Modern solid state chemistry is inconceivable without theoretical treatment of solids thanks to the availability of efficient and accurate computational methods. Being developed mainly by physicist's community and deeply rooted in the formalism of reciprocal space, they often lack connections to familiar chemical concepts, indispensable for the chemical understanding of matter. Quantum chemical topology approach is a powerful theory able to efficiently recover chemical entities from the abstract description of a system given by its density matrices. It can be used to partition any many-electron system into the atoms, using the topology of electron density or for instance into atomic shells, using the topology of ELI-D field. Various characteristics of interactions between these chemical building blocks can be obtained applying bonding indicators, e.g. from the analysis of domain-averaged properties. Quantum chemical topology methods have been extended in the current work for the applications on the diversity of theoretical methods widely used for the description of solids nowadays – from the mean field Kohn-Sham density functional theory to the reduced one-electron density matrices functional theory or from the scalar-relativistic methods to the many-component formalisms employing spinor wavefunctions. It has been shown, that they provide chemically meaningful description of the bonding which is universally applicable to any class of extended systems, be it ionic insulator, covalent solid or metal. It has been shown, that the relativistic effects on the chemical bonding can be easily revealed using extensions of bonding indicators developed in the current work. Classical chemical concepts like Zintl-Klemm concept can be easily recovered with these descriptions. Intimate connection between the class of the material and the degree of chemical bonding delocalization has been also established. All these methods have been successfully applied to the various classes of solids and delivered novel insights on their crystal structure, properties, solid state transitions and reactivity.

Quantum mechanics became a foundation for incessant development of versatile computational methods for analysis of chemical and physical properties of molecules and crystals. A huge progress has been made in the fifield of density functional theory, since nowadays this theory offers the best compromise between precision of results and efficiency fiof computation. The chemical bonding analysis can be easily performed with real space methods based on chemical concepts introduced via partitioning of real space into chemically meaningful domains, since the orbital based approach is not well applicable due to the delocalized nature of plane waves. However the practical usage of those methods often requires a signifificant amount of computational resources. Some methods require the evaluation of so called domain overlap matrices, that is a formidable task for complex and low-symmetry systems. In the present research the author enables the investigation of complex solid compounds with real space chemical bonding indicators by introducing the derivation of the expression for the evaluation of the domain overlap matrix elements from the projected-augmented wave method. The corresponding program module was developed, which is capable to perform the real space chemical bonding analysis with a number of methods, like electron localizability indicators, electron localization function, localization/delocalization indices and domain averaged Fermi hole orbitals. The efficiency and the accuracy of the developed implementation is demonstrated by the comparison with the domain overlap matrix elements evaluation from the full-potential linearized augmented plane wave method on a set of simple compounds with three atoms per primitive cell at most. A set of complex periodic structures is analyzed and the capability of the present implementation to unravel intricate chemical bonding patterns is demonstrated.

Modern solid state chemistry is inconceivable without theoretical treatment of solids thanks to the availability of efficient and accurate computational methods. Being developed mainly by physicist's community and deeply rooted in the formalism of reciprocal space, they often lack connections to familiar chemical concepts, indispensable for the chemical understanding of matter. Quantum chemical topology approach is a powerful theory able to efficiently recover chemical entities from the abstract description of a system given by its density matrices. It can be used to partition any many-electron system into the atoms, using the topology of electron density or for instance into atomic shells, using the topology of ELI-D field. Various characteristics of interactions between these chemical building blocks can be obtained applying bonding indicators, e.g. from the analysis of domain-averaged properties. Quantum chemical topology methods have been extended in the current work for the applications on the diversity of theoretical methods widely used for the description of solids nowadays – from the mean field Kohn-Sham density functional theory to the reduced one-electron density matrices functional theory or from the scalar-relativistic methods to the many-component formalisms employing spinor wavefunctions. It has been shown, that they provide chemically meaningful description of the bonding which is universally applicable to any class of extended systems, be it ionic insulator, covalent solid or metal. It has been shown, that the relativistic effects on the chemical bonding can be easily revealed using extensions of bonding indicators developed in the current work. Classical chemical concepts like Zintl-Klemm concept can be easily recovered with these descriptions. Intimate connection between the class of the material and the degree of chemical bonding delocalization has been also established. All these methods have been successfully applied to the various classes of solids and delivered novel insights on their crystal structure, properties, solid state transitions and reactivity.

Quantum mechanics became a foundation for incessant development of versatile computational methods for analysis of chemical and physical properties of molecules and crystals. A huge progress has been made in the fifield of density functional theory, since nowadays this theory offers the best compromise between precision of results and efficiency fiof computation. The chemical bonding analysis can be easily performed with real space methods based on chemical concepts introduced via partitioning of real space into chemically meaningful domains, since the orbital based approach is not well applicable due to the delocalized nature of plane waves. However the practical usage of those methods often requires a signifificant amount of computational resources. Some methods require the evaluation of so called domain overlap matrices, that is a formidable task for complex and low-symmetry systems. In the present research the author enables the investigation of complex solid compounds with real space chemical bonding indicators by introducing the derivation of the expression for the evaluation of the domain overlap matrix elements from the projected-augmented wave method. The corresponding program module was developed, which is capable to perform the real space chemical bonding analysis with a number of methods, like electron localizability indicators, electron localization function, localization/delocalization indices and domain averaged Fermi hole orbitals. The efficiency and the accuracy of the developed implementation is demonstrated by the comparison with the domain overlap matrix elements evaluation from the full-potential linearized augmented plane wave method on a set of simple compounds with three atoms per primitive cell at most. A set of complex periodic structures is analyzed and the capability of the present implementation to unravel intricate chemical bonding patterns is demonstrated.

This work is dedicated to the investigation on intermetallic compounds of beryllium and magnesium with late transition metals. By conducting fundamental research, the objective is to unveil novel intermetallic compounds possessing distinctive chemical bonding and interesting physical properties, with the aim to identify potential semiconductor materials for further thermoelectric applications. Following the recent discovery of the semiconducting properties of Be5Pt, it was initially hypothesised that replacing Be with Mg, while preserving the semiconducting properties, could enhance the widespread applicability of said material considering the lower toxicity of magnesium compared to that of beryllium. The study of the already well-investigated Mg–Pt system, revealed that a phase with composition Mg5Pt does not exist, instead two new phases, Mg3Pt2 and Mg29-xPt4+y (x = 0.47, y = 0.07), were discovered. Mg3Pt2 can be synthesised by direct reaction of its constituent elements or through spark plasma sintering (SPS) using MgH2 and PtCl2 as precursors. An in-depth analysis of the chemical bonding in Mg3Pt2 allowed to conclude that belonging to the same structural prototype (Eu3Ga2) does not necessarily indicate the same chemical bonding scenario. The isolation of single crystals for diffraction experiments combined with atomic-resolution transmission electron microscopy (TEM), enabled the determination and examination of the crystal structure of Mg29-xPt4+y, the existence of which had previously only been hinted on the basis of powder diffraction or metallography analysis. The investigation of the chemical bonding in Mg29-xPt4+y revealed a unique characteristic, that distinguishes it from other complex intermetallic compounds (CMAs). Notably, a spatial separation of regions with different bonding features was observed, explaining a distinctive mixed Mg/Pt site occupancy near the origin of the unit cell. Beryllium has garnered considerable interest due to its versatile behaviour when combined with other elements. These combinations can give rise to materials exhibiting distinctive physical properties and intriguing chemical bonding characteristics. However, the high toxicity associated with beryllium and its compounds as well as difficulties in characterisation, e.g. very low X-ray scattering power, has limited systematic investigations of Be–based intermetallic compounds. This comprehensive study focuses on the binary Be–Ru system. The redetermination of the Be3Ru crystal structure, showed that it crystallises with TiCu3–type structure. The crystal structure can be derived by ‘colouring’ the hexagonal closest packing of spheres characteristic for large groups of intermetallic compounds. Be3Ru exhibits diamagnetic properties, and its metallic electrical resistivity is in good agreement both with electronic structure calculations and experimental measurements. Be2Ru crystallises with Fe2P–type structure, instead of the previously reported MgZn2–type one. Detailed investigations using single crystal X-ray diffraction experiments together with atomic-resolution electron microscopy have revealed the presence of minor orthorhombic inclusions dispersed within the hexagonal Fe2P–type matrix crystal structure. Despite these structural variations, both atomic arrangements primarily consist of similar structural layers and exhibit comparable chemical bonding characteristics. It has been also discovered that Be3Ru2 crystallises with U3Si2–type structure, in contrast to the previously reported (Mn0.5Fe0.5)2O3–type structure. Be7Ru4 and Be12Ru7 represent two new phases in the Be–Ru system. They possess a very close atomic composition (63.6 at. % Be and 63.2 at. % Be, respectively) and are situated between Be2Ru and Be3Ru2 in the Be–Ru phase diagram. Together with Be2Ru, these two new phases form a series of two-dimensional intergrowth structures, incorporating building blocks of Be2Ru and Be3Ru2 (Fe2P– and U3Si2– type structure). The first one is comprised of hexagonal channels of Ru atoms accompanied by embedded columns of [Be@Be6] trigonal prisms, while the second structure consists of columns composed of tetragonal [Be@Ru8] and trigonal [Be@Ru6] prisms. The structural organisation observed in Be7Ru4 and Be12Ru7 has not been documented previously, indicating that these two phases represent novel structural prototypes. A careful investigation of the crystal structure of Be17Ru3, revealed that the center of a cage [X@Be12] around at the origin of the unit cell, is not completely empty, but rather partly occupied by either Be or Ru. Furthermore, it was observed that this cage can be filled by rare earth and actinide elements giving rise to a novel family of ternary compounds with composition RBe68Ru12 (R = U, Th, Ce, Pr, Gd, Ho). Finally, two new Be–based Laves phases C15–Be2Fe1-xRux (x = 0.52) and C14–Be2Fe1-xOsx (x= 0.57) were discovered through alloying Ru and Os to C14–Be2Fe Laves phase. This study confirmed that the stability of C15 or C14 AB2 Laves phases cannot be predicted by simple reasoning such as atomic size ratio between the A and B atoms, difference in electronegativity or valence electron concentration (VEC), particularly when all three elements, Fe, Ru and Os, belong to the same group of the periodic table. Despite their different chemical behaviour, the investigation of chemical bonding using quantum chemical techniques in the Be– and Mg–based intermetallic compounds with late transition metals, unveiled shared characteristics whereby their crystal structures are stabilised by the formation of polar multiatomic bonds. The observed charge transfer not only serves a decisive role in stabilising the atomic configurations, but also contributes to the emergence of distinct structuring of the calculated electronic density of states of states, DOS, i.e. appearance of more or less prominent dips in the vicinity of the Fermi level, implying their proximity to a semiconducting state, in particular as far as Be–based intermetallic compounds are concerned.