Nowadays, reactions on surfaces are attaining great scientific interest because of their diverse applications. Some well known examples are production of ammonia on metal surfaces for fertilizers and reduction of poisonous gases from automobiles using catalytic converters. More recently, also photoinduced reactions at surfaces, useful, textit{e.g.}, for photocatalysis, were studied in detail. Often, very short laser pulses are used for this purpose. Some of these reactions are occurring on femtosecond (1 fs=$10^{-15}$ s) time scales since the motion of atoms (which leads to bond breaking and new bond formation) belongs to this time range. This thesis investigates the femtosecond laser induced associative photodesorption of hydrogen, H$_2$, and deuterium, D$_2$, from a ruthenium metal surface. Many interesting features of this reaction were explored by experimentalists: (i) a huge isotope effect in the desorption probability of H$_2$ and D$_2$, (ii) the desorption yield increases non-linearly with the applied visible (vis) laser fluence, and (iii) unequal energy partitioning to different degrees of freedom. These peculiarities are due to the fact that an ultrashort vis pulse creates hot electrons in the metal. These hot electrons then transfer energy to adsorbate vibrations which leads to desorption. In fact, adsorbate vibrations are strongly coupled to metal electrons, textit{i.e.}, through non-adiabatic couplings. This means that, surfaces introduce additional channels for energy exchange which makes the control of surface reactions more difficult than the control of reactions in the gas phase. In fact, the quantum yield of surface photochemical reactions is often notoriously small. One of the goals of the present thesis is to suggest, on the basis of theoretical simulations, strategies to control/enhance the photodesorption yield of H$_2$ and D$_2$ from Ru(0001). For this purpose, we suggest a textit{hybrid scheme} to control the reaction, where the adsorbate vibrations are initially excited by an infrared (IR) pulse, prior to the vis pulse. Both textit{adiabatic} and textit{non-adiabatic} representations for photoinduced desorption problems are employed here. The textit{adiabatic} representation is realized within the classical picture using Molecular Dynamics (MD) with electronic frictions. In a quantum mechanical description, textit{non-adiabatic} representations are employed within open-system density matrix theory. The time evolution of the desorption process is studied using a two-mode reduced dimensionality model with one vibrational coordinate and one translational coordinate of the adsorbate. The ground and excited electronic state potentials, and dipole function for the IR excitation are taken from first principles. The IR driven vibrational excitation of adsorbate modes with moderate efficiency is achieved by (modified) $pi$-pulses or/and optimal control theory. The fluence dependence of the desorption reaction is computed by including the electronic temperature of the metal calculated from the two-temperature model. Here, our theoretical results show a good agreement with experimental and previous theoretical findings. We then employed the IR+vis strategy in both models. Here, we found that vibrational excitation indeed promotes the desorption of hydrogen and deuterium. To summarize, we conclude that photocontrol of this surface reaction can be achieved by our IR+vis scheme. / Heutzutage werden Reaktionen auf Oberflächen wegen ihrer vielfältigen Anwendungen intensiv untersucht. Einige der bekannten Beispiele sind die Herstellung von Ammoniak auf Metalloberflächen für die Kunstdüngerproduktion und die Reduktion giftiger Abgase in Autokatalysatoren. In letzter Zeit wurden auch photoinduzierte Reaktionen an Oberflächen eingehender untersucht, die z.B. für die Photokatalyse verwandt werden können. Häufig werden in diesen Untersuchungen sehr kurze Laserpulse benutzt. Einige der Reaktionen finden auf einer Femtosekunden-Zeitskala mbox{(1 fs =10$^{-15}$ s)} statt, da die Bewegungen einzelner Atome in derart kurzen Zeitspannen ablaufen (durch die der Bindungsbruch und das Knüpfen neuer Bindungen verursacht wird). Diese Arbeit untersucht die femtosekunden-laserinduzierte assoziative Photodesorption von Wasserstoff, H$_2$, und Deuterium, D$_2$, von einer Rutheniumoberfläche. Viele interessante Eigenschaften dieser Reaktion wurden in Experimenten entdeckt: (i) ein großer Isotopeneffekt in der Desorptionswahrscheinlichkeit von H$_2$ und D$_2$, (ii) die Desorptionsausbeute steigt nicht-linear mit der (vis) Laserfluenz an und (iii) eine Nicht-Gleichverteilung der Energie auf die einzelnen Freiheitsgrade. Diese Auffälligkeiten sind durch den Umstand verursacht, dass der ultrakurze vis-Laserpuls heiße Elektronen im Metall erzeugt. Die heißen Elektronen transferieren dann Energie in die Schwingungen des Adsorbats, was zur Desorption führt. Tatsächlich sind die Adsorbatschwingungen stark an die Elektronen gekoppelt, nämlich durch nicht-adiabatische Kopplungen. Dies bedeutet, dass durch Oberflächen neue Kanäle für den Energietransfer geöffnet werden, was die Kontrolle von Oberflächenreaktionen im Vergleich zu solchen in der Gasphase erschwert. In der Tat sind die Quantenausbeuten von photochemischen Oberflächenreaktionen bekannterweise klein. Eines der Ziele in der vorliegenden Arbeit ist es auf der Basis von theoretischen Simulationen Strategien vorzuschlagen, um die Photodesorptionsausbeute von H$_2$ und D$_2$ von Ru(0001) zu kontrollieren bzw. zu verbessern. Zu diesem Zweck schlagen wir ein gemischtes Kontrollschema für die Reaktion vor, bei dem zunächst die Adsorbatschwingungen vor dem vis-Puls durch einen infraroten (IR) Puls angeregt werden. Sowohl adiabatische als auch nicht-adiabatische Repräsentationen für photoinduzierte Desorptionsprozesse werden dabei benutzt. Die adiabatische Repräsentation ist in klassischen Molekulardynamik-Simulationen mit elektronischer Reibung verwirklicht. In einer quantenmechanischen Beschreibung werden nicht-adiabatische Repräsentationen innerhalb der Dichtematrixtheorie für offene Quantensysteme verwandt. Die zeitliche Entwicklung des Desorptionsprozesses wird in einem Zwei-Modenmodell reduzierter Dimensionalität mit einer Schwingungs- und einer Translationskoordinate des Adsorbats beschrieben. Die Potentiale für den elektronische Grundzustand und den angeregten Zustand sind abgeleitet aus quantenchemischen Rechnungen (textsl{first principles}). Die IR-getriebene Schwingungsanregung der Adsorbatmoden mit moderatem Wirkungsgrad wird mit (modifizierten) $pi$-Pulsen und/oder der Theorie der optimalen Kontrolle erreicht. Die Abhängigkeit der Desorption von der Fluenz wird mit Hilfe der elektronischen Temperatur des Metalls berechnet, welche im Rahmen des Zwei-Temperatur-Modells bestimmt wird. Dabei weisen unsere Ergebnisse eine gute Übereinstimmung mit experimentellen und früheren theoretischen Arbeiten auf. Daraufhin wandten wir die IR+vis Strategie in beiden Modellen an. Dadurch konnten wir zeigen, dass Schwingungsanregung in der Tat die Desorption von Wasserstoff und Deuterium begünstigt. Zusammenfassend stellen wir fest, dass die Photokontrolle dieser Oberflächenreaktion durch unser IR+vis Schema erreichbar ist.

In this thesis the path integral formalism is applied to the calculation of the dynamics of dissipative quantum systems. The time evolution of a system of bilinearly coupled bosonic modes is treated using the real-time path integral technique in coherent-state representation. This method is applied to a damped harmonic oscillator within the Caldeira-Leggett model. In order to get the stationary trajectories the corresponding Lagrangian function is diagonalized and then the path integrals are evaluated by means of the stationary-phase method. The time evolution of the reduced density matrix in the basis of coherent states is given in simple analytic form for weak system-bath coupling, i.e. the so-called rotating-wave terms can be evaluated exactly but the non-rotating-wave terms only in a perturbative manner. The validity range of the rotating-wave approximation is discussed from the viewpoint of spectral equations. In addition, it is shown that systems without initial system-bath correlations can exhibit initial jumps in the population dynamics even for rather weak dissipation. Only with initial correlations the classical trajectories for the system coordinate can be recovered. The path integral formalism in a combined phase-space and coherent-state representation is applied to the problem of curve-crossing dynamics. The system of interest is described by two coupled one-dimensional harmonic potential energy surfaces interacting with a heat bath. The mapping approach is used to rewrite the Lagrangian function of the electronic part of the system. Using the Feynman-Vernon influence-functional method the bath is eliminated whereas the non-Gaussian part of the path integral is treated using the perturbation theory in the small coordinate shift between potential energy surfaces. The vibrational and the population dynamics is considered in a lowest order of the perturbation. The dynamics of a Gaussian wave packet is analyzed along a one-dimensional reaction coordinate. Also the damping rate of coherence in the electronic part of the relevant system is evaluated within the ordinary and variational perturbation theory. The analytic expressions for the rate functions are obtained in the low and high temperature regimes.

This thesis presents the benchmarking and development of a method to study ground state properties of hydrogen clusters using molecular dynamics. Benchmark studies are performed on our Path Integral Molecular Dynamics code using the Langevin equation for finite temperature studies and our Langevin equation Path Integral Ground State code to study systems in the zero-temperature limit when all particles occupy their nuclear ground state. A simulation is run on the first 'real' system using this method, a parahydrogen molecule interacting with a fixed water molecule using a trivial unity trial wavefunction. We further develop a systematic method of optimizing the necessary parameters required for our ground state simulations and introduce more complex trial wavefunctions to study parahydrogen clusters and their isotopologues orthodeuterium and paratritium. The effect of energy convergence with parameters is observed using the trivial unity trial wavefunction, a Jastrow-type wavefunction that represents a liquid-like system, and a normal mode wavefunction that represents a solid-like system. Using a unity wavefunction gives slower energy convergence and is inefficient compared to the other two. Using the Lindemann criterion, the normal mode wavefunction acting on floppy systems introduces an ergodicity problem in our simulation, while the Jastrow does not. However, even for the most solid-like clusters, the Jastrow and the normal mode wavefunctions are equally efficient, therefore we choose the Jastrow trial wavefunction to look at properties of a range of cluster sizes. The energetic and structural properties obtained for parahydrogen and orthodeuterium clusters are consistent with previous studies, but to our knowledge, we may be the first to predict these properties for neutral paratritium clusters. The results of our ground state simulations of parahydrogen clusters, namely the distribution of pair distances, are used to calculate Raman vibrational shifts and compare to experiment. We investigate the accuracy of four interaction potentials over a range of cluster sizes and determine that, for the most part, the ab initio derived interaction potentials predict shifts more accurately than the empirically based potentials for cluster sizes smaller than the first solvation shell and the trend is reversed as the cluster size increases. This work can serve as a guide to simulate any system in the nuclear ground state using any trial wavefunction, in addition to providing several applications in using this ground state method.

Noncovalent interactions in complex chemical systems are examined by considering model systems which capture the essential physics of the interactions and applying correlated electronic structure techniques to these systems. Noncovalent interactions are critical to understanding a host of energetic and structural properties in complex chemical systems, from base pair stacking in DNA to protein folding in organic solids. Complex chemical and biophysical systems, such as enzymes and proteins, are too large to be studied using computational techniques rigorous enough to capture the subtleties of noncovalent interactions. Thus, the larger chemical system must be truncated to a smaller model system to which rigorous methods can be applied in order to capture the essential physics of the interaction. Computational methodologies which can account for high levels of electron correlation, such as second-order perturbation theory and coupled-cluster theory, must be used. These computational techniques will be used to study several types (pi stacking, S/pi, and C-H/pi) of noncovalent interactions in two chemical contexts: biophysical systems and organic solids.

Propriedades dinâmicas de sistemas quânticos de muitos corpos é um tópico de grande interesse em física da matéria condensada. Estas propriedades nos dão informação sobre a propagação de excitações elementares e de mecanismos de relaxação em sistemas interagentes. Neste contexto, as funções de correlação tem se tornado ainda mais relevantes devido a experimentos em sistemas de átomos frios e íons armadilhados que medem diretamente no domínio temporal os comportamentos assintóticos no tempo. No entanto, até o momento a maioria dos estudos em cadeias de spin quânticas focaram-se em correlações de um único spin. Utilizando a cadeia de spin XX unidimensional, nós estudamos métodos exatos para calcular as funções de correlação das componentes do tensor de dois spins, Tabi,j = SaiSbj. Estes operadores aparecem, por exemplo, como a resposta da seção de choque de espalhamento inelástico de raios X. Baseados no teorema de Wick, nós mostramos que algumas funções de correlação das componentes locais do tensor de dois operadores de spins de sítios vizinhos, na representação de férmions, podem ser escritas como uma combinação de funções de Green de uma única partícula. Utilizamos diagramas de Feynman para organizar esta combinação e calcular as funções de correlação. Em seguida, considerando esses propagadores para tempos longos e grandes distâncias ao longo do cone de luz, encontramos o comportamento dessas funções de correlação como leis de potência oscilatórias que decaem com o tempo e distância. Uma aplicação direta das funções de correlação é para o estudo de quantidades conservadas e não conservadas, uma análise sobre algumas dessas quantidades foi feita. Discutimos também as funções de correlação das componentes do tensor que não são locais na representação fermiônica. Nesse caso os cálculos foram mais desafiadores, mas usamos o fato que funções de correlação dependente do tempo podem ser expressadas em termos dos determinantes de Fredholm. / Dynamical properties of quantum many body systems is a major topic of interest in condensed matter physics. These properties tell us about the propagation of elementary excitation and mechanisms of relaxation in interacting systems. In this context correlation functions have became even more relevant due the experiments in systems of cold atoms and trapped ions that measure real time dependence directly out to relatively long times. However, most studies in quantum spins chains so far have focused on correlations of single spins. Using the one dimensional XX spin chain, we study exact methods to calculate the correlation functions of the components of the tensor operator involving two spins, Tabi,j = SaiSbj. This operator appear, for example, as a response of inelastic x-ray scattering cross section. Based on Wick\'s theorem, we show that some correlation functions of local components of the tensor operator of two pairs of neighbor sites, in the fermion space, can be written as a combination of Greens functions of a single particle. We have used Feynman diagrams to organize this combination and calculate the correlation functions. Then, considering these propagators for long times and large distances along the light cone, we found the behavior of these correlation functions as a oscillatory and power law decay on time. A direct application of correlation functions is to study conserved and non-conserved quantities, and such analysis has been made. We also considered other two-spin operators which are not local in the fermionic representation. In this case the calculation is more challenging, but the time-dependent correlation functions can be expressed in terms of Fredholm determinants.

We utilize the multi Davydov-Ansatz, an Ansatz of the bosonic many-body wave function in terms of moving Gaussian basis functions, to illuminate several aspects of open quantum system dynamics and quantum many-body theory. By two artifices alongside the time-dependent variational principle we extract from this Ansatz, commonly considered ill-behaved and not converging, a highly stable and converging method. Its extremely favourable scaling of the numerical effort with the number of degrees of freedom facilitates exploration of the zero and non-zero temperature physics of both system and environment of open quantum systems in the strong coupling regime, even in cases where the system is laser-driven. The discovery that strongly coupling a system to an environment may, apart from the introduction of dissipation and decoherence also serve as a resource for the system has fuelled the research on strongly correlated open quantum systems. Although the advent of ultra powerful data processors enables advanced methods to tackle these systems, their explicit treatment without further assumptions remains an eminently challenging task. With the multi Davydov-Ansatz we numerically exactly calculate the dynamics of various open systems coupled strongly to an environment. In particular, we illuminate diverse aspects of laser-driven molecular dynamics in dissipative environments. Based on a rigorous investigation of the time-dependent variational principle for moving Gaussian basis functions, we systematically develop a linear algebra formulation of the system of equations of motion for the Ansatz parameters. On its basis we precisely isolate the origin of the issues related to the multi Davydov-Ansatz and solve the long-standing convergence problem of the method by a regularization termed apoptosis. We show exemplary for the ohmic and sub-ohmic Spin-Boson model that apoptosis renders the multi Davydov-Ansatz a highly stable method with an outstanding speed of convergence, suited to numerically exactly reproduce the dynamics of the model at surprisingly humble numerical effort even for strong coupling strengths. Furthermore, since they are not suited to efficiently reproduce Fock number states in many-body systems, we shed some light on possible extensions of the Gaussian basis functions in the multi Davydov-Ansatz in terms of displaced number states and in terms of squeezed states. In particular we argue that due to the emergence of an inappropriate number of equations of motion, there is no straightforward generalization of the multi Davydov-Ansatz by displaced number states. For the purpose of further optimization of the multi Davydov-Ansatz, we investigate in detail the impact on the numerical effort of different representations of an open system's environment. In particular, different frequency discretizations for given continuous spectral densities are examined with respect to the speed of convergence of the system dynamics to the continuum limit. We utilize a Windowed Fourier Transform as an a priori measure for the quality of the discretized representation of bath correlations. Furthermore, efficient representations of the environment for shifted initial conditions in general and non-zero temperature in particular are found systematically. As an alternative representation of an environment of mutually uncoupled harmonic oscillators, we investigate an environment represented in terms of a linear chain of effective modes. In this context we detail how to consistently reformulate the effective mode representation in second quantization, removing inadvertent double excitations introduced by the original formulation. We show that the alternative representation is beneficial in cases where the bath spectral density is highly structured, while for the ohmic and sub-ohmic spectral density of the Spin-Boson model it is of no advantage. Once we have identified the numerically most efficient representation of the environment, we apply the multi Davydov-Ansatz in order to illuminate several aspects of open quantum system dynamics whose investigation has previously remained occlusive. In particular, the access to the exact dynamics of the environmental degrees of freedom allows to shed light on the question for the channels through which energy can be interchanged between system and environment in the considered systems. Firstly, in a system-bath setup we survey the vibrational relaxation dynamics of deuterium dimers at a silicon surface. The investigation of the relaxation dynamics requires the quantum mechanical treatment of multiple system levels, which in turn prohibits a treatment of the environmental dynamics on a perturbative level. We demonstrate that the multi Davydov-Ansatz allows for a numerically exact calculation of the system dynamics with multiple system levels and a huge number of surface vibrations explicitly taken into account. Furthermore, due to the structure of the spectral density of the environment, the effective mode representation allows for this system to dramatically reduce the numerical effort. Secondly we shall investigate in detail the relaxation dynamics of an exciton in a one-dimensional molecular crystal. Since the strong coupling regime renders highly complicated the phonon dynamics, apoptosis turns out to be inevitably required in order to reliably converge the system dynamics. We show that the multi Davydov-Ansatz equipped with apoptosis allows for an extremely efficient calculation of the exciton and phonon dynamics, for both large hopping integrals and large molecular crystals. Furthermore we illuminate diverse aspects of laser-driven molecular dynamics in a dissipative environment. By restriction to two electronic energy levels we determine the channels through which system and environment interchange energy in the vicinity of an avoided crossing in a dissipative Landau-Zener model. In particular, we reveal that the final transition probability can be tuned by coupling to the environment for both diagonal and off-diagonal coupling. By appropriately adjusting the initial excitation of the system, the final transition probability is shown to converge to a fixed value for increasing coupling. Finally, we investigate in detail laser-induced population transfer by rapid adiabatic passage in a dissipative environment. By application of the multi Davydov-Ansatz it is shown for zero as well as for non-zero temperature that strongly coupling the system to an environment can serve as a resource for the population inversion. In particular, we shall examine how the coupling to the environment compensates for the decay channels in the system even if the laser pulse is only weakly chirped.:1. Introduction 2. Prerequisites 2.1. Harmonic oscillator basics 2.2. Canonical coherent states of the harmonic oscillator 2.3. Overcompleteness of CS and the Segal-Bargmann transformation 2.4. Density operator representation in terms of CS 2.5. Ideal squeezed states 2.6. Displaced number states 2.7. On the variational principle 3. Real time propagation with CS 3.1. Variational principle with CS 3.1.1. Gauge freedom in the vMCG Ansatz 3.1.2. Equations of motion for the vMCG Ansatz 3.2. Standard form of the linear system 3.3. Regularity of the coefficient matrix 3.3.1. Regularization in the case of vanishing coefficients 3.3.2. Apoptosis of CS 3.4. The route to Semiclassics 3.5. Variational principle with DNS and squeezed states 3.6. The multi Davydov-Ansatz 3.7. The multi Davydov-Ansatz at non-zero temperature 4. Open Quantum Systems 4.1. System-Bath Hamiltonian 4.2. The road to classical dissipation 4.3. The impact of apoptosis and regularization of the 𝜌-matrix 4.3.1. Multi Davydov-Ansatz for the Quantum Rabi model 4.3.2. Multi Davydov-Ansatz and the Spin-Boson model 4.3.2.1. Spin-Boson model in the ohmic regime 4.3.2.2. Spin-Boson model in the sub-ohmic regime 4.4. The Windowed Fourier Transform 4.5. The sub-ohmic case and the problem of oversampling 4.5.1. On the polarized initial condition 4.5.2. On the treatment of non-zero temperature 4.6. The Effective Mode Representation 5. Applications 5.1. Vibrational relaxation dynamics at surfaces 5.2. Relaxation dynamics of the Holstein polaron 5.3. The dissipative Landau Zener Model 5.3.1. Coupling to a single environmental mode 5.3.2. Coupling to multiple environmental modes 5.4. Rapid Adiabatic Passage with a dissipative environment 6. Summary And Outlook List of abbreviations Appendix A. Closure relation of displaced number states B. Hamilton equations: classical vs. CCS for a Morse oscillator C. Equations of motion for the multi Davydov-Ansatz C.1. D2-Ansatz C.2. D1-Ansatz D. Details of implementation E. Calculation of the BCF F. Calculation of the polarized initial condition for 𝑇 = 0 Bibliography List of publications

We investigate thermalization in finite quantum systems using coherent state-based approaches to solve the time-dependent Schr\'odinger equation. Earlier, a lot of work has been done in the quantum realm, to study thermalization in spin systems, but not for the case of continuous systems. Here, we focus on continuous systems. We study the zero temperature thermalization i.e., we consider the ground states of the bath oscillators (environment). In order to study the quantum dynamics of a system under investigation, we require numerical methods to solve the time-dependent Schr\'odinger equation. We describe different numerical methods like the split-operator fast fourier transform, coupled coherent states, static grid of coherent states, semiclassical Herman-Kluk propagator and the linearized semiclassical initial value representation to study the quantum dynamics. We also give a comprehensive comparison of the most widely used coherent state based methods. Starting from the fully variational coherent states method, after a first approximation, the coupled coherent states method can be derived, whereas an additional approximation leads to the semiclassical Herman-Kluk method. We numerically compare the different methods with another one, based on a static rectangular grid of coherent states, by applying all of them to the revival dynamics in a one-dimensional Morse oscillator, with a special focus on the number of basis states (for the coupled coherent states and Herman-Kluk methods the number of classical trajectories) needed for convergence. We also extend the Husimi (coherent state) based version of linearized semiclassical theories for the calculation of correlation functions to the case of survival probabilities. This is a case that could be dealt with before only by use of the Wigner version of linearized semiclassical theory. Numerical comparisons of the Husimi and the Wigner case with full quantum results as well as with full semiclassical ones is given for the revival dynamics in a Morse oscillator with and without coupling to an additional harmonic degree of freedom. From this, we see the quantum to classical transition of the system dynamics due to the coupling to the environment (bath harmonic oscillator), which then can lead ultimately to our final goal of thermalization for long-time dynamics. In regard to thermalization in quantum systems, we address the following questions--- is it enough to increase the interaction strength between the different degrees of freedom in order to fully develop chaos which is the classical prerequisite for thermalization, or if, in addition, the number of those degrees of freedom has to be increased (possibly all the way to the thermodynamic limit) in order to observe thermalization. We study the ``toppling pencil'' model, i.e., an excited initial state on top of the barrier of a symmetric quartic double well to investigate thermalization. We apply the method of coupled coherent states to study the long-time dynamics of this system. We investigate if the coupling of the central quartic double well to a finite, environmental bath of harmonic oscillators in their ground states will let the central system evolve towards its uncoupled ground state. This amounts to thermalization i.e., a cooling down to the bath ``temperature'' (strictly only defined in the thermodynamic limit) of the central system. It is shown that thermalization can be achieved in finite quantum system with continuous variables using coherent state-based methods to solve the time-dependent Schr\'odinger equation. Also, here we witness thermalization by coupling the system to a bath of only few oscillators (less than ten), which until now has been seen for more than ten to twenty bath oscillators.

We study the time evolution of driven quantum systems using analytic, algebraic, and numerical methods. First, we obtain analytic solutions for driven free and oscillator systems by shifting the coordinate and phase of the undriven wave function. We also factorize the quantum evolution operator using the generators of the Lie algebra comprising the Hamiltonian. We obtain coupled ODE's for the time evolution of the Lie algebra parameters. These parameters allow us to find physical properties of oscillator dynamics. In particular we find phase-space trajectories and transition probabilities. We then search for chaotic behavior in the Lie algebra parameters as a signature for dynamical chaos in the quantum system. We plot the trajectories, transition probabilities, and Lyapunov exponents for a wide range of the following physical parameters: strength and duration of the driving force, frequency difference, and anharmonicity of the oscillator. We identify conditions for the appearance of chaos in the system.

La photo-isomérisation par ouverture de cycle du benzopyrane a été étudiée à l'aide de la méthode MCTDH (Multi-Configuration Time-Dependent Hartree). Nous avons introduit différentes stratégies pour contrôler la conversion du benzopyrane en mérocyanine à l'aide d'impulsions laser. Nous avons utilisé un modèle pour le potentiel électronique à six dimensions développé dans le cadre d'un travail antérieur. Le modèle repose sur une généralisation des Hamiltoniens modèles standards pour les couplages vibroniques et utilise les six coordonnées les plus importantes pour le processus. Le principal objectif est de fournir des stratégies de contrôle qui pourront être utilisées par les expérimentateurs par la suite. Plus précisément, nous avons proposé: (i) une technique de type pompe-sonde pour contrôler la photostabilité, (ii) une stratégie en deux étape avec une préexcitation vibrationnel du système,(iii) une stratégie reposant sur un contrôle par effet Stark induit par un laser non-résonant. / The ring-opening photoisomerization of benzopyran, which occurs via a photochemical route involving a conical intersection,has been studied with quantum dynamics calculations using the multi-configuration time-dependent Hartree method (MCTDH). We introduce a mechanistic strategy to control the conversion of benzopyran to merocyanine with laser pulses. We use asix-dimensional model developed in a previous work for the potential energy surfaces (PES) based on an extension of thevibronic-coupling Hamiltonian model (diabatization method by ansatz), which depends on the most active degrees of freedom. The main objective of these quantum dynamics simulations is to provide a set of strategies that could help experimentalists tocontrol the photoreactivity vs. photostability ratio (selectivity). In this work we present:(i) a pump-dump technique used tocontrol the photostability, (ii) a two-step strategy to enhance the reactivity of the system: first, a pure vibrational excitation inthe electronic ground state that prepares the system and, second, an ultraviolet excitation that brings the system to the firstadiabatic electronic state; (iii) finally the effect of a non-resonant pulse (Stark effect) on the dynamics.

In der vorliegenden Arbeit wird eine einheitliche und allumfassende Theorie der Nicht-linearen Polarisationsspektroskopie in der Frequenzdomäne (NLPF) aufgestellt. Dies Methode basiert auf der in einer isotropen Farbstofflösung durch ein polarisiertes, monochromatisches Laserfeldes (pump) erzeugten Anisotropie, die mittels eines weiteren monochromatischen Laserfeldes (probe), mit einer um 45° gegenüber dem Pumpfeld gedrehten Polarisationsrichtung geprobt wird. Ausgehend von den grundlegenden Gleichungen für den nichtlinearen Respons molekularer Systeme auf elektromagnetische Felder wird das zweidimensional NLPF-spektrum hergeleitet, und zwar sowohl in der niedrigsten Ordnung Störungstheorie als auch unter Verwendung eines selbstkonsistenten Ansatzes für beliebige Pumpfeldstärken. In der niedrigsten Ordnung Störungstheorie können drei in ihrer Frequenzabhängigkeit sich unterscheidende Arten von Ausdrücke explizit angegeben werden. Diese sind drei Areten von Peaks im NLPF-spektrum zuzuordnen: Den T2-peaks, dem T1-peaks und den Zweiphotonen-peaks. Letztere sind unter Normalbedingungen im allgemeinen nicht beobachtbar und wurden daher nicht weiter behandelt. Die in dieser Arbeit erstmals gelungene, allgemeine und einheitliche theoretische Beschreibung der T1- und T2-peaks in NLPF-spektren von Mehrniveausystemen stellt einen Durchbruch hin zu einer allumfassenden Subbandenanalyse mittels NLPF dar. Durch Einbeziehung der teilweise bereits bekannten Auswirkungen homogener und inhomogener Linienverbreiterung und spektraler Diffusion auf NLPF-spektren, sowie deren Verallgemeinerung im Ramen der Theorie nichtmarkowscher Dissipationsprozesse, konnte eine Methodik entwickelt werden, die es erlaubt, NLPF-spektren molekularer und supramolekularer Systeme in Bezug auf das ihnen zugrundeliegende Termschema mit Übergangsfrequenzen und -dipolen, die homogenen und inhomogenen Linienbreiten, sowie dem zugeordneten Energierelaxations- und -transferpfad mitsamt zugehörigen Raten zu analysieren. Die in dieser Arbeit vorgestellte und über frühere rudimentäre Ansätze weit hinausgehende Theorie der NLPF bei starken Pumpfeldern, die auf einem selbstkonsistenten Ansatz für den Fourier-transformierten statistischen Operator beruhen, eröffnet ein komplett neues Feld von Anwendungen der NLPF. Für Zweiniveausysteme konnten die selbstkonsistenten Gleichung vollständig analytisch gelöst werden. Dabei konnten die Querverbindungen zur nichtlinearen Absorption und zum optischen Starkeffekt aufgezeigt werden. Aus der resultierenden Sättigungskurve für das NLPF-signal kann die Sättigungsintensität mit hoher Genauigkeit bestimmt werden. Diese kann unter Heranziehen der aus Analyse des T1-peaks bei niedrigen Intensitäten gewonnen Energierelaxationsrate und der analog aus T2-peakanalyse erhaltenen homogenen Linienbreite zur Bestimmung der Dipolstärke des Übergangs ohne Bestimmung der Farbstoffkonzentration verwendet werden. Dies erweist sich insbesondere bei der Analyse molekularer Aggregation als vorteilhaft. Durch Abbildung auf das gelöste Zweiniveauproblem konnte die Methodik auch auf spezielle Mehrniveausysteme übertragen werden. Eine analytische Lösung für allgemeine Mehrniveausysteme scheiterte jedoch an der komplizierten Orientierungsmittelung über die isotrope Verteilung der Übergangsdipole. Beide oben beschriebenen Methoden, Subbandanalyse bei niedrigen und Bestimmung der Übergangsdipolstärke bei hohen Pumpintensitäten, wurden in der vorliegenden Arbeit zur Untersuchung der Natur der angeregten Zustände in photosynthetischen Antennen von Purpurbakterien und höheren Pflanzen eingesetzt. Für die periphere lichtsammelnde Antenne LH2 des Purpurbakteriums Rhodobacter sphaeroides ergab die T2-peakanalyse der B850-absorptionsbande überraschenderweise zwei Subbanden, die im Absorptionsspektrum selbst bei tiefsten Temperaturen nicht aufzufinden gewesen wären. Eine Erklärung für die in Bezug auf die Oszilatorstärke asymmetrische Aufspaltung der B850-bande konnte allerdings nicht gefunden werden. Für den LH2 des sehr ähnliche Purpurbakterium Rhodospirillium molischianum konnte keine Aufspaltung der B850-bande festgestellt werden. Vielmehr liegt eine überwiegend homogen verbreiterte Bande mit einer homogener Linienbreite (FWHM) von 474±10 cm-1 und einem oberen limit für die inhomogene Linienbreite von 120 cm-1 vor. Daher wurde Rhodospirillium molischianum ausgewählt, um Delokalisation der Anregung im B850-aggregat mittels pumpintensitätsabhängiger NLPF zu untersuchen. Die Frage nach der Delokalisationslänge im B850-aggregat gab und gibt teilweise immer noch Anlass zu hitzigen Debatten. Das Ergebnis einer Ausdehnung der Anregung über 3-4 Bakteriochlorophylle des B850-aggregats der vorliegenden Arbeit unterstützt die aus Exciton-Exciton gewonnen Resultate. Weder eine vollständig lokalisierte noch vollständig delokalisierte Beschreibung war mit dem hier präsentierten Ergebnis in Übereinstimmung zu bringen. Auch im Hauptlichtsammelkomplex höherer Pflanzen LHC II konnte mittels pumpintensitätsabhängiger NLPF-spektren Delokalisation der Anregung über mindestens ein Chlì¥Á / In the work be presented a standard theory of non-linear polarization spectroscopy in the frequency domain (NLPF) will be established. The NLPF technique based on anisotropy induced in a dye-solution, which is isotropic elsewhere, by a polarized monochromatic pump laser field. This is probed by a second laser field, which polarization direction is turned of 45 degree in respect to that of the pump. From the fundamental equations describing the non-linear response of molecular systems on electromagnetic fields, the two-dimensional NLPF spectrum is deduced for arbitrary pump-intensities. At low pump-intensities a subband analysis by NLPF has been established. This allows one to study the term scheme and energy relaxation path of molecular and supra-molecular systems by their NLPF-spectra. This includes the determination of transition-frequencies and -dipole orientations, homogeneous and inhomogeneous linewidths, as well as energy relaxation rates. Furthermore, using a self-connsistent approach, the pump-fieled dependence of the NLPF-spectrum has been deduced for the two-level system in general and also for specific multi-level systems. This method allows one to determine the oscillator strength without knowledge of the concentration, what is quite useful for studying molecular aggregates. Applications are presented to the peripheral light harvesting antenna LH2 of purple bacteria and the light harvesting complexes LHC II and CP 29 of higher plants.