Rozprawy doktorskie na temat „Open Shell Molecular Systems”

This PhD thesis reports original research results concerning the development of theoretical models and computational protocols for the quantification and analysis of two of the most important quantum observables of open-shell systems: the electron spin density and the phosphorescence energy gap. In the first part, a comprehensive theory of the electron spin density topology is proposed for the first time [1]. Several new notions (spin density critical points, molecular spin graphs, spin density basins, spin maxima and spin minima joining paths etc.) and descriptors (local and integral spin polarization indeces, basin average spin density etc.) are introduced. This analysis reveals that the spin density topology, based on precise mathematical notions, can unveil precious information on the physical structure of spin-polarized systems. In particular, it enables to describe and quantify spin polarization and delocalization mechanisms and, at the same time, to evaluate the dependence of spin density distributions on the adopted level of theory. In the second part instead, the performance of the domain-based local pair natural orbital (DLPNO) variant of the “gold standard” CCSD(T) method for the prediction of phosphorescence energies of aromatic chromophores is investigated for the first time [2]. An extensive analysis of both accuracy and computational cost of the main parameters of the method (basis set, triples correction approximation, dimension of PNOs space) is conducted. Two procedures, the Gold DLPNO-CCSD(T) aimed at maximizing the accuracy and the Silver DLPNO-CCSD(T) aimed at minimizing the computational cost, which result in an excellent agreement with experimental data, are proposed. 1. G. Bruno, G. Macetti, L. Lo Presti and C. Gatti, “Spin Density Topology,” Molecules, 25, 3537, 2020. 2. G. Bruno, B. de Souza, F. Neese, and G. Bistoni, “Can domain-based local pair natural orbitals approaches accurately predict phosphorescence energies?,” Phys. Chem. Chem. Phys., 24, 14228–14241, 2022.

This thesis focuses on two different, but equally challenging, areas of computational chemistry: transition metal organic molecule interactions and parameterisation of organic conjugated polymers for molecular dynamics simulations. The metal-binding properties are important for understanding of biomolecular action of type 2 diabetes drug and development of novel protocols for redox calculations of copper systems. In this area the challenge is mainly related to the complex electronic structure of the open-shell transition metals. The main challenges for the parameterisation of conjugated polymers are due to the size of the studied systems, their conjugated nature and inclusion of environment. Metal-binding properties as well as electronic structures of copper complexes of type 2 diabetes drug metformin (Metf) and other similar, but often inactive, compounds were examined using DFT method. It was found that for neutral compounds it is not possible to explain the differences in their biological effects solely by examining the copper-binding properties. Further, the proposed mechanism potentially explaining the difference in the biomolecular mode of action involves a possible deprotonation of biguanide and Metf compounds under higher mitochondrial pH which would lead to formation of more stable copper complexes and potentially affecting the mitochondrial copper homeostasis. In addition, redox properties of copper-biguanide complexes could interfere with the sensitive redox chemistry or interact with important metalloproteins in the mitochondria. Understanding the copper-binding properties is also important for a systematic development and testing of computational protocols for calculations of reduction potentials of copper complexes. Copper macrocyclic complexes previously used as model systems for redox-active metalloenzymes and for which experimentally determined redox potentials are available were used as model systems. First adequacy of using single reference methods such as DFT was examined for these systems and then various DFT functionals and basis sets were tested in order to develop accurate redox potential protocol. It was shown that good relative cor-relations were obtained for several functionals while the best absolute agreement was obtained with either the M06/cc-pVTZ functional with the SMD or either M06L or TPSSTPSS functional with cc-pVTZ basis set and the PCM solvation model. Organic conjugated polymers have a great potential due to their application in organic optoelectronics. Various wavefunction and DFT methods are utilized in order to systematically develop parameterisation scheme that can be used to derive selected force-field parameters such as torsional potentials between monomer units that are critical for these systems and partial charges. Moreover, critical points of such a parameterisation are addressed in order to obtain accurate MD simulations that could provide valuable insight into material morphology and conformation that affect their optical properties and conductivity. It was shown that a two step approach of geometry optimisation with CAM-B3LYP/631G* and single point (SP) energy scan with CAM-B3LYP/cc-pVTZ is able to yield accurate dihedral potentials in agreement with the potentials calculated using higher level methods such as MP2 and CBS limit CCSD(T). Further, investigating partial charge distribution for increasing backbone length of fluorene and thiophene it has been found that it is possible to obtain a three residue model of converged charge distributions using the RESP scheme. The three partial charge residues can be then used to build and simulate much longer polymers without the need to re-parametrize charge distributions. In the case of side-chains, it was found that it is not possible to obtain converged charge sets for sidechain lengths of up to 10 carbons due to the strong asymmetry between the side-chain ends. Initial validation of derived force-field parameters performed by simulations of 32mers of fluorene with octyl side-chains (PF8) and thiophene with hexyl side-chains (P3HT) in chloroform and calculation of persistence lengths and end-to-end lengths showed close correspondence to experimentally obtained values.

In this thesis, the implementation of the incremental scheme for open-shell systems with unrestricted Hartree-Fock reference wave functions is described. The implemented scheme is tested within robustness and performance with respect to the accuracy in the energy and the computation times. New approaches are discussed to implement a fully automated incremental scheme in combination with the domain-specific basis set approximation. The alpha Domain Partitioning and Template Equalization are presented to handle unrestricted wave functions for the local correlation treatment. Both orbital schemes are analyzed with a test set of structures and reactions. As a further goal, the DSBSenv orbital basis sets and auxiliary basis sets are optimized to be used as environmental basis in the domain-specific basis set approach. The performance with respect to the accuracy and computation times is analyzed with a test set of structures and reactions. In another project, a scheme for the optimization of auxiliary basis sets for uranium is presented. This scheme was used to optimize the MP2Fit auxiliary basis sets for uranium. These auxiliary basis enable density fitting in quantum chemical methods and the application of the incremental scheme for systems containing uranium. Another project was the systematical analysis of the binding energies of four water dodecamers. The incremental scheme in combination with the CCSD(T) and CCSD(T)(F12*) method were used to calculate benchmark energies for these large clusters.

The question posed in this work is how one would model and predict the rotational spectrum of open-shell open-shell van der Waals complexes. There are two secondary questions that arise: the nature of radical-radical interactions in such systems and the modelling of the large amplitude motion of the constituent molecules. Four different systems were studied in this work, each providing part of the answer to the main question. Starting with the large amplitude motion, there are two theoretical approaches that may be adopted: to either model the whole complex as a semi-rigid molecule, or to perform quantum dynamical calculations. We recorded and analysed the rotational spectrum (using Fourier transform microwave spectroscopy) of the molecule of tertiary butyl acetate (TBAc) which exhibits a high degree of internal rotation; and of the weakly-bound complex between a neon atom and a nitrogen dioxide molecule (Ne-NO2). We used the semi-rigid approach for TBAc and the quantum dynamical approach for Ne-NO2. We also explored the compatibility of these two approaches. Moreover, we were able to predict and analyse the fine and hyperfine structure of the Ne-NO2 spectrum using spherical tensor operator algebra and the results of our dynamics calculations. To explore the nature of the interactions in an radical-radical van der Waals complex we calculated the PESs of the possible states that the complex may be formed in, when an oxygen and a nitrogen monoxide molecule meet on a plane using a number of high level ab initio methods. Finally, our conclusions were tested and applied when we performed the angular quantum dynamics to predict the rotational spectrum of the complex between an oxygen and a nitrogen dioxide molecule, and account for the effect of nuclear spin statistics in that system.

The microwave spectrum of the open-shell van der Waals complex NO-HF has been recorded in the region 6-20GHz using a pulsed nozzle Fourier transform microwave spectrometer. This is the first observation of the microwave spectrum of a open-shell van der Waals complex between two molecules. The spectrum exhibits a rich hyperfine structure with the observation of intermolecular hyperfine interactions in an isolated system providing a sensitive probe of electron transfer in the complex. The spectrum consists of four fine structure transitions 5/2(e)-3/2(e), 3/2(e)-1/2(e), 5/2(f)-3/2(f), 3/2(f)-1/2(f) which have been fitted to a semi-rigid Hamiltonian developed to include the effects of the orbital and spin angular momenta of the unpaired electron on NO. A new treatment to account for the intermolecular hyperfine interaction was developed. The structure of the complex has been determined and is significantly bent with an angle of between 37 degrees and 49 degrees between the NO internuclear axis and the a-axis of the complex. The Renner-Teller parameter, epsilon 2, is very large and negative having the value of -10 449.32(4)GHz indicating that configuration with the unpaired electron in the plane of the complex is more stable. The analysis of the hyperfine interactions of the hydrogen and fluorine nuclei uses two constants for each nucleus, one for the spatial relationship between the magnetic moments of the unpaired electron and the nuclear magnetic moment and a Fermi-contact term. The Fermi-contact term for hydrogen is the first strong evidence of intermolecular charge transfer in an isolated van der Waals molecule.

This thesis investigates the applicability of a range of computational techniques across a range of open shell chemical systems from the geometrically simple but electronically complex to the geometrically complex but electronically simple. Initially an investigation into a range of geometrically simple but electronically complicated systems is presented. The Monte Carlo Configuration Interaction method (MCCI) is applied to challenging transition metals dimers such as ScNi in order to establish the ground state potential energy surface, from equilibrium bond lengths through to dissociation using highly compact wavefunctions compared to Full Configuration Interaction (FCI). It shall be demonstrated that the ScNi dimer represents the current limit of this technique. Software development of MCCI is then undertaken in order to perform calculations of spin-orbit coupling interactions. Results on B, C, O, F, Si, S, F, Cl, OH, NO, CN and C2 species are shown to be comparable with other techniques using the one-electron Breit-Pauli Hamiltonian. The application of quantum chemistry to geometrically complex but electronically simple systems is then considered. Density Functional Theory (DFT) is used to investigate the mechanism and energetic barriers leading to ring inversion of the biscalix[4]arene supra-molecule. A minimum barrier height of 19.31 kcalmol−1 to inversion is elucidated along with details of the complete mechanistic pathway to inversion. The focus then moves to polymetallic clusters of calix[4]arene. A DFT study is made of the preferential binding of calix[4]arene towards first row transition metals of various oxidation and spin states. Results indicate that Cu3+ (singlet) species will preferentially bind to the lower rim over other metals in the study. The final DFT-related work presented is a study of the preferential binding at the upper rim of polymetallic calix[4]arene clusters towards a range of important small gas molecules. It was found that gases such as NH3 and SO2 bind most strongly to the upper rim with the inclusion of a transition metal at the lower rim providing strengthening of the host-guest binding.

In this work the semiclassical hybrid dynamics is extended in order to be capable of treating open quantum systems considering finite baths. The corresponding phenomena, i.e. decoherence and dissipation, are investigated for various scenarios.

In the first part of the dissertation, we develop a theoretical approach to analyze nonlinear spectroscopy experiments based on the formalism of quantum state (QST) and process tomography (QPT). In it, a quantum system is regarded as a black box which can be systematically tested in its performance, very much like an electric circuit is tested by sending a series of inputs and measuring the corresponding outputs, but in the quantum sense. We show how to collect a series of pump-probe or photon-echo experiments, and by varying polarizations and frequency components of the perturbations, reconstruct the quantum state (density matrix) of the probed system for a set of different initial conditions, hence simultaneously achieving QST and QPT. Furthermore, we establish the conditions under which a set of two-dimensional optical spectra also yield the desired results. Simulations of noisy experiments with inhomogeneous broadening show the feasibility of the protocol. A spin-off of this work is our suggestion of a witness that distinguishes between spectroscopic time-oscillations corresponding to vibronic only coherences against their electronic counterparts. We conclude by noting that the QST/QPT approach to nonlinear spectroscopy sheds light on the amount of quantum information contained in the output of an experiment, and hence, is a convenient theoretical and experimental paradigm even when the goal is not to perform a full QPT. In the second part of the thesis, we discuss a methodology to study the electronic dynamics of complex molecular systems, such as photosynthetic units, in the framework of time-dependent density functional theory (TD-DFT). By treating the electronic degrees of freedom as the system and the nuclear ones as the bath, we develop an open quantum systems (OQS) approach to TD-DFT. We formally extend the theoretical backbone of TD-DFT to OQS, and suggest a Markovian bath functional which can be readily included in electronic structure codes.

New dynamical applications of quantum beat spectroscopy (QBS) to molecular dynamics are employed to probe the angular momentum polarization effects in photodissociation and molecular collisions. The magnitude and the dynamical behaviour of angular momentum alignment and orientation, two types of polarization, can be measured via QBS technique on a shot-by-shot basis. The first part of this thesis describes the experimental studies of collisional angular momentum depolarization for the electronically excited state radicals in the presence of the collider partners. Depolarization accompanies both inelastic collisions, giving rise to rotational energy transfer (RET), and elastic collisions. Experimental results also have a fairly good agreement with the results of quasi-classical trajectory scattering calculations. Chapter 1 provides the brief theories about the application of the QBS technique and collisional depolarization. Chapter 2 describes the method and instrumentation employed in the experiments of this work. In Chapter 3, the QBS technique is used to measure the total elastic plus elastic depolarization rate constants under thermal conditions for NO(A,v=0) in the presence of He, Ar, N2, and O2. In the case of NO(A) with Ar, and particularly with He, collisional depolarization is significantly smaller than RET, reflecting the weak long-range forces in these systems. In the case of NO(A)+N2/O2, collisional depolarization and RET are comparable, reflecting the relatively strong long-range forces in these systems. In Chapter 4, the QBS technique is used to measure the elastic and inelastic depolarization and total RET rate constants for OH(A,v=0) under thermal conditions in the presence of He and Ar, as well as the total depolarization rate constants under superthermal conditions. In the case of OH(A)+He, elastic depolarization is sensitive to the N rotational state, and inelastic depolarization is strongly dependent on the collision energy. In the case of OH(A)+Ar, elastic depolarization is insensitive to N, and inelastic depolarization is less sensitive to the collision energy, reflecting that the relatively strong long-range force in OH(A)+Ar system. The second part of this thesis describes the experimental studies of photodissociation under thermal conditions. Chapter 5 provides a brief introduction about several polarization parameter formalisms used for photodissociation, and the incorporation of the QBS technique to measure these polarization parameters. In this thesis, most polarization parameters of the molecular photofragments are measured using the LIF method, and the QBS technique is used as a complementary tool to probe these polarization parameters. In Chapter 6, rotational orientation in the OH(X,v=0) photofragments from H2O2 photodissociation using circularly polarized light at 193 nm is observed. Although H2O2 can be excited to both the A and B electronic states by 193 nm, the observed orientation is only related to the A state dynamics. A proposed mechanism about the coupling between a polarized photon and the H2O2 parent rotation is simulated, and the good agreement between the experimental and simulation results further confirms the validity of this mechanism. In Chapter 7, rotational orientation in the NO(X,v) photofragments from NO2 photodissociation using circularly polarized light at 306 nm (v=0,1,2) and at 355 nm (v=0,1) is observed. Two possible mechanisms, the parent molecular rotation and the coherent effect between multiple electronic states, are discussed. NOCl is photodissociated using circularly polarized light at 306 nm, and NO(X,v) rotational distributions (v=0,1) and rotational orientation (v=0) are measured. For the case of NOCl, the generation of orientation is attributed to the coherent effect.

In this thesis, quantum dynamical simulations are performed in order to describe the vibrational motion of diatomic molecules in a highly quantum environment, so-called helium droplets. We aim to reproduce and explain experimental findings which were obtained from dimers on helium droplets. Nanometer-sized helium droplets contain several thousands of 4-He atoms. They serve as a host for embedded atoms or molecules and provide an ultracold “refrigerator” for them. Spectroscopy of molecules in or on these droplets reveals information on both the molecule and the helium environment. The droplets are known to be in the superfluid He II phase. Superfluidity in nanoscale systems is a steadily growing field of research. Spectra obtained from full quantum simulations for the unperturbed dimer show deviations from measurements with dimers on helium droplets. These deviations result from the influence of the helium environment on the dimer dynamics. In this work, a well-established quantum optical master equation is used in order to describe the dimer dynamics effectively. The master equation allows to describe damping fully quantum mechanically. By employing that equation in the quantum dynamical simulation, one can study the role of dissipation and decoherence in dimers on helium droplets. The effective description allows to explain experiments with Rb-2 dimers on helium droplets. Here, we identify vibrational damping and associated decoherence as the main explanation for the experimental results. The relation between decoherence and dissipation in Morse-like systems at zero temperature is studied in more detail. The dissipative model is also used to investigate experiments with K-2 dimers on helium droplets. However, by comparing numerical simulations with experimental data, one finds that further mechanisms are active. Here, a good agreement is obtained through accounting for rapid desorption of dimers. We find that decoherence occurs in the electronic manifold of the molecule. Finally, we are able to examine whether superfluidity of the host does play a role in these experiments
In dieser Dissertation werden quantendynamische Simulationen durchgeführt, um die Schwingungsbewegung zweiatomiger Moleküle in einer hochgradig quantenmechanischen Umgebung, sogenannten Heliumtröpfchen, zu beschreiben. Unser Ziel ist es, experimentelle Befunde zu reproduzieren und zu erklären, die von Dimeren auf Heliumtröpfchen erhalten wurden. Nanometergroße Heliumtröpfchen enthalten einige tausend 4-He Atome. Sie dienen als Wirt für eingebettete Atome oder Moleküle und stellen für dieseeinen ultrakalten „Kühlschrank“ bereit. Durch Spektroskopie mit Molekülen in oder auf diesen Tröpfchen erhält man Informationen sowohl über das Molekül selbst als auch über die Heliumumgebung. Man weiß, dass sich die Tröpfchen in der suprafluiden He II Phase befinden. Suprafluidität in Nanosystemen ist ein stetig wachsendes Forschungsgebiet. Spektren, die für das ungestörte Dimer durch voll quantenmechanische Simulationen erhalten werden, weichen von Messungen mit Dimeren auf Heliumtröpfchen ab. Diese Abweichungen lassen sich auf den Einfluss der Heliumumgebung auf die Dynamik des Dimers zurückführen. In dieser Arbeit wird eine etablierte quantenoptische Mastergleichung verwendet, um die Dynamik des Dimers effektiv zu beschreiben. Die Mastergleichung erlaubt es, Dämpfung voll quantenmechanisch zu beschreiben. Durch Verwendung dieser Gleichung in der Quantendynamik-Simulation lässt sich die Rolle von Dissipation und Dekohärenz in Dimeren auf Heliumtröpfchen untersuchen. Die effektive Beschreibung erlaubt es, Experimente mit Rb-2 Dimeren zu erklären. In diesen Untersuchungen wird Dissipation und die damit verbundene Dekohärenz im Schwingungsfreiheitsgrad als maßgebliche Erklärung für die experimentellen Resultate identifiziert. Die Beziehung zwischen Dekohärenz und Dissipation in Morse-artigen Systemen bei Temperatur Null wird genauer untersucht. Das Dissipationsmodell wird auch verwendet, um Experimente mit K-2 Dimeren auf Heliumtröpfchen zu untersuchen. Wie sich beim Vergleich von numerischen Simulationen mit experimentellen Daten allerdings herausstellt, treten weitere Mechanismen auf. Eine gute Übereinstimmung wird erzielt, wenn man eine schnelle Desorption der Dimere berücksichtigt. Wir stellen fest, dass ein Dekohärenzprozess im elektronischen Freiheitsgrad des Moleküls auftritt. Schlussendlich sind wir in der Lage herauszufinden, ob Suprafluidität des Wirts in diesen Experimenten eine Rolle spielt

Zusammenfassung in PostScript In dieser Arbeit wird die photoinduzierte Dynamik offener Molekularsysteme unter dem Einfluß intensiver und ultrakurzer Laserpulse untersucht. Die Anregung eines Moleküls durch einen optischen ultrakurzen Laserpuls führt zu Übergängen zwischen verschiedenen elektronischen Zuständen. Dieser Anregungsprozeß wird begleitet von dissipativen Vorgängen wie Energie-- und Phasenrelaxation. Die Beschreibung dieser photoinduzierten Dynamik erfolgt mit Hilfe der Methode der Dichtematrixtheorie. Dabei zeigt die Ableitung der Quanten--Master--Gleichung im Rahmen des Projektionsoperator--Formalismus, daß die wirkenden äußeren Felder einmal direkt im reversiblen Anteil der Bewegungsgleichung auftreten, aber auch einen indirekten Einfluß über den die Dissipation beschreibenden Dissipations--Superoperator ausüben. In dieser Arbeit wird zum ersten Mal die durch ultrakurze Laserpulse induzierte Feldabhängigkeit des Dissipations--Superoperators berücksichtigt. Im Rahmen der Darstellung der Quanten--Master--Gleichung im Floquetbild kann eine anschauliche Deutung dieses feldabhängigen Effektes gegeben werden: die die Dissipation beschreibende frequenzabhängige Spektraldichte der Umgebungsmoden wird feldabhängig bei verschiedenen Frequenzen abgefragt. Analytische Untersuchungen zum Zwei--Niveau--System zeigen, daß die Feldabhängigkeit dann relevant wird, wenn die Pulslänge vergleichbar ist mit der Zeitskala, auf der die Autokorrelationsfunktion der Umgebungsfreiheitsgrade abklingt. Um den Einfluß auf experimentelle Größen zu untersuchen, wird ein zweifarbiges Pump--Test--Experiment zum Laserfarbstoffmolekül IR 125 betrachtet, bei welchem die spektral und zeitlich aufgelöste Transmission auf einer Femtosekunden-- und Pikosekunden--Zeitskala gemessen wurde. Im Rahmen des Modells einer effektiven Schwingungsmode wird eine Anpassungsrechnung an das Experiment vorgenommen. Dabei wird zunächst die Standard-Redfield-Theorie verwendet, um ein Referenzmodell zu gewinnen. Es gelingt, eine gute Übereinstimmung mit dem Experiment zu erreichen. Die exakte Berücksichtigung des Einflusses der internen Konversion zwischen den angeregten elektronischen Zuständen führt zu einem Anstieg der Transmission innnerhalb einer Pikosekunde. Es ist notwendig, die Dichtematrixgleichungen exakt zu lösen, da eine vergleichende Untersuchung mit Hilfe der nichtlinearen Suszeptibilität dritter Ordnung eine deutliche Abweichung zum exakten Resultat zeigt. Ausgehend vom Referenzfall feldunabhängiger Dissipation wird dann die Feldabhängigkeit der Relaxationsraten bestimmt sowie der Einfluß auf Observablen wie der relativen Transmission untersucht. In Übereinstimmung mit den analytischen Ergebnissen zeigt sich, daß der feldabhängige Effekt am größen ausgeprägt ist, wenn die Pulslänge kleiner als die Korrelationszeit der Umgebungsfreiheitsgrade wird und die wirkenden Felder hinreichend intensiv sind.Damit wird eine Kontrolle von Dissipation möglich. Ein Einfluß des feldabhängigen Effektes auf experimentelle Observablen wird vorhergesagt.
abstract in PostScript This thesis investigates the influence of intense and ultrashort laser pulses on the photoinduced dynamics of open molecular systems. The excitation of a molecule by an optical ultrashort laser pulse induces transitions between different electronic states. This excitation process is accompanied by the dissipative processes of energy and vibrational relaxation. This excitation process is described within the method of the density matrix theory. Thereby, the derivation of the quantum master equation in the framework of the projection operator formalism demonstrates that the external fields are present in the reversible part of the equation of motion and also exert an indirect influence by acting on the dissipation superoperator which accounts for dissipation. In this thesis the field--dependency of the dissipation superoperator which is induced by the external fields is considered for the first time. By a representation of the quantum master equation in the Floquet picture, an interpretation of this field--dependent effect can be given: the frequency--dependent spectral density of the environmental modes which describe dissipation is determined at different field--dependent frequencies. Analytical investigations for the two level system demonstrate that the field dependence becomes relevant if the pulse length is comparable with the time scale on which the autocorrelation function of the environmental degrees of freedom decays.To investigate the influence on experimental quantities, a two--color pump--probe experiment for the laser dye molecule IR 125 is considered for which the spectrally and temporally resolved transmission on a femtosecond and picosecond time scale has been measured. Within the model of one effective vibrational mode the experimental data is fitted. The standard Redfield theory is used to provide a reference model. A high degree of concurrence between the theory and the results of the experiment is achieved. The exact treatment of internal conversion between the excited electronic states leads to a rise in transmission within one picosecond. It is necessary to solve the density matrix equations exactly because a comparative investigation with the nonlinear susceptibility of third order leads to a clear viation from the exact result. Starting from the reference case of field--independent dissipation, the field--dependency of the relaxation rates is determined and the influence on observables for example the relative transmission is investigated. The analytical results show that the field--dependent effect is strongest if the pulse length becomes smaller than the correlation time of the environmental modes and if the acting fields are sufficiently strong. Thereby, a control of dissipation becomes possible. An influence of the field--dependent effect on experimental observables is predicted.

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.

The work summarizes basic theory of relaxation, energy transfer and decoher- ence in photosynthetic molecular aggregates described as open quantum systems and basic theory of third order coherent non-linear spectroscopy. The work presents two methods for calculation of photo-induced dynamics of molecular aggregates. The methods relax certain approximations of the theories commonly used to model the relaxation and energy transfer in the molecular systems on the sub-picosecond time scale. The first theory derived in the formalism of para- metric projection operators accounts for correlations in a second-order non-linear response-function that are usually neglected in the formalism of master equations. The second theory represents stochastic model of exact dynamics via the cumulant expansion. The work also presents an analysis of importance of the secular and the Markov approximations in the description of dynamics derived in the second-order perturbation theory in the system-bath coupling with emphasis on the excitonic coherence lifetime.

In this thesis, quantum dynamical simulations are performed in order to describe the vibrational motion of diatomic molecules in a highly quantum environment, so-called helium droplets. We aim to reproduce and explain experimental findings which were obtained from dimers on helium droplets. Nanometer-sized helium droplets contain several thousands of 4-He atoms. They serve as a host for embedded atoms or molecules and provide an ultracold “refrigerator” for them. Spectroscopy of molecules in or on these droplets reveals information on both the molecule and the helium environment. The droplets are known to be in the superfluid He II phase. Superfluidity in nanoscale systems is a steadily growing field of research. Spectra obtained from full quantum simulations for the unperturbed dimer show deviations from measurements with dimers on helium droplets. These deviations result from the influence of the helium environment on the dimer dynamics. In this work, a well-established quantum optical master equation is used in order to describe the dimer dynamics effectively. The master equation allows to describe damping fully quantum mechanically. By employing that equation in the quantum dynamical simulation, one can study the role of dissipation and decoherence in dimers on helium droplets. The effective description allows to explain experiments with Rb-2 dimers on helium droplets. Here, we identify vibrational damping and associated decoherence as the main explanation for the experimental results. The relation between decoherence and dissipation in Morse-like systems at zero temperature is studied in more detail. The dissipative model is also used to investigate experiments with K-2 dimers on helium droplets. However, by comparing numerical simulations with experimental data, one finds that further mechanisms are active. Here, a good agreement is obtained through accounting for rapid desorption of dimers. We find that decoherence occurs in the electronic manifold of the molecule. Finally, we are able to examine whether superfluidity of the host does play a role in these experiments.
In dieser Dissertation werden quantendynamische Simulationen durchgeführt, um die Schwingungsbewegung zweiatomiger Moleküle in einer hochgradig quantenmechanischen Umgebung, sogenannten Heliumtröpfchen, zu beschreiben. Unser Ziel ist es, experimentelle Befunde zu reproduzieren und zu erklären, die von Dimeren auf Heliumtröpfchen erhalten wurden. Nanometergroße Heliumtröpfchen enthalten einige tausend 4-He Atome. Sie dienen als Wirt für eingebettete Atome oder Moleküle und stellen für dieseeinen ultrakalten „Kühlschrank“ bereit. Durch Spektroskopie mit Molekülen in oder auf diesen Tröpfchen erhält man Informationen sowohl über das Molekül selbst als auch über die Heliumumgebung. Man weiß, dass sich die Tröpfchen in der suprafluiden He II Phase befinden. Suprafluidität in Nanosystemen ist ein stetig wachsendes Forschungsgebiet. Spektren, die für das ungestörte Dimer durch voll quantenmechanische Simulationen erhalten werden, weichen von Messungen mit Dimeren auf Heliumtröpfchen ab. Diese Abweichungen lassen sich auf den Einfluss der Heliumumgebung auf die Dynamik des Dimers zurückführen. In dieser Arbeit wird eine etablierte quantenoptische Mastergleichung verwendet, um die Dynamik des Dimers effektiv zu beschreiben. Die Mastergleichung erlaubt es, Dämpfung voll quantenmechanisch zu beschreiben. Durch Verwendung dieser Gleichung in der Quantendynamik-Simulation lässt sich die Rolle von Dissipation und Dekohärenz in Dimeren auf Heliumtröpfchen untersuchen. Die effektive Beschreibung erlaubt es, Experimente mit Rb-2 Dimeren zu erklären. In diesen Untersuchungen wird Dissipation und die damit verbundene Dekohärenz im Schwingungsfreiheitsgrad als maßgebliche Erklärung für die experimentellen Resultate identifiziert. Die Beziehung zwischen Dekohärenz und Dissipation in Morse-artigen Systemen bei Temperatur Null wird genauer untersucht. Das Dissipationsmodell wird auch verwendet, um Experimente mit K-2 Dimeren auf Heliumtröpfchen zu untersuchen. Wie sich beim Vergleich von numerischen Simulationen mit experimentellen Daten allerdings herausstellt, treten weitere Mechanismen auf. Eine gute Übereinstimmung wird erzielt, wenn man eine schnelle Desorption der Dimere berücksichtigt. Wir stellen fest, dass ein Dekohärenzprozess im elektronischen Freiheitsgrad des Moleküls auftritt. Schlussendlich sind wir in der Lage herauszufinden, ob Suprafluidität des Wirts in diesen Experimenten eine Rolle spielt.

Tesis (Doctor en Física)--Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física, 2010.
En este trabajo se estudia, bajo un tratamiento cuántico completo, la dinámica de la interacción entre un sistema observado con otro no-observado (y no-controlado), con un enfoque de sistema cuántico abierto. El aporte original consiste en mantener esta visión en toda la escala temporal del operador de evolución. Esto brinda una clara distinción y comprensión de los procesos de dinámica Liouvilliana aislada, decoherencia cuántica adiabática, decoherencia cuántica y relajación. Esto lleva, como contribución original, al entendimiento de la irreversibilidad introducida por la decoherencia cuántica como un concepto local del sistema observado, con origen en el tratamiento cuántico del ambiente, que permite evolucionar al estado del sistema hacia el quasi-equilibrio. Se concluye que este estado de quasi-equilibrio es parte de la caracterización de la dinámica cuántica completa, como un estadio intrínseco de la misma, que finaliza con la termalización del sistema observado bajo relajación. Se aplican estas ideas al estudio del sistema de espines de los protones en los cristales líquidos nemáticos con Resonancia Magnética Nuclear, realizando experimentos y cálculos numéricos desde primeros principios, sin aproximaciones. Además, se diseña y construye un espectrómetro de RMN, para prestaciones de técnicas de pulsos avanzadas, con control de temperatura.
In this work we study the dynamics of the interaction between an observed and a non-observed (and uncontrolled) system, by introducing a full-quantum approach, in which the observed system is considered an open quantum system. The originality of the proposal resides in involving this quantum view along the whole timescale of the dynamics. This treatment provides insight on the different dynamical processes involved, allowing to distinguish the Liouvillian dynamics of an isolated system, adiabatic decoherence, quantum decoherence and relaxation. Through this treatment we could also identify the irreversibility introduced by quantum decoherence as a local concept of the observed system, but originated in the quantum treatment of the environment or non-observed system, which allows the evolution of the quantum state towards the quasi-equilibrium description. This description is part of the complete characterization of the quantum dynamics, as an intrinsic state of the system, which culminates with the thermalization of the observed system with the lattice, driven by relaxation processes. These ideas were applied in the study of the proton spin system of a nematic liquid crystal with Nuclear Magnetic Resonance (NMR) technics, including experiments and numerical calculations from first principles, which need no approximations. In addition, an NMR spectrometer was constructed with facilities for advanced pulsed sequences and temperature control.
Héctor Hugo Segnorile.