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NR 20140805

Nonradiative decay of excitons is a competing process to Multi-Exciton Generation (MEG) in nanoparticles. Nonradiative decay of single excitons with sufficient energy to generate bi-excitons in Cd₂₀ Se₁₉ and Cd₈₃ Se₈₁ nanoparticles was studied using Tully's Molecular Dynamics with Quantum Transitions (MDQT) method and a CdSe pseudopo- tential. Exciton decay rates increase with increases in nanoparticle temperature and density of lower-lying excitonic states. There did not appear a significant effect of size on energy decay rates. The decay dynamics generally follow a gradual decay with transitions between nearby states. This is punctuated by periodic, short-lived periods of rapid downhill tran- sitions that result in a large proportion of excess exciton energy being transferred to the vibrational motion of the nanoparticle. The time for relaxation to below the 2.0E[subscript g] cutoff was on the order of 1ps. / text

Nonadiabatic dynamical processes are ubiquitous in chemistry and biology. Such events are directly connected to the treatment of energetically close lying states which gives rise to strong vibronic interactions in which case the Born-Oppenheimer approximation tends to break down. In case of biradicals, nonadiabatic events are facilitated by conical intersections, as a result of symmetry lowering of degenerate electronic states due to Jahn-Teller distortion. A central problem in the treatment of the nonadiabatic molecular dynamics is posed by the representation of potential energy surfaces. A point by point calculation of a potential energy surface on a multi-dimensional grid is very cumbersome and in general does not provide with an analytical functional form of the potential. This becomes even more complicated when the adiabatic surfaces have cusps, where the function becomes non-differentiable. Vibronic model Hamiltonians, which represent the potential in the form of a potential matrix which contains the electronic energies as well as the couplings in a diabatic basis. A Taylor series expansion of the potential matrix can be done to get a smooth analytical functional form of the potential matrix elements. These models can then be used to perform nuclear dynamics using either exact diagonalization time-independent method or the wavepacket propagation based time-dependent methods. Thus, vibronic models provide a compact representation of complicated coupled potential energy surfaces, which can be used in conjunction with non-adiabatic nuclear dynamics Vibronic models have been constructed for selected biradicals, for which photodetachment spectra have been simulated using the time-independent (VIBRON) as well as time-dependent (MCTDH) methods. Consistent results have been obtained with both the approaches for small systems. This also assures the use of MCTDH program for larger systems, where the time-independent methods are not applicable. Moreover, for biradicals, the parent anionic state also undergoes a Jahn-Teller distortion, or often the ground state potential energy surface is highly anharmonic in nature. This requires the description of anionic ground state by a vibronic model. Therefore, in order to simulate the photodetachment spectra of biradicals, three vibronic models are constructed for each simulation. The first model describes the ground and excited states of the parent anionic (neutral) species. Two other vibronic models describe singlet and triplet states of the target neutral (cation) species, and the spectrum is simulated using the vibronic ground state(s) of the anion (neutral) as the absorbing state in VIBRON/MCTDH. The electronic states and vibronic model parameters are obtained using the IP-EOM-CCSD and DIP-STEOM-CCSD methodology as coded in the ACESII quantum chemistry program package. The photodetachment spectra of nitrate radical, cyclobutadiene negative ion and trimethylene negative ion have been studied using this methodology.

Nonadiabatic dynamical processes are ubiquitous in chemistry and biology. Such events are directly connected to the treatment of energetically close lying states which gives rise to strong vibronic interactions in which case the Born-Oppenheimer approximation tends to break down. In case of biradicals, nonadiabatic events are facilitated by conical intersections, as a result of symmetry lowering of degenerate electronic states due to Jahn-Teller distortion. A central problem in the treatment of the nonadiabatic molecular dynamics is posed by the representation of potential energy surfaces. A point by point calculation of a potential energy surface on a multi-dimensional grid is very cumbersome and in general does not provide with an analytical functional form of the potential. This becomes even more complicated when the adiabatic surfaces have cusps, where the function becomes non-differentiable. Vibronic model Hamiltonians, which represent the potential in the form of a potential matrix which contains the electronic energies as well as the couplings in a diabatic basis. A Taylor series expansion of the potential matrix can be done to get a smooth analytical functional form of the potential matrix elements. These models can then be used to perform nuclear dynamics using either exact diagonalization time-independent method or the wavepacket propagation based time-dependent methods. Thus, vibronic models provide a compact representation of complicated coupled potential energy surfaces, which can be used in conjunction with non-adiabatic nuclear dynamics Vibronic models have been constructed for selected biradicals, for which photodetachment spectra have been simulated using the time-independent (VIBRON) as well as time-dependent (MCTDH) methods. Consistent results have been obtained with both the approaches for small systems. This also assures the use of MCTDH program for larger systems, where the time-independent methods are not applicable. Moreover, for biradicals, the parent anionic state also undergoes a Jahn-Teller distortion, or often the ground state potential energy surface is highly anharmonic in nature. This requires the description of anionic ground state by a vibronic model. Therefore, in order to simulate the photodetachment spectra of biradicals, three vibronic models are constructed for each simulation. The first model describes the ground and excited states of the parent anionic (neutral) species. Two other vibronic models describe singlet and triplet states of the target neutral (cation) species, and the spectrum is simulated using the vibronic ground state(s) of the anion (neutral) as the absorbing state in VIBRON/MCTDH. The electronic states and vibronic model parameters are obtained using the IP-EOM-CCSD and DIP-STEOM-CCSD methodology as coded in the ACESII quantum chemistry program package. The photodetachment spectra of nitrate radical, cyclobutadiene negative ion and trimethylene negative ion have been studied using this methodology.

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.

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.

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.

No description available.

Chemische Reaktionen in der Natur sowie Prozesse in synthetischen Materialien werden oft erst durch die Wechselwirkung von Licht mit Materie ausgelöst. Üblicherweise werden diese komplexen Prozesse mit Hilfe von Näherungen beschrieben. Im ersten Teil der Arbeit wird die Gültigkeit der Born-Oppenheimer Näherung in einem vibronischen Modellsystem (Trans-Polyacetylene) unter Photoelektronenspektroskopie im Gleichgewicht sowie zeitaufgelöster Photoelektronenspektroskopie im Nichtgleichgewicht überprüft. Die vibronische Spektralfunktion zeigt aufgrund des faktorisierten Anfangs- und Endzustandes in der Born-Oppenheimer Näherung zusätzliche Peaks, die in der exakten Spektralfunktion nicht auftreten. Im Nichtgleichgewicht zeigen wir für eine Franck-Condon Anregung und eine Anregung mit Pump-Probe Puls, wie die Bewegung des vibronischen Wellenpaktes im zeitabhängigen Photoelektronenspektrum verfolgt werden kann. Im zweiten Teil der Arbeit werden sowohl die Materie als auch das Licht quantisiert behandelt. Für eine volle quantenmechanische Beschreibung des Elektron-Licht Systems, verwenden wir die kürzlich entwickelte quantenelektrodynamische Dichtefunktionaltheorie (QEDFT) für gekoppelte Elektron-Photon Systeme. Wir zeigen erste numerische QEDFT-Berechnungen voll quantisierter Atome und Moleküle in optischen Kavitäten, die an das quantisierte elektromagnetische Feld gekoppelt sind. Mit Hilfe von Fixpunktiterationen berechnen wir das exakte Kohn-Sham Potential im diskreten Ortsraum, wobei unser Hauptaugenmerk auf dem Austausch-Korrelations-Potential liegt. Wir zeigen die erste Näherung des Austausch-Korrelations-Potentials mit Hilfe eines optimierten effektiven Potential Ansatzes angewandt auf einen Jaynes-Cummings-Dimer. Die dieser Arbeit zugrunde liegenden Erkenntnisse und Näherungen ermöglichen es neuartige Phänomene an der Schnittstelle zwischen den Materialwissenschaften und der Quantenoptik zu beschreiben. / Many natural and synthetic processes are triggered by the interaction of light and matter. All these complex processes are routinely explained by employing various approximations. In the first part of this work, we assess the validity of the Born-Oppenheimer approximation in the case of equilibrium and time-resolved nonequilibrium photoelectron spectra for a vibronic model system of Trans-Polyacetylene. We show that spurious peaks appear for the vibronic spectral function in the Born-Oppenheimer approximation, which are not present in the exact spectral function of the system. This effect can be traced back to the factorized nature of the Born-Oppenheimer initial and final photoemission states. In the nonequilibrium case, we illustrate for an initial Franck-Condon excitation and an explicit pump-pulse excitation how the vibronic wave packet motion can be traced in the time-resolved photoelectron spectra as function of the pump-probe delay. In the second part of this work, we aim at treating both, matter and light, on an equal quantized footing. We apply the recently developed quantum electrodynamical density-functional theory, (QEDFT), which allows to describe electron-photon systems fully quantum mechanically. We present the first numerical calculations in the framework of QEDFT. We focus on the electron-photon exchange-correlation contribution by calculating exact Kohn-Sham potentials in real space using fixed-point inversions and present the performance of the first approximate exchange-correlation potential based on an optimized effective potential approach for a Jaynes-Cummings-Hubbard dimer. This work opens new research lines at the interface between materials science and quantum optics.