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Van der Waals (vdW) solids have attracted great attention ever since the discovery of graphene, with the essential feature being the weak chemical bonding across the vdW gap. The nature of these weak interactions is decisive for many extraordinary properties, but it is a strong challenge for current theory to accurately model long-range electron correlations. Here we use synchrotron X-ray diffraction data to precisely determine the electron density in the archetypal vdW solid, TiS2, and compare the results with density functional theory calculations. Quantitative agreement is observed for the chemical bonding description in the covalent TiS2 slabs, but significant differences are identified for the interactions across the gap, with experiment revealing more electron deformation than theory. The present data provide an experimental benchmark for testing theoretical models of weak chemical bonding.

An accurate X-ray diffraction study at 20 K combined with DFT theoretical calculations has been performed for the estriol crystal with two conformationally different molecules in the asymmetric unit. The electron density has been modeled via a multipole expansion, using both experimental and theoretical structure factors, and a topological analysis has been performed. The experimental molecular geometry, hydrogen bonding, atomic charges, dipole moments, and other topological characteristics are compared with those calculated theoretically. In particular, the molecular electrostatic potential has been extracted and compared with those reported for other estrogen molecules exhibiting different binding affinities to the estrogen receptors (ERα and ERβ).

The electron density distribution of two substituted norbornene derivatives (cis-5-norbornene-endo-2,3-dicarboxylic anhydride (1) and 7-oxabicylo[2.2.1]hept-5-ene-exo-2,3-dicarboxylic anhydride (2) has been determined from low-temperature (20 K) X-ray diffraction data and from DFT calculations with periodic boundary conditions. Topological analysis of the electron density is discussed with respect to exo-selective additions, the partial retro-Diels-Alder (rDA) character of the ground state, and intermolecular interaction energies.

The charge density of 2,6-dinitrophenol has been carefully determined from low temperature (20 K) single crystal X-ray diffraction data and periodic ab initio theoretical calculations. The topological analysis performed on the refined densities within the framework of the Quantum Theory of Atoms in Molecules (QTAIM), allowed us to characterize, both qualitatively and quantitatively, the various intra- and intermolecular interactions existing in the crystal structure of this compound. Notably two strong intramolecular noncovalent interactions have been characterized (O···H, De > 60 kJ/mol; O···O, De ∼ 19 kJ/mol). In addition, a series of weaker intermolecular interactions (O···N, O···O, O···C, and C···C) with estimated dissociation energies of 1–9 kJ/mol have been identified.

This paper presents topological analysis of charge density from multipolar refinement and ab initio calculations for both melamine-barbital co-crystal and isolated molecules. The comparison of electron density properties for the isolated molecules and for the co-crystal allowed one to unravel the factors contributing to the formation of specific hydrogen bond patterns in the co-crystal structure. The inspection of charge density properties revealed that N1A of barbital and N3B of melamine compete for H1A atom in hydrogen bond formation. The hydrogen bond shows an intermediate character between closed and shared shell interaction. The tendency of barbital to adopt tautomeric forms in solution which can be correlated with the shift of electron density (mesomeric effect) was emphasized. Charge density studies confirmed the existence of the mesomeric form B of barbital in the studied co-crystal. The form B was also reported in polar co-crystals comprised of barbital and barbituric acid.

X-ray/neutron (X/N) diffraction data measured at very low temperature (15 K) in conjunction with ab initio theoretical calculations were used to model the crystal charge density (CD) of the host-guest complex of hydroquinone (HQ) and acetonitrile. Due to pseudosymmetry, information about the ordering of the acetonitrile molecules within the HQ cavities is present only in almost extinct, very weak diffraction data, which cannot be measured with sufficient accuracy even by using the brightest X-ray and neutron sources available, and the CD model of the guest molecule was ultimately based on theoretical calculations. On the other hand, the CD of the HQ host structure is well determined by the experimental data. The neutron diffraction data provide hydrogen anisotropic thermal parameters and positions, which are important to obtain a reliable CD for this light-atom-only crystal. Atomic displacement parameters obtained independently from the X-ray and neutron diffraction data show excellent agreement with a |ΔU| value of 0.00058 Å(2) indicating outstanding data quality. The CD and especially the derived electrostatic properties clearly reveal increased polarization of the HQ molecules in the host-guest complex compared with the HQ molecules in the empty HQ apohost crystal structure. It was found that the origin of the increased polarization is inclusion of the acetonitrile molecule, whereas the change in geometry of the HQ host structure following inclusion of the guest has very little effect on the electrostatic potential. The fact that guest inclusion has a profound effect on the electrostatic potential suggests that nonpolarizable force fields may be unsuitable for molecular dynamics simulations of host-guest interaction (e.g., in protein-drug complexes), at least for polar molecules.

The discovery of the ultra-high thermoelectric figure of merit of 2.6 in SnSe has drawn attention to other lead-free IV-VI orthorhombic semiconductors. GeSe has been predicted to possess thermoelectric performances comparable to SnSe. Here, a complete structural study is reported of GeSe with temperature by means of high-resolution synchrotron powder X-ray diffraction. In the orthorhombic phase, the evolution of the bond distances with temperature is shown to deviate significantly with respect to SnSe. Analysis of the chemical bonding within the Quantum Theory of Atoms in Molecules shows that GeSe is ionic with van der Waals interlayer interactions. The signature of the N shell lone pair of Ge is also evident from both the electron density Laplacian and the ELF topologies.

We present a combined experimental and theoretical charge density study of the coordination polymer Zn(HCOO)(2)(H(2)O)(2), which serves as a nonmagnetic reference for the isostructural magnetic compounds containing 3d transition metals. The charge density has been modeled using the multipole formalism against a high-resolution single-crystal X-ray diffraction data set collected at 100 K. The theoretical model is based on periodic density functional theory calculations in the experimental geometry. To gauge the degree of systematic bias from the multipole model, the structure factors of the theoretical model were also projected into a multipole model and the two theoretical models are compared with the experimental results. All models, both experiment and theory, show that the Zn atom densities are highly spherical but show small accumulations of charge toward the negative ligands. The metal-ligand interactions are found to be primarily ionic, but there are subtle topological indications of covalent contributions to the bonds. The source function calculated at the bond critical points reveals a rather delocalized picture of the density in the bridging carboxylates, and this presumably reflects the exchange pathway in the magnetic analogues.

Octahedral monodisperse a-MnS and MnO nanoparticles have been synthesized by decomposing manganese oleate and elemental sulfur in octadecene at high (250-320 °C) temperature. The chemical composition of the obtained NPs depends on the Mn:S ratio in an unexpected way. Pure a-MnS NP samples are obtained when S:Mn >= 2:1, whereas pure MnO NPs require S:Mn

Catalysts comprising amorphous Fe2O3 nanoparticles dispersed on silica and silica-zirconia are presented. A molecular Fe precursor was grafted on the oxide support surface by an equilibrium-adsorption method. Afterward, calcination of the material produced amorphous Fe2O3 nanoparticles on the oxide support surface. The different nature of the oxide support (SixZr1-xO2, 0.715 < x < 1) imparted tunable electronic (studied by UV-vis diffuse reflectance spectroscopy), dimensional (studied by electron paramagnetic resonance spectroscopy, EPR), and redox (studied by thermal programmed reduction, TPR) properties to the samples, with following down toward their catalytic properties. The different support surfaces were covered by the iron oxide phase (from 5 to 10%), constituted of nanosized particles in a narrow size interval (between 2 and 9 nm, studied by EPR line shape and transmission electron microscopy, TEM, analyses). Homogeneous surface distribution was achieved in any case (studied by scanning electron micrographs coupled with energy dispersive X-ray spectroscopy, SEM-EDS). The precise arrangement and nuclearity of the iron oxide nanoparticles on the surface depended on the support nature. Besides, from Fe2O3 nanoaggregates (3d and 2d nanoparticles), the presence of isolated Fe3+ ions in strong interaction with the oxide support was revealed, the amount increasing with the zirconia content in the support.

The electronic structure of Co4Sn6–xTe6+x (x = 0, 1) ternary skutterudite systems has been investigated using ab -initio band structure computation. The x = 0 system is a semiconductor like the binary Co4Sb12, but with a lower band gap. The best dopant concentration for Co4Sn6Te6 is estimated to be lower than that of Co4Sb12, with the highest electronic fig- ure-of-merit ZeT for the n-doped system. Finally, the increased charge transfer between the 8c Co and 24g Sn and Te atoms in Co4Sn6Te6 compared to that of Co4Sb12 could be one reason for the observed decrease of thermal conductivity in ternary skutterudite systems. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

The electron density distributions in both polymorphs of the promising photovoltaic material iron disulfide have been determined by multipole modelling against state-of-the-art synchrotron X-ray diffraction data collected at 10 K using minute single crystals with dimensions less than 10 μm. Charge density analysis of FeS2 pyrite and marcasite offers a unique opportunity to relate local atomic properties, such as 2-center chemical bonding, atomic charges and d-orbital populations, to polymorphism in extended crystal structures. In combination with results from periodic calculations on the compounds in the experimental geometries using WIEN2k, the study provides unambiguous answers to a number of unsolved issues regarding the nature of the bonding in FeS2. The Fe–S bonds exhibit all the virtues of polar covalent bonds, with only minor charge accumulation but significantly negative energy densities at the bond critical points. Compared to a non-interacting model, the density is found to be concentrated along the Fe–S interaction line in support of a partial covalent bonding description. The homopolar covalent S–S interaction is seemingly stronger in pyrite than in marcasite, determined not only from the shorter distance but also from all topological indicators. The study also clarifies that the atomic charges are significantly smaller than the estimation based on crystal-field theory of Fe2+, S−1. The experimentally derived Fe d-orbital populations are found to deviate from the commonly assumed full t2g set, empty eg set, and they fit exceptionally well with the theoretical individual atomic orbitals projected density of states showing a higher dxy participation in the valence band in marcasite compared with pyrite. Thus, the differences between the two polymorphic compounds are directly reflected in their valence density distributions and d-orbital populations.

CoSb3is 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 CoSb3framework 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.

\({\mathrm{FeSb }}_{2}\) exhibits extraordinary physical properties with a colossal thermopower reaching 45 mV/K at \(\sim \)10 K, while maintaining fairly low electrical resistivity. This results in extremely high thermoelectric power factors exceeding 2,000 \(\upmu {\mathrm{W }}/({\mathrm{K }}^{2} \cdot \,{\mathrm{cm }})\). If the thermal conductivity can be reduced to a few W/(K\(\cdot \)m), then a thermoelectric figure of merit of unity is within reach at cryogenic temperatures opening up for a new solid state cooling technology. Furthermore, the physical properties of \(\mathrm{FeSb }_{2}\) are also of immense fundamental interest since the material is believed to be a strongly correlated narrow band gap semiconductor. In the last decade a wide range of studies have explored the synthesis, structure and properties of \(\mathrm{FeSb }_{2}\) and related materials, and here an overview of the efforts is provided.

One of the most basic concepts in chemical bonding theory is the octet rule, which was introduced by Lewis in 1916, but later challenged by Pauling to explain the bonding of third-row elements. In the third row, the central atom was assumed to exceed the octet by employing d orbitals in double bonding leading to hypervalency. Ever since, polyoxoanions such as SO(4)(2-), PO(4)(3-), and ClO(4)(-) have been paradigmatic examples for the concept of hypervalency in which the double bonds resonate among the oxygen atoms. Here, we examine S-O bonding by investigating the charge density of the sulfate group, SO(4)(2-), within a crystalline environment based both on experimental and theoretical methods. K(2)SO(4) is a high symmetry inorganic solid, where the crystals are strongly affected by extinction effects. Therefore, high quality, very low temperature single crystal X-ray diffraction data were collected using a small crystal (∼30 μm) and a high-energy (30 keV) synchrotron beam. The experimental charge density was determined by multipole modeling, whereas a theoretical density was obtained from periodic ab initio DFT calculations. The chemical bonding was jointly analyzed within the framework of the Quantum Theory of Atoms In Molecules only using quantities derived from an experimental observable (the charge density). The combined evidence suggests a bonding situation where the S-O interactions can be characterized as highly polarized, covalent bonds, with the "single bond" description significantly prevailing over the "double bond" picture. Thus, the study rules out the hypervalent description of the sulfur atom in the sulfate group.

Fully filled CaCo4Sb12 system is selected as a test case for probing how the ab-initio modeled electronic transport properties are affected by the computational level. The periodic wave functions for the various adopted models are calculated by means of the Density Functional Theory (DFT) approach using local gaussian atomic basis sets, while the relevant electronic transport properties are obtained from the band structure using the semi-classical Boltzmann transport theory. This two-step computational procedure is tested against the atomic basis set quality, the band structure adopted in the frozen band approach and the DFT functional form. From this extensive test, a reliable computational level for CaCo4Sb12 is identified and the experimental findings on the Ca-filled systems are discussed in the light of, and compared with, the results from computations.

The experimental charge density (CD) distributions in both polymorphs of the photovoltaic compound iron-disulphide (FeS2; cubic pyrite and orthorhombic marcasite) will be described.[1] The CDs are determined by multipole modelling using synchrotron X-ray diffraction data collected at 10 K on extremely small single crystals (

CoSb3 is a highly important host-guest material for the engineering of high-performance thermoelectric materials.[1] Its crystal structure has empty cavities and when guest atoms are added to CoSb3, its thermoelectric properties are greatly enhanced due to decreased thermal conductivity.[2] In order to understand the origin of the thermoelectric properties of this family of materials, it is important to understand the crystal structure and chemical bonding of the un-doped host material.[3] This can be achieved through analysis of the charge density, which in principle can be obtained from modeling of accurate X-ray diffraction data.[4] However, considering the heavy elements, the high symmetry and the perfect crystallinity of this inorganic network structure one cannot think of a much more challenging case for experimental charge density analysis. In the present study we analyze several low-temperature experimental X-ray diffraction data sets collected at different sources using different experimental conditions. These are compared with high-level ab-initio periodic DFT calculations. The results clearly show that in the current study the data obtained from synchrotron sources were superior to data obtained from conventional sources. Some important experimental requirements are that the data need to be collected on a high-intensity, high-energy source using very small crystals so as to diminish extinction and absorption effects. The data collected at SPring8 seem to fulfill these requirements most satisfactorily.[5]References [1] D.T. Morelli et al., Phys. Rev. B 51 (1995) 9622. [2] J.-L. Mi, M. Christensen, E. Nishibori, B.B. Iversen. Phys. Rev. B 84 (2011) 064114. [3] T. Caillat, A. Borshchevsky, J.-P. Fleurial. J. Appl. Phys. 80 (1996) 4442-4449. [4] A. Ohno et al., Phys. Rev. B 76 (2007) 064119. [5] M. Schmøkel, L. Bjerg, F.K. Larsen, J. Overgaard, S. Cenedese, M. Christensen, G.K.H. Madsen, C. Gatti, A. Pinkerton, E. Nishibori, K. Sugimoto, M. Takata, B.B. Iversen. In preparation.