This thesis presents a development of classical canonical formalism and the usual transition schema to quantum dynamics. The question of transition from relativistic mechanics to relativistic quantum dynamics is answered by developing a homogeneous formalism which is relativistically invariant. Using this formalism the Klein-Gordon equation is derived as the relativistic analog of the Schroedinger equation. Using this formalism further, a method of generating other relativistic equations (with spin) is presented.

The aim of this thesis is the quantum dynamical study of two examples of scanning tunneling microscope (STM)-controllable, Si(100)(2x1) surface-mounted switches of atomic and molecular scale. The first example considers the switching of single H-atoms between two dangling-bond chemisorption sites on a Si-dimer of the Si(100) surface (Grey et al., 1996). The second system examines the conformational switching of single 1,5-cyclooctadiene molecules chemisorbed on the Si(100) surface (Nacci et al., 2008). The temporal dynamics are provided by the propagation of the density matrix in time via an according set of equations of motion (EQM). The latter are based on the open-system density matrix theory in Lindblad form. First order perturbation theory is used to evaluate those transition rates between vibrational levels of the system part. In order to account for interactions with the surface phonons, two different dissipative models are used, namely the bilinear, harmonic and the Ohmic bath model. IET-induced vibrational transitions in the system are due to the dipole- and the resonance-mechanism. A single surface approach is used to study the influence of dipole scattering and resonance scattering in the below-threshold regime. Further, a second electronic surface was included to study the resonance-induced switching in the above-threshold regime. Static properties of the adsorbate, e.g., potentials and dipole function and potentials, are obtained from quantum chemistry and used within the established quantum dynamical models. / Die vorliegende Doktorarbeit befasst sich mit kleinsten schaltbaren Einheiten in Form des Moleküls Cyclooctadien (COD) und dem Wasserstoff-Atom, die chemisch fest mit einer Oberfläche aus kristallinem Silizium verbunden sind. Jeder dieser Schalter kann mittels einer winzigen Spitze, eines so genannten Rastertunnelmikroskops (RTM), von atomarem Durchmesser in zwei unterscheidbare und stabile Schaltpositionen gebracht werden. Dabei besteht das Schalten entweder in einer Änderung der Geometrie des molekularen Schalters oder im Brechen und Neu-knüpfen chemischer Bindungen. Dabei ist es entscheidend, dass durch die geringe Grösse dieser Schalter eine hohe Anzahl dieser Schalter auf einer Oberfläche deponiert werden können. Mit der in den Schaltern speicherbaren Informationen an oder aus, 0 oder 1 ließen sich sehr hohe Speicherkapazitäten erreichen. Vor einer Anwendung dieser Art ist es wichtig zunächst ein grundlegendes Verständnis der Schaltprozesse auf der Oberfläche zu gewinnen. Wenn alle wesentlichen Faktoren berücksichtigt wurden und der Mechanismus des Schaltens verstanden ist, kann das Ergebnis des Experiments mit Hilfe eines theoretischen Modells vorhergesagt werden. Für die Handhabbarkeit muss sich das theoretisches Modell auf wesentliche Einflüsse beschränken und diese so einfach wie möglich beschreiben. So wurde die simultane Bewegung der 12 Atome des COD in die Bewegung eines gemittelten Massenpunktes entlang von einer oder von zwei räumlichen Freiheitsgraden übersetzt. Dabei kann der Massenpunkt im klassischen Bild anschaulich als eine rollende Kugel beschrieben werden, die in einer Seite einer Doppelmulde gefangen ist. Die Kugel kann durch äußere Anregung zum Schwingen gebracht werden und schließlich über eine Barriere in die benachbarte Mulde schalten. Nun muss die Schwingung der Kugel gebremst werden, um ein Zurück-Schwingen der Kugel zu verhindern. Die Anregung erfolgt durch elektrische Ladungen die von der Spitze des RTM zur Oberfläche wandern oder durch eine schwingende, d.h. warme Oberfläche. Das Bremsen wird über die elastische Bindung zu einer kalten Oberfläche vermittelt. Um Quanteneffekte wie das Tunneln der Kugel durch die Barriere zu beschreiben wurde die Kugel durch ein Wellenpaket beschrieben und dessen Aufenthaltswahrscheinlichkeit in der Doppelmulde untersucht. Im Fall des Wasserstoffatoms war die experimentelle Prüfung des entworfenen Modells für ein Schalten bei starkem Strom leider nicht möglich. Für das COD Molekül konnte jedoch nicht nur die Übereinstimmung mit den experimentellen Befunden, sondern im Fall des Schaltens in Abhängigkeit der Oberflächentemperatur auch die Vorhersagefähigkeit des Modells unter Beweis gestellt werden.

The study of noncovalent interactions between aromatic rings and various functional groups is a very popular topic in current computational chemistry. The research presented in this thesis takes steps to bridge the gap between theoretical prototypes and real-world systems. The non-additive contributions to the interaction energy in stacked aromatic systems are measured by expanding the prototype benzene dimer into trimeric and tetrameric systems. We show that the three- and four-body interaction terms generally do not contribute significantly to the overall interaction energy, and that the two-body terms are essentially the same as in the isolated dimer. The sulfur-pi interaction is then studied by using the hydrogen sufide-benzene dimer as a prototype system for theoretical predictions. We obtain higly-accurate potential energy curves, as well as an interaction energy extrapolated to the complete basis set limit. Energy decomposition analysis using symmetry-adapted perturbation theory shows that the sulfur-pi interaction is primarily electrostatic in nature. These theoretical results are then compared to an analysis of real sulfur-pi contacts found by searching protein structures in the Brookhaven Protein DataBank. We find that the most frequently seen configuration does not correspond to the theoretically predicted equilibrium for sydrogen sulfide-benzene, but instead to a configuration that suggests an alkyl-pi interaction involving the carbon adjacent to the sulfur atom. We believe our findings indicate that environmental effects within proteins are altering the energetics of the sulfur-pi interaction so that other functional groups are preferred for interacting with the aromatic ring.

The dynamic structure factor of liquid para-hydrogen and ortho-deuterium in corresponding thermodynamic states, (T = 20.0 K, n = 21.24 nm⁻³) and (T = 23.0 K, n = 24.61 nm⁻³) respectively, has been computed by both the Feynman-Kleinert linearized path-integral (FK-LPI) and Ring-Polymer Molecular Dynamics (RPMD) methods and compared with Inelastic X-ray Scattering spectra. The combined use of computational and experimental methods enables a reduction in experimental uncertainties for the determination of the true sample spectrum. Furthermore, the refined experimental spectrum of para-hydrogen and ortho-deuterium is consistently reproduced by both FK-LPI and RPMD at momentum transfers lower than 12.8nm⁻¹. At larger momentum transfers the F K - LP I results agree with experiment much better for ortho-deuterium than for para-hydrogen. More specifically we found that for k ~ 20.0 nm⁻¹ para-hydrogen provides a test case for improved approximations to quantum dynamics. We meet this demand for an improved approximate quantum dynamics method by developing two classes of quasi-classical dynamics that are shown to conserve the initial quantum ensemble when used in conjunction with the Feynman-Kleinert approximation of the density operator. As shown, both classes of dynamics are able to recover the exact classical and high temperature limits of the quantum time correlation function, while a subset is able to recover the exact harmonic limit. A comparison of the approximate quantum time correlation functions obtained from both classes of dynamics are made with the exact results for the challenging model problems of the quartic and double-well potentials. It is found that this new Feynman-Kleinert Quasi-Classical Wigner (FK-QCW) method provides a great improvement over the Feynman-Kleinert implementation of the classical Wigner approximation, also known as FK-LPI, in which purely classical dynamics are used. Furthermore, it is shown that the first class of dynamics reduces to Centroid Molecular Dynamics (CMD) when used within the framework of the classical Wigner approximation for the Kubo transformed time correlation function. Finally, we apply the Feynman-Kleinert Quasi-Classical Wigner (FK- QCW) method to the same liquid para-hydrogen and ortho-deuterium system, previously studied using FK-LPI and RPMD. When applied to this challenging system, it is shown that this new FK-QCW method consistently reproduces the experimental dynamic structure factor for all momentum transfers considered. This shows that FK-QCW provides a great improvement over FK-LPI for not only model problems, but also realistic systems. Furthermore, for small momentum transfers, where RPMD is applicable, it is shown that FK-QCW provides nearly the same results as RPMD, thus suggesting that FK-QCW provides a potentially more appealing algorithm than RPMD since one is not limited to correlation functions involving linear operators. This then suggests that the FK-QCW method is a top contender in the realm of approximate quantum dynamics methods which allow for the practical evaluation of time correlation functions. / text

Understanding energy transfer at the molecular scale is both essential for the design of novel molecular level devices and vital for uncovering the fundamental properties of non-equilibrium open quantum systems. In this thesis, we first establish the connection between molecular scale devices -- molecular electronics and phononics -- and open quantum system models. We then develop theoretical tools to study various properties of these models. We extend the standard master equation method to calculate the steady state thermal current and conductance coefficients. We then study the scaling laws of the thermal current with molecular chain size and energy, and apply this tool to investigate the onset of nonlinear thermal current - temperature characteristics, thermal rectification and negative differential conductance. Our master equation technique is valid in the ``on-resonance" regime, referring to the situation in which bath modes in resonance with the subsystem modes are thermally populated. In the opposite ``off-resonance" limit, we develop the Energy Transfer Born-Oppenheimer method to obtain the thermal current scaling without the need to solve for the subsystem dynamics. Finally, we develop a mapping scheme that allows the dynamics of a class of open quantum systems containing coupled subsystems to be treated by considering the separate dynamics in different subsections of the Hilbert space. We combine this mapping scheme with path integral numerical simulations to explore the rich phenomenon of entanglement dynamics within a dissipative two-qubit model. The formalisms developed in this thesis could be applied for the study of energy transfer in different realizations, including molecular electronic junctions, donor-acceptor molecules, artificial solid state qubits and cold-atom lattices.

Understanding energy transfer at the molecular scale is both essential for the design of novel molecular level devices and vital for uncovering the fundamental properties of non-equilibrium open quantum systems. In this thesis, we first establish the connection between molecular scale devices -- molecular electronics and phononics -- and open quantum system models. We then develop theoretical tools to study various properties of these models. We extend the standard master equation method to calculate the steady state thermal current and conductance coefficients. We then study the scaling laws of the thermal current with molecular chain size and energy, and apply this tool to investigate the onset of nonlinear thermal current - temperature characteristics, thermal rectification and negative differential conductance. Our master equation technique is valid in the ``on-resonance" regime, referring to the situation in which bath modes in resonance with the subsystem modes are thermally populated. In the opposite ``off-resonance" limit, we develop the Energy Transfer Born-Oppenheimer method to obtain the thermal current scaling without the need to solve for the subsystem dynamics. Finally, we develop a mapping scheme that allows the dynamics of a class of open quantum systems containing coupled subsystems to be treated by considering the separate dynamics in different subsections of the Hilbert space. We combine this mapping scheme with path integral numerical simulations to explore the rich phenomenon of entanglement dynamics within a dissipative two-qubit model. The formalisms developed in this thesis could be applied for the study of energy transfer in different realizations, including molecular electronic junctions, donor-acceptor molecules, artificial solid state qubits and cold-atom lattices.

This thesis aims at validating a theoretical protocol to develop global potential energy surfaces for use in the spectroscopy and dynamics of transition metal nitrosyl complexes. To get an insight into the homogeneous catalysis of NO with Cu and the chemical reaction dynamics, an accurate prediction of the nature of the interaction, as well as of the global potential energy surfaces (PES) is necessary in the gas phase. Experimental data are difficult to obtain, hence the importance of carrying out calculations of the lowest electronic states as accurate as possible to address the structure , spectroscopy and dynamics of this system. All ab initio calulations we report here were performed at the multi-reference configuration interaction (MRCI) and at the coupled cluster level of theory. We aslo investigate the importance of relativistic effects in the systems. For CuNO system, it is shown that a complete active space involving 18 valence electrons, 11 molecular orbitals and the prior determination of 12 roots in the MCSCF calculation is needed for overall qualitatively correct results from the MRCI calculations. The present calculations yield a bound singlet A' ground state for CuNO and comparared with previous results. We have obtained new, complete potential energy functions of the ground electronic states of CuO and CuN systems. Comparison of the term values for the lowest electronic states of CuO and CuN with those previously reported in the literature shows a quite good agreement. We derived a novel analytical representation of the adiabatic potential energy surface in the ground electronic state of the CuNO system as a sum of two-body and three-body terms. This compact and flexible representation enables us to make a physically correct interpolation of the ab initio data points at the MRCI level of theory. We use a modified Levenberg-Marquardt algorithm for fitting the potential, which has 19 adjustable parameters and which now enables us to do scattering dynamics of the CuNO system. We perform full dimensional quantum dynamical studies with this new potential. Convergence of the time dependent wavepacket calculation has been achieved. We find that the scattering in CuNO is highly inelastic. Intermediate, excited meta stable reaction products CuNO∗ live for about 0.5 to 1 ps and maybe more.

Many-body quantum dynamics is a challenging problem that has induced the development of many different computational techniques. One powerful technique is the multiconfiguration time-dependent Hartree-Fock (MCTDHF) method. This method allows proper consideration of electronic correlation with much less computational overhead compared to other similar methods. In this work, we present our implementation of the MCTDHF method on a non-uniform cylindrical grid. With the one-body limit of our code, we studied the controversial topic of tunneling delay, and showed that our results agree with one recent experiment while disagreeing with another. Using the fully correlated version of the code, we demonstrated the ability of MCTDHF to address correlation by calculating the ground state ionization energies of a few strongly correlated systems.

Chiral perturbation theory is a useful tool in the study of low energy reactions involving light particles. However the inclusion of heavy particles in chiral perturbation theory results in large contributions from loop diagrams which violate the standard power counting scheme. We review two methods, referred to as heavy baryon chiral perturbation theory and infrared regularization, which remove the high energy effects of the heavy particles and which therefore do not violate the power counting scheme. We then use these two methods to calculate the amplitude for pion photoproduction to fourth order and prove that the two amplitudes are equivalent.

Introduction An atom or ion in a solid is associated with a given lattice site. Translational motion can however occur in solids and such diffusion processes can be studied by nuclear magnetic resonance, tracer diffusion and other methods. In ionic compounds the diffusion is also a mechanism for charge transport and hence there is an associated ionic conductivity. [continued in text ...] NOTE: The Abstract contains many indistinct letters in mathematical formulas and it is impracticable to reproduce it here.