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.

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.

The quest for solid-state materials with tailored chemical and physical features stimulates the search for general prescriptions to recognize and forecast their electronic structures providing valuable information about the experimentally determined bulk properties at the atomic scale. Although the concepts first introduced by Zintl and Hume–Rothery help to understand and forecast the bonding motifs in several intermetallic compounds, there is an emerging group of compounds dubbed as polar intermetallic phases whose electronic structures cannot be categorized by the aforementioned conceptions. These polar intermetallic compounds can be divided into two categories based on the building units in their crystal structures and the expected charge distributions between their components. On the one hand, there are polar intermetallic compounds composed of polycationic clusters surrounded by anionic ligands, while, on the other hand, the crystal structures of other polar intermetallic compounds comprise polyanionic units combined with monoatomic cations. In this review, we present the quantum chemical techniques to gain access to the electronic structures of polar intermetallic compounds, evaluate certain trends from a survey of the electronic structures of diverse polar intermetallic compounds, and show options based on quantum chemical approaches to predict the properties of such materials.

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.