Due to the chemical and physical properties interesting for applications, a better understanding of the composition and bonding in crystal structures of intermetallic compounds is necessary and – at the same time – is a challenge [1]. 

Composed of elements that are located in the periodic table around the Zintl border and on its left side, intermetallic compounds show valence-electron demand in comparison with the normal valent materials, which may be expressed as the number of electrons in the last shell per atom (ELSA). This hinders the application of bonding concepts based on the 8–N rule [2] to understand the organization of these substances in a simple way. In consequence, these materials do not follow the usual valence rules and require special concepts for the understanding of their chemical composition and crystal structure [3]. This was the driving force to extend the 8−N concept by considering the participation of d electrons (penultimate shell) in bonding events (18−N rule). On a natural way, the further resolving of this situation should involve the analysis of multi-atomic bonding as a mechanism of satisfying the local electron demands in a chemical system.

An application of new quantum-chemical tools opens the way to systematic real-space definition of the basic categories for chemical bonding description. The analysis of chemical bonding in position space has developed in the last decades into an important quantum–chemical tool for study the stoichiometric and structural organization of intermetallic compounds. Using this approach – also under ELSA deficiency conditions - opens the way to systematic real-space definition of the basic categories for chemical bonding description. It allows evaluation of the atomic charges and charge transfer between the atoms, detection and visualization of the interaction between two and more atoms, evaluation of its polarity, quantization of the bond type and bond order, and - finally – calculation of the energetic characteristics of atomic interactions [4].