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.

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 IrAl2.75 , 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 IrAl2.75 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.

Generality of the 18-n Rule: Intermetallic Structural Chemistry Explained through Isolobal Analogies to Transition Metal Complexes.

Intermetallic phases exhibit a vast structural diversity in which electron count is known to be one controlling factor. However, chemical bonding theory has yet to establish how electron counts and structure are interrelated for the majority of these compounds. Recently, a simple bonding picture for transition metal (T)-main group (E) intermetallics has begun to take shape based on isolobal analogies to molecular T complexes. This bonding picture is summarized in the 18-n rule: each T atom in a T-E intermetallic phase will need 18-n electrons to achieve a closed-shell 18-electron configuration, where n is the number of electron pairs it shares with other T atoms in multicenter interactions isolobal to T-T bonds. In this Article, we illustrate the generality of this rule with a survey over a wide range of T-E phases. First, we illustrate how three structural progressions with changing electron counts can be accounted for, both geometrically and electronically, with the 18-n rule: (1) the transition between the fluorite and complex ß-FeSi2 types for TSi2 phases; (2) the sequence from the marcasite type to the arsenopyrite type and back to the marcasite type for TSb2 compounds; and (3) the evolution from the AuCu3 type to the ZrAl3 and TiAl3 types for TAl3 phases. We then turn to a broader survey of the applicability of the 18-n rule through a study of the following 34 binary structure types: PtHg4, CaF2 (fluorite), Fe3C, CoGa3, Co2Al5, Ru2B3, ß-FeSi2, NiAs, Ni2Al3, Rh4Si5, CrSi2, Ir3Ga5, Mo3Al8, MnP, TiSi2, Ru2Sn3, TiAl3, MoSi2, CoSn, ZrAl3, CsCl, FeSi, AuCu3, ZrSi2, Mn2Hg5, FeS2 (oP6, marcasite), CoAs3 (skutterudite), PdSn2, CoSb2, Ir3Ge7, CuAl2, Re3Ge7, CrP2, and Mg2Ni. Through these analyses, the 18-n rule is established as a framework for interpreting the stability of 341 intermetallic phases and anticipating their properties.

Defusing Complexity in Intermetallics: How Covalently Shared Electron Pairs Stabilize the FCC Variant Mo2Cu(x)Ga(6-x) (x ≈ 0.9).

Simple sphere packings of metallic atoms are generally assumed to exhibit highly delocalized bonding, often visualized in terms of a lattice of metal cations immersed in an electron gas. In this Article, we present a compound that demonstrates how covalently shared electron pairs can, in fact, play a key role in the stability of such structures: Mo2Cu(x)Ga(6-x) (x ≈ 0.9). Mo2Cu(x)Ga(6-x) adopts a variant of the common TiAl3 structure type, which itself is a binary coloring of the fcc lattice. Electronic structure calculations trace the formation of this compound to a magic electron count of 14 electrons/T atom (T = transition metal) for the TiAl3 type, for which the Fermi energy coincides with an electronic pseudogap. This count is one electron/T atom lower than the electron concentration for a hypothetical MoGa3 phase, making this structure less competitive relative to more complex alternatives. The favorable 14 electron count can be reached, however, through the partial substitution of Ga with Cu. Using DFT-calibrated Hückel calculations and the reversed approximation Molecular Orbital (raMO) method, we show that the favorability of the 14 electron count has a simple structural origin in terms of the 18 - n rule of T-E intermetallics (E = main group element): the T atoms of the TiAl3 type are arranged into square nets whose edges are bridged by E atoms. The presence of shared electron pairs along these T-T contacts allows for 18 electron configurations to be achieved on the T atoms despite possessing only 18 - 4 = 14 electrons/T atom. This bonding scheme provides a rationale for the observed stability range of TiAl3 type TE3 phases of ca. 13-14 electrons/T atom, and demonstrates how the concept of the covalent bond can extend even to the most metallic of structure types.

Orbital origins of helices and magic electron counts in the Nowotny chimney ladders: the 18 - n rule and a path to incommensurability.

Valence electron count is one of the key factors influencing the stability and structure of metals and alloys. However, unlike in molecular compounds, the origins of the preferred electron counts of many metallic phases remain largely mysterious. Perhaps the clearest-cut of such electron counting rules is exhibited by the Nowotny chimney ladder (NCL) phases, compounds remarkable for their helical structural motifs in which transition metal (T) helices serve as channels for a second set of helices formed from main group (E) elements. These phases exhibit density of states pseudogaps or band gaps, and thus special stability and useful physical properties, when their valence electron count corresponds to 14 electrons per T atom. In this Article, we illustrate, using DFT-calibrated Hückel calculations and the reversed approximation Molecular Orbital analysis, that the 14-electron rule of the NCLs is, in fact, a specific instance of an 18 - n rule emerging for T-E intermetallics, where n is the number of E-supported T-T bonds per T atom. The structural flexibility of the NCL series arises from the role of the E atoms as supports for these T-T bonds, which simply requires the E atoms to be as uniformly distributed within the T sublattice as possible. This picture offers a strategy for identifying other intermetallic structures that may be amenable to incommensurability between T and E sublattices.

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.

Isolobal analogies in intermetallics: the reversed approximation MO approach and applications to CrGa4- and Ir3Ge7-type phases.

Intermetallic phases offer a wealth of unique and unexplained structural features, which pose exciting challenges for the development of new bonding concepts. In this article, we present a straightforward approach to rapidly building bonding descriptions of such compounds: the reversed approximation Molecular Orbital (raMO) method. In this approach, we reverse the usual technique of using linear combinations of simple functions to approximate true wave functions and employ the fully occupied crystal orbitals of a compound as a basis set for the determination of the eigenfunctions of a simple, chemically transparent model Hamiltonian. The solutions fall into two sets: (1) a series of functions representing the best-possible approximations to the model system's eigenstates constructible from the occupied crystal orbitals and (2) a second series of functions that are orthogonal to the bonding picture represented by the model Hamiltonian. The electronic structure of a compound is thus quickly resolved into a series of orthogonal bonding subsystems. We first demonstrate the raMO analysis on a familiar molecule, 1,3-butadiene, and then move to illustrating its use in discovering new bonding phenomena through applications to three intermetallic phases: the PtHg4-type CrGa4 and the Ir3Ge7-type compounds Os3Sn7 and Ir3Sn7. For CrGa4, a density of states (DOS) minimum coinciding with its Fermi energy is traced to 18-electron configurations on the Cr atoms. For Os3Sn7 and Ir3Sn7, 18-electron configurations also underlie DOS pseudogaps. This time, however, the 18-electron counts involve multicenter interactions isolobal with classical Ir-Ir or Os-Os covalent bonds, as well as Sn-Sn single bonds serving as electron reservoirs. Our results are based on DFT-calibrated Hückel calculations, but in principle the raMO analysis can be implemented in any method employing one-electron wave functions.