solids; a "semiconductor" has a narrow bandgap across which electrons can be excited by light; these classifications are therefore based on measurable, macroscopic properties. A fingerprint of five coexisting identifiers was recently used to define a concept termed "metavalent" bonding (MVB): [4,5] metavalent solids show i) moderate electronic conductivity (≈10 2 -10 4 S cm −1 ); ii) increased coordination numbers incompatible with the (8-N) rule for semiconductors; iii) large optical dielectric constants, ε ∞ ; iv) large bond polarizability, as measured by Born effective charges, Z*; and v) large lattice anharmonicity, as measured by the Grüneisen parameter, |γ TO |. In terms of conductivity and coordination numbers, metavalent solids are therefore located between the covalent and metallic regimes-but they are distinctly different from both because they show anomalously large response properties [5] and a unique bond-breaking mechanism [4] not observed in either covalent or metallic solids. This definition based on a set of observable properties directly led to a revision of the "resonant bonding" model (which had previously been widely used to describe the bonding in PCMs [6] ) by showing that the response properties of PCMs are fundamentally different from those of resonantly bonded benzene and graphite. [5] A 2D map is created for solid-state materials based on a quantum-mechanical description of electron sharing and electron transfer. This map intuitively identifies the fundamental nature of ionic, metallic, and covalent bonding in a range of elements and binary compounds; furthermore, it highlights a distinct region for a mechanism recently termed "metavalent" bonding. Then, it is shown how this materials map can be extended in the third dimension by including physical properties of application interest. Finally, it is shown how the map coordinates yield new insight into the nature of the Peierls distortion in phase-change materials and thermoelectrics. These findings and conceptual approaches provide a novel avenue to tailor material properties. Materials DesignThe ORCID identification number(s) for the author(s) of this article can be found under https://doi.

and β-As 2 Te 3 ) and GaSe are investigated. Atom probe tomography studies reveal that four of the seven sesqui-chalcogenides (Bi 2 Te 3 , Bi 2 Se 3 , Sb 2 Te 3 , and β-As 2 Te 3 ) show an unconventional bond-breaking mechanism. The same four compounds evidence a remarkable property portfolio in density functional theory calculations including large Born effective charges, high optical dielectric constants, low Debye temperatures and an almost metal-like electrical conductivity. These results are indicative for unconventional bonding leading to physical properties distinctively different from those caused by covalent, metallic, or ionic bonding. The experiments reveal that this bonding mechanism prevails in four sesqui-chalcogenides, characterized by rather short interlayer distances at the van der Waals like gaps, suggestive of significant interlayer coupling. These conclusions are further supported by a subsequent quantum-chemistry-based bonding analysis employing charge partitioning, which reveals that the four sesqui-chalcogenides with unconventional properties are characterized by modest levels of charge transfer and sharing of about one electron between adjacent atoms. Finally, the 3D maps for different properties reveal discernible property trends and enable material design.The ORCID identification number(s) for the author(s) of this article can be found under https://doi.org/10.1002/adma.201904316.Chalcogenides are attracting considerable attention due to their striking properties. These characteristics enable a wide range of applications ranging from phase-change materials (PCMs) [1][2][3] to thermoelectrics [4] and topological insulators [5,6] for the heavier chalcogenides. The remarkable application potential has been attributed to an unconventional property portfolio. [2,[7][8][9] Adv. Mater. 2019, 31, 1904316

Understanding chemical bonding is of significant interest since it allows us to comprehend and tailor certain material properties, [1,2] which could be utilized, e.g., to optimize phase-change materials (PCMs) [3-7] or thermoelectrics. [8,9] The first steps to understand the nature of the chemical bond were already taken almost a century ago by Linus Pauling [10] and others. [11,12] In the meantime, enormous developments have taken place in both, quantum-mechanical and experimental techniques, [13-15] which help us to explore chemical bonding with unprecedented detail. Recently, these advances have also led to the concept of metavalent bonding (MVB), describing a bonding mechanism in between electron delocalization (i.e., metallic bonding) and electron localization at the ion cores (i.e., ionic bonding) as well as within the interatomic region (i.e., covalent bonding). [16-18] Metavalent bonding has been categorized by combining both quantummechanical and experimentally accessible bonding descriptors. [16-18] The 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 quantummechanical 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 β-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 (γ TO)), 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 ε 2 (ω). Hence, the insights gained from this study highlight the technological relevance of the concept of metavalent bonding and its potential for materials design.

Quantum chemical bonding descriptors have recently been utilized to design materials with tailored properties. We will review their usage to facilitate a quantitative description of bonding in chalcogenides as well as the transition between different bonding mechanisms. More importantly, these descriptors will also be employed as property predictors for several important material characteristics, including optical and transport properties. Hence, these quantum chemical bonding descriptors can be utilized to tailor material properties of chalcogenides relevant for thermoelectrics, photovoltaics and phase change memories.Relating material properties to bonding mechanisms also shows that there is a class of materials, which are characterized by unconventional properties such as a pronounced anharmonicity, a large chemical bond polarizability, and strong optical absorption. This unusual property portfolio is attributed to a novel bonding mechanism, fundamentally different from ionic, metallic and covalent bonding, which has been called 'metavalent'. In the concluding chapter, a number of promising research directions are sketched, which explore the nature of the property changes upon changing bonding mechanism and extend the concept of quantum chemical property predictors to more complex compounds.

We study the performance of fourth-order gradient expansions of the kinetic energy density (KED) in semi-local kinetic energy functionals depending on the density-dependent variables.The formal fourth-order expansion is convergent for periodic systems and small molecules but does not improve over the second-order expansion (Thomas-Fermi term plus one-ninth of von Weizsäcker term). Linear fitting of the expansion coefficients somewhat improves on the formal expansion. The tuning of the fourth order expansion coefficients allows for better reproducibility of Kohn-Sham kinetic energy density than the tuning of the second-order expansion coefficients alone. The possibility of a much more accurate match with the Kohn-Sham kinetic energy density by using neural networks trained using the terms of the 4 th order expansion as densitydependent variables is demonstrated. We obtain ultra-low fitting errors without overfitting. Small single hidden layer neural networks can provide good accuracy in separate KED fits of each compound, while for joint fitting of KEDs of multiple compounds multiple hidden layers were required to achieve good fit quality. The critical issue of data distribution is highlighted. We also show the critical role of pseudopotentials in the performance of the expansion, where in the case of a too rapid decay of the valence density at the nucleus with some pseudopotentials, numeric instabilities arise.