Isolobal Analogies in Intermetallics: The Reversed Approximation MO Approach and Applications to CrGa4- and Ir3Ge7-Type Phases

Emergent Transitions: Discord between Electronic and Chemical Pressure Effects in the REAl3 (RE = Sc, Y, Lanthanides) Series

Atomic packing and electronic structure are key factors underlying the crystal structures adopted by solid-state compounds. In cases where these factors conflict, structural complexity often arises. Such is born in the series of REAl₃ (RE = Sc, Y, lanthanides), which adopt structures with varied stacking patterns of face-centered cubic close packed (FCC, AuCu₃ type) and hexagonal close packed (HCP, Ni₃Sn type) layers. The percentage of the hexagonal stacking in the structures is correlated with the size of the rare earth atom, but the mechanism by which changes in atomic size drive these large-scale shifts is unclear. In this Article, we reveal this mechanism through DFT-Chemical Pressure (CP) and reversed approximation Molecular Orbital (raMO) analyses. CP analysis illustrates that the Ni₃Sn structure type is preferable from the viewpoint of atomic packing as it offers relief to packing issues in the AuCu₃ type by consolidating Al octahedra into columns, which shortens Al-Al contacts while simultaneously expanding the RE atom's coordination environment. On the other hand, the AuCu₃ type offers more electronic stability with an 18-n closed-shell configuration that is not available in the Ni₃Sn type (due to electron transfer from the RE d_z² atomic orbitals into Al-based states). Based on these results, we then turn to a schematic analysis of how the energetic contributions from atomic packing and the electronic structure vary as a function of the ratio of FCC and HCP stacking configurations within the structure and the RE atomic radius. The minima on the atomic packing and electronic surfaces are non-overlapping, creating frustration. However, when their contributions are added, new minima can emerge from their combination for specific RE radii representing intergrowth structures in the REAl₃ series. Based on this picture, we propose the concept of emergent transitions, within the framework of the Frustrated and Allowed Structural Transitions principle, for tracing the connection between competing energetic factors and complexity in intermetallic structures.

Metavalent bonding in chalcogenides: DFT-chemical pressure approach

Understanding the chemical bond nature has attracted considerable attention as it is crucial to analyze and comprehend the different physical and chemical properties of materials. This work is considered a complementary part of our previous work in studying the nature of different types of bonding interactions in a wide variety of molecules and materials using the DFT Chemical Pressure (CP) approach. Recently, a new type of chemical bond, the metavalent bond (MVB), has been defined. We show how the CP formalism can be used to analyze and study the establishment of MVB in two chalcogenides, GeSe and PbSe, in a similar fashion as the electron localization function (ELF) profiles. This is accomplished by analyzing the CP maps of these two chalcogenides at different pressures (up to 40 GPa for GeSe and 10 GPa for PbSe). The CP maps show distinctive features related to the MVB, providing insights into the existence of such chemical interaction in the crystal structure of the two compounds. Similar to ELF profiles, CP maps can visualize and track the strength of the MVB in GeSe and PbSe under pressure.

Frustrated Packing in Simple Structures: Chemical Pressure Hindrance to Isolobal Bonds in the TiAl3 type and ZrAl2.6Sn0.4

While simple close-packed arrangements convey a sense of optimization, they can, in fact, host competition between different types of interactions. The TiAl₃ structure type, for example, represents one of a series of ordered TE₃ variants (T = transition metal, E = main group element) of the face-centered cubic structure, alongside the AuCu₃ and ZrAl₃ types. These structures differ in their T-T connectivity corresponding to the 18-n rule: electronic pseudogaps occur at electron concentrations of 18-n/T atom, where n is the number of electron pairs each T atom shares with other T atoms in T-T isolobal bonds. Facile stacking variations interrelate these structures, presumably setting the stage for an electronically precise series. However, the prototype of the TiAl₃ type itself violates the 18-n rule, with its count of 13 electrons/Ti atom calling for n = 5 rather than the 4 isolobal T-T bonds/T atom available in this type. Here, we investigate the factors underlying this deviation from the 18-n rule and their relation to the new TiAl₃-type compound ZrAl_3-xSn_x (x ∼ 0.4). First, the relative stabilities of the TiAl₃ and ZrAl₃ types are compared for TAl₃ compounds (T = Zr and Ti). While for T = Zr, the structure adhering to the 18-n rule is highly preferred, for T = Ti, the energy difference essentially vanishes. This trend is connected through DFT-Chemical Pressure (CP) analysis to a tension that emerges in TiAl₃ between the optimization of the T-T isolobal bonds and the space requirements of Al-Al contacts elsewhere. This picture elucidates the transition of ZrAl₃ from its own type to the TiAl₃-type upon partial Sn substitution in ZrAl_2.6Sn_0.4: the incorporation of Sn brings the electron count closer to that predicted for the TiAl₃ type, while electronegativity and CP direct the larger Sn atoms to the site that resists isolobal bond formation in TiAl₃.

At the Limits of Isolobal Bonding: π-Based Covalent Magnetism in Mn2Hg5

Magnetic ordering in inorganic materials is generally considered to be a mechanism for structures to stabilize open shells of electrons. The intermetallic phase Mn₂Hg₅ represents a remarkable exception: its crystal structure is in accordance with the 18-n bonding scheme and non-spin-polarized density functional theory (DFT) calculations show a corresponding pseudogap near its Fermi energy. Nevertheless, it exhibits strong antiferromagnetic ordering virtually all the way up to its decomposition temperature. In this Article, we examine how these two features of Mn₂Hg₅ coexist through the development of a DFT implementation of the reversed approximation Molecular Orbital (raMO) analysis. In the non-spin-polarized electronic structure, the DFT-raMO approach confirms that Mn₂Hg₅ adheres to the 18-n rule: its chains of Mn atoms are linked through isolobal triple bonds, with three electron pairs being shared at each Mn-Mn contact in one σ-type and two π-type functions. Because each Mn atom has 6 isolobal Mn-Mn bonds, it achieves a filled 18-electron count at the compound's electron concentration of 18 - 6 = 12 electrons/Mn. A pseudogap thus occurs at the Fermi energy. Upon the introduction of antiferromagnetic order, the original pseudogap widens and deepens, suggesting enhancement of a stabilizing effect already present in the nonmagnetic state. A raMO analysis reveals that antiferromagnetism enlarges the gap by allowing diradical character to enter into the Mn-Mn isolobal π bonds, reminiscent of the dissociation of a classic covalent bond. Antiferromagnetism is accompanied by residual bonding in the π system, making Mn₂Hg₅ a vivid realization of the concept of covalent magnetism.

Bond-breaking induced Lifshitz transition in robust Dirac semimetal VAI3

Understanding the relation between crystal structure and electronic properties is crucial for designing new quantum materials with desired functionality. So far, controlling a chemical bond is less considered as an effective way to manipulate the topological electrons. In this paper, we show that the V–Al bond acts as a shield for protecting the topological electrons in Dirac semimetal VAl3. The Dirac electrons remain intact in the V1−xTixAl3 solid solutions, even after a substantial part of V atoms have been replaced. A Lifshitz transition from Dirac semimetal to trivial metal occurs as long as the V–Al bond is completely broken. Our finding highlights a rational approach for designing new quantum materials via controlling their chemical bond.

Topological electrons in semimetals are usually vulnerable to chemical doping and environment change, which restricts their potential application in future electronic devices. In this paper, we report that the type-II Dirac semimetal VAl3 hosts exceptional, robust topological electrons which can tolerate extreme change of chemical composition. The Dirac electrons remain intact, even after a substantial part of V atoms have been replaced in the V1−xTixAl3 solid solutions. This Dirac semimetal state ends at x=0.35, where a Lifshitz transition to p-type trivial metal occurs. The V–Al bond is completely broken in this transition as long as the bonding orbitals are fully depopulated by the holes donated from Ti substitution. In other words, the Dirac electrons in VAl3 are protected by the V–Al bond, whose molecular orbital is their bonding gravity center. Our understanding on the interrelations among electron count, chemical bond, and electronic properties in topological semimetals suggests a rational approach to search robust, chemical-bond-protected topological materials.

Entropy-Driven Incommensurability: Chemical Pressure-Guided Polymorphism in PdBi and the Origins of Lock-In Phenomena in Modulated Systems

Incommensurate order, in which two or more mismatched periodic patterns combine to make a long-range ordered yet aperiodic structure, is emerging as a general phenomenon impacting the crystal structures of compounds ranging from alloys and nominally simple salts to organic molecules and proteins. The origins of incommensurability in these systems are often unclear, but it is commonly associated with relatively weak interactions that become apparent only at low temperatures. In this article, we elucidate an incommensurate modulation in the intermetallic compound PdBi that arises from a different mechanism: the controlled increase of entropy at higher temperatures. Following the synthesis of PdBi, we structurally characterize two low-temperature polymorphs of the TlI-type structure with single crystal synchrotron X-ray diffraction. At room temperature, we find a simple commensurate superstructure of the TlI-type structure (comm-PdBi), in which the Pd sublattice distorts to form a 2D pattern of short and long Pd-Pd contacts. Upon heating, the structure converts to an incommensurate variant (incomm-PdBi) corresponding to the insertion of thin slabs of the original TlI type into the superstructure. Theoretical bonding analysis suggests that comm-PdBi is driven by the formation of isolobal Pd-Pd bonds along shortened contacts in the distorted Pd network, which is qualitatively in accord with the 18-n rule but partially frustrated by the population of competing Bi-Bi bonding states. The emergence of incomm-PdBi upon heating is rationalized with the DFT-Cemical Pressure (CP) method: the insertion of TlI-type slabs result in regions of higher vibrational freedom that are entropically favored at higher temperatures. High-temperature incommensurability may be encountered in other materials when bond formation is weakened by competing electronic states, and there is a path for accommodating defects in the CP scheme.

Frustrated and Allowed Structural Transitions: The Theory-Guided Discovery of the Modulated Structure of IrSi

To the experienced molecular chemist, predicting the geometries and reactivities of a system is an exercise in balancing simple concepts such as sterics and electronics. In this Article, we illustrate how recent theoretical developments can give this combination of concepts a similar predictive power in intermetallic chemistry through the anticipation and discovery of structural complexity in the nominally MnP-type compound IrSi. Analysis of the bonding scheme and DFT-Chemical Pressure (CP) distribution of the reported MnP-type structure exposes issues pointing toward new structural behavior. The placement of the Fermi energy below an electronic pseudogap indicates that this structure is electron-poor, an observation that can be traced via the 18-n rule to the structure's Ir-Ir connectivity. In parallel with this, the structure's CP scheme highlights facile paths of atomic motion that could enable a structural response to this electronic deficiency. Combined, these analyses suggest that IrSi may adopt a more complex structure than previously recognized. Through synthesis and detailed structural investigation of this phase, we confirm this prediction: single-crystal X-ray diffraction reveals an incommensurately modulated structure with the (3+1)D superspace group P2₁/n(0βγ)00 and q ≈ -0.22b* + 0.29c*. The structural modulations increase the average number of Ir-Ir bonds to nearly match the 18-n expectations of the phase through Ir-Ir trimerization along negative CPs with the incommensurability arising from the difficulty of contracting and stretching the Ir-Ir contacts in a regular pattern without expanding the structure along directions of negative Si-Si CP. Integrating these results with prior analyses of related systems points to a simple guideline for materials design, the Frustrated and Allowed Structural Transitions (FAST) principle: the ease with which competing structural phenomena can be experimentally realized is governed by the degree to which they are supported by the coordination of the atomic packing and electronic factors.

Cation Clustering in Intermetallics: The Modular Bonding Schemes of CaCu and Ca2Cu

Electropositive metals such as the alkaline earths or lanthanides are generally assumed to act largely as spectator cations in solid state compounds. In polar intermetallic phases, atoms of such elements are indeed often placed at the peripheries of anions or polyanionic fragments. However, they also show a pronounced tendency to cluster with each other in these peripheral regions in a manner suggestive of multicenter bonding. In this Article, we theoretically investigate the bonding schemes that underlie these cationic cluster arrangements, focusing on CaCu (whose two polymorphs are based on the intergrowth of the FeB- and CrB-types) and Ca₂Cu (a Ca-intercalated derivative of CaCu). The structures of these phases are based on Cu zigzag chains embedded in matrices of Ca atoms arranged into increasingly well-developed fragments of closest-packed arrangements. Using reversed approximation Molecular Orbital (raMO) analysis, the Cu chains of both structures are revealed to be connected via nearly fully occupied Cu-Cu isolobal σ-bonds, such that the Cu atoms control 11.67 of the 13 and 15 electrons/formula unit of CaCu and Ca₂Cu, respectively. Most of the remaining electrons are drawn to multicenter bonding functions in the Ca sublattices despite the availability of additional Cu 4p orbitals, indicating that the electronegativity difference between Ca and Cu is insufficient to achieve formal Cu oxidation states far beyond -1. The metallic nature of the Ca-based bonding subsystem is reflected in the raMO analysis by a plurality of resonance structures that can be generated from the occupied crystal orbitals. Across these bonding schemes, a separation of the electronic structure into largely self-contained Ca-Ca and Ca-Cu states is a consistent theme. This modularity in the bonding can be correlated to the ease with which this and related systems rearrange FeB- and CrB-type features, which may provide clues to identifying other intermetallic families with similar degrees of structural versatility.

Principles of weakly ordered domains in intermetallics: the cooperative effects of atomic packing and electronics in Fe2Al5

Many complex intermetallic structures feature a curious juxtaposition of domains with strict 3D periodicity and regions of much weaker order or incommensurability. This article explores the basic principles leading to such arrangements through an investigation of the weakly ordered channels of Fe2Al5. It starts by experimentally confirming the earlier crystallographic model of the high-temperature form, in which nearly continuous columns of electron density corresponding to disordered Al atoms emerge. Then electronic structure calculations on ordered models are used to determine the factors leading to the formation of these columns. These calculations reveal electronic pseudogaps near 16 electrons/Fe atom, an electron concentration close to the Al-rich side of the phase's homogeneity range. Through a reversed approximation Molecular Orbital (raMO) analysis, these pseudogaps are correlated with the filling of 18-electron configurations on the Fe atoms with the support of isolobal σ Fe-Fe bonds. The resulting preference for 16 electrons/Fe requires a fractional number of Al atoms in the Fe2Al5 unit cell. Density functional theory-chemical pressure (DFT-CP) analysis is then applied to investigate how this nonstoichiometry is accommodated. The CP schemes reveal strong quadrupolar distributions on the Al atoms of the channels, suggestive of soft atomic motions along the undulating electron density observed in the Fourier map that allow the Al positions to shift easily in response to compositional changes. Such a combination of preferred electron counts tied to stoichiometry and continuous paths of CP quadrupoles could provide predictive indicators for the emergence of channels of disordered or incommensurately spaced atoms in intermetallic structures.

Pseudogap Control of Physical and Chemical Properties in CeFeSi-Type Intermetallics

We describe the synthesis of the new ternary compound CaRuSi whose chemical and physical properties help draw a clear picture of how electronic structure controls the behavior of an isostructural series of intermetallics. DFT calculations reveal that an electronic pseudogap arises near the Fermi level ( E_F), corresponding to 14 valence electrons per RuSi unit. The closed-shell-like character is further investigated by comparisons with the electronic structures of CaCoSi (15 electrons), where the E_F lies above the corresponding pseudogap, and its hydride CaCoSiH, where formation of H anions restores the 14-electron count on the metal sublattice, returning the E_F to the pseudogap. The chemical origin of the 14-electron pseudogap is interpreted with a reversed approximation Molecular Orbital analysis. Here, the pseudogap is shown to coincide with the filling of Ru 16 electron configurations isolobal to the d⁸ square planar complexes of coordination chemistry (but where 4 electron pairs are shared covalently between Ru atoms such that only 12 electrons are required), and the occupation of Si lone pairs (2 electrons). Experimentally, the pseudogap is confirmed with heat capacity measurements, which indicate that the 14-electron systems CaRuSi and CaCoSiH each exhibit  a smaller electronic density of states at the E_F than the 15-electron system CaCoSi. Importantly, the 14-electron pseudogap also significantly affects the chemical properties of the compounds, as evidenced by the difference in the stabilities of CaCoSiH and CaRuSiH observed in hydrogen desorption measurements. These results may support the design of functional materials for superconductivity, hydrogen storage, and catalysis involving hydrogenation.

Paths to Stabilizing Electronically Aberrant Compounds: A Defect-Stabilized Polymorph and Constrained Atomic Motion in PtGa2

The structures and properties of intermetallic phases are intimately connected to electron count; unfavorable electron counts can result in structural rearrangements or new electrical or magnetic behavior when no such transformation is available. The compound PtGa₂ appears to teeter on the border between these two scenarios with its two polymorphs: a cubic fluorite type form (c-PtGa₂) and a complex tetragonal superstructure (t-PtGa₂) whose Pt-Pt connectivity aligns with the 18- n electron counting rule. Here, we investigate the factors underlying this polymorphism. Electronic structure calculations show that the transition to t-PtGa₂ opens a pseudogap at the Fermi energy that can be traced to Pt-Pt isolobal bond formation, in line with the 18- n bonding scheme. Conversely, DFT-chemical pressure (CP) analysis reveals a network of positive local pressures along Pt-Ga contacts, requiring that the c-PtGa₂ to t-PtGa₂ transition follows tightly concerted atomic motions. Experimentally, a series of samples with varying Pt:Ga ratios were synthesized to examine the stability ranges of the polymorphs. Ga-poor samples yield exclusively the cubic polymorph over the full range of temperatures studied, which can be correlated to the enhanced incorporation of interstitial Pt atoms (at points of negative pressure in the CP scheme). At more Ga-rich compositions, however, t-PtGa₂ emerges as a low-temperature form. In these samples, the t-PtGa₂ to c-PtGa₂ transition is found to be reversible, but with a large hysteresis that in single crystals can exceed 100 °C. Together, the theoretical and experimental results indicate that the c-PtGa₂ phase is buttressed at its unfavorable electron count by the interstitial atoms and networks of positive CPs that restrict atomic motion, suggesting more general strategies for achieving exotic electronic structures in intermetallic materials.

[Co@Sn6 Sb6 ]3- : An Off-Center Endohedral 12-Vertex Cluster

We report on the asymmetric occupation of a 12-vertex cluster centered by a single metal atom. Three salts of related intermetalloid cluster anions, [Co@Sn₆ Sb₆ ]^3- (1), [Co₂ @Sn₅ Sb₇ ]^3- (2), and [Ni₂ @Sn₇ Sb₅ ]^3- (3) were synthesized, which have pseudo-C_4v -symmetric or pseudo-D_4h -symmetric 12-vertex Sn/Sb shells and interstitial Co^- ions or Ni atoms. Anion 1 is a very unusual single-metal-"centered" 12-atom cluster, with the inner atom being clearly offset from the cluster center for energetic reasons. Quantum chemistry served to assign atom types to the atomic positions and relative stabilities of this cluster type. The studies indicate that the structures are strictly controlled by the total valence electron count-which is particularly variable in ternary intermetalloid cluster anions. Preliminary ¹¹⁹ Sn NMR studies in solution, supported by quantum-chemical calculations of the shifts, illustrate the complexity regarding Sn:Sb distributions of such ternary systems.

Parallels in Structural Chemistry between the Molecular and Metallic Realms Revealed by Complex Intermetallic Phases

The structural diversity of intermetallic phases poses a great challenge to chemical theory and materials design. In this Account, two examples are used to illustrate how a focus on the most complex of these structures (and their relationships to simpler ones) can reveal how chemical principles underlie structure for broad families of compounds. First, we show how experimental investigations into the Fe-Al-Si system, inspired by host-guest like features in the structure of Fe₂₅Al₇₈Si₂₀, led to a theoretical approach to deriving isolobal analogies between molecular and intermetallic compounds and a more general electron counting rule. Specifically, the Fe₈Al_17.6Si_7.4 compound obtained in these syntheses was traced to a fragmentation of the fluorite-type structure (as adopted by NiSi₂), driven by the maintenance of 18-electron configurations on the transition metal centers. The desire to quickly generalize these conclusions to a broader range of phases motivated the formulation of the reversed approximation Molecular Orbital (raMO) approach. The application of raMO to a diverse series of compounds allowed us recognize the prevalence of electron pair sharing in multicenter functions isolobal to classical covalent bonds and to propose the 18 - n electron rule for transition metal-main group (T-E) intermetallic compounds. These approaches provided a framework for understanding the 14-electron rule of the Nowotny Chimney Ladder phases, a temperature-driven phase transition in GdCoSi₂, and the bcc-structure of group VI transition metals. In the second story, we recount the development of the chemical pressure approach to analyzing atomic size and packing effects in intermetallic structures. We begin with how the stability of the Yb₂Ag₇-type structure of Ca₂Ag₇ over the more common CaCu₅ type highlights the pressing need for approaches to assessing the role of atomic size in crystal structures, and inspired the development of the DFT-Chemical Pressure (CP) method. Examples of structural phenomena elucidated by this approach are then given, including the Y/Co₂ dumbbell substitution in the Th₂Zn₁₇-type phase Y₂Co₁₇, and local icosahedral order in the Tsai-type quasicrystal approximant CaCd₆. We next discuss how deriving relationships between the CP features of a structure and its phonon modes provided a way of both validating the method and visualizing how local arrangements can give rise to soft vibrational modes. The themes of structural mechanisms for CP relief and soft atomic motions merge in the discovery and elucidation of the incommensurately modulated phase CaPd₅. In the conclusion of this Account, we propose combining raMO and CP methods for focused predictions of structural phenomena.

Chemical Pressure Maps of Molecules and Materials: Merging the Visual and Physical in Bonding Analysis

The characterization of bonding interactions in molecules and materials is one of the major applications of quantum mechanical calculations. Numerous schemes have been devised to identify and visualize chemical bonds, including the electron localization function, quantum theory of atoms in molecules, and natural bond orbital analysis, whereas the energetics of bond formation are generally analyzed in qualitative terms through various forms of energy partitioning schemes. In this Article, we illustrate how the chemical pressure (CP) approach recently developed for analyzing atomic size effects in solid state compounds provides a basis for merging these two approaches, in which bonds are revealed through the forces of attraction and repulsion acting between the atoms. Using a series of model systems that include simple molecules (H₂, CO₂, and S₈), extended structures (graphene and diamond), and systems exhibiting intermolecular interactions (ice and graphite), as well as simple representatives of metallic and ionic bonding (Na and NaH, respectively), we show how CP maps can differentiate a range of bonding phenomena. The approach also allows for the partitioning of the potential and kinetic contributions to the interatomic interactions, yielding schemes that capture the physical model for the chemical bond offered by Ruedenberg and co-workers.

Tiered Electron Anions in Multiple Voids of LaScSi and Their Applications to Ammonia Synthesis

Electrides-compounds in which electrons localized in interstitial spaces periodically serve as anions-have attracted broad attention for their exotic properties, such as extraordinary electron-donating ability. In our efforts to expand this small family of phases, LaScSi emerges as a promising candidate. Its electron count is 2e^- f.u.^-1 in excess of that expected from the Zintl concept, while its structure offers interstitial spaces that can accommodate these extra electrons. Herein, this potential is explored through density functional theory (DFT) calculations and property measurements on LaScSi. DFT calculations (validated by heat capacity and electrical transport measurements) reveal electron density peaks at two symmetry-distinct interstitial sites. Importantly, this electride-like character is combined with chemical stability in air and water, an advantage for catalysis. Ru-loaded LaScSi shows outstanding catalytic activity for ammonia synthesis, with a turnover frequency (0.1 s^-1 at 0.1 MPa, 400 °C) an order of magnitude higher than those of oxide-based Ru catalysts, e.g., Ru/MgO. As with other electrides, LaScSi's ability to reversibly store hydrogen prevents the hydrogen poisoning of Ru surfaces. The better performance of LaScSi, however, hints at the importance of the high concentration (>1.6 × 10²² cm^-3 ) and tiered nature of its anionic electrons, which offers guidance toward new catalysts.

Inducing Complexity in Intermetallics through Electron-Hole Matching: The Structure of Fe14 Pd17 Al69

We illustrate how the crystal structure of Fe₁₄ Pd₁₇ Al₆₉ provides an example of an electron-hole matching approach to inducing frustration in intermetallic systems. Its structure contains a framework based on IrAl_2.75 , a binary compound that closely adheres to the 18-n rule. Upon substituting the Ir with a mixture of Fe and Pd, a competition arises between maintaining the overall ideal electron concentration and accommodating the different structural preferences of the two elements. A 2×2×2 supercell results, with Pd- and Fe-rich regions emerging. Just as in the original IrAl_2.75 phase, the electronic structure of Fe₁₄ Pd₁₇ Al₆₉ exhibits a pseudogap at the Fermi energy arising from an 18-n bonding scheme. The electron-hole matching approach's ability to combine structural complexity with electronic pseudogaps offers an avenue to new phonon glass-electron crystal materials.

Electron-counting in intermetallics made easy: the 18-n rule and isolobal bonds across the Os–Al system

Electron count is one of the key factors controlling the formation of complex intermetallic structures. The delocalized nature of bonding in metals, however, has made it difficult to connect these electron counts to the various structural features that make up complex intermetallics. In this article, we illustrate how structural progressions in transition metal-main group intermetallics can in fact be simply understood with the 18-

π-Conjugation in Gd13Fe10C13 and its oxycarbide: unexpected connections between complex carbides and simple organic molecules

Carbometalates are a diverse family of solid state structures formed from transition metal (TM)-carbon polyanionic frameworks whose charges are balanced by rare earth (RE) cations. Remarkable structural features, such as transition metal clusters, are often encountered in these phases, and a pressing challenge is to explain how such features emerge from the competing interaction types (RE-TM, TM-TM, TM-C, etc.) in these systems. In this Article, we describe a joint experimental and theoretical investigation of two compounds, Gd13Fe10C13 and its oxycarbide Gd13Fe10C(13-x)O(x) (x ≈ 1), which add a new dimension to the structural chemistry of carbometalates: π-conjugation through both TM-C and TM-TM multiple bonds. The crystal structures of both compounds are built from layers of Fe-centered Gd prisms stacked along c and surrounded by an Fe-C network, and differ chiefly in the stacking sequence of these layers. The phases' identical local structures have two types of Fe environment: trigonal planar FeC3 sites and H-shaped Fe2C4 sites, with unusually short Fe-Fe and Fe-C bonds. (57)Fe Mössbauer spectroscopy and DFT-calibrated Hückel calculations on Gd13Fe10C13 build a picture of covalent Fe-C σ bonds and conjugated π systems for which Lewis structures can be drawn. Using the reversed approximation Molecular Orbital approach, we can draw isolobal analogies between the Fe centers of this compound and molecular TM complexes: 18-electron configurations could be achieved through σ and π bonds with 18 electrons/Fe for the FeC3 site and 18-n (n = 2 for an Fe═Fe double bond) electrons/Fe for the Fe2C4 site. In this way, the vision of a unified bonding scheme of carbometalates and organometallics proffered by earlier studies is realized in a visual manner, directly from the 1-electron wave functions of the Hückel model. The bonding analysis predicts that Gd13Fe10C13 is one electron/formula unit short of an ideal electron count, explaining the tendency of the system toward a small degree of oxygen substitution. Analogies between the π bonding in Gd13Fe10C13 and that of the allyl anion help rationalize the presence of trigonal planar Fe and linear C units in the structure. The isolobal analogy between Gd13Fe10C13 and an 18-electron coordination complex is expected to apply to carbometalates as a whole, and will be extended to other examples in our future work.