Pomocou COHP analýzy sme študovali chemickú väzbu v diboridoch prechodných kovov ako aj v zliatine Ni2MnGa. Elektrónová štruktúra študovaných materiálov bola vypočítaná použitím výpočtov z prvých princípov pomocou metódy PAW. V prípade diboridov tranzitných kovov z výsledkov vyplýva, že sila väzby bór-bór je silne závislá od transferu elektrónov na atómy bóru. Zvyšujúci sa počet valenčných elektrónov v kove spôsobuje destabilizáciu alfa štruktúry kvôli vzájomnej interakcii elektrónov prislúchajúcich jednému atómu (on-site interakcie) v blízkosti Fermiho hladiny. Pre zliatinu s tvarovou pamäťou Ni2MnGa bola použitá metóda DFT+ U upravujúca popis lokalizácie elektrónov. V prípade použitia parametra U na Ni dochádza k destabilizácii kubického austenitu a k stabilizácii tetragonálneho nemodulovaného martenzitu. Naopak, zvýšenie lokalizácie elektrónov mangánu martenzit destabilizuje. Analýza väzieb ukázala, že najsilnejšou väzbou je Ni-Ga s kovalentným charakterom. Zvýšená lokalizácia valenčných elektrónov Mn zvyšuje podiel kovalentnosti Mn-Ni väzby a kovový charakter Ni-Ni väzby. Vplyvom zvýšenej lokalizácie Ni elektrónov sa Mn-Ni väzba stáva viac kovovou.

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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 chemical calculations at the gradient-corrected (BP86) density-functional calculations with various basis sets (SVP, TZVPP) have been carried out for Mo(CO)4 complexes of Nheterocyclic carbene and analogues-NHEMe (called tetrylenes) with E = C, Si, Ge, Sn, Pb. The equilibrium structures of complexes [Mo(CO)4-NHEMe] (Mo4-NHEMe) exhibit an interesting trend which the lightest adduct Mo4-NHCMe has a trigonal bipyramidal coordination mode where the ligand NHCMe occupies an equatorial position. In contrast, the heavier species from Mo4-NHSiMe to Mo4-NHPbMe possess a square pyramidal structure where the ligands from NHSiMe to NHPbMe occupy a basal position. The slighter complexes Mo4-NHEMe possess end-on-bonded NHEMe ligands when E = C, Si, Ge with the bending angles, α, are 180° whereas the heavier adducts Mo4-NHSnMe and Mo4-NHPbMe exhibit strongly side-on-bonded ligands which the bending angle, α become more acute. The trend of the bond dissociations energies-De [kcal/mol] (BDEs) for the Mo-E bonds is Mo4-NHCMe > Mo4-NHSiMe > Mo4-NHGeMe > Mo4-NHSnMe > Mo4-NHPbMe. Bonding analysis shows that the Mo-E bonds have a significant contribution from (CO)4Mo ← NHEMe π-donation. This is because the energy levels of the π-type donor orbitals of Mo4-NHCMe − Mo4-NHPbMe are higher lying than the σ-type donor orbitals. The NHEMe ligands in Mo4- NHEMe are strong electron donors. This review intends to provide a comprehensive data for plant biology research in the future. / Tính toán hóa lượng tử sử dụng lý thuyết phiếm hàm mật độ kết hợp điều chỉnh gradient (BP86) từ các bộ hàm cơ sở khác nhau (SVP, TZVPP) được thực hiện cho việc tính toán lý thuyết của phức giữa Mo(CO)4 và phối tử N-heterocyclic carbene và các phức tương tự NHEMe (gọi là tetrylenes) với E = C, Si, Ge, Sn, Pb. Cấu trúc của phức [Mo(CO)4-NHEMe] (Mo4-NHEMe) thể hiện sự khác biệt khá thú vị từ Mo4-NHCMe đến Mo4-NHPbMe, phức Mo4-NHCMe có cấu trúc phối trí lưỡng tháp tam giác trong đó phối tử NHCMe chiếm ở vị trí xích đạo. Ngược lại, những phức có phân tử khối lớn hơn từ Mo4-NHSiMe đến Mo4-NHPbMe lại có cấu trúc tháp vuông và các phối tử từ NHSiMe đến NHPbMe chiếm vị trí cạnh (basal – cạnh hướng về bốn đỉnh của đáy vuông). Các cấu trúc của phức Mo4-NHEMe cho thấy các phối tử NHEMe với E = C-Ge tạo với phân tử Mo(CO)4 một góc thẳng α =180.0°, ngược lại, các phức nặng hơn Mo4-NHEMe thì phối tử NHEMe với E = Sn, Pb liên kết với phân tử Mo(CO)4 tạo góc cong và góc cong, α, càng trở nên nhọn hơn khi nguyên tử khối của E càng lớn. Năng lượng phân ly liên kết của liên kết Mo- E giảm dần: Mo4-NHCMe > Mo4-NHSiMe > Mo4-NHGeMe > Mo4-NHSnMe > Mo4-NHPbMe. Phân tích liên kết Mo-E cho thấy có sự đóng góp đáng kể của sự cho liên kết π (CO)4Mo ← NHEMe. Điều này có thể do mức năng lượng của orbital π-cho của Mo4-NHCMe − Mo4-NHPbMe nằm cao hơn orbital σ-cho. Từ kết quả tính toán có thể kết luận rằng phối tử NHEMe trong phức Mo4- NHEMe là chất cho điện tử mạnh. Kết quả nghiên cứu lý thuyết về hệ phức Mo4-NHEMe lần đầu tiên cung cấp một cơ sở dữ liệu hoàn chỉnh cho các nghiên cứu về sinh học thực vật trong tương lai.

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.

Quantum chemical calculations at the gradient-corrected (BP86) density-functional calculations with various basis sets (SVP, TZVPP) have been carried out for Mo(CO)4 complexes of Nheterocyclic carbene and analogues-NHEMe (called tetrylenes) with E = C, Si, Ge, Sn, Pb. The equilibrium structures of complexes [Mo(CO)4-NHEMe] (Mo4-NHEMe) exhibit an interesting trend which the lightest adduct Mo4-NHCMe has a trigonal bipyramidal coordination mode where the ligand NHCMe occupies an equatorial position. In contrast, the heavier species from Mo4-NHSiMe to Mo4-NHPbMe possess a square pyramidal structure where the ligands from NHSiMe to NHPbMe occupy a basal position. The slighter complexes Mo4-NHEMe possess end-on-bonded NHEMe ligands when E = C, Si, Ge with the bending angles, α, are 180° whereas the heavier adducts Mo4-NHSnMe and Mo4-NHPbMe exhibit strongly side-on-bonded ligands which the bending angle, α become more acute. The trend of the bond dissociations energies-De [kcal/mol] (BDEs) for the Mo-E bonds is Mo4-NHCMe > Mo4-NHSiMe > Mo4-NHGeMe > Mo4-NHSnMe > Mo4-NHPbMe. Bonding analysis shows that the Mo-E bonds have a significant contribution from (CO)4Mo ← NHEMe π-donation. This is because the energy levels of the π-type donor orbitals of Mo4-NHCMe − Mo4-NHPbMe are higher lying than the σ-type donor orbitals. The NHEMe ligands in Mo4- NHEMe are strong electron donors. This review intends to provide a comprehensive data for plant biology research in the future. / Tính toán hóa lượng tử sử dụng lý thuyết phiếm hàm mật độ kết hợp điều chỉnh gradient (BP86) từ các bộ hàm cơ sở khác nhau (SVP, TZVPP) được thực hiện cho việc tính toán lý thuyết của phức giữa Mo(CO)4 và phối tử N-heterocyclic carbene và các phức tương tự NHEMe (gọi là tetrylenes) với E = C, Si, Ge, Sn, Pb. Cấu trúc của phức [Mo(CO)4-NHEMe] (Mo4-NHEMe) thể hiện sự khác biệt khá thú vị từ Mo4-NHCMe đến Mo4-NHPbMe, phức Mo4-NHCMe có cấu trúc phối trí lưỡng tháp tam giác trong đó phối tử NHCMe chiếm ở vị trí xích đạo. Ngược lại, những phức có phân tử khối lớn hơn từ Mo4-NHSiMe đến Mo4-NHPbMe lại có cấu trúc tháp vuông và các phối tử từ NHSiMe đến NHPbMe chiếm vị trí cạnh (basal – cạnh hướng về bốn đỉnh của đáy vuông). Các cấu trúc của phức Mo4-NHEMe cho thấy các phối tử NHEMe với E = C-Ge tạo với phân tử Mo(CO)4 một góc thẳng α =180.0°, ngược lại, các phức nặng hơn Mo4-NHEMe thì phối tử NHEMe với E = Sn, Pb liên kết với phân tử Mo(CO)4 tạo góc cong và góc cong, α, càng trở nên nhọn hơn khi nguyên tử khối của E càng lớn. Năng lượng phân ly liên kết của liên kết Mo- E giảm dần: Mo4-NHCMe > Mo4-NHSiMe > Mo4-NHGeMe > Mo4-NHSnMe > Mo4-NHPbMe. Phân tích liên kết Mo-E cho thấy có sự đóng góp đáng kể của sự cho liên kết π (CO)4Mo ← NHEMe. Điều này có thể do mức năng lượng của orbital π-cho của Mo4-NHCMe − Mo4-NHPbMe nằm cao hơn orbital σ-cho. Từ kết quả tính toán có thể kết luận rằng phối tử NHEMe trong phức Mo4- NHEMe là chất cho điện tử mạnh. Kết quả nghiên cứu lý thuyết về hệ phức Mo4-NHEMe lần đầu tiên cung cấp một cơ sở dữ liệu hoàn chỉnh cho các nghiên cứu về sinh học thực vật trong tương lai.