Fragment Orbitals Extracted from First-Principles Plane-Wave Calculations.

Decomposing extended structures into smaller, molecular, even functional groups or simple fragments has a long tradition in chemistry because it allows for understanding certain electronic peculiarities in truly chemical terms. By doing so, invaluable property information is chemically accessible, for example, needed to rationalize catalytic or magnetic or optical nature. In order to also follow that train of thought for periodic materials, we have developed a tool which in a straightforward manner derives fragment molecular orbitals from plane-wave electronic-structure data of whatever kind of solid-state material. We here report on the mathematical apparatus of the method dubbed linear combination of fragment orbitals (LCFO) used for that purpose, implemented within the LOBSTER code. The method is illustrated from various sorts of molecular entities contained in such crystalline materials, together with an assessment of both accuracy and robustness of the new tool.

Synthesis and Characterization of Iron Bispyridine Bisdicyanamide, Fe[C5H5N]2[N(CN)2]2.

Fe[C5H5N]2[N(CN)2]2 (1) was synthesized from a reaction of stoichiometric amounts of NaN(CN)2 and FeCl2·4H2O in a methanol/pyridine solution. Single-crystal and powder diffraction show that 1 crystallizes in the monoclinic space group I2/m (no. 12), different from Mn[C5H5N]2[N(CN)2]2 (P21/c, no. 14) due to tilted pyridine rings, with a = 7.453(7) Å, b = 13.167(13) Å, c = 8.522(6) Å, ß = 114.98(6)° and Z = 2. ATR-IR, AAS, and CHN measurements confirm the presence of dicyanamide and pyridine. Thermogravimetric analysis shows that π-stacking interactions of the pyridine rings play an important role in structural stabilization. Based on DFT-optimized structures, a chemical bonding analysis was performed using a local-orbital framework by projection from a plane-wave basis. The resulting bond orders and atomic charges are in good agreement with the expectations based on the structure analysis. SQUID magnetic susceptibility measurements show a high-spin state FeII compound with predominantly antiferromagnetic exchange interactions at lower temperatures.

Examination of a Structural Preference in Quaternary Alkali-Metal (A) Rare-Earth (R) Copper Tellurides by Combining Experimental and Quantum-chemical Means.

In the quest for materials addressing the grand challenges of the future, there is a critical need for a broad understanding of their electronic structures because the knowledge of the electronic structure of a given solid allows us to recognize its structural preferences and to rationalize its properties. As previous research on quaternary chalcogenides containing active metals (a group-I- or -II-element), early transition-metals, and late transition-metals indicated that such materials could pose as alluring systems in the developments of thermoelectrics, our impetus was stimulated to probe the suitability of tellurides belonging to the prolific A3R4Cu5Te10-family. In doing so, we first used quantum-chemical techniques to explore the electronic and vibrational properties of representatives crystallizing with different A3R4Cu5Te10 structure types. The outcome of these explorations indicated that the aspects that control the formation of a given type of A3R4Cu5Te10 structure are rather subtle so that transitions between different types of A3R4Cu5Te10 structures could be induced by manipulating the ambient conditions. To probe this prediction, we explored the thermal behavior for the example of one quaternary telluride, that is, Rb3Er4Cu5Te10, and thereby identified a new type of A3R4Cu5Te10 structure. Because understanding the structural features of the A3R4Cu5Te10 family plays an important role in the analyses of the aforementioned explorations, we also present an overview about the structural features and the members of this class of quaternary tellurides. In this connection, we also provide a structural report of four tellurides, that is, K3Tb4Cu5Te10 and Rb3R4Cu5Te10 (R = Tb, Dy, Ho), which have been obtained from high-temperature solid-state reactions for the very first time.

Chemical Reactions and Phase Stabilities in the Si-Te System at High Pressures and High Temperatures.

Chemical reactions and phase stabilities in the Si-Te system at high pressures were explored using in situ angle-dispersive synchrotron powder diffraction in a large-volume multianvil press together with density functional theory-based calculations. Cubic and rhombohedrally distorted clathrates, with the general formula Te8@(Si38Te8) and wide compositional range, preceded by a hexagonal phase with the composition Si0.14Te, are formed for different mixtures of Si and Te as starting materials. Si0.14Te, with the structural formula Te2(Te0.74Si0.26)3(Te0.94Si0.06)3, is the very first chalcogenide with the Mn5Si3-type structure. Silicon sesquitelluride α-Si2Te3 decomposes into a mixture of phases that includes the clathrate and hexagonal phases at high pressures and high temperatures. The higher the pressure, the lower the temperature for the two phases to occur. Regardless of the starting compositions, only the clathrate is quenched to atmospheric conditions, while the hexagonal phase amorphizes on decompression. The rhombohedral clathrates Te8@(Si38Te8) form on quenching of the cubic phases to ambient conditions. There is a high degree of interchangeability of Si and Te not only in the clathrates but also in the Mn5Si3-type structure. The theoretical calculations of enthalpies indicate that the reported decomposition of α-Si2Te3 is energetically favorable over its transformation to another polymorph of the A2X3 type at extreme conditions.

The Mineral Stützite: a Zintl-Phase or Polar Intermetallic? A Case Study Using Experimental and Quantum-Chemical Techniques.

Differing reports regarding the structural features of the mineral stützite, Ag5-xTe3 (-0.25 ≤ x ≤ 1.44), and the quest for tellurides with low-dimensional fragments stimulated our impetus to review this system by employing experimental as well as quantum-chemical methods. Determination of the crystal structures for three samples with compositions Ag4.72(3)Te3 (I), Ag4.66(1)Te3 (II), and Ag4.96(2)Te3 (III) revealed considerable positional disorders for the Ag and Te sites and previously unknown structure models for I and II, which differ from that of III through the stacking sequences of honeycomb-fashioned Te layers. The crystal structures comprise [Te@Ag9]@Te14 units in the forms of bicapped hexagonal Te antiprisms that enclose Te-centered tricapped trigonal Ag prisms, while each Te atom is encapsulated by Ag atoms assembling diverse types of coordination polyhedra. The vibrational and electronic properties were determined for three models approximating the actual crystal structure of stützite by means of techniques based on first principles. From analyses of the electronic structures and projected crystal orbital Hamilton populations (pCOHP), it is clear that the amounts and distributions of the Ag atoms within the Te network should be influenced by the subtle interplay between the attempts to achieve an electronically favorable situation with a gap at EF and minimize the occupations of antibonding states.

Revisiting the Si-Te System: SiTe2 Finally Found by Means of Experimental and Quantum-Chemical Techniques.

Through explorations of the silicon-tellurium system we identified the extremely air-sensitive, red Si1.67(4)Te3≡Si1.11(3)Te2 that is a silicon-deficient relative of the previously reported Si2Te3. The crystal structure features hexagonal closest packed layers of tellurium atoms with disordered [Si2] dumbbells residing in about 50% of the octahedra of every second layer enclosed by the tellurium atoms. In addition to the determination of the crystal structure for this silicon telluride, we probed the opportunity of the existence of a SiTe2 adopting the Si2Te3-structure by means of quantum chemical techniques. The investigations of the electronic structures and a subsequent chemical bonding analysis based on the projected Crystal Orbital Hamilton Population (pCOHP) technique for two "SiTe2" models revealed a tendency to align the [Si2] dumbbells parallel to the c axis to maximize Si-Te bonding. However, the disorder of the [Si2] dumbbells appears to be a consequence of non-equilibrium condensation into the solid state.

High-Pressure NiAs-Type Modification of FeN.

The combination of laser-heated diamond anvil cells and synchrotron Mössbauer source spectroscopy were used to investigate high-temperature high-pressure chemical reactions of iron and iron nitride Fe2 N with nitrogen. At pressures between 10 and 45 GPa, significant magnetic hyperfine splitting indicated compound formation after annealing at 1300 K. Subsequent in situ X-ray diffraction reveals a new modification of FeN with NiAs-type crystal structure, as also rationalized by first-principles total-energy and chemical-bonding studies.

Unexpected Ge-Ge Contacts in the Two-Dimensional Ge4 Se3 Te Phase and Analysis of Their Chemical Cause with the Density of Energy (DOE) Function.

A hexagonal phase in the ternary Ge-Se-Te system with an approximate composition of GeSe0.75 Te0.25 has been known since the 1960s but its structure has remained unknown. We have succeeded in growing single crystals by chemical transport as a prerequisite to solve and refine the Ge4 Se3 Te structure. It consists of layers that are held together by van der Waals type weak chalcogenide-chalcogenide interactions but also display unexpected Ge-Ge contacts, as confirmed by electron microscopy analysis. The nature of the electronic structure of Ge4 Se3 Te was characterized by chemical bonding analysis, in particular by the newly introduced density of energy (DOE) function. The Ge-Ge bonding interactions serve to hold electrons that would otherwise go into antibonding Ge-Te contacts.

Electron counting rules and electronic structure in tetrameric transition-metal (T)-centered rare-Earth (R) cluster complex halides (X).

Electron partition schemes are a beneficial means to systematize bonding networks and to identify structure-bonding relationships in polar intermetallics. One prolific class of polymetal networks with simple counterions is the broad family of transition-metal (T)-centered rare-earth metal (R) cluster halides (X), which can be isolated or condensed to oligomers and chains. While the electronic structures of R cluster monomers and chains encapsulating T atoms have been studied systematically, the band structures of oligomers, in particular, the most frequent Friauf-type {T(4)R(16)} tetramers, have been investigated to a lesser extent. Therefore, the band structures of prototypical compounds with {T(4)R(16)}-type tetramers, while maintaining different compositions, were analyzed employing density functional theory based methods. Furthermore, these theoretical examinations provide insight into the origin of the 15 electron rule, which is significant for this class of compounds and correlates with the closed-shell configurations for these structures. Additional research focused on the band structure of monoclinic {Ru(4)Gd(16)}Br(23), which is composed of rhomboid-shaped {Ru(4)Gd(16)} tetramers.

From the Ternary Eu(Au/In)2 and EuAu4(Au/In)2 with Remarkable Au/In Distributions to a New Structure Type: The Gold-Rich Eu5Au16(Au/In)6 Structure.

The ternary Eu(Au/In)2 (EuAu(0.46)In(1.54(2))) (I), EuAu4(Au/In)2 (EuAu(4+x)In(2-x) with x = 0.75(2) (II), 0.93(2), and 1.03(2)), and Eu5Au16(Au/In)6 (Eu5Au(17.29)In(4.71(3))) (III) have been synthesized, and their structures were characterized by single-crystal X-ray diffraction. I and II crystallize with the CeCu2-type (Pearson Symbol oI12; Imma; Z = 4; a = 4.9018(4) Å; b = 7.8237(5) Å; c = 8.4457(5) Å) and the YbAl4Mo2-type (tI14; I4/mmm; Z = 2; a = 7.1612(7) Å; c = 5.5268(7) Å) and exhibit significant Au/In disorder. I is composed of an Au/In-mixed diamond-related host lattice encapsulating Eu atoms, while the structure of II features ribbons of distorted, squared Au8 prisms enclosing Eu, Au, and In atoms. Combination of these structural motifs leads to a new structure type as observed for Eu5Au16(Au/In)6 (Eu5Au(17.29)In(4.71(3))) (oS108; Cmcm; Z = 4; a = 7.2283(4) Å; b = 9.0499(6) Å; c = 34.619(2) Å), which formally represents a one-dimensional intergrowth of the series EuAu2-"EuAu4In2". The site preferences of the disordered Au/In positions in II were investigated for different hypothetical "EuAu4(Au/In)2" models using the projector-augmented wave method and indicate that these structures attempt to optimize the frequencies of the heteroatomic Au-In contacts. A chemical bonding analysis on two "EuAu5In" and "EuAu4In2" models employed the TB-LMTO-ASA method and reveals that the subtle interplay between the local atomic environments and the bond energies determines the structural and site preferences for these systems.

Crystal structure and bonding in BaAu5Ga2 and AeAu4+xGa3-x (Ae = Ba and Eu): hexagonal diamond-type Au frameworks and remarkable cation/anion partitioning in the Ae-Au-Ga systems.

Five new polar intermetallic compounds in the Ae-Ga-Au system (Ae = Ba, Eu), BaAu(5)Ga(2) (I), BaAu(4.3)Ga(2.7) (II), Ba(1.0)Au(4.5)Ga(2.4 )(III), EuAu(4.8)Ga(2.2) (IV), and Eu(1.1)Au(4.4)Ga(2.2) (V), have been synthesized and their crystal structures determined by single-crystal X-ray diffraction. I crystallizes in the orthorhombic crystal system with a large unit cell [Pearson symbol oP64; Pnma, Z = 8, a = 8.8350(5) Å, b = 7.1888(3)Å, c = 20.3880(7) Å], whereas all other compounds are hexagonal [hP24; P6̅2m, Z = 3, a = 8.54-8.77(1) Å, c = 7.19-7.24(1) Å]. Both structures contain mutually orthogonal layers of Au(6) hexagons in chair and boat conformations, resulting in a hexagonal diamond-like network. Ae atoms and additional (Au/Ga)(3) groups are formally encapsulated by (Au(6))(2) distorted hexagonal prisms formed of three edge-sharing hexagons in the boat conformation or, alternatively, lie between two Au(6) hexagons in the chair conformation. The (Au/Ga)(3) groups can be substituted by Ae atoms in some of the hexagonal structures with no change to the structural symmetry. Tight-binding electronic structure calculations using linear-muffin-tin-orbital methods on idealized models "BaAu(5)Ga(2)" and "BaAu(4)Ga(3)" show both compounds to be metallic with evident pseudogaps near the corresponding Fermi levels. The integrated crystal orbital Hamilton populations are dominated by Au-Au and Au-Ga orbital interactions, although Ba-Au and Ba-Ga contributions are significant. Furthermore, Au-Au interactions vary considerably along different directions in the unit cells, with the largest values for the hexagons in the boat conformation and the lowest values for those in the chair conformation. II revealed that partial substitution of Au atoms in the hexagonal diamond net by a post-transition element (Ga) may occur in this family, whereas the sizes of the (Au/Ga)(3) groups and strong Ba-Au covalent interactions allow for their mutual replacement in the voids.

Cation-Poor Complex Metallic Alloys in Ba(Eu)-Au-Al(Ga) Systems: Identifying the Keys that Control Structural Arrangements and Atom Distributions at the Atomic Level.

Four complex intermetallic compounds BaAu(6±x)Ga(6±y) (x = 1, y = 0.9) (I), BaAu(6±x)Al(6±y) (x = 0.9, y = 0.6) (II), EuAu6.2Ga5.8 (III), and EuAu6.1Al5.9 (IV) have been synthesized, and their structures and homogeneity ranges have been determined by single crystal and powder X-ray diffraction. Whereas I and II originate from the NaZn13-type structure (cF104-112, Fm3̅c), III (tP52, P4/nbm) is derived from the tetragonal Ce2Ni17Si9-type, and IV (oP104, Pbcm) crystallizes in a new orthorhombic structure type. Both I and II feature formally anionic networks with completely mixed site occupation by Au and triel (Tr = Al, Ga) atoms, while a successive decrease of local symmetry from the parental structures of I and II to III and, ultimately, to IV correlates with increasing separation of Au and Tr on individual crystallographic sites. Density functional theory-based calculations were employed to determine the crystallographic site preferences of Au and the respective triel element to elucidate reasons for the atom distribution ("coloring scheme"). Chemical bonding analyses for two different "EuAu6Tr6" models reveal maximization of the number of heteroatomic Au-Tr bonds as the driving force for atom organization. The Fermi levels fall in broad pseudogaps for both models allowing some electronic flexibility. Spin-polarized band structure calculations on the "EuAu6Tr6" models hint to singlet ground states for europium and long-range magnetic coupling for both EuAu6.2Ga5.8 (III) and EuAu6.1Al5.9 (IV). This is substantiated by experimental evidence because both compounds show nearly identical magnetic behavior with ferromagnetic transitions at TC = 6 K and net magnetic moments of 7.35 µB/f.u. at 2 K. The effective moments of 8.3 µB/f.u., determined from Curie-Weiss fits, point to divalent oxidation states for europium in both III and IV.

Nickel hexa-yttrium deca-iodide, [NiY6]I10.

Comproportionation reactions of yttrium triiodide, yttrium and nickel led to the formation of the compound [NiY6]I10, which is isostructural with the prototypical [RuY6]I10. In particular, [NiY6]I10 is composed of isolated nickel centered yttrium octa-hedra (site symmetry -1) that are further surrounded by iodide ligands to construct a three-dimensional cluster complex framework. Although this compound has been previously detected by powder X-ray diffraction techniques [Payne & Corbett (1990 ▶). Inorg. Chem. 29, 2246-2251], details of the crystal structure for triclinic [NiY6]I10 were not provided.

Identifying a structural preference in reduced rare-earth metal halides by combining experimental and computational techniques.

The structures of two new cubic {TnLa(3)}Br(3) (Tn = Ru, Ir; I4(1)32, Z = 8; Tn = Ru: a = 12.1247(16) Å, V = 1782.4(4) Å(3); Tn = Ir: a = 12.1738(19) Å, V = 1804.2(5) Å(3)) compounds belonging to a family of reduced rare-earth metal halides were determined by single-crystal X-ray diffraction. Interestingly, the isoelectronic compound {RuLa(3)}I(3) crystallizes in the monoclinic modification of the {TnR(3)}X(3) family, while {IrLa(3)}I(3) was found to be isomorphous with cubic {PtPr(3)}I(3). Using electronic structure calculations, a pseudogap was identified at the Fermi level of {IrLa(3)}Br(3) in the new cubic structure. Additionally, the structure attempts to optimize (chemical) bonding as determined through the crystal orbital Hamilton populations (COHP) curves. The Fermi level of the isostructural {RuLa(3)}Br(3) falls below the pseudogap, yet the cubic structure is still formed. In this context, a close inspection of the distinct bond frequencies reveals the subtleness of the structure determining factors.

Exploring the subtle factors that control the structural preferences in Cu7Te4.

In the quest for materials suited as components in future technologies, the copper-rich regions of the binary Cu-Te system have been of great interest. In this context, several explorative efforts were also focused on Cu7Te4which was reported to crystallize with different types of structure. To explore the structural preferences for two Cu7Te4structure models, both experimental as well as quantum-chemical means were employed. The crystal structures of both Cu7Te4types are composed of hexagonal closest packed layers of tellurium atoms, and differ in the respective distributions of the copper atoms between these layers. The analysis of the electronic structures was accomplished based on the densities-of-states, Mulliken charges, projected crystal orbital Hamilton populations, and electron localization functions of both structure models, and its outcome indicates that the factors that control the formation of a respective type of structure are rather subtle.

Bonding diversity in rock salt-type tellurides: examining the interdependence between chemical bonding and materials properties.

Future technologies are in need of solid-state materials showing the desired chemical and physical properties, and designing such materials requires a proper understanding of their electronic structures. In this context, recent research on chalcogenides, which were classified as 'incipient metals' and included phase-change data storage materials as well as thermoelectrics, revealed a remarkable electronic behavior and possible state (dubbed 'metavalency') proposed for the frontier between entire electron localization and delocalization. Because the members of the family of the polar intermetallics vary widely in their properties as well as electronic structures, one may wonder if the aforementioned electronic characteristics are also achieved for certain polar intermetallics. To answer this question, we have employed quantum-chemical tools to examine the electronic structures of the rock salt-type YTe and SnTe belonging to the families of the polar intermetallics and incipient metals, respectively. To justify these classifications and argue as to why an application of the Zintl-Klemm concept (frequently employed to relate the structural features of tellurides to their electronic structures) could be misleading for YTe and SnTe, the electronic structures of YTe and SnTe were first compared to that of the rock salt-type SrTe. In addition, we carried out a Gedankenexperiment by subsequently modifying the chemical composition from YTe to SnTe, and, by doing so, we shed new light on the interdependence between chemical bonding and materials properties. Gradual changes in the former do not necessarily translate into the latter which may undergo discontinuous modifications.

Long-Range Forces in Rock-Salt-Type Tellurides and How they Mirror the Underlying Chemical Bonding.

Chemical bonding in main-group IV chalcogenides is an intensely discussed topic, easily understandable because of their remarkable physical properties that predestine these solid-state materials for their widespread use in, for instance, thermoelectrics and phase-change memory applications. The atomistic origin of their unusual property portfolio remains somewhat unclear, however, even though different and sometimes conflicting chemical-bonding concepts have been introduced in the recent years. Here, it is proposed that projecting phononic force-constant tensors for pairs of atoms along differing directions and ranges provide a suitable and quantitative descriptor of the bonding nature for these materials. In combination with orbital-based quantitative measures of covalency such as crystal orbital Hamilton populations (COHP), it is concluded that the well-established many-center and even n-center bonding is an appropriate picture of the underlying quantum-chemical bonding mechanism, supporting the recent proposal of hyperbonded phase-change materials.

Probing the Validity of the Zintl-Klemm Concept for Alkaline-Metal Copper Tellurides by Means of Quantum-Chemical Techniques.

Understanding the nature of bonding in solid-state materials is of great interest for their designs, because the bonding nature influences the structural preferences and chemical as well as physical properties of solids. In the cases of tellurides, the distributions of valence-electrons are typically described by applying the Zintl-Klemm concept. Yet, do these Zintl-Klemm treatments provide adequate pictures that help us understanding the bonding nature in tellurides? To answer this question, we followed up with quantum-chemical examinations on the electronic structures and the bonding nature of three alkaline-metal copper tellurides, i.e., NaCu3Te2, K2Cu2Te5, and K2Cu5Te5. In doing so, we accordingly probed the validity of the Zintl-Klemm concept for these ternary tellurides, based on analyses of the respective projected crystal orbital Hamilton populations (-pCOHP) and Mulliken as well as Löwdin charges. Since all of the inspected tellurides are expected to comprise Cu-Cu interactions, we also paid particular attention to the possible presence of closed-shell interactions.

Discovering Electron-Transfer-Driven Changes in Chemical Bonding in Lead Chalcogenides (PbX, where X = Te, Se, S, O).

Understanding the nature of chemical bonding in solids is crucial to comprehend the physical and chemical properties of a given compound. To explore changes in chemical bonding in lead chalcogenides (PbX, where X = Te, Se, S, O), a combination of property-, bond-breaking-, and quantum-mechanical bonding descriptors are applied. The outcome of the explorations reveals an electron-transfer-driven transition from metavalent bonding in PbX (X = Te, Se, S) to iono-covalent bonding in ß-PbO. Metavalent bonding is characterized by adjacent atoms being held together by sharing about a single electron (ES ≈ 1) and small electron transfer (ET). The transition from metavalent to iono-covalent bonding manifests itself in clear changes in these quantum-mechanical descriptors (ES and ET), as well as in property-based descriptors (i.e., Born effective charge (Z*), dielectric function ε(ω), effective coordination number (ECoN), and mode-specific Grüneisen parameter (γTO )), and in bond-breaking descriptors. Metavalent bonding collapses if significant charge localization occurs at the ion cores (ET) and/or in the interatomic region (ES). Predominantly changing the degree of electron transfer opens possibilities to tailor material properties such as the chemical bond (Z*) and electronic (ε∞ ) polarizability, optical bandgap, and optical interband transitions characterized by ε2 (ω). Hence, the insights gained from this study highlight the technological relevance of the concept of metavalent bonding and its potential for materials design.

Identifying the Origins of Vacancies in the Crystal Structures of Rock Salt-type Chalcogenide Superconductors.

The tailored (computational) design of materials addressing future challenges requires a thorough understanding of their electronic structures. This becomes very apparent for a given material existing in a certain homogeneity range, as its particular composition influences its electronic structure and, eventually, its physical properties. This led us to explore the influence and, furthermore, the origin of vacancies in the crystal structures of rock salt-type superconductors by means of quantum-chemical techniques. In doing so, we examined the vibrational properties, electronic band structures, and nature of bonding for a series of superconducting transition-metal sulfides, i.e., MS (M = Sc, Y, Zr, Lu), which were identified to exist over certain homogeneity ranges. The outcome of our research indicates that the subtle competing interplay between two electronically unfavorable situations at the Fermi levels, i.e., the occupations of flat bands and the populations of antibonding states, appears to control the presence of vacancies in the crystal structures of the sulfides.