Ziel dieser Arbeit war die Entwicklung einer allgemein anwendbaren Methode für die Simulation von ultraschnellen Prozessen und experimentellen Observablen. Hierfür wurden die Berechnung der elektronischen Struktur mit der zeitabhängigen Dichtefunktionaltheorie (TDDFT) und das Tully-Surface-Hopping-Verfahren für die nichtadiabatische Kerndynamik auf der Basis klassischer Trajektorien miteinander kombiniert. Insbesondere wurde eine Beschreibung der nichtadiabatischen Kopplungen für TDDFT entwickelt. Diese Methode wurde für die Simulation noch komplexerer Systeme durch die Tight-Binding-Näherung für TDDFT erweitert. Da die zeitaufgelöste Photoelektronenspektroskopie (TRPES) ein exzellentes experimentelles Verfahren für die Echtzeitbeobachtung von ultraschnellen Prozessen darstellt, wurde eine TDDFT-basierte Methode für die Simulation von TRPES entwickelt. Der Methode liegt die Idee zu Grunde, das System aus Kation und Photoelektron näherungsweise durch angeregte Zustände des neutralen Moleküls oberhalb der Ionisierungsgrenze zu beschreiben. Um diese Zustände mit TDDFT berechnen zu können wurde eine Beschreibung der Übergangsdipolmomente zwischen angeregten TDDFT-Zuständen entwickelt. Des Weiteren wurden Simulationen im Rahmen des Stieltjes-Imaging-Verfahrens, das eine Möglichkeit der Rekonstruktion des Photoelektronenspektrums aus den spektralen Momenten bietet, durchgeführt. Diese spektralen Momente wurden aus den diskreten TDDFT-Zuständen berechnet. Die breite Anwendbarkeit der entwickelten theoretischen Methoden für die Simulation von komplexen Systemen wurde an der Photoisomerisierung in Benzylidenanilin sowie der ultraschnellen Photodynamik in Furan, Pyrazin und mikrosolvatisiertem Adenin illustriert. Die dargestellten Beispiele demonstrieren, dass die nichtadiabatische Dynamik im Rahmen von TDDFT bzw. TDDFTB sehr gut für die Untersuchung und Interpretation der ultraschnellen photoinduzierten Prozesse in komplexen Molekülen geeignet ist. / The goal of this thesis was the development of a generally applicable theoretical framework for the simulation of ultrafast processes and experimental observables in complex molecular systems. For this purpose, a combination of the time-dependent density functional theory (TDDFT) for the description of the electronic structure with the Tully''s surface hopping procedure for the treatment of nonadiabatic nuclear dynamics based on classical trajectories was employed. In particular, a new approach for the calculation of nonadiabatic couplings within TDDFT was devised. The method was advanced for the description of more complex systems such as chromophores in a solvation shell by employing the tight binding approximation to TDDFT. Since the time-resolved photoelectron spectroscopy (TRPES) represents a powerful experimental technique for real-time observation of ultrafast processes, a TDDFT based approach for the simulation of TRPES was developed. The basic idea is the approximate representation of the combined system of cation and photoelectron by excited states of the neutral species above the ionization threshold. In order to calculate these states with TDDFT, a formulation of the transition dipole moments between excited states within TDDFT was devised. Moreover, simulations employing the Stieltjes imaging (SI) procedure were carried out providing the possibility to reconstruct photoelectron spectra from spectral moments. In this work, the spectral moments were calculated from discrete TDDFT states. The scope of the developed theoretical methods was illustrated on the photoisomerization in benzylideneaniline as well as on the ultrafast photodynamics in furan, pyrazine, and microsolvated adenine. The examples demonstrate that the nonadiabatic dynamics simulations based on TDDFT and TDDFTB are particularly suitable for the investigation and interpretation of ultrafast photoinduced processes in complex molecules.

Submitted by WELDER FRANZINI AMARAL CALLERA null (weldercallera@hotmail.com) on 2017-08-28T21:25:00Z No. of bitstreams: 1 TESE - Welder F A Callera OK.pdf: 2324966 bytes, checksum: 979c488a0e341117b537d2d5a1ec77b2 (MD5) / Rejected by Luiz Galeffi (luizgaleffi@gmail.com), reason: Solicitamos que realize uma nova submissão seguindo a orientação abaixo: O arquivo submetido está sem a ficha catalográfica. A versão submetida por você é considerada a versão final da dissertação/tese, portanto não poderá ocorrer qualquer alteração em seu conteúdo após a aprovação. Corrija esta informação e realize uma nova submissão contendo o arquivo correto. Agradecemos a compreensão. on 2017-08-29T18:03:23Z (GMT) / Submitted by WELDER FRANZINI AMARAL CALLERA null (weldercallera@hotmail.com) on 2017-08-29T18:41:29Z No. of bitstreams: 1 TESE - Welder F A Callera OK.pdf: 2349810 bytes, checksum: 0b00e94e2ccb5b74f2521ba559748736 (MD5) / Approved for entry into archive by Luiz Galeffi (luizgaleffi@gmail.com) on 2017-08-29T18:53:53Z (GMT) No. of bitstreams: 1 callera_wfa_dr_araiq.pdf: 2349810 bytes, checksum: 0b00e94e2ccb5b74f2521ba559748736 (MD5) / Made available in DSpace on 2017-08-29T18:53:53Z (GMT). No. of bitstreams: 1 callera_wfa_dr_araiq.pdf: 2349810 bytes, checksum: 0b00e94e2ccb5b74f2521ba559748736 (MD5) Previous issue date: 2017-08-04 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Esta tese de doutoramento apresentou o entendimento de processos redox enzimáticos, detalhando o mecanismo envolvido na troca eletrônica, a qual resulta na formação de um produto, por catálise enzimática. Observou-se a influência de um eletrodo sob a ação de um potencial estacionário aplicado (E) na reação enzima/substrato. Realizou-se eletroanálises, como: Voltametria Cíclica (VC) e Espectroscopia de Impedância Eletroquímica (EIE), para a penicilinase. Os resultados obtidos dão indícios de que a reação enzimática se beneficia de determinados potenciais, pois o parâmetro utilizado, Rct, resistência à transferência de cargas, sugere que ocorre maior troca eletrônica em alguns potenciais ótimos (faixa de -0,3 a -0,5 V). A Simulação Molecular serviu para estudar o comportamento atomístico por métodos clássicos (Dinâmica Molecular – DM) para as condições impostas experimentalmente, esclarecendo o mecanismo de reação enzimática por métodos quânticos (DFT – Teoria do Funcional de Densidade) e híbridos (QM/MM), cabendo salientar que a penicilinase não pertence à classe das enzimas oxirredutivas. / This doctoral thesis presented the understanding of enzymatic redox processes, detailing the mechanism involved in the electronic exchange, which results in the formation of a product by enzymatic catalysis. The influence of an electrode under the action of an applied stationary potential (E) on the enzyme/substrate reaction was observed. Electroanalysis was performed, such as: Cyclic Voltammetry (VC) and Electrochemical Impedance Spectroscopy (EIS), for the penicilinase. The results obtained indicate that the enzymatic reaction benefits from certain potentials, since the parameter used, Rct, resistance to the transfer of charges, suggests that there is greater electronic exchange in some optimal potentials (range the -0.3 to -0.5 V). The Molecular Simulation was used to study the atomistic behavior by classical methods (Molecular Dynamics - DM) for experimentally imposed conditions, clarifying the mechanism of enzymatic reaction by quantum methods (DFT) and hybrids (QM/MM). That penicillinase does not belong to the class of oxidoreductive enzymes.

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Diese Arbeit ist eine umfassende und systematische Untersuchung der Adsorption von Wasser auf der Fe2O3(0001)-Oberfläche. Sie deckt eine Vielzahl der Probleme auf, die während des Anfangs der Wasseradsorption auf den Übergangsmetalloxidoberflächen auftreten. Dazu gehören die Stabilität der reinen Oberfläche, die Rolle der Oberflächendefekte, der Einfluss der kristallographischen und elektronischen Strukturen, die elementare Kinetik der adsorbierten Arten von Wasser auf der Oberfläche, die Eigenschaften bei niedrigem und hohem Bedeckungsgrad und die Auswirkungen der Wasserstoffbrückenbindung auf die Adsorption und das XPS-Spektrum. Niedrige und hohe Bedeckungsgrade von 0.25 bis 1 Monolage werden untersucht, um die Grundlage für die folgende Erhöhung der Wasserbedeckung, die normalerweise in Experimenten beobachtet wird, zu ermitteln. Das Einzeladsorptionsregime wurde erweitert, um eine echte Wasserdampfumgebung mittels der Gibbs-Energie zu berücksichtigen. Die Ensemblemethode wurde benutzt, um die durchschnittlichen Werte der energisch entarteten Adsorptionskonfigurationen zu interpretieren. Der Abstandsmatrixansatz wurde entwickelt, um die statistische Analyse zu ermöglichen. Die Methode reduziert mithilfe der Oberflächensymmetrie die Gesamtzahl der Adsorptionskonfigurationen, die zu berücksichtigen sind. Das XPS-Spektrum wird für verschiedene Wasserdampftemperaturen und Drücke simuliert. Es wird eine gute Übereinstimmung zwischen theoretischen und experimentellen Spektren erreicht und die geringen Unterschiede werden erklärt. Die Hauptmerkmale des XPS-Spektrums beim Anstieg von relativer Feuchtigkeit des Wasserdampfs werden beschrieben. Die Ähnlichkeiten und Unterschiede der Wasseradsorption auf Fe2O3 und Al2O3 werden betont und die wichtigsten Tendenzen werden abgeleitet. Auf Grund dieser Arbeit kann der Anfangsprozess der Fe2O3(0001)-Oberflächenbenetzung erklärt werden. / The present study is a comprehensive systematic theoretical investigation of the water adsorption on the Fe2O3(0001) surface. It covers a broad number of problems inherent to the initial stage of the water adsorption on the transition metal oxide surface: clean surface stability, the influence of surface oxygen defects, the role of the crystallographic and electronic structures on the adsorption configuration, elementary kinetics, the particular qualities of the low and high adsorption coverage regimes and the effect of the hydrogen bonding on adsorption and on the XPS spectra simulation. The low and high coverage regimes from 0.25 up to 1 monolayer water coverage were considered to form a basis for the following increase of water loading mainly observed in experiments. A single adsorption energy picture was expanded to take into account the water vapour environment through the Gibbs free energy. The statistical ensemble was employed to classify and interpret the averaged values of the adsorption configurations set rather than the ``invisible'' in experiment quantities intrinsic to the particular single adsorption configuration. In order to make the statistical analysis feasible an effective distance matrix scheme was developed. It helped to reduce the total number of structures to consider without loss of generality by virtue of the surface space symmetry. Based on the statistical contribution of each individual adsorption configuration, the O-1s XPS was simulated for the various water vapour environments. A good agreement between the simulated and experimental spectra was found. Wherever it was important, the similarities and differences between water adsorption on the Fe2O3, Al2O3 and Fe3O4 surfaces were stressed and the main tendencies were deduced. Based on the present study, the whole picture of the initial stage of the Fe2O3(0001) surface wetting process was established.

Leaflet replacement in aortic valve repair (AVr) is associated with increased long-term repair failure. Hemodynamic performance and mechanical stress levels were investigated after porcine AVr with 5 types of clinically relevant replacement materials to ascertain which material(s) would be best suited for repair. Porcine aortic roots with intact aortic valves were placed in a left-heart simulator mounted with a high-speed camera for baseline valve assessment. Then, the non-coronary leaflet was excised and replaced with autologous porcine pericardium (APP), glutaraldehyde-fixed bovine pericardial patch (BPP; Synovis™), extracellular matrix scaffold (CorMatrix™), or collagen-impregnated Dacron (HEMASHIELD™). Hemodynamic parameters were measured over a range of cardiac outputs (2.5–6.5L/min) post-repair. Material properties of the above materials along with St. Jude Medical™ Pericardial Patch with EnCapTM Technology (SJM) were determined using pressurization experiments. Finite element models of the aortic valve and root complex were then constructed to verify the hemodynamic characteristics and determine leaflet stress levels. This study demonstrates that APP and SJM have the closest profiles to normal aortic valves; therefore, use of either replacement material may be best suited. Increased stresses found in BPP, HEMASHIELD™, and CorMatrix™ groups may be associated with late repair failure.

Leaflet replacement in aortic valve repair (AVr) is associated with increased long-term repair failure. Hemodynamic performance and mechanical stress levels were investigated after porcine AVr with 5 types of clinically relevant replacement materials to ascertain which material(s) would be best suited for repair. Porcine aortic roots with intact aortic valves were placed in a left-heart simulator mounted with a high-speed camera for baseline valve assessment. Then, the non-coronary leaflet was excised and replaced with autologous porcine pericardium (APP), glutaraldehyde-fixed bovine pericardial patch (BPP; Synovis™), extracellular matrix scaffold (CorMatrix™), or collagen-impregnated Dacron (HEMASHIELD™). Hemodynamic parameters were measured over a range of cardiac outputs (2.5–6.5L/min) post-repair. Material properties of the above materials along with St. Jude Medical™ Pericardial Patch with EnCapTM Technology (SJM) were determined using pressurization experiments. Finite element models of the aortic valve and root complex were then constructed to verify the hemodynamic characteristics and determine leaflet stress levels. This study demonstrates that APP and SJM have the closest profiles to normal aortic valves; therefore, use of either replacement material may be best suited. Increased stresses found in BPP, HEMASHIELD™, and CorMatrix™ groups may be associated with late repair failure.

<p dir="ltr">The generalization error of a classifier is related to the complexity of the set of functions among which the classifier is chosen. We study a family of low-complexity classifiers consisting of thresholding a random one-dimensional feature. The feature is obtained by projecting the data on a random line after embedding it into a higher-dimensional space parametrized by monomials of order up to k. More specifically, the extended data is projected n-times and the best classifier among those n, based on its performance on training data, is chosen. </p><p dir="ltr">We show that this type of classifier is extremely flexible, as it is likely to approximate, to an arbitrary precision, any continuous function on a compact set as well as any Boolean function on a compact set that splits the support into measurable subsets. In particular, given full knowledge of the class conditional densities, the error of these low-complexity classifiers would converge to the optimal (Bayes) error as k and n go to infinity. On the other hand, if only a training dataset is given, we show that the classifiers will perfectly classify all the training points as k and n go to infinity. </p><p dir="ltr">We also bound the generalization error of our random classifiers. In general, our bounds are better than those for any classifier with VC dimension greater than O(ln(n)). In particular, our bounds imply that, unless the number of projections n is extremely large, there is a significant advantageous gap between the generalization error of the random projection approach and that of a linear classifier in the extended space. Asymptotically, as the number of samples approaches infinity, the gap persists for any such n. Thus, there is a potentially large gain in generalization properties by selecting parameters at random, rather than optimization. </p><p dir="ltr">Given a classification problem and a family of classifiers, the Rashomon ratio measures the proportion of classifiers that yield less than a given loss. Previous work has explored the advantage of a large Rashomon ratio in the case of a finite family of classifiers. Here we consider the more general case of an infinite family. We show that a large Rashomon ratio guarantees that choosing the classifier with the best empirical accuracy among a random subset of the family, which is likely to improve generalizability, will not increase the empirical loss too much. </p><p dir="ltr">We quantify the Rashomon ratio in two examples involving infinite classifier families in order to illustrate situations in which it is large. In the first example, we estimate the Rashomon ratio of the classification of normally distributed classes using an affine classifier. In the second, we obtain a lower bound for the Rashomon ratio of a classification problem with a modified Gram matrix when the classifier family consists of two-layer ReLU neural networks. In general, we show that the Rashomon ratio can be estimated using a training dataset along with random samples from the classifier family and we provide guarantees that such an estimation is close to the true value of the Rashomon ratio.</p>