In dieser Dissertation diskutiere ich theoretische Methoden zur Simulation von Grenzflächen zwischen Metallen und Molekülen auf atomarer Maßstabsebene, die für die Speicherung und Erzeugung "sauberer" Energie von Bedeutung sind, und wende sie an. Wir verwenden die Dichtefunktionaltheorie für das elektronische Subsystem und verschiedene Methoden wie die (quasi-)harmonische Näherung und die Pfadintegral-Molekulardynamik, um die Quanteneigenschaften des nuklearen Subsystems zu berücksichtigen. Wir berechnen den Isotopeneffekt auf die Arbeitsfunktion von Cyclohexan, das an der Rh(111)-Oberfläche adsorbiert wird, ein Effekt, der sich aus der Elektron-Phonon-Kopplung nur dann ergibt, wenn die nuklearen Freiheitsgrade quantenmechanisch behandelt werden. Deuteriertes Cyclohexan C6D12 hat einen größeren Adsorptionsabstand als gewöhnliches Cyclohexan. Pfadintegral-Molekulardynamiksimulationen zeigen auch eine temperaturabhängige Renormierung der elektronischen Zustandsdichte in diesem System. Schließlich befassen wir uns mit Oberflächenreaktionen auf einer geladenen metallischen Oberfläche. Wir stellen unsere Implementierung der Nudged-Elastic-Band-Methode (NEB) im i-PI-Paket vor und diskutieren ihre Leistungsfähigkeit. Anschließend setzen wir die Methode ein, um die Energiebarriere der Wasserspaltungsreaktion auf einer Pd(111)-Oberfläche zu berechnen, die einem elektrischen Feld unterschiedlicher Intensität ausgesetzt ist. Wir zeigen, dass die niedrigste Dissoziationsbarriere auftritt, wenn das Feld eine Stärke erreicht, die eine geometrische Frustration des auf der Oberfläche adsorbierten Wassermoleküls hervorruft, und dass die Nullpunktenergiebeiträge zur Barriere dieser Reaktion über den weiten Bereich der auf das System angelegten elektrischen Feldstärken nahezu konstant bleiben. Wir erklären dies durch eine gegenseitige Aufhebung der Rot- und Blauverschiebungen einzelner Schwingungsmoden zwischen Reaktant und Übergangszustand. / In this thesis, I discuss and apply theoretical methods for simulating interfaces between metals and molecules of relevance to "clean" energy storage and production on an atomistic scale. We use density-functional theory for the electronic subsystem and various methods such as (quasi-)harmonic approximation and path integral molecular dynamics to account for quantum properties of the nuclear subsystem, determining which methods are sufficient to grasp the essential phenomena while remaining computationally affordable. We calculate isotope effect on the work function of cyclohexane adsorbed on Rh(111) surface, an effect that emerges from electron-phonon coupling only when the nuclear degrees of freedom are treated quantum-mechanically. Deuterated cyclohexane C6D12 has larger adsorption distance than ordinary cyclohexane. Path integral molecular dynamics simulations also show a temperature-dependent renormalization of the electronic density of states in this system, induced by both thermal and quantum fluctuations of nuclei. Finally, we address surface reactions on a charged metallic surface. We present our implementation of the nudged elastic band (NEB) method in i-PI package and discuss its performance. We then employ the method to calculate the energy barrier of water splitting reaction on a Pd(111) surface subjected to electric fields of different strengths. We show that the lowest dissociation barrier takes place when the field reaches a strength that induces a geometric frustration of the water molecule adsorbed on the surface, and that the zero-point energy contributions to the barrier of this reaction remain nearly constant across the wide range of electric field strengths applied to the system. We explain this by a mutual cancellation of the red and blue shifts of individual vibrational modes between reactant and transition states.

In dieser Doktorarbeit untersuchen wir den Einfluss von Elektron-Phonon-Wechselwirkungen (EPW) auf die Bandlueckenrenormierung in kristallinen Festkoerpern bei endlichen Temperaturen. Das Hauptziel besteht darin, den Einfluss der Kernbewegung und der thermischen Ausdehnung des Gitters auf die Bandstruktur in einer Vielzahl von Materialien zu quantifizieren. Zu diesem Zweck wird der Temperatureinfluss auf das EPW in harmonischen Naeherungen unter Verwendung der stochastischen Abtastmethode und vollstaendig anharmonisch durch Durchführung von ab initio Molekulardynamiksimulationen (aiMD). Die Bandluecke bei endlichen Temperaturen wird aus der thermodynamisch gemittelten Spektralfunktion extrahiert, die unter Verwendung der Bandentfaltungstechnik berechnet wird. Waehrend die Verwendung von aiMD bereits fuer Berechnungen von EPW verwendet wurde, wurde die Kombination von aiMD und Bandentfaltung zur Behandlung der Bandluecken renormalisierung erst kuerzlich verwendet. In dieser Doktorarbeit haben wir eine verbesserte Bandentfaltungstechnik verwendet, um die Berechnung effektiv zu verwalten. Diese verbesserte Methode enthaelt mehrere methodische Neuerungen, die dazu dienen, den Rechenaufwand zu verringern und das statistische Rauschen in den Endergebnissen zu minimieren. Die aktualisierte Methode wurde gruendlich bewertet, dokumentiert und mit einer benutzerfreundlichen Oberflaeche gestaltet. Wir praesentieren eine umfassende Untersuchung der numerischen Aspekte der thermodynamischen Mittelung, der Schaetzung von Fehlerbalken und der Bewertung der Konvergenz in Bezug auf die Groesse der Simulationssuperzelle. Unser etabliertes Protokoll ermoeglicht die Berechnung der Bandlückenrenormierung bei endlichen Temperaturen, was in guter Uebereinstimmung mit frueheren theoretischen Studien und experimentellen Daten steht. / In this thesis, we investigate the influence of electron-phonon interactions (EPI) on the band gap renormalization in crystalline solids at finite temperatures. The main goal is to identify the impact of the nuclear motion and the lattice thermal expansion on the band structure in a wide range of materials. For this purpose, the temperature influence on the EPI is calculated in the harmonic approximations by utilizing the stochastic sampling methodology and fully anharmonically, by performing ab initio molecular dynamics simulations (aiMD). The band gap at finite temperatures is extracted from the thermodynamically averaged spectral function, which is calculated using band-unfolding technique. While utilization of aiMD was already used for calculations of EPI the combination of aiMD and band-unfolding to treat the band gap renormalization was used only recently. In this thesis, we employed an improved band unfolding technique in order to effectively manage the calculations. This improved method incorporates several methodological innovations that serve to mitigate computational cost and minimize statistical noise in the final results. The updated method was thoroughly benchmarked, documented, and designed with a user-friendly interface. We present a comprehensive examination of the numerical aspects of thermodynamic averaging, the estimation of error bars, and the evaluation of convergence with respect to the size of the simulation supercell. Our established protocol enables the calculation of band gap renormalization at finite temperatures, which is in good agreement with prior theoretical studies and experimental data.

Die vorliegende Habilitationsschrift bespricht aktuelle Ergebnisse zur Struktur und Reaktivität von Übergangsmetalloxidoberflächen. Es werden eingangs Grundlagen zur Berechnung von Eigenschaften von Oberflächen mittels Dichtefunktionaltheorie vorgestellt. Des Weiteren werden anhand von drei untersuchten Oxiden, nämlich dem Vanadium(III)-oxid, dem Cer(IV)-oxid, und dem Eisen(II,III)-oxid, der aktuelle Forschungsstand im Hinblick auf Oberflächenstruktur und Reaktivität von Phasengrenzen, wie z.B. der Phasengrenze zwischen Vanadium(V)-oxid und Cer(IV)-oxid und der Phasengrenze zwischen Wasser und Eisen(II,III)-oxid dargelegt. / The present habilitation thesis discusses results on structure and reactivity of transition metal oxide surfaces obtained using state-of-the-art density functional theory methods. First, fundamental issues of density functional theory are presented. Furthermore, the current state in research with respect to surface structure on one hand and reactivities of interfaces between different oxides like vanadium(III) and cerium(IV) oxide or water and iron(II,III) oxide on the other hand are developed.

The bifunctional formalism presents an alternative how to obtain the functional value from its functional derivative by exploiting homogeneous density scaling. In the bifunctional formalism the density dependence of the functional derivative is suppressed. Consequently, those derivatives have to be treated as formal functional derivatives. For a pointwise correspondence between the true and the formal functional derivative, the bifunctional expression yields the same value as the density functional. Within the bifunctional formalismthe functional value can directly be obtained fromits derivative (while the functional itself remains unknown). Since functional derivatives are up to a constant uniquely defined, this approach allows for a pointwise comparison between approximate potentials and reference potentials. This aspect is especially important in the field of orbital-free density functional theory, where the burden is to approximate the kinetic energy. Since in the bifunctional approach the potential is approximated directly, full control is given over the latter, and consequently over the final electron densities obtained from variational procedure. Besides the bifunctional formalismitself another concept is introduced, dividing the total non-interacting kinetic energy into a known functional part and a remainder, called Pauli kinetic energy. Only the remainder requires further approximations. For practical purposes sufficiently accurate Pauli potentials for application on atoms, molecular and solid-state systems are presented.

Chemische Reaktionen in der Natur sowie Prozesse in synthetischen Materialien werden oft erst durch die Wechselwirkung von Licht mit Materie ausgelöst. Üblicherweise werden diese komplexen Prozesse mit Hilfe von Näherungen beschrieben. Im ersten Teil der Arbeit wird die Gültigkeit der Born-Oppenheimer Näherung in einem vibronischen Modellsystem (Trans-Polyacetylene) unter Photoelektronenspektroskopie im Gleichgewicht sowie zeitaufgelöster Photoelektronenspektroskopie im Nichtgleichgewicht überprüft. Die vibronische Spektralfunktion zeigt aufgrund des faktorisierten Anfangs- und Endzustandes in der Born-Oppenheimer Näherung zusätzliche Peaks, die in der exakten Spektralfunktion nicht auftreten. Im Nichtgleichgewicht zeigen wir für eine Franck-Condon Anregung und eine Anregung mit Pump-Probe Puls, wie die Bewegung des vibronischen Wellenpaktes im zeitabhängigen Photoelektronenspektrum verfolgt werden kann. Im zweiten Teil der Arbeit werden sowohl die Materie als auch das Licht quantisiert behandelt. Für eine volle quantenmechanische Beschreibung des Elektron-Licht Systems, verwenden wir die kürzlich entwickelte quantenelektrodynamische Dichtefunktionaltheorie (QEDFT) für gekoppelte Elektron-Photon Systeme. Wir zeigen erste numerische QEDFT-Berechnungen voll quantisierter Atome und Moleküle in optischen Kavitäten, die an das quantisierte elektromagnetische Feld gekoppelt sind. Mit Hilfe von Fixpunktiterationen berechnen wir das exakte Kohn-Sham Potential im diskreten Ortsraum, wobei unser Hauptaugenmerk auf dem Austausch-Korrelations-Potential liegt. Wir zeigen die erste Näherung des Austausch-Korrelations-Potentials mit Hilfe eines optimierten effektiven Potential Ansatzes angewandt auf einen Jaynes-Cummings-Dimer. Die dieser Arbeit zugrunde liegenden Erkenntnisse und Näherungen ermöglichen es neuartige Phänomene an der Schnittstelle zwischen den Materialwissenschaften und der Quantenoptik zu beschreiben. / Many natural and synthetic processes are triggered by the interaction of light and matter. All these complex processes are routinely explained by employing various approximations. In the first part of this work, we assess the validity of the Born-Oppenheimer approximation in the case of equilibrium and time-resolved nonequilibrium photoelectron spectra for a vibronic model system of Trans-Polyacetylene. We show that spurious peaks appear for the vibronic spectral function in the Born-Oppenheimer approximation, which are not present in the exact spectral function of the system. This effect can be traced back to the factorized nature of the Born-Oppenheimer initial and final photoemission states. In the nonequilibrium case, we illustrate for an initial Franck-Condon excitation and an explicit pump-pulse excitation how the vibronic wave packet motion can be traced in the time-resolved photoelectron spectra as function of the pump-probe delay. In the second part of this work, we aim at treating both, matter and light, on an equal quantized footing. We apply the recently developed quantum electrodynamical density-functional theory, (QEDFT), which allows to describe electron-photon systems fully quantum mechanically. We present the first numerical calculations in the framework of QEDFT. We focus on the electron-photon exchange-correlation contribution by calculating exact Kohn-Sham potentials in real space using fixed-point inversions and present the performance of the first approximate exchange-correlation potential based on an optimized effective potential approach for a Jaynes-Cummings-Hubbard dimer. This work opens new research lines at the interface between materials science and quantum optics.

In this thesis, a series of computational studies based on density functional theory (DFT) and density functional tight-binding (DFTB) is presented to deeply understand experimental results on the synthesis of endohedral fullerenes and graphene/iron hybrids at atomic level. In the first part, a simple and efficient model is proposed to evaluate the strain experienced by clusters encapsulated in endohedral metallofullerenes (EMFs). Calculations for the sole cluster, either in the neutral or the charged state, cannot be used for this goal. However, when the effect of the carbon cage is mimicked by small organic π-systems (such as pentalene and sumanene), the cluster has sufficient freedom to adopt the optimal configuration, and therefore the energetic characteristics of the EMF-induced distortion of the cluster can be evaluated. Both nitride and sulfide clusters were found to be rather flexible. Hence, they can be encapsulated in carbon cages of different size and shape. For carbide M2C2 cluster the situation is more complex. The optimized cluster can adopt either butterfly or linear shapes, and these configurations have substantially different metal-metal distance. Whereas for Sc2C2 both structures are isoenergetic, linear form of the Y2C2 cluster is substantially less stable than the butterfly-shaped configuration. These results show that phenomenon of the “nanoscale fullerene compression” once proposed by Zhang et al. (J. AM. CHEM. SOC. (2012),134(20)) should be “nanoscale fullerene stretching”. Finally, the results also reveal that both Ti2S and Ti2C2 cluster are strained in corresponding EMF molecules, but the origin of the strain is opposite: C78-D3h(5) cage imposes too long Ti···Ti distance for the sulfide cluster and too short distance for the carbide cluster. In the second part of the thesis, possible fullerene geometries and electronic structures have been explored theoretically for the species detected in mass spectra of the Sc-EMF extract synthesized using CH4 as a reactive gas. Two most promising candidates, namely Sc4C@C80-Ih(7) and Sc4C3@C80-Ih(7), have been identified and further studied at the DFT level. For Sc4C@C80, the tetrahedral Sc4 cluster with the central μ4-C atom was found to be 10 kJ/mol more stable than the square cluster. For Sc4C3@C80, the calculation showed that the most stable is the Sc4C3 cluster in which the triangular C3 moiety is η3- and η2-coordinated to Sc atoms. Whereas Sc4C@C80 has rather small HOMO-LUMO gap and low ionization potential, the HOMO-LUMO gap of Sc4C3@C80 is substantially higher and exceeds that of Sc4C2@C80. In the third part, computational studies of structures and reactivity are described for a new type of EMFs with a heptagon that has been produced in the arc-discharge synthesis. DFT computations predict that LaSc2N@Cs(hept)-C80 is more stable than LaSc2N@D5h-C80, so the former should be synthesized in much higher yield than observed. This disagreement may be ascribed to the kinetic factors rather than thermodynamic stability. Because of prospective applications of this EMFs by introducing functional groups, the influence of the heptagon on the chemical properties have been further evaluated. Thermodynamically and kinetically preferred reaction sites are studied computationally for Prato and Bingel-Hirsch cycloaddition reactions. In both types of reactions the heptagon is not affected, and chemical reactivity is determined by the adjacent pentalene units. Thermodynamically controlled Prato addition is predicted to proceed regioselectively across the pentagon/pentagon edges, whereas the most reactive sites in kinetically-controlled Bingel-Hirsch reaction are the carbon atoms next to the pentagon/pentagon edge. Fourth, although various EMFs have been successfully synthesized and characterized, the formation mechanism is still not known in details, and hence control of the synthesis products is rather poor. Therefore, EMF self-assembly process in Sc/carbon vapor in the presence and absence of cooling gas (helium) and reactive gas (NH3 and CH4) is systematically investigated using quantum chemical molecular dynamics (QM/MD) simulations based on the DFTB potentials. The cooling gas effect is that the presence of He atoms accelerates formation of pentagons and hexagons and reduces the size of formed carbon cages in comparison to the analogous He-free simulations. As a result, the Sc/C/He system yields a large number of successful trajectories (i.e. leading to the Sc-EMFs) with more realistic cage-size distribution than the Sc/C system. Encapsulation of Sc atoms within the carbon cage was found to proceed via two parallel mechanisms. The main mechanism involves nucleation of the several hexagons and pentagons with Sc atoms already at the early stages of the carbon vapor condensation. In such proto-cages, both Sc–C σ-bonds and coordination bonds between Sc atoms and the π-system of the carbon network are present. Sc atoms are thus rather labile and can move along the carbon network, but the overall bonding is sufficiently strong to prevent dissociation even at high temperatures. Further growth of the carbon cage results in encapsulation of one or two Sc atoms within the forming fullerene. Another encapsulation mechanism is observed in rare cases. In this process, the closed cage is formed with Sc being a part of the carbon network, i.e. being bonded by three or four Sc–C σ-bonds. However, such intermediates are found to be unstable, and transform into the endohedral fullerenes within few picoseconds of annealing. In perfect agreement with experimental studies, extension of the simulation to Fe and Ti showed that Fe-EMFs are not formed at all, whereas Ti is prone to form Ti-EMFs with small cage sizes, including Ti@C28-Td and Ti@C30-C2v(3). The role of “reactive gas” in the EMF synthesis is revealed in dedicated simulations of the fullerene formation in the presence of several molecules of CH4 or NH3. When concentration of reactive gas is high, carbon vapor tends to form graphene flakes or other carbon species terminated by hydrogen atoms, whereas the yield of empty fullerenes is very low. Conversely, with additional metal atoms (Sc) and the same number of NH3 molecules, the yield of fullerenes constantly increase from 5 to 65% which is ascribed to the catalytic activity of metal atoms in the nucleation of carbon cages already at early stage. Moreover, due to the presence of hydrogen atoms from the reactive gas, the carbon cage formation requires much longer time, which provides sufficient reaction time to encapsulate 3 or 4 Sc atoms within one cage. It explains preferential formation of clusterfullerenes in experiments with reactive gas. At the same time, monometallofullerenes and dimetallofullerenes are the main products in absence of reactive gas. We also provide possible growth mechanisms of carbide and cyano-clusterfullerenes in details to elucidate how the intracluster goes into the cage. A possible growth mechanism of nitride clusterfullerenes has been proposed based on DFT results. In the last part, a free-standing crystalline single-atom thick layer of Fe has been studied theoretically. By investigating the energy difference, ΔE, between a suspended Fe monolayer and a nanoparticle using the equivalent number of Fe atoms, one can estimate that the largest stable membrane should be ca. 12 atoms wide or 3 × 3 nm2 which is in excellent agreement with the experimental observation. Otherwise, the possibility of C, O, N atoms embedded into the Fe membrane can been fully excluded by DFTB and DFT simulations, which agrees with electron energy loss spectroscopy (EELS) measurement. A significantly enhanced magnetic moment for single atom thick Fe membranes (3.08 μB) is predicted by DFT as compared to the bulk BCC Fe (2.1 μB), which originates from the 2D nature of the Fe membrane since the dz2 orbital is out-of-plane while the dxy orbital is in-plane.

The electronic structure of the zero-gap two-dimensional graphene has a charge neutrality point exactly at the Fermi level that limits the practical application of this material. There are several ways to modify the Fermi-level-region of graphene, e.g. adsorption of graphene on different substrates or different molecules on its surface. In all cases the so-called dispersion or van der Waals interactions can play a crucial role in the mechanism, which describes the modification of electronic structure of graphene. The adsorption of water on graphene is not very accurately reproduced in the standard density functional theory (DFT) calculations and highly-accurate quantum-chemical treatments are required. A possibility to apply wavefunction-based methods to extended systems is the use of local correlation schemes. The adsorption energies obtained in the present work by means of CCSD(T) are much higher in magnitude than the values calculated with standard DFT functional although they agree that physisorption is observed. The obtained results are compared with the values available in the literature for binding of water on the graphene-like substrates. / Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG-geförderten) Allianz- bzw. Nationallizenz frei zugänglich.

Unter Verwendung von Dichtefunktionaltheorie werden die katalytischen Eigenschaften von Cerdioxidoberflächen mit verschiedenen Terminierungen untersucht. Cerdioxid wird auch als Trägermaterial in der heterogenen Katalyse eingesetzt, um Aktivität, Selektivität und Stabilität der aktiven Komponente zu erhöhen. In dieser Arbeit werden geträgerte Vanadiumoxidcluster diskutiert. Dabei wird die oxidative Dehydrierung von Methanol als Modellreaktion zur Aktivierung von C-H-Bindungen genutzt. Ceroxidpartikel werden oft in wässriger Lösung synthetisiert. Damit hängt die Form der Nanokristallite direkt von der relativen Stabilität der unterschiedlichen Terminierungen in der Gegenwart von Wasser ab. Außerdem ist Wasser an zahlreichen Reaktionen entweder als Produkt, Edukt oder Lösungsmittel beteiligt. Aus diesem Grund werden auch die Wasser-Oberflächenwechselwirkungen untersucht. Des Weiteren wird die Genauigkeit von drei verschiedenen Funktionalen (B3LYP, HSE und PBE+U) durch den Vergleich mit experimentellen Daten evaluiert. Diese beinhalten Barrieren, die mittels Temperatur-programmierter Desorptionsspektroskopie erhalten wurden, und Schwingungsspektren. / Density functional theory is applied to study the catalytic properties of ceria surfaces with different terminations. Ceria is also used as a support material in heterogeneous catalysis to improve activity, selectivity, and stability of the active component. In this work, supported vanadia clusters are discussed. The oxidative dehydrogenation of methanol is used as a model reaction for C–H bond activation. Ceria catalysts are often prepared in aqueous solution. As a result, the shape of ceria nanocrystallites depends on the relative stability of the different surface terminations in the presence of water. Furthermore, many reactions involve water either as a product, as a reagent, or as a solvent. Hence, water–surface interactions are studied as well. Furthermore, the accuracy of three different functionals (B3LYP, HSE, and PBE+U) is assessed by comparison to experimental data such as barriers obtained via temperature-programmed desorption and infrared spectra.

Die vorliegende Arbeit ist ein Beitrag auf dem Gebiet der theoretischen Chemie und beschäftigt sich mit der Entwicklung effizienter Berechnungsmethoden für die Elektronendichte und die Energie des Grundzustands molekularer und periodischer Systeme im Rahmen der Kohn-Sham-Dichtefunktionaltheorie (Kohn-Sham-DFT) und unter Verwendung von lokalen Basisfunktionen. Im Vordergrund steht dabei die einheitliche Beschreibung von Molekülen und ausgedehnten Systemen beliebiger Periodizität (zum Beispiel Volumenkristalle, dünne Filme und Polymere) mit einfachen Algorithmen bei einem hohen Maß an numerischer Genauigkeit und Recheneffizienz. Dafür hat der Verfasser bewährte molekulare Simulationsmethoden in neuartiger Form auf periodische Randbedingungen erweitert und zu einer vollständigen DFT-Methode vereint. Von diesen Methoden ist das völlig neue Konzept für die RI-Methode (resolution of identity, Zerlegung der Einheit), die auf den Coulomb-Term angewendet wird, die Schlüsseltechnologie in dieser Arbeit. Ein Merkmal der Methode ist, dass sie ausschließlich im direkten Raum arbeitet. Neben der RI-Methode wurden weitere methodische Ansätze entwickelt werden, um eine gute Speicher- und Zeiteffizienz der gesamten DFT-Methode zu gewährleisten. Dazu gehören die Komprimierung der speicherintensiven Dichte- und Kohn-Sham-Matrizes und die numerische Integration des Austausch-Korrelationsterms durch die Anwendung eines adaptiven, numerischen Integrationsschemas. Die vorgestellten Methoden werden zum Prototypen eines RI-DFT-Programms zusammengefügt. Dieses Programm ermöglicht die Berechnung von single point-Energien am Gamma-Punkt für Systeme mit abgeschlossenen Schalen. Anhand von Berechnungen werden die numerische Genauigkeit und Effizienz bewertet. Das Programm bildet die Basis für ein effizientes und leistungsfähiges DFT-Programm, das Moleküle und periodische Systeme methodisch einheitlich und numerisch genau behandelt. / This work contributes to the field of theoretical chemistry and is aimed at the development of efficient methods for computation of the electron density and the energy belonging to the ground state of molecular and periodic systems. It is based on the use of Kohn Sham density functional theory (Kohn Sham DFT) and local basis functions. In this scope, the molecular and the periodic systems of any dimensionality (e.g., bulk crystals, thin films, and polymers) are treated on an equal footing using methods which are easy to implement, numerically accurate, and highly efficient. For this, the author has augmented established methods of molecular simulations for their use with periodic boundary conditions applying novel techniques. These methods have been combined to a complete DFT method. Among these methods, the innovative approach for the RI (resolution of identity) method applied to the Coulomb term represents the key technology of this work. As a striking feature, this approach operates exclusively in real space. Although the RI method is the chief ingredient, the development of further methods is required to achieve overall efficiency for the consumption of storage and time. One of these methods is used to compress the density and Kohn Sham matrices. Moreover, numerical integration of the exchange-correlation term has been improved applying an adaptive numerical integration scheme. The methods presented in this thesis are combined to the prototype of an RI-DFT program. Using this program single point energies on the gamma point can be calculated for systems with closed shells. Calculations have been performed and the results are used to assess the accuracy and efficiency achieved. This program forms the foundation of an efficient and competitive DFT code. It works numerically accurate and treats molecules and periodic systems on an equal footing.

Diese Arbeit ist ein Beitrag zur theoretischen Chemie sowie zur Oberflächenchemie. Durch Kombination von computergestützten und experimentellen Untersuchungen wird die atomare Struktur von dünnen SiO2-Filmen auf Ru(0001)-Unterlagen, von eisendotierten SiO2-Filmen auf diesen Unterlagen und von H2O-Filmen auf MgO(001)-Oberflächen bestimmt. Die atomaren Strukturmodelle wurden entweder mit dem neu entworfenen und im Paket DoDo implementierten genetischen Algorithmus oder mittels auf Sachkenntnis gestützter Vermutungen erhalten. Die simulierten Eigenschaften der so erhaltenen Strukturen stimmen sehr gut mit den experimentellen Daten (Raster-Tunnel-Mikroskopie, Infrarot-Spektroskopie) überein. Die erfolgreiche Strukturbestimmung mithilfe des DoDo-Programms zeigt, dass genetische Algorithmen zur systematischen und extensiven Erkundung der Energielandschaften 2D-periodischer Systeme geeignet sind. / This work is a contribution in the field of theoretical chemistry and surface science. The joint computational and experimental studies investigated the atomic structure of ultrathin silica and iron-doped silica films formed on the Ru(0001) surface and water films formed on the MgO(001) surface. The atomic structure models were obtained using either the educated guess approach or the genetic algorithm that was designed and implemented within the DoDo package. The properties simulated for the resulting models are in a very good agreement with the experimental data (scanning tunnelling microscopy, infrared spectroscopy). The successful structure determination using the DoDo program shows that the genetic algorithm technique is capable of systematic and extensive exploration of the energy landscapes for 2D-periodic systems.