Exploratory Synthesis: The Fascinating and Diverse Chemistry of Polar Intermetallic Phases†This article is based on J. D. Corbett’s address upon receipt of the 2008 American Chemical Society’s F. Albert Cotton Award in Synthetic Inorganic Chemistry sponsored by the F. Albert Cotton Endowment Fund

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.

Yet Another Case of Lithium Metal Atoms and Germanium Atoms Sharing Chemistry in the Solid State: Synthesis and Structural Characterization of Ba2 LiGe3

Several Ba-Li-Ge ternary phases are known and structurally characterized, including the title compound Ba2 LiGe3 . Its structure is reported to contain [Ge6 ]10- anions that exhibit delocalized bonding with a Hückel-like aromatic character. The Ge atoms are in the same plane with the Li atoms, and if both types of atoms are considered as covalently bonded, [LiGe3 ]4- honeycomb-like layers will result. The latter are separated by slabs of Ba2+ cations. However, based on the systematic work detailed herein, it is necessary to re-evaluate the phase as Ba2 Li1-x Ge3+x (x<0.05). Although small, the homogeneity range is clearly demonstrated in the gradual change of the unit cell for four independent samples. Subsequent characterization by single-crystal X-ray diffraction methods shows that the Ba2 Li1-x Ge3+x structure, responds to the varied number of valence electrons and the changes are most pronounced for the refined lengths of the Li-Ge and Ge-Ge bonds. Indirectly, the changes in the Ge-Li/Ge distances within layers affect the stacking too, and these changes can be correlated to the variation of the c-cell parameter. Chemical bonding analysis based on TB-LMTO-ASA level calculations affirms the notion for covalent character of the Ge-Ge bonds; the Ba-Ge and Li-Ge interactions also show some degree of covalency.

From Laves Phases to Quasicrystal Approximants in the Na-Au-Cd System

The exploratory synthesis of gold-based polar intermetallic phases has revealed many new compounds with unprecedented crystal structures, unique bonding arrangements, and interesting electronic features. Here, we further understand the complexity of gold's crystal chemistry by studying the Na-Au-Cd ternary composition space. A nearly continuous structure transformation is observed between the seemingly simple binary NaAu₂-NaCd₂ phases, yielding three new intermetallic compounds with the compositions Na(Au_0.89(5)Cd_0.11(5))₂, Na(Au_0.51(4)Cd_0.49(4))₂, and Na₈Au_3.53(1)Cd_13.47(1). Two compounds adopt different Laves phases, while the third crystallizes in a complex decagonal quasicrystal approximant. All three compounds are related through Friauf-Laves polyhedral building units with the gold/cadmium ratio found to control the transition among the unique crystal structures. Electronic structure calculations subsequently revealed the metallic nature of all three compounds with a combination of polar covalent Na-(Au/Cd) interactions and covalent (Au/Cd)-(Au/Cd) bonding interactions stabilizing each structure. These results highlight the crystal and electronic structure relationship among Laves phases and quasicrystal approximants enabled by the unique chemistry of gold.

Influence of Disorder on the Bad Metal Behavior in Polar Amalgams

The two new ternary amalgams K_1-xRb_xHg₁₁ [x = 0.472(7)] and Cs_3-xCa_xHg₂₀ [x = 0.20(3)] represent two different examples of how to create ternary compounds from binaries by statistical atom substitution. K_1-xRb_xHg₁₁ is a Vegard-type mixed crystal of the isostructural binaries KHg₁₁ and RbHg₁₁ [cubic, BaHg₁₁ structure type, space group Pm3̅m, a = 9.69143(3) Å, Rietveld refinement], whereas Cs_3-xCa_xHg₂₀ is a substitution variant of the Rb₃Hg₂₀ structure type [cubic, space group Pm3̅n, a = 10.89553(14) Å, Rietveld refinement] for which a fully substituted isostructural binary Ca phase is unknown. In K_1-xRb_xHg₁₁, the valence electron concentration (VEC) is not changed by the substitution, whereas in Cs_3-xCa_xHg₂₀, the VEC increases with the Ca content. Amalgams of electropositive metals form polar metal bonds and show "bad metal" properties. By thermal analysis, magnetic susceptibility and resistivity measurements, and density functional theory calculations of the electronic structures, we investigate the effect of the structural disorder introduced by creating mixed-atom occupation on the physical properties of the two new polar amalgam systems.

La26Ge19M5O5 (M = Ag, Cu): Rare-Earth Metal Suboxide Superconductors with [La18O5] Cluster Units

Herein we report two reduced rare-earth metal-based superconductors, La₂₆Ge₁₉M₅O₅ (M = Ag, Cu), that feature an unprecedented [La₁₈O₅] cluster composed of five oxygen-centered [La₆O] octahedra condensed through shared faces and capped with [Ge₄] butterfly rings. The structure, determined by single-crystal X-ray diffraction, crystallizes in a tetragonal space group (P4/nmm), with a = 15.508(2) Å and c = 11.238(2) Å. Resistivity and magnetic susceptibility measurements show onsets of superconductivity at T_c = 5.4 and 6.4 K for the Ag and Cu compounds, respectively. Applying high pressures, up to 1.3 GPa, results in increased superconducting transition temperatures (T_c = 6.8 K for Ag and 7.2 K for Cu compounds), with no sign of saturation.

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.

Al4Ir: An Al-Ir Binary-Phase Superstructure of the Ni2Al3 Type

A binary phase with Al₄Ir composition has been discovered in the Al-Ir binary system. Single-crystal X-ray diffraction analysis reveals that it crystallizes in the trigonal space group P3c1 with the unit cell parameters a = 12.8802(2) Å and c = 9.8130(2) Å. This structure is derived from the Ni₂Al₃ structure type. The supercell is due to the ordering of the aluminum atoms, which replace the nickel atoms in the prototype structure. The crystal structure was directly imaged by atomic-scale scanning transmission electron microscopy, and the misalignment of the Al site responsible for the supercell has been clearly evidenced. Its metastable nature has been confirmed by differential thermal analysis measurements. The atomic and electronic structures of Al₄Ir have also been investigated by density functional theory. The structural optimization leads to lattice parameters and atomic positions in good agreement with the experimental ones. The compound is metallic, with a minimum in the density of states located more than 1 eV above the Fermi energy. This suggests a metastable system, in agreement with the electron count found much above 18 electrons per Ir atom, deviating from the Hume-Rothery rule and with the presence of occupied antibonding states revealed by the crystal orbital Hamiltonian population analysis. The relative stability of the compound is ensured by the hybridization between sp-Al and d-Ir states within Ir-centered clusters, while covalent-like interactions in-between the clusters are indicated by the analysis of the electron localizability function.

Recent developments in germanium containing clusters in intermetallics and nanocrystals

Multimetallic clusters can be described as building blocks in intermetallics, compounds prepared from all metals and/or semi-metals, and in Zintl phases, a subset of intermetallics containing metals with large differences in electronegativity. In many cases, these intermetallic and Zintl phases provide the first clue for the possibilities of bond formation between metals and semi-metals. Recent advances in multimetallic clusters found in Zintl phases and nanoparticles focusing on Ge with transition metals and semi-metals is presented. Colloidal routes to Ge nanocrystals provide an opportunity for kinetically stabilized Ge-metal and Ge-semi-metal bonding. These routes provide crystalline nanoclusters of Ge, hereafter referred to as nanocrystals, that can be structurally characterized. Compositions of Ge nanocrystals containing transition metals, and the semi-metals, Sb, Bi, and Sn, whose structures have recently been elucidated through EXAFS, will be presented along with potential applications.

A novel ternary bismuthide, NaMgBi: crystal and electronic structure and electrical properties

A new ternary sodium magnesium bismuthide, NaMgBi, has been synthesized from the constituent metals, and its crystal structure was determined by single-crystal X-ray diffraction. NaMgBi crystallizes in a tetragonal PbFCl-type structure corresponding to the space group P4/nmm, where Z = 2, a = 4.7123(4) and c = 7.8158(7) Å. The structure is composed of layers formed by edge-sharing Bi tetrahedra centered with Mg stacked in the c-axis direction, and these layers sandwich the Na atoms. First-principles computations based on density functional theory calculations have verified that the most stable atomic configuration is the one in which the Na and Mg atoms occupy the 2a and 2c sites, respectively. The electrical resistivity measured for a sintered polycrystalline sample of NaMgBi with a relative density of 70% was found to gradually decrease from 868 to 26.4 mΩ cm upon increasing the temperature from 297 to 506 K, and the Seebeck coefficient decreased from 273 to 180 μV K−1 upon increasing the temperature from 298 to 496 K. Electronic structure calculations have revealed that NaMgBi must be a semiconductor with a small band gap of ∼0.1 eV.

Exploring the frontier between polar intermetallics and Zintl phases for the examples of the prolific ALnTnTe3-type alkali metal (A) lanthanide (Ln) late transition metal (Tn) tellurides

Understanding electronic structures is important in order to interpret and to design the chemical and physical properties of solid-state materials. Among those materials, tellurides have attracted an enormous interest, because several representatives of this family are at the cutting edge of basic research and technologies. Despite this relevance of tellurides with regard to the design of materials, the interpretations of their electronic structures have remained challenging to date. For instance, most recent research on tellurides, which primarily comprise post-transition elements, revealed a remarkable electronic state, while the distribution of the valence electrons in tellurides comprising group-I/II elements could be related to the structural features by applying the Zintl-Klemm-Busmann concept. In the cases of tellurides containing transition metals the applications of the aforementioned idea should be handled with care, as such tellurides typically show characteristics of polar intermetallics rather than Zintl phases. And yet, how may the electronic structure look like for a telluride that consists of a transition metal behaving like a p metal? To answer this question, we examined the electronic structure for the quaternary RbTbCdTe3 and provide a brief report on the crystal structures of the isostructural compounds RbErZnTe3 and RbTbCdTe3, whose crystal structures have been determined by means of X-ray diffraction experiments for the very first time.

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.

Synthesis and Characterization of NaCd0.92Sn1.08, Na(Cd0.28Sn0.72)2 and Na2CdSn5 with Three-Dimensional Cd-Sn Frameworks

The crystal structures of three new ternary compounds, NaCd0.92Sn1.08 (I), Na(Cd0.28Sn0.72)2 (II), and Na2CdSn5 (III) synthesized in a sodium-cadmium-tin system were determined by single-crystal X-ray analysis to be the following: (I) LiGeZn-type structure (hexagonal, a = 4.9326(1) Å, c = 10.8508(3) Å, space group P-6m2); (II) CaIn2-type structure (hexagonal, a = 4.8458(2) Å, c = 7.7569(3) Å, P63/mmc); and (III) isotype with tI-Na2ZnSn5 (tetragonal, a = 6.4248(1) Å, c = 22.7993(5) Å, I-42d). Each compound has a three-dimensional framework structure mainly composed of four-fold coordinated Cd and Sn atoms with Na atoms located in the framework space. Elucidation of the electrical properties of the polycrystalline samples indicated that compounds (I) and (II) are polar intermetallics with metallic conductivity, and compound (III) is a semiconducting Zintl compound. These properties were consistent with the electronic structures calculated using the ordered structure models of the compounds.

Revealing the Bonding Nature in an ALnZnTe3-Type Alkaline-Metal (A) Lanthanide (Ln) Zinc Telluride by Means of Experimental and Quantum-Chemical Techniques

Tellurides have attracted an enormous interest in the quest for materials addressing future challenges, because many of them are at the cutting edge of basic research and technologies due to their remarkable chemical and physical properties. The key to the tailored design of tellurides and their properties is a thorough understanding of their electronic structures including the bonding nature. While a unique type of bonding has been recently identified for post-transition-metal tellurides, the electronic structures of tellurides containing early and late-transition-metals have been typically understood by applying the Zintl−Klemm concept; yet, does the aforementioned formalism actually help us in understanding the electronic structures and bonding nature in such tellurides? To answer this question, we prototypically examined the electronic structure for an alkaline metal lanthanide zinc telluride, i.e., RbDyZnTe3, by means of first-principles-based techniques. In this context, the crystal structures of RbLnZnTe3 (Ln = Gd, Tb, Dy), which were obtained from high-temperature solid-state syntheses, were also determined for the first time by employing X-ray diffraction techniques.

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.

Revisiting the Zintl‒Klemm Concept for ALn2Ag3Te5-Type Alkaline-Metal (A) Lanthanide (Ln) Silver Tellurides

Understanding the bonding nature of solids is decisive, as knowledge of the bonding situation for any given material provides valuable information about its structural preferences and physical properties. Although solid-state tellurides are at the forefront of several fields of research, the electronic structures, particularly their nature of bonding, are typically understood by applying the Zintl‒Klemm concept. However, certain tellurides comprise ionic as well as strong (polar) mixed-metal bonds, in obvious contrast to the full valence-electron transfers expected by Zintl‒Klemm’s reasoning. How are the valence-electrons really distributed in tellurides containing ionic as well as mixed-metal bonds? To answer this question, we carried out bonding and Mulliken as well as Löwdin population analyses for the series of ALn2Ag3Te5-type tellurides (A = alkaline-metal; Ln = lanthanide). In addition to the bonding analyses, we provide a brief description of the crystal structure of this particular type of telluride, using the examples of RbLn2Ag3Te5 (Ln = Ho, Er) and CsLn2Ag3Te5 (Ln = La, Ce), which have been determined for the first time.

Ir6In32S21, a polar, metal-rich semiconducting subchalcogenide

Subchalcogenides are uncommon, and their chemical bonding results from an interplay between metal-metal and metal-chalcogenide interactions. Herein, we present Ir₆In₃₂S₂₁, a novel semiconducting subchalcogenide compound that crystallizes in a new structure type in the polar P31m space group, with unit cell parameters a = 13.9378(12) Å, c = 8.2316(8) Å, α = β = 90°, γ = 120°. The compound has a large band gap of 1.48(2) eV, and photoemission and Kelvin probe measurements corroborate this semiconducting behavior with a valence band maximum (VBM) of -4.95(5) eV, conduction band minimum of -3.47(5) eV, and a photoresponse shift of the Fermi level by ∼0.2 eV in the presence of white light. X-ray absorption spectroscopy shows absorption edges for In and Ir do not indicate clear oxidation states, suggesting that the numerous coordination environments of Ir₆In₃₂S₂₁ make such assignments ambiguous. Electronic structure calculations confirm the semiconducting character with a nearly direct band gap, and electron localization function (ELF) analysis suggests that the origin of the gap is the result of electron transfer from the In atoms to the S 3p and Ir 5d orbitals. DFT calculations indicate that the average hole effective masses near the VBM (1.19m _e) are substantially smaller than the average electron masses near the CBM (2.51m _e), an unusual feature for most semiconductors. The crystal and electronic structure of Ir₆In₃₂S₂₁, along with spectroscopic data, suggest that it is neither a true intermetallic nor a classical semiconductor, but somewhere in between those two extremes.

Na3Pt10Si5: A Non-Centrosymmetric Superconductor Having Rattling Na Atoms in the Tunnel Framework Structure

Single crystals of a novel Na-Pt-Si ternary compound, Na₃Pt₁₀Si₅, were synthesized by heating the constituent elements at 1423 K. It crystallizes in a non-centrosymmetric trigonal structure of space group R32 (Z = 3) with lattice constants of a = 10.1536(3) Å and c = 10.1539(3) Å at 300 K. The structure consists of a three-dimensional framework made of Pt and Si atoms, and the Na atoms are contained in the tunnels of the framework. The large magnitude and the temperature dependence of the atomic displacement parameter of the Na site reveal a large thermal vibration indicative of a "rattling" motion of Na atoms in the oversized tunnel. The electronic structure calculations explain the observed metallic properties on the basis of the covalent bonds between the Pt and Si atoms in the framework and the ionic bonding of the Na atoms to the framework. A type II superconductivity with a transition temperature of 2.9 K and an upper critical field of 2.5 kOe are observed for a polycrystalline sintered bulk sample of Na₃Pt₁₀Si₅ prepared by heating at 1353 K in Na vapor. Heat capacity measurements reveal a strong coupling superconductivity that is probably caused by an electron-phonon interaction enhanced by the rattling motion of the Na atoms.

Crystallographic and Theoretical Investigations of Er2 @C2 n (2 n=82, 84, 86): Indication of Distance-Dependent Metal-Metal Bonding Nature

Successful isolation and characterization of a series of Er-based dimetallofullerenes present valuable insights into the realm of metal-metal bonding. These species are crystallographically identified as Er₂ @C_s (6)-C₈₂ , Er₂ @C_3v (8)-C₈₂ , Er₂ @C₁ (12)-C₈₄ , and Er₂ @C_2v (9)-C₈₆ , in which the structure of the C₁ (12)-C₈₄ cage is unambiguously characterized for the first time by single-crystal X-ray diffraction. Interestingly, natural bond orbital analysis demonstrates that the two Er atoms in Er₂ @C_s (6)-C₈₂ , Er₂ @C_3v (8)-C₈₂ , and Er₂ @C_2v (9)-C₈₆ form a two-electron-two-center Er-Er bond. However, for Er₂ @C₁ (12)-C₈₄ , with the longest Er⋅⋅⋅Er distance, a one-electron-two-center Er-Er bond may exist. Thus, the difference in the Er⋅⋅⋅Er separation indicates distinct metal bonding natures, suggesting a distance-dependent bonding behavior for the internal dimetallic cluster. Additionally, electrochemical studies suggest that Er₂ @C_82-86 are good electron donors instead of electron acceptors. Hence, this finding initiates a connection between metal-metal bonding chemistry and fullerene chemistry.

Stacking polytypes of mixed alkali gallides/indides A 1–2(Ga/In)3 (A=K, Rb, Cs): synthesis, crystal chemistry and chemical bonding

The Ga/In phase width (y) and the distribution of the two triels within the polyanions of known binary (x = 1, 2) and new ternary ‘intermediate’ (x = 1–2) alkali trielides Ax (Ga1− y In y )3 (A = K, Rb, Cs) was investigated in a synthetic (slow cooling of the melts of the three elements), crystallographic (X-ray single crystal) and bond theoretical (FP-LAPW DFT bandstructure calculation) study. The Cs2In3-type structure (x = 2, series A, tetragonal, I 4/mmm) exhibits layers of four-connected closo octahedra [M 6]4−. Ternary K compounds of this type were yielded within a large range (y = 0–0.87), whereas isotypic Rb/Cs trielides exist only at higher In contents (>52/69%). Geometric criteria determine not only the Ga/In stability ranges but also the occurrence of a commensurate superstructure at approx. 33% In (K2Ga2.17In0.83: P 42/ncm, a = 879.83(4), c = 1557.66(10) pm, R 1 = 0.0887), in which the octahedra are slightly tilted against the layers. Cesium compounds of the RbGa3-type structure (x = 1, C, tetragonal, I 4̅m2), which exhibits a 3D network of all-exo bonded closo dodecahedra [M 8]2− and four-bonded M − anions, are stable throughout the whole substitutional range CsGa3–CsIn3. The maximum possible In content increases with increasing size of A + (Cs: 100%, Rb: 30%, K: 8% In). The similarities between these two tetragonal structures are consistent with the occurrence of two new structure types of ‘intermediate’ compounds A 7 M 15 (x = 1.4, 1 B/2 B), which differ in the stacking sequences of double layers of novel six-fold exo-bonded pentagonal bipyramidal closo clusters [M 7]3− connected via four-bonded M − (e.g. 1 B: Cs7Ga8.4In6.6, P 4̅m2, a = 656.23(3), c = 1616.0(1) pm, R 1 = 0.0742; 2 B: Rb7Ga8.1In6.9, P 42/nmc, a = 665.64(2), c = 3140.9(2) pm, R 1 = 0.0720). The Rb/Cs compounds of these types are only stable in a limited Ga/In region and with a distinct Ga/In distribution within the [M 7] clusters. According to the close relation between the structures A, B and C, the structure family is characterised by the occurrence of stacking faults and diffuse scattering, indicating the existence of further members of this series. The new compound Cs5Ga3.1In5.9 (x = 1.667, P 4̅m2, a = 654.62(2), c = 3281.5(2) pm, R 1 = 0.1005) is a reasonably periodically ordered stacking variant containing layers A and double layers B in parallel.

Revealing the Nature of Chemical Bonding in an ALn2Ag3Te5-Type Alkaline-Metal (A) Lanthanide (Ln) Silver Telluride

Although the electronic structures of several tellurides have been recognized by applying the Zintl-Klemm concept, there are also tellurides whose electronic structures cannot be understood by applications of the aforementioned idea. To probe the appropriateness of the valence-electron transfers as implied by Zintl-Klemm treatments of ALn2Ag3Te5-type tellurides (A = alkaline-metal; Ln = lanthanide), the electronic structure and, furthermore, the bonding situation was prototypically explored for RbPr2Ag3Te5. The crystal structure of that type of telluride is discussed for the examples of RbLn2Ag3Te5 (Ln = Pr, Nd), and it is composed of tunnels which are assembled by the tellurium atoms and enclose the rubidium, lanthanide, and silver atoms, respectively. Even though a Zintl-Klemm treatment of RbPr2Ag3Te5 results in an (electron-precise) valence-electron distribution of (Rb+)(Pr3+)2(Ag+)3(Te2−)5, the bonding analysis based on quantum-chemical means indicates that a full electron transfer as suggested by the Zintl-Klemm approach should be considered with concern.

Development of a robust tool to extract Mulliken and Löwdin charges from plane waves and its application to solid-state materials

Chemically understanding the electronic structure of a given material provides valuable information about its chemical as well as physical nature and, hence, is the key to designing materials with desired properties. For example, to rationalize the structures of solid-state materials in terms of the valence-electron distribution, highly schematic, essentially non-quantum-mechanical electron-partitioning models such as the Zintl–Klemm concept have been introduced by assuming idealized ionic charges. To go beyond the limits of the aforementioned concept, a Mulliken and Löwdin population analytical tool has been developed to accurately calculate the charges in solid-state materials solely from first-principles plane-wave-based computations. This population analysis tool, which has been implemented into the LOBSTER code, has been applied to diverse solid-state materials including polar intermetallics to prove its capability, including quick access to Madelung energies. In addition, a former weakness of the population analysis (namely, the basis-set dependency) no longer exists for the present approach which therefore represents a comparatively fast and accurate wave-function-based alternative for plane-wave calculations for which density-based charge approaches (e.g., Bader like) have been very popular.

A robust tool to extract Mulliken and Löwdin charges for (extended) solids from plane waves has been developed and applied.

The Crystal Orbital Hamilton Population (COHP) Method as a Tool to Visualize and Analyze Chemical Bonding in Intermetallic Compounds

Recognizing the bonding situations in chemical compounds is of fundamental interest for materials design because this very knowledge allows us to understand the sheer existence of a material and the structural arrangement of its constituting atoms. Since its definition 25 years ago, the Crystal Orbital Hamilton Population (COHP) method has been established as an efficient and reliable tool to extract the chemical-bonding information based on electronic-structure calculations of various quantum-chemical types. In this review, we present a brief introduction into the theoretical background of the COHP method and illustrate the latter by diverse applications, in particular by looking at representatives of the class of (polar) intermetallic compounds, usually considered as “black sheep” in the light of valence-electron counting schemes.

Electron-Poor Polar Intermetallics: Complex Structures, Novel Clusters, and Intriguing Bonding with Pronounced Electron Delocalization

Intermetallic compounds represent an extensive pool of candidates for energy related applications stemming from magnetic, electric, optic, caloric, and catalytic properties. The discovery of novel intermetallic compounds can enhance understanding of the chemical principles that govern structural stability and chemical bonding as well as finding new applications. Valence electron-poor polar intermetallics with valence electron concentrations (VECs) between 2.0 and 3.0 e^-/atom show a plethora of unprecedented and fascinating structural motifs and bonding features. Therefore, establishing simple structure-bonding-property relationships is especially challenging for this compound class because commonly accepted valence electron counting rules are inappropriate. During our efforts to find quasicrystals and crystalline approximants by valence electron tuning near 2.0 e^-/atom, we observed that compositions close to those of quasicrystals are exceptional sources for unprecedented valence electron-poor polar intermetallics, e.g., Ca₄Au₁₀In₃ containing (Au₁₀In₃) wavy layers, Li_14.7Mg_36.8Cu_21.5Ga₆₆ adopting a type IV clathrate framework, and Sc₄Mg_xCu_15-xGa_7.5 that is incommensurately modulated. In particular, exploratory syntheses of AAu₃T (A = Ca, Sr, Ba and T = Ge, Sn) phases led to interesting bonding features for Au, such as columns, layers, and lonsdaleite-type tetrahedral frameworks. Overall, the breadth of Au-rich polar intermetallics originates, in part, from significant relativistics effect on the valence electrons of Au, effects which result in greater 6s/5d orbital mixing, a small effective metallic radius, and an enhanced Mulliken electronegativity, all leading to ultimate enhanced binding with nearly all metals including itself. Two other successful strategies to mine electron-poor polar intermetallics include lithiation and "cation-rich" phases. Along these lines, we have studied lithiated Zn-rich compounds in which structural complexity can be realized by small amounts of Li replacing Zn atoms in the parent binary compounds CaZn₂, CaZn₃, and CaZn₅; their phase formation and bonding schemes can be rationalized by Fermi surface-Brillouin zone interactions between nearly free-electron states. "Cation-rich", electron-poor polar intermetallics have emerged using rare earth metals as the electropositive ("cationic") component together metal/metalloid clusters that mimic the backbones of aromatic hydrocarbon molecules, which give evidence of extensive electronic delocalization and multicenter bonding. Thus, we can identify three distinct, valence electron-poor, polar intermetallic systems that have yielded unprecedented phases adopting novel structures containing complex clusters and intriguing bonding characteristics. In this Account, we summarize our recent specific progress in the developments of novel Au-rich BaAl₄-type related structures, shown in the "gold-rich grid", lithiation-modulated Ca-Li-Zn phases stabilized by different bonding characteristics, and rare earth-rich polar intermetallics containing unprecedented hydrocarbon-like planar Co-Ge metal clusters and pronounced delocalized multicenter bonding. We will focus mainly on novel structural motifs, bonding analyses, and the role of valence electrons for phase stability.

An Icosahedral Quasicrystal and Its 1/0 Crystalline Approximant in the Ca-Au-Al System

A new icosahedral quasicrystalline phase, CaAu_4.5-xAl_1.5+x [0.11 ≤ x ≤ 0.40(6); CaAu_4.4Al_1.6, a_QC = 5.383(4) Å, and Pm3̅ 5̅], and its lowest-order 1/0 cubic crystalline approximant phase, CaAu_3+xAl_1-x [0 ≤ x ≤ 0.31(1); a = 9.0766(5)-9.1261(8) Å, Pa3̅ (No. 205), and Pearson symbol cP40], have been discovered in the Ca-poor region of the Ca-Au-Al system. In the crystalline approximant, eight [Au_3-xAl_1+x] tetrahedra fill the unit cell, and each tetrahedron is surrounded by four Ca atoms, thus forming a three-dimensional network of {Ca_4/4[Au_3-xAl_1+x]} tetrahedral stars. A computational study of Au and Al site preferences concurs with the experimental results, which indicate a preference for near-neighbor Au-Al interactions over Au-Au and Al-Al interactions. Analysis of the electronic density of states and the associated crystal orbital Hamilton population curves was used to rationalize the descriptions of CaAu_4.5-xAl_1.5+x [0.11 ≤ x ≤ 0.46(6)] and CaAu_3+xAl_1-x [0 ≤ x ≤ 0.31(1)] as polar intermetallic species, whereby Ca atoms engage in polar covalent bonding with the electronegative, electron-deficient [Au_3-xAl_1+x] tetrahedral clusters and the observed phase width of the crystalline approximant.

RE 3Au5Zn (RE = Y, Sm, Gd–Ho) – A new structure type with five- and six-membered rings as building units in a gold network

RE 3Au5Zn (RE = Y, Sm, Gd–Ho) intermetallic compounds were synthesized by melting the elements in sealed tantalum tubes. They exhibit a new structure type which was studied by X-ray diffraction on powders and refined from single crystal diffraction data: Cmcm, a = 736.9(2), b = 1489.4(2), c = 1330.4(3) pm, wR2 = 0.0371, 1184 F 2 values and 55 variables for Y3Au4.92Zn1.08 and a = 739.0(1), b = 1495.8(2), c = 1339.2(2) pm, wR2 = 0.0325, 1410 F 2 values and 54 variables for Tb3Au5Zn. The network consists of five- and six-membered gold rings in puckered conformations. Atoms of the rare earth elements are placed within the cavities of this network where every third cavity is filled by a Zn2 dumbbell. The structure is discussed in detail and compared with the gold substructure of Hf7Au10.

Crystal structure of Sr2CdPt2 containing linear platinum chains

The ternary inter-metallic title phase, distrontium cadmium diplatinum, was prepared from stoichiometric amounts of the elements at 1123 K for one day. The crystal structure adopts the ortho-rhom-bic Ca2GaCu2 structure type in space group Immm. Its main features are characterized by linear (Pt-Pt⋯Pt-Pt) n chains that are aligned along [010] and condensed through cadmium atoms forming Cd-centred Pt2Cd2/2 rectangles to build up sheets parallel to (001). These sheets are connected to each other via alternating (001) sheets of strontium atoms along [001]. The strontium sheets consists of corrugated Sr4 units that are condensed to each other through edge-sharing parallel to [100].

Electron-deficient copper pnictides: A2Mg3Cu9Pn7 (A = Sr, Eu; Pn = P, As) and Eu5Mg2.39Cu16.61As12

Five pnictide Zintl compounds, A₂Mg₃Cu₉Pn₇ (A = Sr, Eu; Pn = P, As) and Eu₅Mg_2.39Cu_16.61As₁₂, were synthesized from the Pb-flux reactions. The anion structures of these compounds can be described as being composed of edge- or corner-sharing CuPn₄ tetrahedra, which construct complex 3D frameworks with cations filled into the cavities.

Endohedral gallide cluster superconductors and superconductivity in ReGa5

We present transition metal-embedded (T@Gan) endohedral Ga-clusters as a favorable structural motif for superconductivity and develop empirical, molecule-based, electron counting rules that govern the hierarchical architectures that the clusters assume in binary phases. Among the binary T@Gan endohedral cluster systems, Mo8Ga41, Mo6Ga31, Rh2Ga9, and Ir2Ga9 are all previously known superconductors. The well-known exotic superconductor PuCoGa5 and related phases are also members of this endohedral gallide cluster family. We show that electron-deficient compounds like Mo8Ga41 prefer architectures with vertex-sharing gallium clusters, whereas electron-rich compounds, like PdGa5, prefer edge-sharing cluster architectures. The superconducting transition temperatures are highest for the electron-poor, corner-sharing architectures. Based on this analysis, the previously unknown endohedral cluster compound ReGa5 is postulated to exist at an intermediate electron count and a mix of corner sharing and edge sharing cluster architectures. The empirical prediction is shown to be correct and leads to the discovery of superconductivity in ReGa5. The Fermi levels for endohedral gallide cluster compounds are located in deep pseudogaps in the electronic densities of states, an important factor in determining their chemical stability, while at the same time limiting their superconducting transition temperatures.

Synthesis, crystal structure, and bonding analysis of the hypoelectronic cubic phase Ca5Pd6Ge6

The title compound, Ca5Pd6Ge6, was obtained during a systematic investigation of the Ca-Pd-Ge ternary phase diagram. The crystal structure was determined and refined from single-crystal X-ray diffraction data. It crystallizes in a new structure variant of the Y4PdGa12-type structure (Im3̅m, a = 8.7764(4) Å) that features an arrangement of vertex-sharing body-centered cubes of calcium, Ca@Ca8, with a hierarchical bcc network, interpenetrating a second (Pd6Ge6) network consisting of Ge2 dumbbells surrounded by Pd in a strongly flattened octahedron with Pd(μ(2)-η(2),η(4)-Ge2)-like motifs. These octahedra are condensed through the Pd to form a 3D open fcc network. Theoretical band structure calculations suggested that the compound is hypoelectronic with predominantly multicenter-type interatomic interactions involving all three elements and essentially a Hume-Rothery-like regime of electronic stabilization. The similar electronegativity between germanium and palladium atoms has a decisive impact on the bonding picture of the system.

Alkaline earth-gold-aluminides: synthesis and structure of SrAu3Al2, SrAu2.83Al2.17, BaAu2.89Al2.11 and BaAu7.09Al5.91

New alkaline earth-gold-aluminides were synthesized from the elements in sealed tantalum or quartz ampoules in muffle furnaces at maximum annealing temperatures of 1325 K. The structures were refined from single crystal X-ray diffractometer data. SrAu3Al2 crystallizes in an ordered version of the LT-SrZn5 structure: Pnma, a = 1315.9(3), b = 549.0(1), c = 684.5(3) pm, wR2 = 0.0232, 930 F 2 values, 35 variables. SrAu2.83Al2.17 (a = 1065.0(2), b = 845.0(2), c = 548.1(1) pm, wR2 = 0.0416, 452 F 2 values, 22 variables) and BaAu2.89Al2.11 (a = 1096.1(3), b = 835.7(3), c = 554.0(1) pm, wR2 = 0.0280, 501 F 2 values, 22 variables) both adopt the BaZn5 type, space group Cmcm with Au/Al mixing on the 4c site. The gold and aluminum atoms in both types form three-dimensional networks of condensed tetrahedra with the strontium and barium atoms in large cavities. BaAu7.09Al5.91 is a new member of the NaZn13 type: Fm3̅c, a = 1257.6(2) pm, wR2 = 0.0267, 168 F 2 values, 12 variables. Both the 96i and 8b sites show Au/Al mixing. The crystal chemical details are discussed.

Crystal structure of the inter-metallic compound SrCdPt

The title compound crystallizes in the TiNiSi structure type in the space group Pnma. St atoms are bonded to each other, forming six-membered rings with chair conformation whilst Pt atoms form zigzag chains of cadmium-centred tetra­hedra, building up the three-dimensional network.

The crystal structure of the title compound, strontium cadmium platinum, adopts the TiNiSi structure type with the Sr atoms on the Ti, the Cd atoms on the Ni and the Pt atoms on the Si positions, respectively. The Pt atoms form cadmium-centred tetra­hedra that are condensed into a three-dimensional network with channels parallel to the b-axis direction in which the Sr atoms are located. The latter are bonded to each other in the form of six-membered rings with chair conformations. All atoms in the SrCdPt structure are situated on a mirror plane.