binary and ternary liquid alloys of aluminum with 3d-transition metals (TM) was studied by the X-ray diffraction method and Reverse Monte Carlo simulations. The causes of the presence of the prepeak and asymmetric shape of the second peak on the experimental total structure factors were discussed. The effect of the transition metal atom type on the short-range order of Al-based liquid alloys was demonstrated.

Change in the short-range order in binary Al-Mn melts during partial substitution of manganese atoms by nickel or cobalt

The structure of ternary melts Al80Mn14.7Ni5.3 (at 1233 K) and Al66.6Mn16.7Co16.7 (at 1393 K), the compositions of which correspond to ternary intermetallic compounds, is studied by X-ray diffraction. Structural models are constructed for the melts using experimental structure factor curves and the reverse Monte Carlo method. The structural models are analyzed by the Voronoi-Delaunay method of partitioning. Local atomic ordering is shown to change noticeably when passing from binary Al-Mn to the ternary melts. The causes of the appearance of a prepeak and the asymmetry of the second maximum in the experimental structure factor curves are discussed. Correlations between the short-range orders in the ternary melts and crystalline and pseudocrystalline phases are found.

Effective ion–ion potentials in warm dense matter

The effective ion–ion potential is extracted from first principle simulations and from experimental structure factors for several warm dense matter systems. Results of three different methods are compared for simple elements like hydrogen or beryllium as well as for composite materials like lithium-hydride and hydrogen–helium plasmas. It is shown that iterative techniques based on the pair distribution function are not unique in their solution and direct force-matching from first principle simulations is subject to finite size effects. Moreover, both methods are not able to provide potentials for small distances. These disadvantages can be avoided by using the static structure factor as input, although higher order correlations are only accounted for within the hypernetted chain approximation in this case. Furthermore, we discuss possibilities to use the extracted effective potentials to investigate the dielectric function beyond linear response.

Dipolar solute rotation in ionic liquids, electrolyte solutions and common polar solvents: Emergence of universality

Here we develop a molecular theory attempting to answer the long-standing questions regarding the decoupling of dielectric friction from dipolar solute rotation in various liquid systems: ionic liquids, electrolyte solutions and polar solvents. Using both experimental and model solvent structure factors, we show insignificant dielectric friction and provide microscopic explanation for the experimentally observed domination of hydrodynamics in solute rotation in these media. Our analyses lead to a macro–micro relation indicating a quasi-universality in solute rotation for a wide variety of solute–solvent combinations. We demonstrate that both the quasi-universality and the domination of hydrodynamics originate from packing at liquid-like density.

A critical analysis of dipole-moment calculations as obtained from experimental and theoretical structure factors

Three models of charge-density distribution - Hansen-Coppens multipolar, virtual atom and kappa - of different complexities, different numbers of refined parameters, and with variable levels of restraints, were tested against theoretical and high-resolution X-ray diffraction structure factors for 2-methyl-4-nitro-1-phenyl-1H-imidazole-5-carbonitrile. The influence of the model, refinement strategy, multipole level and treatment of the H atoms on the dipole moment was investigated. The dipole moment turned out to be very sensitive to the refinement strategy. Also, small changes in H-atom treatment can greatly influence the calculated magnitude and orientation of the dipole moment. The best results were obtained when H atoms were kept in positions determined by neutron diffraction and anisotropic displacement parameters (obtained by SHADE, in this case) were used. Also, constraints on kappa values of H atoms were found to be superior to the free refinement of these parameters. It is also shown that the over-parametrization of the multipolar model, although possibly leading to better residuals, in general gives worse dipole moments.

Tetrahedral germanium in amorphous phase change materials: Exploring the isochemical scenario

AbstractThe structural, vibrational, and electronic properties of low‐temperature supercooled GeTe4 are studied using density functional theory (DFT). Two models have been considered: an ordinary melt‐quenched system containing a majority of defect‐octahedral germanium atoms, and a relaxed one obtained from a quenched SiTe4 rescaled structure which contains mostly tetrahedral germanium, while leaving the Te environment preserved. The tetrahedral system exhibits an increased agreement with the experimental structure factor S(k), the pair distribution function g(r), and the infrared absorption spectrum. It is suggested that the fraction of tetrahedral Ge must be higher as usually believed. In addition, we provide the calculation of the 125Te wideline NMR spectra. While the latter do not agree with recent experimental findings, both systems exhibit important significant differences in the widths of the computed spectra. These exploratory calculations clearly show that NMR will be an interesting probe that deserves further investigations for the experimental determination of the local geometry.

On the Structure of Aqueous Cesium Fluoride and Cesium Iodide Solutions: Diffraction Experiments, Molecular Dynamics Simulations, and Reverse Monte Carlo Modeling

A detailed study of the microscopic structure of two electrolyte solutions, cesium fluoride (CsF) and cesium iodide (CsI) in water, is presented. For revealing the influence of salt concentration on the structure, CsF solutions at concentrations of 15.1 and 32.3 mol % and CsI solutions at concentrations of 1.0 and 3.9 mol % are investigated. For each concentration, we combine total scattering structure factors from neutron and X-ray diffraction and 10 partial radial distribution functions from molecular dynamics simulations in one single structural model, generated by reverse Monte Carlo modeling. For the present solutions we show that the level of consistency between simulations that use simple pair potentials and experimental structure factors is at least semiquantitative for even the extremely highly concentrated CsF solutions. Remaining inconsistencies seem to be caused primarily by water-water distribution functions, whereas slightly problematic parts appear on the ion-oxygen partials, too. As a final result, we obtained particle configurations from reverse Monte Carlo modeling that were in quantitative agreement with both sets of diffraction data and most of the MD simulated partial radial distribution functions. From the particle coordinates, distributions of the number of first neighbors as well as angular correlation functions were calculated. The average number of water molecules around cations in both materials decreases from about 8.0 to about 5.1 as concentration increases, whereas the same quantity for the anions (X) changes from about 5.3 to about 3.7 in the case of CsF and from about 6.2 to about 4.0 in the case of CsI. The average angle of X···H-O particle arrangements, characteristic of anion-water hydrogen bonds, is closer to 180° than that found for O···H-O arrangements (water-water hydrogen bonds) at higher concentrations.

Modeling particle scattering structure factor for branched bio-inspired polymers in solution: A small angle X-ray scattering study

We present a study which illustrates the modeling of the Particle Scattering Structure Factor of an hyperbranched biopolymer in water solution using the Small Angle X-ray Scattering (SAXS) data. The studied sample was a sodium carboxilate terminated poly(amidoamine) dendrimer (generation 2.5) dispersed in water medium. The experimental inter-dendrimer structure factor S(q) has been analyzed in the framework of liquid integral equation theory for charged systems in solution. From that, we derive an effective interparticle interaction composed of a screened Coulombic plus hard-sphere repulsion potential, which allows the estimation of the dendrimer effective charge Zeff. The present analysis strongly supports the finding that structures and interaction of dendrimer are strongly influenced by charge effects. As a result, this quantity can be considered as a crucial parameter for the modulation of the degree of structural organization in solution, suitable for a number of potential applications. We conclude our form factor analysis with the investigation of the long-range assembly conditions during the growth of the intermediate nanoaggregates generated by the inclusion of aluminosilicate components of zeolite 13X on the surface of dendrimers.

Magnetism in melt grown dilute magnetic semiconductor Ge1−xMnx from electron density

Dilute magnetic semiconductor materials Ge1−xMnx (x=0.04, 0.06 and 0.10) have been grown via a melt growth technique. The influence of the intermetallic secondary phases like Mn-poor Ge8Mn11 and Mn-rich Ge3Mn5 has been analyzed quantitatively from charge density studies. Three-dimensional charge density pictures, arrangement of charges on two-dimensional Miller planes and one-dimensional charge density profiles between nearest neighbors along the bond path have been enumerated using a statistical approach, the maximum entropy method using experimental X-ray structure factors. The Rietveld method and pair distribution functions (PDF) have been used to analyze the X-ray information for local structural features. A correlation between spatial charge distribution and magnetic behavior of the chosen system has been achieved using a charge density route.

The liquid structure of some food aromas: Joint X-ray diffraction, all-atom molecular dynamics and reverse Monte Carlo investigations of dimethyl sulfide, dimethyl disulfide and dimethyl trisulfide

Following synchrotron X-ray diffraction measurements on liquid dimethyl sulfide, dimethyl disulfide and dimethyl trisulfide, all-atom molecular dynamics (MD) simulations were carried out for these materials which are known widely used food aromas. The X-ray weighted structure factor calculated from the MD particle configurations was in reasonably good agreement with the experimental data for each liquid. For refining the structure, series of Reverse Monte Carlo (RMC) simulations using various combinations of the experimental structure factor, MD-based partial radial distribution functions, as well as constraints on cosine distribution of bond angles were carried out. The best representation of the structure could be achieved by the simultaneous application of all the above constraints, thus providing an MD-aided RMC structural model of the three liquids. The largest inconsistency between MD and the experimental structure factor showed up in terms of the SH partial radial distribution function for dimethyl sulfide and disulfide. The coherency between MD results and the experimental structure factor increased with the number of sulfur atoms in the molecule. It is shown that a great deal of information on the intramolecular structure is contained in the X-ray weighted structure factor, whereas intermolecular correlations are represented to a somewhat lesser extent.

Structural Heterogeneity and Unique Distorted Hydrogen Bonding in Primary Ammonium Nitrate Ionic Liquids Studied by High-Energy X-ray Diffraction Experiments and MD Simulations

Liquid structure and the closest ion-ion interactions in a series of primary alkylammonium nitrate ionic liquids [C(n)Am(+)][NO(3)(-)] (n = 2, 3, and 4) were studied by means of high-energy X-ray diffraction (HEXRD) experiments with the aid of molecular dynamics (MD) simulations. Experimental density and X-ray structure factors are in good accordance with those evaluated with MD simulations. With regard to liquid structure, characteristic peaks appeared in the low Q (Q: a scattering vector) region of X-ray structure factors S(Q)'s for all ionic liquids studied here, and they increased in intensity with a peak position shift toward the lower Q side by increasing the alkyl chain length. Experimentally evaluated S(Q(peak))(r(max)) functions, which represent the S(Q) intensity at a peak position of maximum intensity Q(peak) as a function of distance (actually a integration range r(max)), revealed that characteristic peaks in the low Q region are related to the intermolecular anion-anion correlation decrease in the r range of 10-12 Å. Appearance of the peak in the low Q region is probably related to the exclusion of the correlations among ions of the same sign in this r range by the alkyl chain aggregation. From MD simulations, we found unique and rather distorted NH···O hydrogen bonding between C(n)Am(+) (n = 2, 3, and 4) and NO(3)(-) in these ionic liquids regardless of the alkyl chain length. Subsequent ab initio calculations for both a molecular complex C(2)H(5)NH(2)···HONO(2) and an ion pair C(2)H(5)NH(3)(+)···ONO(2)(-) revealed that such distorted hydrogen bonding is specific in a liquid state of this family of ionic liquids, though the linear orientation is preferred for both the N···HO hydrogen bonding in a molecular complex and the NH···O one in an ion pair. Finally, we propose our interpretation of structural heterogeneity in PILs and also in APILs.

In-plane pyridinium cation reorientation in bis-thiourea chloride, bromide and iodide: quasielastic neutron scattering combined with molecular dynamics simulations

We have studied the dynamics of bis-thiourea pyridinium chloride and bromide by means of quasielastic neutron scattering (QENS). The QENS data allow describing the geometry of the in-plane motion of the pyridinium cation and reveal that it is similar to the motion previously observed in bis-thiourea pyridinium iodide. Molecular dynamics (MD) simulations have been performed to investigate the cation dynamics on the high temperature phase of the full series of compounds: bis-thiourea pyridinium chloride, bromide and iodide. Three different models of intermolecular potential have been tested and the agreement between the simulated and experimental elastic incoherent structure factors (EISFs) is used to select the more realistic one. The detailed analysis of the MD results indicates that Coulombic interactions together with the formation of hydrogen bonds between the pyridinium cation and the host sublattice influence strongly the geometry of the in-plane cation reorientation.