In this thesis quantum-classical dynamics is applied to the study of quantum condensed phase processes. This approach is based on the quantum-classical Liouville equation where the dynamics of a small subset of the degrees of freedom are treated quantum mechanically while the remaining degrees of freedom are treated by classical mechanics to a good approximation. We use this approach as it is computationally tractable, and the resulting equation of motion accurately accounts for the quantum and classical dynamics, as well as the coupling between these two components of the system. By recasting the quantum-classical Liouville equation into the form of a generalized master equation we investigate connections to surface-hopping. The link between these approaches is decoherence arising from interaction of the subsystem with the environment. We derive an evolution equation for the subsystem which contains terms accounting for the effects of the environment. One of these terms involves a memory kernel that accounts for the coherent dynamics. If this term decays rapidly, a Markovian approximation can be made. By lifting the resulting subsystem master equation into the full phase space, we obtain a Markovian master equation that prescribes surface-hopping-like dynamics. Our analysis outlines the conditions under which such a description is valid. Next, we consider the calculation of the rate constant for a quantum mechanical barrier crossing process. Starting from the reactive-flux autocorrelation function, we derive a quantum-classical expression for the rate kernel. This expression involves quantum-classical evolution of a species operator averaged over the initial quantum equilibrium structure of the system making it possible to compute the rate constant via computer simulation. Using a simple model for a proton transfer reaction we compare the results of the rate calculation obtained by quantum-classical Liouville dynamics with that of master equation dynamics. The master equation provides a good approximation to the full quantum-classical Liouville calculation for our model and a more stable algorithm results due to the elimination of oscillating phase factors in the simulation. Finally, we make use of the theoretical framework established in this thesis to analyze some aspects of decoherence used in popular surface-hopping techniques.

Doctor of Philosophy / Department of Chemistry / Christine Aikens / Thiolate-protected noble metal nanoparticles (~2 nm size) are efficient solar photon harvesters, as they favorably absorb within the visible region. Clear mechanistic insights regarding the photo-physics of the excited state dynamics in thiolate-protected noble metal nanoclusters are important for future photocatalytic, light harvesting and photoluminescence applications. Herein, the core and higher excited states lying in the visible range are investigated using the time-dependent density functional theory method for different thiolate-protected nanoclusters. Nonadiabatic molecular dynamics simulations are performed using the fewest switches surface hopping approach with a time-dependent Kohn-Sham (FSSH-TDKS) description of the electronic states with decoherence corrections to study the electronic relaxation dynamics. Calculations on the [Au₂₅ (SH)₁₈]⁻¹ nanocluster showed that relaxations between core excited states occur on a short time scale (2-18 ps). No semiring or other states were observed at an energy lower than the core-based S₁ state, which suggested that the experimentally observed picosecond time constants could be core-to-core transitions rather than core-to-semiring transitions. Electronic relaxation dynamics on [Au₂₅ (SH)₁₈]⁻¹ with different R ligands (R = CH₃, C₂H₅, C₃H₇, MPA) [MPA = mercaptopropanoic acid] showed that all ligand clusters including the simplest SH model follow a similar trend in decay within the core states. In the presence of higher excited states, R= H, CH₃, C₂H₅, C₃H₇ demonstrated similar relaxations trends, whereas R=MPA showed a different relaxation of core states due to a smaller LUMO+1-LUMO+2 gap. Overall, the S₁ state gave the slowest decay in all ligated clusters. An examination of separate electron and hole relaxations in the [Au₂₅ (SCH₃)₁₈]⁻¹ nanocluster showed how the independent electron and hole relaxations contribute to its overall relaxation dynamics. Relaxation dynamics in the Au₁₈(SH)₁₄ nanocluster revealed that the S₁ state has the slowest decay, which is a semiring to core charge transfer state. Hole relaxations are faster than electron relaxations in the Au₁₈(SH)₁₄ cluster due its closely packed HOMOs. The dynamics in the Au₃₈(SH)₂₄ nanocluster predicted that the slowest decay, the decay of S₁₁ or the combined S₁₁-S₁₂, S₁-S₂-S₄-S₇ and S₄-S₅-S₉-S₁₀ decay, involves intracore relaxations. The phonon spectral densities and vibrational frequencies suggested that the low frequency (25 cm⁻¹) coherent phonon emission reported experimentally could be the bending of the bi-icosahedral Au₂₃ core or the “fan blade twisting” mode of two icosahedral units. Relaxation dynamics of the silver nanoparticle [Ag₂₅ (SR)₁₈]⁻¹ showed that both [Ag₂₅(SH)₁₈]⁻¹ and [Au₂₅ (SH)₁₈]⁻¹ follow a common decay trend within the core states and the higher excited states.

No description available.

The ability of the nucleic acids to absorb ultraviolet light and remain relatively photostable is a property upon which life depends. The nucleobases, which are the primary chromophores, when irradiated display rapid radiationless decay back to the ground state, in general faster than is needed for photoreaction. Fluorescent analogs of these bases have structures similar to the nucleic acid bases, but display much longer excited state lifetimes. Theoretical investigations using quantum mechanical methods can provide insight into the precise mechanisms of these decay processes, and to the molecular specifics that contribute to them. The results of multi-reference configuration interaction (MRCI) ab initio investigations into these mechanisms are presented, with emphasis on cytosine and its fluorescent analog 5-methyl-2-pyrimidinone (5M2P). A comprehensive picture of the potential energy surfaces of these two bases is given, including stationary points and conical intersections, where radiationless transitions are promoted, between up to three state surfaces, as well as pathways connecting these points for each base. Cytosine is shown to have two different energetically accessible radiationless decay channels. The fluorescence of 5M2P is also demonstrated theoretically, with mechanism proposed. The potential energy surfaces of the two bases have many close similarities, with the different photophysical properties being attributed to subtle energetic differences between the two bases. Nonadiabatic coupling and the geometric phase effect are analyzed in detail near conical intersections in cytosine, including in a region close to a three-state conical intersection. A substituent effect study on the 2-pyrimidinone ring system shows that the presence, position and orientation of the amino group in cytosine is central to its photophysical properties, particularly its high absorption energy, and can be explained with a simple Frontier Molecular Orbital model. The effects of water solvent on the excitation energies of cytosine and uracil are theoretically investigated using two multi-reference ab initio methods, a quantum mechanical molecular mechanics method using MRCI (MRCI-QM/MM), and the fragment molecular orbital multiconfiguration self-consistent field method (FMO-MCSCF). The solvatochromic shifts calculated from both methods agree well with other more expensive methods and experimental data. The effects of water on the photophysical pathways of cytosine is also investigated using MRCI-QM/MM, including considerations of solvent reorganization. Results show that the overall effect of water on the decay mechanisms is small, with neither decay channel being significantly blocked or favored. / Chemistry

Soluções não-adiabáticas em coordenadas hiperesférica para sistemas coulombianos de três corpos são apresentadas. Energias altamente precisas para o estado fundamental do hélio são obtidas, pela primeira vez, no método adiabática hiperesferico (HAA). Com a inclusão de somente três curvas de potencial e os correspondentes acoplamentos, precisão de partes por milhão foram obtidas. Concluímos que o HAA, usado exaustivamente para descrever semi-quantitativamente sistemas atômicos e moleculares, não está mais obstruído pela falata de prescrição para se obter funções de onda de precisão arbritária para sitemas coulombianos. / Non-adiabatic solutions for the Coulombic three-body systems in hyperspherical coordinates are presented. Highly accurated energies for the helium ground state are obtained, by the first time, in the hyperspherical adiabatic approach (HAA). With the inclusion of only three potential curves and the corresponding couplings, precision of parts per million have been achieved. We conclude that the HAA, exhaustively used to describe semi-quantitatively both molecular and atomic systems, is no longer more hampered by the lack of prescription for the obtainment of arbitrary precision wave functions for Coulombic systems.

Made available in DSpace on 2015-05-15T11:46:09Z (GMT). No. of bitstreams: 1 ArquivoTotalOsvaldo.pdf: 1490620 bytes, checksum: 022e9b1169cd35f90c2e82c9ae74fe26 (MD5) Previous issue date: 2008-12-19 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / We present the own mathematic formalism to, first of all, study the holonomy interpretations of the adiabatic geometric phase presented by Berry-Simon and Aharanov-Anadan and, after this, the similirities found with the theory of representation groups, particularly, with the Borel-Weil-Bott theorem. These relations are made through classification of complex bundle line, and these results are used to introduce a cranked Hamiltonian. In general, we also show that the parameter space is a flag manifold or a submanifold of her and present a topologic argument of this space that indicates the relation between the structure Riemannian and the Berry s connection. / Apresentamos o formalismo matemático próprio para, primeiramente, estudarmos as interpretações holonômicas da fase geométrica adiabática apresentadas por Berry-Simon e Aharanov-Anadan e, em seguida, as similaridades encontradas com a Teoria de Representações de Grupos, em particular, com o teorema de Borel-Weil-Bott. Estas relações são feitas via classificação de fibrados linha complexos, e esses resultados são usados para introduzir um procedimento que trata a não-adiabaticidade e a adiabaticidade da fase de Berry por meio de uma modificação na hamiltoniana. Mostramos, também, que em geral, o espaço de parâmetros é uma variedade de bandeira ou uma subvariedade dela e apresentamos um argumento topológico desse espaço, que indica a relação entre a estrutura Riemanniana e a conexão de Berry.

Soluções não-adiabáticas em coordenadas hiperesférica para sistemas coulombianos de três corpos são apresentadas. Energias altamente precisas para o estado fundamental do hélio são obtidas, pela primeira vez, no método adiabática hiperesferico (HAA). Com a inclusão de somente três curvas de potencial e os correspondentes acoplamentos, precisão de partes por milhão foram obtidas. Concluímos que o HAA, usado exaustivamente para descrever semi-quantitativamente sistemas atômicos e moleculares, não está mais obstruído pela falata de prescrição para se obter funções de onda de precisão arbritária para sitemas coulombianos. / Non-adiabatic solutions for the Coulombic three-body systems in hyperspherical coordinates are presented. Highly accurated energies for the helium ground state are obtained, by the first time, in the hyperspherical adiabatic approach (HAA). With the inclusion of only three potential curves and the corresponding couplings, precision of parts per million have been achieved. We conclude that the HAA, exhaustively used to describe semi-quantitatively both molecular and atomic systems, is no longer more hampered by the lack of prescription for the obtainment of arbitrary precision wave functions for Coulombic systems.

Cette thèse concerne l'ouverture de cycle des spiropyranes (SP) et leur utilisation comme interrupteurs contrôlés par impulsions laser. Nous avons élaboré un modèle théorique pour étudier cette réaction photochimique et développer des stratégies de contrôle.Les SP présentent des effets non adiabatiques impliquant un traitement quantique pour les électrons et les noyaux. L'approche multiconfigurationnelle dépendante du temps (MCTDH) est idéale car elle peut traiter des dynamiques quantiques impliquant plusieurs états électroniques. MCTDH a été appliqué avec succès aux calculs de spectres électroniques de systèmes montrant de forts effets non adiabatiques. Cependant, cette approche requiert au préalable les surfaces d'énergie potentielle (PES). Ces applications sont basées sur un modèle de couplage vibronique local de la PES à proximité du point de Franck-Condon (FC). Contrairement aux calculs de spectres de photoabsorbtion impliquant souvent de courtes échelles de temps et de faibles déformations autour du point de FC, la simulation de réactions photochimiques requiert une représentation adéquate des mouvements de large amplitude. Ce modèle doit donc être rendu plus flexible. Les modes normaux, utilisés dans le modèle standard, n'étant pas adaptés aux grandes déformations, nous avons choisi d'utiliser la méthode MCTDH en coordonnées curvilignes avec une reformulation systématique du modèle en coordonnées polysphériques afin d'obtenir une énergie cinétique nucléaire séparable.Même si le processus n'implique que l'état fondamental et le premier état excité, leurs configurations électroniques dominantes peuvent changer fortement le long de mouvements de grande amplitude. Nous avons donc développé une approche générale basée sur une étude systématique de quelques données ab initio pour générer le meilleur jeu d'états diabatiques d'un problème donné.De premières applications au benzopyrane (chromophore des SP) ont montré un bon accord avec l'expérience. / The focus of this thesis is the ring opening of spiropyrans (SP), and how these molecules can be used as photoswitches controlled with laser pulses. We have built a theoretical model to study this photochemical reaction and develop strategies for control.SP exhibit nonadiabatic effects, and therefore, their modelling requires a quantum description for both the electrons and the nuclei. The multiconfiguration time-dependent Hartree (MCTDH) approach is ideal in this case because it can treat quantum dynamics involving several electronic states. MCTDH was successfully applied to electronic spectra calculations of systems showing strong nonadiabatic effects. However, the corresponding potential energy surfaces (PES) for this approach are required first. These applications are based on a local vibronic coupling model of the PES in the neighbourhood of the Franck-Condon (FC) point.As opposed to calculating photoabsorption spectra that often involves short timescales and small deformations around the FC geometry, simulating photochemical reactions requires an adequate representation of large-amplitude motions. Thus, this model must be made more flexible.Normal modes, usually used for the standard model, are not adapted to large-amplitude deformations. We thus chose to run MCTDH in curvilinear coordinates and recast systematically the model in terms of polyspherical coordinates to produce a separable form for the nuclear kinetic energy.Even if only the ground and the first excited electronic states are involved in the process, their dominant electronic configurations may change significantly along large-amplitude motions. We have developed a general approach based on a systematic analysis of a few ab initio data to generate the best set of diabatic states for a given problem.Preliminary results applied to benzopyran (the chromophore of the SP) showed good agreement with the experiments.

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.

<p>Quantum dynamics is the study of time-dependent phenomena in fundamental processes of atomic and molecular systems. This thesis focuses on systems where nature reveals its quantum aspect; e.g. in vibrational resonance structures, in wave packet revivals and in matter wave interferometry. Grid based numerical methods for solving the time-dependent Schrödinger equation are implemented for simulating time resolved molecular vibrations and to compute photo-electron spectra, without the necessity of diagonalizing a large matrix to find eigenvalues and eigenvectors.</p><p>Pump-probe femtosecond laser spectroscopy on the sodium potassium molecule, showing a vibrational period of 450 fs, is theoretically simulated. We find agreement with experiment by inclusion of the finite length laser pulse and finite temperature effects.</p><p>Complicated resonance structures observed experimentally in photo-electron spectra of hydrogen- and deuterium chloride is analyzed by a numerical computation of the spectra. The dramatic difference in the two spectra arises from non-adiabatic interactions, i.e. the interplay between nuclear and electron dynamics. We suggest new potential curves for the 3²Σ⁺ and 4²Σ⁺ states in HCI⁺.</p><p>It is possible to guide slow atoms along magnetic potentials like light is guided in optical fibers. Quantum mechanics dictates that matter can show wave properties. A proposal for a multi mode matter wave interferometer on an atom chip is studied by solving the time-dependent Schrödinger equation in two dimensions. The results verifies a possible route for an experimental realization.</p><p>An improved representation for wave functions using a discrete set of coherent states is presented. We develop a practical method for computing the expansion coefficients in this non-orthogonal set. It is built on the concept of frames, and introduces an iterative method for computing a representation of the identity operator. The phase-space localization property of the coherent states gives adaptability and better sampling efficiency.</p>