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Here, it is investigated how optical properties of single scatterers in interacting multi‐particle systems influence measurable structure factors. Both particles with linear gradients of their scattering length density and core–shell structures evoke characteristic deviations between the weighted sum ⟨S(Q)⟩ of partial structure factors in a multi‐component system and experimentally accessible measurable structure factors SM(Q). While ⟨S(Q)⟩ contains only the structural information of self‐organizing systems, SM(Q) is additionally influenced by the optical properties of their constituents, resulting in features such as changing amplitudes, additional peaks in the low‐wavevector region or splitting of higher‐order maxima, which are not related to structural reasons. It is shown that these effects can be systematically categorized according to the qualitative behaviour of the form factor in the Guinier region, which enables assessing the suitability of experimentally obtained structure factors to genuinely represent the microstructure of complex systems free from any particular model assumption. Hence, a careful data analysis regarding size distribution and optical properties of single scatterers is mandatory to avoid a misinterpretation of measurable structure factors. [ABSTRACT FROM AUTHOR]

In molten metals, the atomic dynamics have been studied in the present study with the help of equations of motion in terms of the velocity autocorrelation function (VACF), power spectrum $ G(\omega) $ G (ω) , and mean square displacement $ {r^2}(t) $ r 2 (t). The pair correlation function $ g(r) $ g (r) is used to produce VACF for molten metals in the current study with the help of three different types of structure factor methods i.e. hard sphere Yukawa (HSY) method, optimised random phase approximation (ORPA) method and charged hard sphere (CHS) method. The presently obtained results for molten metals of different groups like Na (Z = 1), Mg (Z = 2), Al (Z = 3), Sn (Z = 4), and Sb (Z = 5) are compared with the molecular dynamic (MD) study and also with the other theoretical data available in the literature. For the present study, our own developed pseudopotential has been used for the calculations of the above-mentioned properties. The screening effect is also been observed over and beyond the bare ion potential with Hartree (H) and the effects of exchanges and correlation were computed using procedures given by Taylor (T) and Nagy (N). [ABSTRACT FROM AUTHOR]

The superstructure spots that appear in diffraction patterns of tilted perovskites are well documented and easily calculated using crystallographic software. Here, by considering a distortion mode as a perturbation of the prototype perovskite structure, it is shown how the structure‐factor equation yields Boolean conditions for the presence of superstructure reflections. This approach may have some advantages for the analysis of electron diffraction patterns of perovskites. [ABSTRACT FROM AUTHOR]

An innovative strategy is presented that incorporates deep auto‐encoder networks into a least‐squares fitting framework to address the potential inversion problem in small‐angle scattering. To evaluate the performance of the proposed approach, a detailed case study focusing on charged colloidal suspensions was carried out. The results clearly indicate that a deep learning solution offers a reliable and quantitative method for studying molecular interactions. The approach surpasses existing deterministic approaches with respect to both numerical accuracy and computational efficiency. Overall, this work demonstrates the potential of deep learning techniques in tackling complex problems in soft‐matter structures and beyond. [ABSTRACT FROM AUTHOR]

Diffraction intensities from a crystallographic experiment include contributions from the entire unit cell of the crystal: the macromolecule, the solvent around it and eventually other compounds. These contributions cannot typically be well described by an atomic model alone, i.e. using point scatterers. Indeed, entities such as disordered (bulk) solvent, semi-ordered solvent (e.g. lipid belts in membrane proteins, ligands, ion channels) and disordered polymer loops require other types of modeling than a collection of individual atoms. This results in the model structure factors containing multiple contributions. Most macromolecular applications assume two-component structure factors: one component arising from the atomic model and the second one describing the bulk solvent. A more accurate and detailed modeling of the disordered regions of the crystal will naturally require more than two components in the structure factors, which presents algorithmic and computational challenges. Here an efficient solution of this problem is proposed. All algorithms described in this work have been implemented in the computational crystallography toolbox (CCTBX) and are also available within Phenix software. These algorithms are rather general and do not use any assumptions about molecule type or size nor about those of its components.

Abstract—The isothermal compressibilities (χT) of individual potassium halides and some binary mixtures, namely, KI–KX (X = F, Cl, Br), are calculated using classical molecular dynamics simulation. The modeling of molten potassium halides using the Born–Mayer–Huggins pair potential shows good agreement between the calculated values of isothermal compressibility and the experimental data. A systematic underestimation of the calculated values is found for individual melts, with the maximum difference between the calculated and experimental values being 24% for potassium chloride. For binary KI–KX (X = F, Cl, Br) mixtures, the experimental concentration dependences of χT during the transition from the bromide ion to the fluoride ion are characterized by an increasing deviation from additivity. Even for a KI–KBr binary mixture, the calculated concentration dependence is shown to have a pronounced nonlinear character. The maximum differences (about 34%) between the calculated and experimental values of χT are observed for a binary equimolar KI–KF mixture. [ABSTRACT FROM AUTHOR]

This article presents an upgrade of the D+ software [Ginsburg et al. (2019). J. Appl. Cryst.52, 219–242], expanding its hierarchical solution X‐ray scattering modeling capabilities for fiber diffraction and single crystallographic orientations. This upgrade was carried out using the reciprocal grid algorithm [Ginsburg et al. (2016). J. Chem. Inf. Model.56, 1518–1527], providing D+ its computational strength. Furthermore, the extensive modifications made to the Python API of D+ are described, broadening the X‐ray analysis performed with D+ to account for the effects of the instrument‐resolution function and polydispersity. In addition, structure‐factor and radial‐distribution‐function modules were added, taking into account the effects of thermal fluctuations and intermolecular interactions. Finally, numerical examples demonstrate the usage and potential of the added features. [ABSTRACT FROM AUTHOR]

Shape2SAS is a web application that allows researchers and students to build intuition about and understanding of small‐angle scattering. It is available at https://somo.chem.utk.edu/shape2sas. The user defines a model of arbitrary shape by combining geometrical subunits, and Shape2SAS then calculates and displays the scattering intensity and the pair distance distribution, as well as a visualization of the user‐defined shape. Simulated data with realistic noise are also generated. Here, it is demonstrated how Shape2SAS can calculate and display the different scattering patterns for various geometrical shapes, such as spheres and cylinders. It is also shown how the effect of structure factors can be visualized. Finally, it is indicated how multi‐contrast particles can readily be generated, and how the calculated scattering may be used to validate and visualize analytical models generated in analysis software for fitting small‐angle scattering data. [ABSTRACT FROM AUTHOR]

The partial structure factors (PSFs) of molten lithium fluoride at a temperature of 1200 K are calculated using the following three methods: ab initio and classical molecular dynamics and the charged hard sphere model in the mean-spherical approximation. Despite the common topology of the PSFs calculated by all three methods, the key feature of the computer simulation results is shown to be the absence of a shoulder on the right side of the first peak of the cation–cation structure factor. The observed difference is assumed to be associated with the softness of the repulsive branch of the Buckingham pair potential in the case of the classical model in the molecular dynamics calculation. The ab initio molecular dynamics calculations also confirm this conclusion. The results of calculating the density–density structure factor by computer simulation methods demonstrate the presence of two maxima at k ≈ 2.4 and ≈4.4 Å–1, respectively. The charged hard sphere model demonstrates the presence of one maximum at k ≈ 3.5 Å–1 and a small shoulder on the left, the position of which coincides with the first maximum obtained by computer simulation methods. The observed differences can be attributed to the fact that the cation–anion PSF curve calculated in terms of the charged hard sphere model has a higher amplitude in the vicinity of a wavevector of ≈3.5 Å–1. [ABSTRACT FROM AUTHOR]

• Colored photovoltaic modules are desirable for various fields. • A detailed analysis about spatial correlations was conducted for the colored photovoltaic modules with integrate disordered media. • The spatial correlations can lead to considerable modifications of the color properties but has a limited impact on the power conversion efficiency. Colored photovoltaic (PV) modules with integrated disordered coatings exhibit attractive potential for generating renewable electricity. However, most existing studies on these modules rely on the assumption that the disordered coatings are random systems, neglecting the effects of spatial correlation. In this work, we thoroughly investigate the effects of spatial correlation on the color properties and performance of colored PV modules with integrated disordered coatings, using the full-wave electromagnetic simulation techniques. Our findings indicate that increasing the degree of spatial correlation results in a sharper and narrower reflectance peak, while having a negligible impact on the peak position. This trend suggests that the spatial correlation offers an alternative strategy for producing more vivid color, although it is less effective in expanding the color range. On the other hand, the spatial correlation has little impact on the power conversion efficiency (PCE) of PV modules. Therefore, it is feasible to produce colored PV modules with more vivid colors without significantly affecting the PCE by simply adjusting the degree of spatial correlation. [ABSTRACT FROM AUTHOR]

It has been recently established that the accuracy of structural parameters from X-ray refinement of crystal structures can be improved by using a bank of aspherical pseudoatoms instead of the classical spherical model of atomic form factors. This comes, however, at the cost of increased complexity of the underlying calculations. In order to facilitate the adoption of this more advanced electron density model by the broader community of crystallographers, a new software implementation called DiSCaMB, 'densities in structural chemistry and molecular biology', has been developed. It addresses the challenge of providing for high performance on modern computing architectures. With parallelization options for both multi-core processors and graphics processing units (using CUDA), the library features calculation of X-ray scattering factors and their derivatives with respect to structural parameters, gives access to intermediate steps of the scattering factor calculations (thus allowing for experimentation with modifications of the underlying electron density model), and provides tools for basic structural crystallographic operations. Permissively (MIT) licensed, DiSCaMB is an open-source C++ library that can be embedded in both academic and commercial tools for X-ray structure refinement.

Small‐angle scattering is an increasingly common method for characterizing particle ensembles in a wide variety of sample types and for diverse areas of application. SASfit has been one of the most comprehensive and flexible curve‐fitting programs for decades, with many specialized tools for various fields. Here, a selection of enhancements and additions to the SASfit program are presented that may be of great benefit to interested and advanced users alike: (a) further development of the technical basis of the program, such as new numerical algorithms currently in use, a continuous integration practice for automated building and packaging of the software, and upgrades on the plug‐in system for easier adoption by third‐party developers; (b) a selection of new form factors for anisotropic scattering patterns and updates to existing form factors to account for multiple scattering effects; (c) a new type of a very flexible distribution called metalog [Keelin (2016). Decis. Anal.13, 243–277], and regularization techniques such as the expectation‐maximization method [Dempster et al. (1977). J. R. Stat. Soc. Ser. B (Methodological), 39, 1–22; Richardson (1972) J. Opt. Soc. Am.62, 55; Lucy (1974). Astron. J.79, 745; Lucy (1994). Astron. Astrophys.289, 983–994], which is compared with fits of analytical size distributions via the non‐linear least‐squares method; and (d) new structure factors, especially for ordered nano‐ and meso‐scaled material systems, as well as the Ornstein–Zernike solver for numerical determination of particle interactions and the resulting structure factor when no analytical solution is available, with the aim of incorporating its effects into the small‐angle scattering intensity model used for fitting with SASfit. [ABSTRACT FROM AUTHOR]

Abstract Background Hospital and ICU structural factors are key factors affecting the quality of care as well as ICU patient outcomes. However, the data from China are scarce. This study was designed to investigate how differences in patient outcomes are associated with differences in hospital and ICU structure variables in China throughout 2019. Methods This was a multicenter observational study. Data from a total of 2820 hospitals were collected using the National Clinical Improvement System Data that reports ICU information in China. Data collection consisted of a) information on the hospital and ICU structural factors, including the hospital type, number of beds, staffing, among others, and b) ICU patient outcomes, including the mortality rate as well as the incidence of ventilator-associated pneumonia (VAP), catheter-related bloodstream infections (CRBSIs), and catheter-associated urinary tract infections (CAUTIs). Generalized linear mixed models were used to analyse the association between hospital and ICU structural factors and patient outcomes. Results The median ICU patient mortality was 8.02% (3.78%, 14.35%), and the incidences of VAP, CRBSI, and CAUTI were 5.58 (1.55, 11.67) per 1000 ventilator days, 0.63 (0, 2.01) per 1000 catheter days, and 1.42 (0.37, 3.40) per 1000 catheter days, respectively. Mortality was significantly lower in public hospitals (β = − 0.018 (− 0.031, − 0.005), p = 0.006), hospitals with an ICU-to-hospital bed percentage of more than 2% (β = − 0.027 (− 0.034, -0.019), p

The design of X-ray optics based on diffraction from crystals depends on the accurate calculation of the structure factors of their Bragg reflections over a wide range of temperatures. In general, the temperature dependence of the lattice parameters, the atomic positions and the atomic thermal vibrations is both anisotropic and nonlinear. Implemented here is a software package for precise and flexible calculation of structure factors for dynamical diffraction. α-Quartz is used as an example because it presents the challenges mentioned above and because it is being considered for use in high-resolution X-ray spectroscopy. The package is designed to be extended easily to other crystals by adding new material files, which are kept separate from the package's stable core. Python 3 was chosen as the language to allow the easy integration of this code into existing packages. The importance of a correct anisotropic treatment of the atomic thermal vibrations is demonstrated by comparison with an isotropic Debye model. Discrepancies between the two models can be as much as 5% for strong reflections and considerably larger (even to the level of 100%) for weak reflections. A script for finding Bragg reflections that backscatter X-rays of a given energy within a given temperature range is demonstrated. The package and example scripts are available on request. Also discussed, in detail, are the various conventions related to the proper description of chiral quartz. [ABSTRACT FROM AUTHOR]

Background: Hospital and ICU structural factors are key factors affecting the quality of care as well as ICU patient outcomes. However, the data from China are scarce. This study was designed to investigate how differences in patient outcomes are associated with differences in hospital and ICU structure variables in China throughout 2019. Methods: This was a multicenter observational study. Data from a total of 2820 hospitals were collected using the National Clinical Improvement System Data that reports ICU information in China. Data collection consisted of a) information on the hospital and ICU structural factors, including the hospital type, number of beds, staffing, among others, and b) ICU patient outcomes, including the mortality rate as well as the incidence of ventilator-associated pneumonia (VAP), catheter-related bloodstream infections (CRBSIs), and catheter-associated urinary tract infections (CAUTIs). Generalized linear mixed models were used to analyse the association between hospital and ICU structural factors and patient outcomes. Results: The median ICU patient mortality was 8.02% (3.78%, 14.35%), and the incidences of VAP, CRBSI, and CAUTI were 5.58 (1.55, 11.67) per 1000 ventilator days, 0.63 (0, 2.01) per 1000 catheter days, and 1.42 (0.37, 3.40) per 1000 catheter days, respectively. Mortality was significantly lower in public hospitals (β = − 0.018 (− 0.031, − 0.005), p = 0.006), hospitals with an ICU-to-hospital bed percentage of more than 2% (β = − 0.027 (− 0.034, -0.019), p < 0.001) and higher in hospitals with a bed-to-nurse ratio of more than 0.5:1 (β = 0.009 (0.001, 0.017), p = 0.027). The incidence of VAP was lower in public hospitals (β = − 0.036 (− 0.054, − 0.018), p < 0.001). The incidence of CRBSIs was lower in public hospitals (β = − 0.008 (− 0.014, − 0.002), p = 0.011) and higher in secondary hospitals (β = 0.005 (0.001, 0.009), p = 0.010), while the incidence of CAUTIs was higher in secondary hospitals (β = 0.010 (0.002, 0.018), p = 0.015). Conclusion: This study highlights the association between specific ICU structural factors and patient outcomes. Modifying structural factors is a potential opportunity that could improve patient outcomes in ICUs. [ABSTRACT FROM AUTHOR]

Many experimental methods are available for the characterization of nanostructures, but most of them are limited by stringent experimental conditions. When it comes to analysing nanostructures in the bulk or in their natural environment – even as ordinary as water at room temperature – small‐angle scattering (SAS) of X‐rays or neutrons is often the only option. The rapid worldwide development of synchrotron and neutron facilities over recent decades has opened unprecedented possibilities for using SAS in situ and in a time‐resolved way. But, in spite of its huge potential in the field of nanomaterials in general, SAS is covered far less than other characterization methods in non‐specialized curricula. Presented here is a rigorous discussion of small‐angle scattering, at a technical level comparable to the classical undergraduate coverage of X‐ray diffraction by crystals and which contains diffraction as a particular case. [ABSTRACT FROM AUTHOR]

Ferroelectric lead-free BaTi1−xZrxO3 ceramic powder samples with various compositions (x = 0, 0.04, 0.06) have been synthesized by conventional high-temperature solid-state reaction method at 1450 °C for 10 h. Influences of Zr doping on the inter-atomic bonding and charge density distributions inside the lattice structure of BaTiO3 were analyzed through powder X-ray diffraction (XRD) and maximum entropy method. Lattice parameter and cell volume values are found to be increasing with the incorporation of Zr content. Calculated average grain sizes are found to be in the range of 23–28 nm. Maximum entropy mapping of electron density analysis reveals the reduction in ionic nature along Ba–O bond and the enhancement of covalent nature along Ti–O bond. Energy band gap values were determined from ultraviolet–visible (UV–Vis) spectra. Surface morphology and microstructures of the samples were analyzed from scanning electron microscopy (SEM) micrographs. Particles with irregular sizes were observed in all the prepared ceramics. Stoichiometry of the samples was further confirmed by energy-dispersive X-ray spectroscopy (EDAX). [ABSTRACT FROM AUTHOR]

This paper aims to explain the evolution of the cultural participation in Colombia between 2018 and 2015, and to empirically analyse the factors associated to the decision of participating in cultural activities in the five main cities during this period. In Bogota, Cali, Medellin, Barranquilla and Cartagena, half of the urban population resides. The effects of a set of individual variables, household and context are evaluated, exploring alongside the traditional determinants, a set of new variables such as the kind of education that children receive, the poverty situation and others concerning the habitat, the social capital and macroeconomic ones. Microdata from households from the Quality of Life Survey – from programmes of citizen monitoring- are used, with which a binomial model is estimated. The results highlight the importance of including the context variables so as to widen the knowledge of the individual decisions of participation.

The development of well ordered nanonetwork materials (in particular gyroid-structured materials) has been investigated using a block-copolymer template for templated electroless plating as an example system for the examination of network formation using X-ray scattering. By taking advantage of the nucleation and growth mechanism of templated electroless plating, gyroid-structured Au was successfully fabricated through the development of Au nanoparticles, then tripods and branched tripods, and finally an ordered network. Each stage in the development of the network phase could then be examined by combining real-space transmission electron microscopy observations with reciprocal-space small-angle X-ray scattering results. The fingerprint scattering profile of the building block for the network (i.e. the tripod of the gyroid) could be well fitted with the form factor of an effective sphere, and the diffraction results from the ordered network could thus be reasonably addressed. As a result, the examination of well ordered network materials can be simplified as the scattering from the form factor of a sphere convoluted with the nodes of its structure factor, providing a facile method of identifying the network phases from X-ray scattering data.

We present the results of molecular dynamic studies of collective dynamics in a system of hard disks confined to a narrow quasi-one-dimensional (quasi-1D) channel. The computer simulations have been performed for the specific channel width of 3/2 of disk diameter in which the disk arrangement at close packing resembles zigzag ordering characteristic of a vertically oriented two-dimensional (2D) triangular lattice. In such a quasi-1D system, which is intermediate between 1D and 2D arrays of hard disks, the transverse excitations obey very specific dispersion law typical of the usual optical transverse modes. This is in a sharp contrast both to the 1D case, where transverse excitations are not possible, and to the 2D case, where the regular shear waves with a propagation gap were observed. Other peculiarities of the dispersion of collective excitations as well as some results of disk structuring and thermodynamics of the quasi-1D hard disk system are presented and discussed for a range of hard disk densities typical for fluid and distorted crystal states.

A local structure analysis method based on convergent‐beam electron diffraction (CBED) has been used for refining isotropic atomic displacement parameters and five low‐order structure factors with sin gθ/λ ≤ 0.28 Å−1 of potassium tantalate (KTaO3). Comparison between structure factors determined from CBED patterns taken at the zone‐axis (ZA) and Bragg‐excited conditions is made in order to discuss their precision and sensitivities. Bragg‐excited CBED patterns showed higher precision in the refinement of structure factors than ZA patterns. Consistency between higher precision and sensitivity of the Bragg‐excited CBED patterns has been found only for structure factors of the outer zeroth‐order Laue‐zone reflections with larger reciprocal‐lattice vectors. Correlation coefficients among the refined structure factors in the refinement of Bragg‐excited patterns are smaller than those of the ZA ones. Such smaller correlation coefficients lead to higher precision in the refinement of structure factors. [ABSTRACT FROM AUTHOR]

This study examined psychosocial factors and structural factors influencing science, technology, engineering, and mathematics (STEM) students’ experiences at six historically Black colleges and universities (HBCUs) in different locations (East, West and South) of the United States. The mixed method design allowed different types of data sources to be collected and analyzed to identify areas of convergence. In this federally funded study, quantitative data served as complementary data to corroborate the emergent qualitative themes. In addition, quantitative and qualitative results provided a comprehensive understanding of different psychosocial factors and structural factors that contributed to African American students’ academic success and retention. [ABSTRACT FROM AUTHOR]

Lens‐less imaging of crystals with coherent X‐ray diffraction offers some unique possibilities for strain‐field characterization. It relies on numerically retrieving the phase of the scattering amplitude from a crystal illuminated with coherent X‐rays. In practice, the algorithms encode this amplitude as a discrete Fourier transform of an effective or Bragg electron density. This short article suggests a detailed route from the classical expression of the (continuous) scattering amplitude to this discrete function. The case of a heterogeneous incident field is specifically detailed. Six assumptions are listed and quantitatively discussed when no such analysis was found in the literature. Details are provided for two of them: the fact that the structure factor varies in the vicinity of the probed reciprocal lattice vector, and the polarization factor, which is heterogeneous along the measured diffraction patterns. With progress in X‐ray sources, data acquisition and analysis, it is believed that some approximations will prove inappropriate in the near future. [ABSTRACT FROM AUTHOR]

Scattering methods are widely used in many research areas to analyze and resolve material structures. Given its importance, a large number of textbooks are devoted to this topic. However, technical details in experiments and disconnection between explanations from different perspectives often confuse and frustrate beginner students and researchers. To create an effective learning path, the core concepts of scattering and structure factor are reviewed in this article in a self‐contained way. Classical examples of scattering photography and intensity scanning are calculated. Sample CPU and GPU codes are provided to facilitate the understanding and application of these methods. [ABSTRACT FROM AUTHOR]

The two‐dimensional wide‐angle X‐ray diffraction technique was applied to a Cm‐doped borosilicate glass in a beryllium container. The experiment involved a high‐energy X‐ray beam and an image plate. It is shown that it is possible to extract the structure factor of the radioactive glass successfully from diffraction patterns and compare it with that of the pristine one. Striking differences appear under the first diffraction peak, revealing new sub‐structures for the radioactive glass. It is suggested that they could be related to structural changes in the medium‐range order, in particular the size distribution of rings or chains under the influence of mixed interactions between the glass network, α‐particles and recoil nuclei. [ABSTRACT FROM AUTHOR]

Measuring the structure factor, S(q), of a dispersion of particles by small‐angle X‐ray scattering provides a unique method to investigate the spatial arrangement of colloidal particles. However, it is impossible to find the exact location of the particles from S(q) because some information is inherently lacking in the measured signal. The two standard ways to analyse an experimental S(q) are then to compare it either with structure factors computed from simulated systems or with analytical ones calculated from approximated systems. However, such approaches may prove inadequate for dispersions of variously polydisperse particles. While Vrij, Bloom and Stell established a mean‐field approach that could yield fairly accurate approximations for experimental S(q), this solution has remained underused because of its mathematical complexity. In the present work, the complete Percus–Yevick solution for general polydisperse hard‐sphere systems is derived in a concise form that is straightforward to use. The form of the solution has been simplified enough to provide experimentalists with ready solutions of several commonly encountered particle‐radius distributions in real systems (Schulz, truncated normal and inverse Gaussian). The approach is also illustrated with a case study of the exponential radius distribution. Finally, the application of the proposed solution to the power‐law radius distribution is discussed in detail by comparing the calculations with experimentally measured S(q) for an Apollonian packing of spherical droplets recently reported in high‐internal‐phase‐ratio emulsions. [ABSTRACT FROM AUTHOR]

An acoustically levitated droplet has been used to collect synchrotron SAXS data on human serum albumin protein solutions up to a protein concentration of 400 mg ml−1. A careful selection of experiments allows for fast data collection of a large amount of data, spanning a protein concentration/solvent concentration space with limited sample consumption (down to 3 µL per experiment) and few measurements. The data analysis shows data of high quality that are reproducible and comparable with data from standard flow‐through capillary‐based experiments. Furthermore, using this methodology, it is possible to achieve concentrations that would not be accessible by conventional cells. The protein concentration and ionic strength parameter space diagram may be covered easily and the amount of protein sample is significantly reduced (by a factor of 100 in this work). Used in routine measurements, the benefits in terms of protein cost and time spent are very significant. [ABSTRACT FROM AUTHOR]

Modern methods of quantum crystallography are techniques firmly rooted in quantum chemistry and, as in many quantum chemical strategies, electron densities are expressed as two‐centre expansions that involve basis functions centred on atomic nuclei. Therefore, the computation of the necessary structure factors requires the evaluation of Fourier transform integrals of basis function products. Since these functions are usually Cartesian Gaussians, in this communication it is shown that the Fourier integrals can be efficiently calculated by exploiting an extension of the Obara–Saika recurrence formulas, which are successfully used by quantum chemists in the computation of molecular integrals. Implementation and future perspectives of the technique are also discussed. [ABSTRACT FROM AUTHOR]

Noble metal nanoparticles exhibit unique physical, chemical, biomedical, catalytic and optical properties. Understanding these properties and further development of production methods entail detailed knowledge of the structure at the atomic scale. Gold nanoparticles with multimodal size distribution were synthesized on porous silica and their atomic scale structure was studied by X‐ray diffraction. The obtained experimental data are compared with molecular dynamics simulations. Spherical models of the Au nanoparticles, defined by ensembles of the Cartesian coordinates of constituent atoms, were generated and their geometry was optimized by applying the LAMMPS software. The comparison was performed in both reciprocal and real space. A good agreement is achieved for the models with disorder that can be related to surface relaxation effects and vacancy defects. The approach adopted here may have wider applications for further structural studies of other nanomaterials, offering direct verification of simulation results by experiment. [ABSTRACT FROM AUTHOR]