Within this work, an additive and a subtractive QM/MM interface were implemented into CAST. The interactions between QM and MM system are described via electrostatic embedding. Link atoms are used to saturate dangling bonds originating from the separation of QM and MM system. Available energy evaluation methods to be combined include force fields (OPLSAA and AMBER), semi-empirical programs (Mopac and DFTB+), and quantum-chemical methods (from Gaussian, Orca, and Psi4). Both the additive and the subtractive interface can deal with periodic boundary conditions. The subtractive scheme was extended to enable QM/QM, three-layer, and multi-center calculations. Another feature only available within the subtractive interface is the microiteration procedure for local optimizations. The novel QM/MM methods were applied to the investigation of the reaction path for the complex formation between rhodesain and K11777. Benchmark calculations show a very good agreement with results from Gaussian-ONIOM. When comparing the relative energies obtained with different options to a computation where the whole system was treated with the “QM method” DFTB3, the electrostatic embedding scheme with option “delM3” gives the best results. “delM3” means that atoms with up to three bonds distance to the QM region are ignored when creating the external charges. This is done in order to avoid a double counting of Coulomb interactions between QM and MM system. The embedding scheme for the inner system in a three-layer calculation, however, does not have a significant influence on the energies. The same is true for the choice of the coupling scheme: Whether the additive or the subtractive QM/MM interface is applied does not alter the results significantly. The choice of the QM region, though, proved to be an important factor. As can be seen from the comparison of two QM systems of different size, bigger is not always better here. Instead, one has to make sure not to separate important (polar) interactions by the QM/MM border. After this benchmark study with singlepoint calculations, the various possibilities of CAST were used to approximate the solution of a remaining problem: The predicted reaction energy for the formation of the rhodesain-K11777 complex differs significantly depending on the starting point of the reaction path. The reason for this is assumed to be an inadequate adjustment of the environment during the scans, which leads to a better stabilization of the starting structure in comparison to the final structure. The first approach to improve this adjustment was performing the relaxed scan with a bigger QM region instead of the minimal QM system used before. While the paths starting from the covalent complex do not change significantly, those starting from the non-covalent complex become more exothermic, leading to a higher similarity of the two paths. Nevertheless, the difference of the reaction energy is still around 15 kcal/mol, which is far from a perfect agreement. For this reason, Umbrella Samplings were run. Here, the adjustment of the environment is not done by local optimizations like in the scans, but by MD simulations. This has the advantage that the system can cross barriers and reach different local minima. The relative free energies obtained by Umbrella Samplings with suitable QM regions are nearly identical, independently of the starting point of the calculation. Thus, \(\Delta A\) evaluated by these computations can be assumed to reproduce the real energy change best. An MD simulation that was started from the transition state in order to mimic a “real-time” reaction indicates a very fast adjustment of the environment during the formation of the complex. This confirms that Umbrella Sampling is probably better suitable to describe the reaction path than a scan, where the environment can never move strong enough to leave the current local minimum. / In dieser Arbeit wurden ein additives und ein subtraktives QM/MM-Interface in CAST implementiert. Die Wechselwirkungen zwischen QM- und MM-System werden durch elektrostatische Einbettung beschrieben. Link-Atome dienen dazu, lose Bindungen abzusättigen, die durch die Trennung von QM- und MM-System entstehen. Als Methoden zur Energieberechnung, die kombiniert werden können, stehen Kraftfelder (OPLSAA und AM- BER), semiempirische Programme (Mopac und DFTB+) und quantenchemische Verfahren (aus Gaussian, Orca und Psi4) zur Verfügung. Sowohl das additive als auch das subtraktive Interface können mit periodischen Randbedingungen verwendet werden. Erweiterungen des subtraktiven Schemas ermöglichen Berechnungen mit QM/QM, drei Schichten o der mehreren QM-Zentren. Ebenfalls nur im subtraktiven Interface verfügbar ist die lokale Optimierung mittels Mikroiterationsschema. ...

Kohlenstoffnanoröhren (Carbon Nanotubes, CNTs) gelten seit einigen Jahren als vielversprechendes neuartiges Material für verschiedenste Anwendungen in der Technik unterschiedlicher Fachgebiete. Von besonderem Interesse, z.B. in Leichtbaustrukturen, sind die postulierten exzellenten mechanischen Eigenschaften der einzelnen CNTs hinsichtlich Steifigkeit und Festigkeit. Diese auf der Nanoskala identifizierten Eigenschaften sollen auch in makroskopischen Bauteilen zu besonders guten mechanischen Eigenschaften führen. Demonstriert werden kann dies zum Beispiel an einer neuartigen Faser, die aus einer Vielzahl individueller Kohlenstoffnanoröhren gesponnen wurde. An dieser Faser durchgeführte Tests zeigen jedoch, dass die Eigenschaften nicht in der gewünschten Höhe von der Nanoskale auf die Makroskale übertragen werden. Um diesen Effekt erklären und evtl. beheben zu können, sowie für das Design von Strukturen aus Nanoröhren ('Superstrukturen') und einige weitere Anwendungen, sind Simulationsmodelle nötig, die die grundlegenden mechanischen (elastischen) Eigenschaften beschreiben können und zudem mit einer sehr großen Anzahl beteiligter CNTs und damit Atome umgehen können. Betrachtet man dies zusätzlich unter dem Aspekt, dass, beispielsweise zu Designzwecken, jeweils Rechnungen zu mehreren Varianten notwendig sind, ist verständlich, dass für jeden Durchlauf nur eine begrenzte Menge an Rechenzeit aufgebracht werden soll. Daher wird in der vorliegenden Arbeit ein mechanisches Modell der Kohlenstoffnanoröhren entwickelt, das die geforderte Aufgabe um ein Vielfaches schneller als quantenmechanische Methoden oder auch klassische Molekulardynamik behandeln kann. Basis hierfür ist ein molekularmechanischer Ansatz, der ein Ersatzmodell der betrachteten Kohlenstoffnanoröhre aus Balkenelementen erzeugt. Die zur Definition des Balkenfachwerks nötigen Balkeneigenschaften werden hierbei aus einem zugrundeliegenden chemischen Kraftfeld abgeleitet, das die kovalenten Bindungen zwischen den Atomen der Nanoröhre beschreibt. Der Ansatz ist damit in die Klasse der 'molecular structural mechanics' (MSM) Ansätze einzuordnen. Ausgangspunkt der vorliegenden Arbeit ist zunächst ein etabliertes MSM-Modell, dessen Schwächen in der vorliegenden Arbeit analysiert werden. Dabei wird festgestellt, dass der bisher verwendete MSM-Ansatz nicht energetisch konsistent zum zugrundeliegenden chemischen Kraftfeld ist. Dieser Umstand wird zunächst durch die Entwicklung eines modifizierten MSM-Modells behoben. Anschließend wird gezeigt, dass dieses Modell energetisch konsistent zum eingesetzten Kraftfeld ist. Um weitere Fortschritte mit dem gewählten molekularmechanischen Ansatz zu erzielen, wird dann ein verallgemeinertes MSM-Modell auf Basis eines fortschrittlichen chemischen Kraftfeldes entwickelt, das weitere Nachteile des ursprünglichen Ansatzes behebt und universeller einsetzbar ist. Das Modell wird dann zur Bestimmung der elastischen Konstanten von Armchair und Zig-zag CNTs eingesetzt und die erhaltenen Ergebnisse diskutiert.:1. Grundlagen 2. Modellbildung und Simulation einwandiger Kohlenstoffnanoröhren 3. Ergebnisse und Diskussion zum Zweck der Modellentwicklung 4. Ergebnisse und Diskussion der elastischen Parameter einwandiger CNTs 5. Zusammenfassung und Ausblick / For several years now, Carbon Nanotubes (CNTs) are seen as a promising new material for manifold applications in new technologies from different fields. The predicted excellent mechanical properties such as high strength and stiffness are of particual interest e.g. in lightweight structures. The nanoscopic propertiers are prone to lead to good mechanical properties also in macrosopic parts. This can be demonstrated for instance on the basis of a novel type of carbon fiber which is spun out of a multitude of individual carbon nanotubes. However, tests of the fibre show that the outstanding properties on the nanoscale are not fully transfered to the macroscale. In order to explain this effect as well as for designing structures made out of nanotubes (so called super structures) and other applications, models for simulations are needed. These models should be capable of reproducing the basic (elastic) mechnical properties of the nanotubes as well as to be capcable of dealing with a large number of participating nanotubes and hence atoms. Considering the additional aspect that multiple calculations of similar systems, e.g. for design purposes, are required, it is easy to understand, that for each calculation only a limited amount of computational effort is affordable. Hence, in the present work a mechanical model for the carbon nanotubes is developed which can fulfil the requested task in a much shorter time than quantummechanical or moleculardynamic calculations. The model is based on a molecular mechanics approach which creates a substitute model for the carbon nanotube based on beam elements. The parameters mandatory to define the beam elements in the beam framework are obtained on the basis of a chemical force field forming the foundation of the approach. The chemical force fields describes the properties of the covalent bonds in the carbon nanotube. As a result, the proposed model can be classified to be part of the molecular structural mechanics (MSM) approaches. Starting point of the present work is a well known MSM-model which is at first analyzed in order to identify its drawbacks. During this investigation it is found, that the model used so far is not consistent in terms of energy to its underlying chemical force field. This problem is fixed by the development of a modified MSM-approach. It is shown that this modified approach is now consistent to the underlying chemical force field in terms of energy. In order to further improve the method, a generalized, advanced MSM-framework is developed on the basis of a sophisticated chemical force field. This advanced framework resolves further drawbacks of the models and enables a more general application of the model. The obtained model is then used to calculate and discuss the elastic constants of Armchair and Zig-zag Carbon Nanotubes.:1. Grundlagen 2. Modellbildung und Simulation einwandiger Kohlenstoffnanoröhren 3. Ergebnisse und Diskussion zum Zweck der Modellentwicklung 4. Ergebnisse und Diskussion der elastischen Parameter einwandiger CNTs 5. Zusammenfassung und Ausblick

Since many years, carbon nanotubes (CNTs) have been considered for a wide range of applications due to their outstanding mechanical properties. CNTs are tubular structures, showing a graphene like hexagonal lattice. Our interest in the calculation of the mechanical properties is motivated by several applications which demand the knowledge of the material behavior. One application in which the knowledge of the material behavior is vital is the CNT based fiber. Due to the excellent stiffness and strength of the individual CNTs, these fibers are expected to be a promising successor for state of the art carbon fibers. However, the mechanical properties of the fibers fall back behind the properties of individual CNTs. It is assumed that this gap in the properties is a result of the van-der-Waals interactions of the individual CNTs within the fiber. In order to understand the mechanical behavior of the fibers we apply a molecular mechanics approach. The mechanical properties of the individual CNTs are investigated by using a modified structural molecular mechanics approach. This is done by calculating the properties of a truss-beam element framework representing the CNT with the help of a chemical force field. Furthermore, we also investigate the interactions of CNTs arranged in basic CNT assemblies, mimicking the ones in a simple CNT fiber. We consider the van-der-Waals interactions in the structure and calculate the potential surface of the CNT assemblies.