Die zuverlässige Berechnung der elektrischen Leitfähigkeit vieler Materialien aus ersten Prinzipien erfordert die Berücksichtigung der anharmonischen Gitterdynamik. Der ab initio Kubo-Greenwood (KG)-Ansatz, der die KG-Leitfähigkeitsformel und die ab initio-Molekulardynamik kombiniert, scheint vielversprechend zu sein, da er die Anharmonizität des Gitters auf natürliche Weise berücksichtigt. Seine Anwendung auf kristalline Materialien hat jedoch bisher nur wenig Beachtung gefunden. Diese Arbeit beschreibt den KG-Ansatz und stellt eine numerische Implementierung dieses Ansatzes für den harmonischen Kristall Si und den anharmonischen Kristall SnSe vor. Die Fallstudie für Si zeigt erhebliche numerische Schwierigkeiten bei den KG-Berechnungen auf. Insbesondere behindert die erforderliche dichte k-Punkt-Abtastung die Konvergenz in Superzellengröße und macht die Berechnungen nur innerhalb der (semi-)lokalen Dichtefunktionaltheorie (DFT) durchführbar. Außerdem führt die notwendige Einführung eines Verbreiterungsparameters (η) zu einer erheblichen Unsicherheit bei der Bestimmung der Leitfähigkeit. Um diese Probleme zu lösen, werden rechnerisch effiziente Strategien diskutiert, darunter: (i) der "Scherenoperator"-Ansatz zur Korrektur des DFT-Bandlückenproblems; (ii) das "Optimal-η-Schema" zur Wahl eines geeigneten Wertes von η; und (iii) die Finite-Size-Scaling-Methode zur Ableitung der Leitfähigkeit in der thermodynamischen Grenze. Es wird festgestellt, dass die KG-Berechnungen mit diesen Strategien Leitfähigkeiten in angemessener Übereinstimmung mit den Experimenten ergeben. Der Vergleich mit früheren ab initio Boltzmann-Transportberechnungen zeigt jedoch, dass das η-Problem und die Frage der Konvergenz in Superzellengröße weiter verbesserte Konzepte erfordern. Die Fallstudie für SnSe zeigt sehr ähnliche numerische Schwierigkeiten wie im Fall von Si. Es werden Einblicke in die Auswirkung der Anharmonizität auf die Konvergenz der Superzellengröße gegeben. / Reliable first-principles calculation of the electrical conductivity in many materials requires accounting for the anharmonic lattice dynamics. The ab initio Kubo-Greenwood (KG) approach, which combines the KG conductivity formula and ab initio molecular dynamics, appears to be promising because it naturally includes lattice anharmonicity. However, its application to crystalline materials has so far received very little attention. This thesis describes the KG approach and presents a numerical implementation of this approach for the harmonic crystal Si and the anharmonic crystal SnSe. The case study for Si identifies considerable numerical difficulties in the KG calculations. In particular, the dense k-point sampling required hinders supercell-size convergence and makes the calculations only feasible within (semi)local density-functional theory (DFT). Besides, the necessary introduction of a broadening parameter (η) introduces a significant uncertainty in determining the conductivity. To address these issues, computationally efficient strategies are discussed, including: (i) the "scissor operator" approach to correct the DFT band-gap problem; (ii) the "optimal-η scheme" to choose an appropriate value of η; and (iii) the finite-size scaling method to deduce the conductivity in the thermodynamic limit. It is found that with these strategies, the KG calculations yield conductivities in reasonable agreement with experiment. Yet, comparison with previous ab initio Boltzmann transport calculations shows that the η problem and the issue of supercell-size convergence still require improved concepts. The case study for SnSe shows very similar numerical difficulties as in the case of Si. Insights into the effect of anharmonicity on the supercell-size convergence are provided.

The catalytic oxidation activity of platinum particles in automobile catalysts is thought to originate from the presence of highly reactive superficial oxide phases which form under oxygen-rich reaction conditions. The thermodynamic stability of platinum oxide surfaces and thin films was studied, as well as their reactivities towards oxidation of carbon compounds by means of first-principles atomistic thermodynamics calculations and molecular dynamics simulations based on density functional theory. On the Pt(111) surface the most stable superficial oxide phase is found to be a thin layer of alpha-PtO2, which appears not to be reactive towards either methane dissociation or carbon monoxide oxidation. A PtO-like structure is most stable on the Pt(100) surface at oxygen coverages of one monolayer, while the formation of a coherent and stress-free Pt3O4 film is favoured at higher coverages. Bulk Pt3O4 is found to be thermodynamically stable in a region around 900 K at atmospheric pressure. The computed net driving force for the dissociation of methane on the Pt3O4(100) surface is much larger than on all other metallic and oxide surfaces investigated. Moreover, the enthalpy barrier for the adsorption of CO molecules on oxygen atoms of this surface is as low as 0.34 eV, and desorption of CO2 is observed to occur without any appreciable energy barrier in molecular dynamics simulations. These results, combined, indicate a high catalytic oxidation activity of Pt3O4 phases that can be relevant in the contexts of Pt-based automobile catalysts and gas sensors.

The catalytic oxidation activity of platinum particles in automobile catalysts is thought to originate from the presence of highly reactive superficial oxide phases which form under oxygen-rich reaction conditions. The thermodynamic stability of platinum oxide surfaces and thin films was studied, as well as their reactivities towards oxidation of carbon compounds by means of first-principles atomistic thermodynamics calculations and molecular dynamics simulations based on density functional theory. On the Pt(111) surface the most stable superficial oxide phase is found to be a thin layer of alpha-PtO2, which appears not to be reactive towards either methane dissociation or carbon monoxide oxidation. A PtO-like structure is most stable on the Pt(100) surface at oxygen coverages of one monolayer, while the formation of a coherent and stress-free Pt3O4 film is favoured at higher coverages. Bulk Pt3O4 is found to be thermodynamically stable in a region around 900 K at atmospheric pressure. The computed net driving force for the dissociation of methane on the Pt3O4(100) surface is much larger than on all other metallic and oxide surfaces investigated. Moreover, the enthalpy barrier for the adsorption of CO molecules on oxygen atoms of this surface is as low as 0.34 eV, and desorption of CO2 is observed to occur without any appreciable energy barrier in molecular dynamics simulations. These results, combined, indicate a high catalytic oxidation activity of Pt3O4 phases that can be relevant in the contexts of Pt-based automobile catalysts and gas sensors.