Tetrahedral Cavities Research Articles

Hydride migration from a triangular face to a tetrahedral cavity in tetranuclear iron carbonyl clusters upon coordination of [AuPPh(3)](+) fragments.

Metal hydrides are of fundamental importance in chemistry, both as solid-state materials and molecular compounds. The first low-valent molecular metal cluster containing an interstitial four-coordinate hydride in a tetrahedral site is decribed, which undergoes hydride migration from the surface to the tetrahedral cavity of the cluster upon coordination of a [AuPPh3 ](+) fragment. The [HFe4 (CO)12 (AuPPh3 )2 ](-) mono-anion, which contains a surface μ3 -H, was obtained from the reaction of [HFe4 (CO)12 ](3-) with two equivalents of [Au(PPh3 )Cl]. This is, in turn, transformed into the neutral [HFe4 (CO)12 (AuPPh3 )3 ] upon addition of a third [AuPPh3 ](+) fragment, with concomitant migration of the unique hydride from the surface of the cluster to its tetrahedral cavity. All of these species have been fully characterized in solution by means of IR and multinuclear NMR spectroscopy, and in the solid state by single-crystal X-ray diffractometry.

Water Release from Pyrophyllite during the Dehydroxylation Process Explored by Quantum Mechanical Simulations

We have investigated one of the most controversial aspects of the dehydroxylation–rehydroxylation process of dioctahedral 2:1 phyllosilicates, that is the release of water from the internal structure of the mineral. We simulate the release of water from a periodic crystal model of pyrophyllite by Car–Parrinello molecular dynamics based on Density Functional Theory. The metadynamics algorithm is employed to accelerate activated processes and compute free energy surfaces. We found that, in spite of the strong hydrogen bonds anchoring water molecules in the tetrahedral cavity, the energy barrier for water release is lower than that for the chemical formation of water molecules from the hydroxyl groups. We then conclude that water release is not the rate-limiting step of the dehydration mechanism.

Three‐Dimensional MOF‐Type Architectures with Tetravalent Uranium Hexanuclear Motifs (U6O8)

Four metal-organic frameworks (MOF) with tetravalent uranium have been solvothermally synthesized by treating UCl4 with rigid dicarboxylate linkers in N,N-dimethylfomamide (DMF). The use of the ditopic ligands 4,4'-biphenyldicarboxylate (1), 2,6-naphthalenedicarboxylate (2), terephthalate (3), and fumarate (4) resulted in the formation of three-dimensional networks based on the hexanuclear uranium-centered motif [U6O4(OH)4(H2O)6]. This motif corresponds to an octahedral configuration of uranium nodes and is also known for thorium in crystalline solids. The atomic arrangement of this specific building unit with organic linkers is similar to that found in the zirconium-based porous compounds of the UiO-66/67 series. The structure of [U6O4(OH)4(H2O)6(L)6]⋅X (L = dicarboxylate ligand; X = DMF) shows the inorganic hexamers connected in a face-centered cubic manner through the ditopic linkers to build up a three-dimensional framework that delimits octahedral (from 5.4 Å for 4 up to 14.0 Å for 1) and tetrahedral cavities. The four compounds have been characterized by using single-crystal X-ray diffraction analysis (or powder diffraction analysis for 4). The tetravalent state of uranium has been examined by using XPS and solid-state UV/Vis analyses. The measurement of the Brunauer-Emmett-Teller surface area indicated very low values (Langmuir <300 m(2) g(-1) for 1, <7 m(2) g(-1) for 2-4) and showed that the structures are quite unstable upon removal of the encapsulated DMF solvent.

Hypoelectronic diruthenaboranes and diosmaboranes having eight to twelve vertices: capped isocloso and bicapped closo structures

The oblate deltahedral structures for the experimentally known 2n − 4 Wadean skeletal electron systems Cp2Re2Bn−2Hn−2 (Cp = η5-R5C5 ligand; R = H, CH3; n = 8 to 12) differ radically from the more nearly spherical 2n skeletal electron isocloso deltahedra such as the known Cp2Fe2C2Bn−4Hn−2 and 2n + 2 skeletal electron closo systems such as the extensive series of known Cp2Co2C2Bn−4Hn−2 derivatives. Density functional theory has now been used to investigate the intermediate “missing” systems, namely the 2n − 2 Wadean skeletal electron systems Cp2M2Bn−2Hn−2 (M = Ru, Os). The lowest energy such structures are predicted to have central deltahedra with n − 1 or n − 2 vertices capped by the remaining BH vertices. This generates larger deltahedra having one or two degree 3 vertices leading to tetrahedral cavities. In all of the lowest energy Cp2M2Bn−2Hn−2 structures the metal atoms are located at the highest degree vertices, most frequently degree 6 vertices. These metal vertices share a deltahedral edge with M–M distances ranging from 2.7 to 2.9 A and Wiberg bond indices of ∼0.3 to ∼0.4. The structural pattern changes drastically for the 12-vertex systems Cp2M2B10H10 (M = Ru, Os) where the lowest energy structures are “isoisocloso” deltahedra having two adjacent degree 6 vertices for the metal atoms as well as eight degree 5 and two degree 4 vertices. Higher energy Cp2M2B10H10 structures are based on a regular icosahedron with all degree 5 vertices having unusually short MM edges of ∼2.2 to ∼2.3 A with corresponding high Wiberg bond indices of ∼1.3 to ∼1.5 suggesting formal metal–metal triple bonds.

Scalar Casimir energies of tetrahedra and prisms

New results for scalar Casimir self-energies arising from interior modes are presented for the three integrable tetrahedral cavities. Since the eigenmodes are all known, the energies can be directly evaluated by mode summation, with a point-splitting regulator, which amounts to evaluation of the cylinder kernel. The correct Weyl divergences, depending on the volume, surface area and the edges, are obtained, which is strong evidence that the counting of modes is correct. Because there is no curvature, the finite part of the quantum energy may be unambiguously extracted. Cubic, rectangular parallelepipedal, triangular prismatic and spherical geometries are also revisited. Dirichlet and Neumann boundary conditions are considered for all geometries. Systematic behavior of the energy in terms of geometric invariants for these different cavities is explored. A smooth interpolation between short and long prisms is further demonstrated. When scaled by the ratio of the volume to the surface area, the energies for the tetrahedra and the prisms of maximal isoareal quotient lie very close to a universal curve. The physical significance of these results is discussed.

Interaction Energies and Spectroscopic Effects in the Adsorption of Formic Acid on Mineral Aerosol Surface Models

Heterogeneous reactions of atmospheric volatile organic compounds (VOCs) on aerosol particles may play an important role in atmospheric chemistry. Silicate particles are present in airborne mineral dust in aerosols, and the atmospheric chemistry in general can be modified by their presence. In this work, the adsorption of a single formic acid molecule on different silicate surface models has been studied using quantum-mechanical methods. Both molecular clusters and a periodic crystal model of the (001) pyrophyllite surface have been employed, and all possible adsorption geometries have been considered. We find that silanol groups are always the most reactive formic acid adsorption sites. In the case of a periodic system, silanol groups at the crystal edges are favored. However, OH groups on the phyllosilicate octahedral sheet are also reactive sites through the tetrahedral cavities. The effect of formic acid adsorption on the spectroscopic properties of the whole system is also analyzed. Significant frequ...

SCALAR CASIMIR ENERGIES OF TETRAHEDRA

New results for scalar Casimir self-energies arising from interior modes are presented for the three integrable tetrahedral cavities. Since the eigenmodes are all known, the energies can be directly evaluated by mode summation, with a point-splitting regulator, which amounts to evaluation of the cylinder kernel. The correct Weyl divergences, depending on the volume, surface area, and the corners, are obtained, which is strong evidence that the counting of modes is correct. Because there is no curvature, the finite part of the quantum energy may be unambiguously extracted. Dirichlet and Neumann boundary conditions are considered and systematic behavior of the energy in terms of geometric invariants is explored.

A simple device to test biodiesel process intensification

In this paper, we have studied the KOH catalyzed transesterification reaction of vegetable oil with methanol in a tubular reactor filled with small spheres of stainless steel of different sizes. Three different packed bed configurations have been tested corresponding to different fluid dynamic situations. The first configuration corresponds to the tubular reactor filled with spheres of 2.5 mm of diameters; in the second configuration an opportune amount of spheres of 1 mm has been added to the mentioned spheres of 2.5 mm for filling the void volume of the octahedral cavities between the bigger spheres; in the third configuration an opportune amount of spheres of 0.39 mm has been added to spheres of 2.5 mm for filling the void volume of the tetrahedral cavities between the bigger spheres. The three mentioned configurations give place to the formation of micro-channels with an approximated size of respectively 1000 μm, 500 μm and 300 μm. These systems, subjected to fluid dynamic characterization, have shown a very high local turbulence (static mixer), in particular, when a packed bed reactor with dual size packing is used. Then, kinetic transesterification runs have been made by using the three mentioned packed bed reactors and a very high productivity has been obtained as a consequence of the induced local micro-mixing. A simplified kinetic model has been developed, which is able to describe many runs in batch conditions reported by the literature. This model resulted unsuitable to simulate the continuous runs performed in the described packed bed reactors. Our conclusion is that monophasic models, often proposed in the literature, are not able to describe the kinetic behavior of KOH catalysed transesterification in microchannels devices. At last, the described microchannels device represents, as it will be discussed, an ideal connection between a traditional tubular packed bed reactor and the recently appeared microreactors that are very efficient in mass and energy transfer operations for process intensification.

Sizes and properties of clusters of magnetic ferrite structures

The structures of the coordination spheres or orbits of hexagonal and cubic crystals and their sizes, coordination numbers, and coordinates of atoms and cavities have been studied. The orbits of atoms of all sublattices of octahedral and tetrahedral cavities have been calculated. The close-packed structures (FCC and HCP) of oxygen ions have been considered as basic structures. In both structures, the metal cations are distributed over octahedral and tetrahedral cavities. The developed method is used for calculating the orbits of clusters with the hexagonal crystal structure of magnetoplumbite, ilmenite, and corundum, as well as with the cubic structure of spinel and perovskite.

Novel MOFs with tetrahedral cavity assembled from 4,4′,4″-s-triazine-2,4,6-triyltribenzoic acid (H3TATB)

Abstract Three novel 3D complexes {H2[Zn6(μ4-O)(TATB)4]}n (1), [Cd3(TATB)2]n (2), and [Mn3(TATB)2]n (3) were synthesized from 4,4′,4″-s-triazine-2,4,6-triyltribenzoic acid (H3TATB) and corresponding metal salts under hydrothermal conditions. These complexes were characterized by elemental analyses, IR spectra, luminescent spectra, thermogravimetric analysis (TGA), and single crystal structure. Complex 1 adopted a straight Zn4(μ4-O) linked by TATB3− subunit to form an adamantane structure with a fully empty tetrahedral cavity. Two naked protons floated in the complex. This structure supports the existence of naked protons in nature. In complexes 2–3, the six deprotonated carboxylic oxygen of TATB3− coordinated to eight metal ions to form a 3D close-packed structure. Its density of 1.837 mg m− 3 made complex 2 one of the most closely packed structure based on H3TATB ever determined. Coordination polyhedral linked each other to form a diamondoid metal–oxygen framework in 2 and 3. All the coordination polymers were thermally stable up to 470 °C. These were the most thermally stable coordination polymers. A high-resolution transmission electron microscope indicated that the metal oxide is porous with pore diameters of ~ 2 nm.

Pentaeuropium dicadmium pentaantimonide oxide, Eu5Cd2Sb5O

The title compound, Eu5Cd2Sb5O adopts the Ba5Cd2Sb5F-type structure (Pearson symbol oC52), which contains nine crystallographically unique sites in the asymmetric unit, all on special positions. One Eu, two Sb, and the Cd atom have site symmetry m..; two other Eu, the third Sb and the O atom have site symmetry m2m; the remaining Eu atom has 2/m.. symmetry. Eu atoms fill penta­gonal channels built from corner-sharing CdSb4 tetra­hedra. The isolated O atom, i.e., an oxide ion O2−, is located in a distorted tetra­hedral cavity formed by four Eu cations.

Nature of disorder in synthetic hectorite

The disorder of synthetic Na-hectorite was investigated using structural simulation of X-ray powder patterns.The method used to characterize this clay mineral was based on the comparison between experimental and calculated X-ray diffraction profiles. The study was achieved in two steps: (i) the quantitative interpretation of 00l reflections enabled the determination of the number of intercalated water molecules, their positions and the stacking mode of the clay mineral layers along the normal to the (a, b) plane; and (ii) the study of the hkl reflections with h and/or k≠0 enabled the characterization of the structural evolution in the (a, b) plane of synthetic hectorite. Many models of disorder with random shifts of ±a/3, a/3+b/3, 80% of a/3+b/3 and 20% of a/3 with a total density of defects of 80%, gave the best fit to the observed data at the level of (02, 11), (20, 13), (04, 22), (15, 24, 31) and (06, 33) bands with 5° of tetrahedral cavity distortion (the rotation angle of the tetrahedra).

Reverse shape selectivity in the adsorption of hexane and xylene isomers in MOF UiO-66

An adsorption study of hexane and xylene isomers mixtures was addressed in a rigid zirconium terephthalate UiO-66 (UiO for University of Oslo) with octahedral and tetrahedral cavities of free diameter close to 1.1 nm and 0.8 nm, respectively. Multicomponent equimolar breakthrough experiments show that the adsorption hierarchy of structural isomers in UiO-66 is opposite to the one observed in conventional adsorbents. For hexane isomers, it was found that the amount adsorbed increases with the degree of branching, being 2,2-dimethylbutane (22DMB) and 2,3-dimethylbutane (23DMB) the more retained molecules. Regarding the xylene isomers, the results show that the adsorption of the bulkier ortho-xylene (oX) is favoured compared to its homologues. The structural similarity between MOF UiO-66 and zeolite MCM-22 suggests that the reverse shape selectivity observed in the adsorption of hexane and xylene isomers might be attributed to the rotational freedom of the molecules inside the small cavities.

Electronic states of hydrogen atom in tetrahedral and similar polyhedral cavities

AbstractElectronic states of an atomic particle situated inside an impenetrable cavity of a simple polyhedral form are studied. The numerical method used here for calculations and its theoretical backgrounds are presented. Numerical estimates for the energy levels of a hydrogen atom inside impenetrable cavities of a tetrahedral, cubic, or more complex shape corresponding to truncated polyhedrons are described. The state ordering of the lowest electronic states for confined hydrogen atom, associated with 1s–3d‐states of a free system, is studied with special attention to the role of the vertexes in tetrahedral cavities. Some details of the state ordering for tetrahedral, octahedral, cubic, and some other polyhedral cavities are analyzed. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011

Crystal structure and bond valence of CaH2 from neutron powder diffraction data

Abstract The crystal structure of CaH2 has been studied from neutron powder diffraction (NPD) at 295 K in a non-deuterated sample; a good quality NPD pattern was obtained in spite of the hydrogen incoherent scattering. The structure was refined by the Rietveld method in the Pnma space group (No. 62), Z = 4, with unit-cell parameters a = 5.9600(1), b = 3.6006(7) and c = 6.8167(1) Å. The two kinds of crystallographically independent H atoms, H1 and H2, are located in tetrahedral and square-pyramidal cavities, respectively, while Ca ions are nine-fold coordinated to hydrogen atoms. The average 〈Ca—H1〉 and 〈Ca—H2〉 bond lengths are 2.279 and 2.544 Å, respectively. Bond valence calculations show that Ca—H1 bonds are under compressive stress, whereas Ca—H2 bonds undergo tensile stress in a structure with a relatively high global instability index. It is also remarkable that the displacement factors for H2 are significantly larger than for H1, suggesting an increased lability for the Ca—H2 bonds. We provide with an analysis of the isotope effect, by comparing the present results on CaH2 with literature data on CaD2; we indeed observe a higher distortion of the H1 and H2 coordination polyhedra with respect to the deuteride, as observed in other isostructural dihydrides.

Diffusion within α-CuI studied using ab initio molecular dynamics simulations

The structure and dynamics of superionicα-CuI are studied in detail by means of ab initio Born–Oppenheimer molecular dynamicssimulations. The extreme cation disorder and a soft immobile face centred cubic sublatticeare evident from the highly diffuse atomic density profiles. The Cu–Cu pair distributionfunction and distribution of Cu–I–Cu bond angles possess distinct peaks at 2.6 Å and60° respectively, which are markedly lower than the values expected from theaverage cationic density, pointing to the presence of pronounced short-rangecopper–copper correlations. Comparison with lattice static calculations showsthat these correlations and the marked shift in the cationic density profile in the⟨111⟩ directions are associated with a locally distorted cation sublattice, and that the movementswithin the tetrahedral cavities involve rapid jumps into and out of shallow basins on thesystem potential energy surface. On average, the iodines are surrounded by three copperswithin their first coordination shell, with the fourth copper being located in a transitionzone between two neighbouring iodine cavities. However, time-resolved analysis revealsthat the local structure actually involves a mixture of threefold-, fourfold- andfivefold-coordinated iodines. Examination of the ionic trajectories shows that the copperions jump rapidly to nearest neighbouring tetrahedral cavities (aligned in the⟨100⟩ directions) following a markedly curved trajectory and often involving short-lived (∼1 ps) interstitial positions. The nature of the correlated diffusion underlying theunusually high fraction of coppers with short residence time can be attributedto the presence of a large number of ‘unsuccessful’ jumps and the likelihood ofcooperative motion of pairs of coppers. The calculated diffusion coefficient at 750 K,DCu = 2.8 × 10−5 cm2 s−1, is in excellent agreement with that found experimentally.

Crystal chemistry of trioctahedral micas in the top sequences of the Colli Albani volcano, Roman Region, central Italy

Trioctahedral mica crystals are frequently found in the volcanoclastic products emplaced during the final stages of the activity of the Colli Albani volcano (Roman Region, central Italy). In the youngest phreatomagmatic deposits, mica is found either as a minor mineral phase in holocrystalline ejecta, scoriae, and coherent pyroclastics, or as loose phenocryst in incoherent pyroclastics. Based on optical and electron microscope investigations, as well as crystal chemical and structural data, the micas selected for this study were divided into two groups, the first one encompassing brownish, Fe-rich crystals (type-A phlogopites, hereafter referred as t-A) with 0.68<Mg/(Mg+Fetotal)<0.85 and 0.062<Tiapfu<0.199, and the other one encompassing colorless, Mg-rich crystals (type-B phlogopites, hereafter referred as t-B) with Mg/(Mg+Fetotal) in excess of 0.85 and 0.007<Tiapfu<0.052. t-A phlogopites also show a tetrahedral ring cavity, overlapped tetrahedral hexagon area, and basal tetrahedron area greater than in the t-B phlogopites.From a petrological point of view, the textural and chemical variations of t-A phlogopites are compatible with fractional crystallization processes taking place within the magma chamber. t-B phlogopites show evidence of a Ti-oxy substitution mechanism, thus suggesting high fO2 conditions. Textural and paragenetic features observed in t-B phlogopite-bearing rock samples, indicate a genesis by thermal metamorphism of a siliceous dolomitic limestone with the input of a variable amount of a potassic magma, possibly the same from which the t-A phlogopites formed, with the exception of one sample, for which a different parental magma is suggested. Indeed, there is an almost continuous spectrum of crystal-chemical and structural parameters starting from t-B and evolving towards t-A phlogopites. The t-A phlogopites displays complex, apparently meaningless relationships in their crystal-chemical parameters, thus indicating interplay of several substitution mechanisms. They possibly formed in polybaric conditions, since their cell volumes differ, but the total size of the cations hosted in the octahedral sheet is the same.

A New Mixed-Valence Ferrite with a Cubic Structure, YBaFe4O7: Spin-Glass-Like Behavior

A new mixed-valence ferrite, YBaFe4O7, has been synthesized. Its unique cubic structure, with a = 8.9595(2) A, is closely related to that of the hexagonal “114” oxides YBaCo4O7 and CaBaFe4O7. It consists of corner-sharing FeO4 tetrahedra, forming triangular and kagome layers parallel to (111)C. In fact, the YBaFe4O7 and CaBaFe4O7 structures can be described as two different “ccc” and “chch” close packings of [BaO3]∞ and [O4]∞ layers, respectively, whose tetrahedral cavities are occupied by Fe2+/Fe3+ cations. The local structure of YBaFe4O7 is characterized by a large amount of stacking faults originating from the presence of “hexagonal” layers in the “ccc” cubic close-packed YBaFe4O7 structure. In this way, they belong to the large family of spinels and hexagonal ferrites studied for their magnetic properties. Differently from all the ferrites and especially from CaBaFe4O7, which are ferrimagnetic, YBaFe4O7 is an insulating spin glass with Tg = 50 K.

High-pressure structural behavior of ingersonite, Ca3Mn2+Sb45+O14: An in-situ single-crystal X-ray study

An in-situ, high-pressure, single-crystal X-ray diffraction study has been carried out at room temperature up to 7.42 GPa on a crystal of ingersonite, ideally Ca 3 Mn 2+ Sb 5+ 4 O 14 , from the type material. Ingersonite is isostructural with the synthetic weberite-3T polytype and related to the pyrochlore structure-type. Owing to the P range investigated and the quality of data, a second-order Birch- Murnaghan Equation of State (EoS) is the best approximation to describe the ingersonite volume evolution with P. The refined EoS parameters are V 0 = 810.6(1) Å 3 and K 0 = 154.5(2.4) GPa. The behavior of ingersonite with pressure is almost isotropic and the decrease of the unit-cell volume is mainly due to the kinking of the polyhedra rather than their volume decrease. The overall mean distances are quite constant, indicating virtually no compressibility of both the A and B polyhedra in the P range investigated. However, some geometrical changes in the pyrochlore-like AB 3 layer can be observed and compared with those observed in synthetic pyrochlore compounds. The largest change is observed for the z atomic coordinate of the O 2 atom. Using an anion-centered polyhedral description, O 2 is the only O atom that is asymmetrically located in an octahedral interstice, this feature being the most remarkable difference between the structure of ingersonite (i.e., weberite-3T type, space group P3 1 21) and that of zirconolite-3T (pyrochlore structure type, space group P3 1 21), where all the O atoms occupy the tetrahedral interstices of a cubic A 2 B 2 array. With the increase of pressure, the O 2 atom migrates from the A 4 B 2 octahedral cavity toward the adjacent AB 3 tetrahedral cavity, suggesting that a transition from weberite-3T to zirconolite-3T structure type could occur at pressures higher than 11 GPa.

Deciphering Chemical Bonding in Golden Cages

The recently developed adaptive natural density partitioning (AdNDP) method has been applied to a series of golden clusters. The pattern of chemical bonding in Au(20) revealed by AdNDP shows that 20 electrons form a four-center-two-electron (4c-2e) bond in each of 10 tetrahedral cavities of the Au(20) cluster. This chemical bonding picture can readily explain the tetrahedral structure of the Au(20) cluster. Furthermore, we demonstrate that the recovered 4c-2e bonds corresponding to independent structural fragments of the cluster provide important information about chemically relevant fragmentation of Au(20). In fact, some of these bonds can be removed from the initial tetrahedral structure together with the associated atomic fragments, leading to the family of smaller gold clusters. Chemical bonding in the systems formed in such a manner is yet closely related to the bonding in the parental systems showing persistence of the 4c-2e bonding motif. Thus, the multicenter bonds in golden cages recovered by the AdNDP analysis correspond to the fragments that should be seen as building blocks of these chemical systems.