Neste trabalho utilizamos sistemas modelos no desenvolvimento, implementação e análise de funcionais orbitais da densidade, focando, em particular, nas correções de autointeração de Perdew-Zunger (PZSIC) e Lundin-Eriksson (LESIC). Aplicamos as correções de auto-interação ao funcional local (LDA) do modelo de Hubbard e de poços quânticos semicondutores, ambos unidimensionais, no caso estático e dependente do tempo, respectivamente. Para o modelo de Hubbard unidimensional, comparamos a LDA, LDA+PZSIC e LDA+LESIC, identificando o desempenho para energias e densidades do estado fundamental, com e sem impurezas locais, além do gap fundamental de energia. Em adição, averiguamos o desempenho diante de cargas fracionárias, estabelecendo conexões com o erro de delocalização da LDA. Mostramos a possibilidade da correta descrição das freqüências das oscilações de Friedel no modelo de Hubbard, além de investigar como a falha da LDA em reproduzir esse aspecto pode estar relacionada com os erros de auto-interação e delocalização. Investigamos ainda as diferentes possibilidades de implementação autoconsistente de qualquer funcional orbital da densidade, analisando a relação entre funcionais aproximados e suas implementações aproximadas. Nos poços quânticos, sob o enfoque dependente do tempo, analisamos a descontinuidade do potencial de troca e correlação ao variarmos o número de partículas, em dois processos distintos: a ionização eletrônica em um poço simples e dissociação de um poço duplo assimétrico. No último caso, avaliamos os efeitos da descontinuidade no número total de partículas em cada poço, revelando os mecanismos que resgatam a neutralidade elétrica durante processos de dissociação, com a correta carga final inteira. / In this work we use model systems to develop, implement and analyse orbital-dependent density functionals, focusing, specifically, on the self-interaction corrections (SICs) of Perdew and Zunger (PZSIC) and of Lundin and Eriksson (LESIC). These self-interaction corrections are applied to the local-density approximation (LDA) for the one-dimensional Hubbard model and for semiconductor quantum wells, in one-dimensional static and time-dependent situations. For the one-dimensional Hubbard model we compare LDA, LDA+PZSIC and LDA+LESIC, and investigate the performance of these approaches for ground-state energies, densities and energy gaps, with and without impurities in the system. We also consider the case of fractional charges, where a connection to the delocalization error of the LDA can be made. We show that in principle a correct description of the frequences of Friedel oscillations in the Hubbard model can be obtained from DFT, and investigate how the failure of the LDA in reproducing this is related to the selfinteraction and delocalization errors. Moreover, we investigate different procedures for the selfconsistent implementation of any orbital-dependent functional, and analyse the question of the interplay between an approximate functional and its approximate implementation. For quantum wells sytems we analyse, in a time-dependent framework, the discontinuity of the exchange-correlation potential under variation of the particle number in two different processes: the ionization of a simple quantum well and the dissociation of an asymmetric double well. In the latter case, we also consider the effect of changes in the particle number in each subwell, thus revealing the mechanism that restores electric neutrality during dissociation, with correct final charge.

Cette thèse de doctorat est dédiée à l’étude, avec des méthodes de calcul ab initio, desplasmons de surface et des états de surface de surfaces d’or, plate ou comportant desmarches (surface vicinale), par la simulation numérique de spectres de perte d’énergieélectronique (EEL) au moyen de la théorie de la fonctionnelle de la densité (DFT) et de lathéorie de perturbation de la fonctionnelle de la densité dépendant du temps (TDDFPT).L’influence du couplage spin-orbite (CSO) et celle de la géométrie de la surface ont étéétudiées. Dans l’or cristallin, j’ai étudié l’effet des électrons de semicoeur sur les spectresEEL à q = 0. J’ai montré en particulier que pour produire un spectre EEL sur une largegamme de fréquences, de 0 à 60 eV, il est nécessaire de tenir compte des électrons desemicoeur dans le pseudopotentiel, et qu’ils peuvent néanmoins être gelés dans le coeurpour l’étude de la partie basse en énergie du spectre EEL, pour des énergies inférieures à20 eV. J’ai réalisé des développements méthodologiques pour la TDDFPT avec CSO cou-plée à l’emploi de pseudopotentiels ultradoux, qui ont permis l’implémentation pratiquede cette approche dans les algorithmes de Liouville-Lanczos et de Sternheimer. J’ai utiliséavec succès ces approches qui m’ont permis de traiter des systèmes à plusieurs centainesd’atomes. J’ai examiné à nouveau le spectre EEL de l’or cristallin à q = 0, montrant enparticulier les traces d’un plasmon écranté dans le spectre EEL calculé sans inclure leseffets de CSO. J’ai ensuite montré que l’inclusion du CSO a un effet petit mais détectablesur le spectre EEL et le pic de plasmon, donnant un meilleur accord avec l’expérienceà q = 0. J’ai trouvé que la dispersion du plasmon acoustique (PAS) de la surface Au(111) est légèrement modifiée par le CSO, provenant du fait que la structure de bandesest elle-même modifiée par le dédoublement de Rashba de certains niveaux électroniques,dédoublement induit par le CSO. Puis, pour étudier les effets de géométrie, j’ai étudié lessurfaces vicinales (322), (455) et (788) de l’or. J’ai en particulier mené l’étude théoriquedes états électroniques de surface, et analysé l’évolution de l’état de surface de Shockleyentre la surface plate Au(111) et les surfaces ayant des marches dont les terrasses avaientdifférentes largeurs. J’ai montré la transition d’un état de surface résonant pour Au(322)à un état localisé pour Au(455) et pour Au(788), ainsi que le passage d’un état 2D étenduà travers la marche pour Au(322) à un état quasi-1D confiné dans la terrasse de la marchepour Au(455) et pour Au(788). Ces résultats sont en accord avec l’expérience, et avecceux d’un modèle de Kronig-Penney de potentiel périodique. J’ai calculé le spectre EELSpour la surface d’or (455) que j’ai modélisé par une tranche de 5 nm d’or séparée de sesvoisines (répétées périodiquement) par 5 nm de vide. J’ai identifié la signature du plas-mon acoustique de surface. J’ai montré que, pour un moment transféré perpendiculaireà la marche de la surface, la dispersion du PAS n’est pas modifiée par rapport à celle duPAS de la surface plate Au(111) pour q < 0.125 Å −1 . Cependant, pour des valeurs plusgrandes du moment transféré, le pic du PAS a une énergie plus basse que celle du PASde Au(111), montrant les signes du confinement du PAS et suggérant que deux types dePAS peuvent se produire: un plasmon intra(sous)bande, similaire à celui de la surfaceAu(111), et un plasmon inter(sub)band, caractéristique de cette surface vicinale. / The PhD thesis is devoted to the ab initio study of surface plasmons and surface states offlat and vicinal surfaces of Au through the simulation of electron energy loss (EEL) spectraby means of the density functional theory (DFT) and the time-dependent density func-tional perturbation theory (TDDFPT). The influence of the spin-orbit coupling (SOC)and of the surface geometry has been investigated. In bulk Au I have studied the effect ofthe inclusion of semi-core electrons on the EEL spectrum at q = 0 and the plasmon peakposition and intensity. In particular, I have shown that in order to reproduce the EELspectrum on a wide frequency range (0-60 eV) it is important to account for semi-coreelectrons in the pseudopotential although they can be frozen in the core in studies of thelow energy part of the spectrum (below 20 eV). I have made methodological developmentsfor TDDFPT with SOC in the ultrasoft pseudopotential scheme that led to the practicalimplementation of SOC in the Liouville-Lanczos and Sternheimer approaches. I have thensuccessfully applied these approaches that allowed me to model systems with hundreds ofatoms. I have revisited the plasmonic excitations in bulk Au, pointing out that, in partic-ular, one can observe traces of an unscreened s-like bulk plasmon in the EEL spectrum atq = 0 calculated without SOC. I have also demonstrated that SOC has a small but notice-able effect on the Au EEL spectrum and plasmon peak, mainly modifying the unscreeneds-like plasmon peak and thus bringing the calculated spectrum into a better agreementwith experimental results at q = 0. Moreover I have observed that the dispersion ofthe acoustic surface plasmon (ASP) on the Au(111) surface is slightly modified by SOC,because the ASP comes from the surface state that itself is modified by SOC through theRashba splitting. To investigate the effect of geometry I have studied the vicinal (322),(455) and (788) surfaces of Au. In particular I have performed the theoretical study of thesurface states, analyzing the evolution of the Shockley surface state from the flat Au(111)surface towards the surfaces with terraces of different width. I have shown the surfaceresonance-to-surface state transition from (322) to (455) and (788) surfaces. I have shownalso the transition from the average-surface-modulated to the terrace-modulated statefrom (322) to (455) and (788) surfaces, as well as the transition from the extended 2Dstate to the quasi-1D state confined within the terrace. These results are in agreementwith experiments and results obtained with the Kronig-Penney periodic potential model.I have performed the EEL spectrum calculations for the Au(455) surface which I havemodeled with a 5 nm sized slab separated from its periodic neighbors by 5 nm of vacuum.I have identified signatures of the ASP in these spectra, showing that indeed, for the caseof the transferred electron wavevector momentum perpendicular to the step, the ASPdispersion is not changed with respect to the ASP dispersion of the Au(111) surface forq < 0.125 Å −1 . For bigger values of q, however, the ASP peak has a lower energy com-pared to the ASP peak of the Au(111) surface, showing signs of the ASP confinement, andsuggesting that two types of the ASP could occur: an intra(sub)band plasmon, similarto the Au(111) surface plasmon, and an inter(sub)band plasmon, characteristic of thisvicinal surface.

No description available.

The non-adiabatic quantum molecular dynamics (NA-QMD) method couples self-consistently classical nuclear motion with time-dependent density functional theory (TDDFT) in basis expansion for the electron dynamics. It has become a versatile approach to study the dynamics of atoms, molecules and clusters in a wide range of scenarios. This work presents applications of the NA-QMD method to important benchmark systems and its systematic extension to include quantum effects in the nuclear motion. Regarding the first objective, a complete study of the strong-field ionization and dissociation dynamics of nature’s simplest molecule H2+ is performed. By including all electronic and nuclear degrees of freedom and all reaction channels, molecular rotation is shown to play an important role in the ionization process. In addition, strong orientation effects in the energy deposition process of the Buckminster fullerene C60 in short intense laser pulses are surprisingly found in full dimensional calculations. Their consequences on the subsequent nuclear relaxation dynamics shed new light on available experimental data and future experiments are proposed to confirm the detailed predictions. Regarding the second objective, the NA-QMD formalism is basically extended to take electron-nuclear correlations into account. This extension is achieved by means of a trajectory surface hopping scheme in the adiabatic Kohn-Sham framework. First studied examples from collision physics and photochemistry illustrate the relevance and importance of quantum effects in the nuclear dynamics.

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.

In this work, experimental and theoretical approaches are applied to the study of chemical reaction dynamics. In Chapter 2, two applications of transition state theory are presented: (1) Application of microcanonical transition state theory to determine the rate constant of dissociation of C2F3I after π∗ ← π excitation. It was found that this reaction has a very fast rate constant and thus is a promising system for testing the statistical assumption of molecular reaction dynamics. (2) A general rate constant expression for the reaction of atoms and molecules at surfaces was derived within the statistical framework of flexible transition state theory. In Chapter 4, a computationally efficient TDDFT approach was found to produce useful potential energy surface landscapes for application to non-adiabatic predissociative dynamics of the molecule CS2 after excitation from the ground state to the singlet C-state. In Chapter 5, ultrafast experimental results of excitation of CS2 to the predissociative neutral singlet C-state is presented. The bandwidth of the excitation laser was carefully tuned to span a two-component scattering resonance with each component differently evolving electronically with respect to excited state character during the quasi-bound oscillation. Scalar time-resolved photoelectron spectra (TRPES) and vector time-resolved photoelectron angular distribution (TRPAD) observables were recorded during the predissociation. The TRPES yield of photoelectrons was found to oscillate with a quantum beat pattern for the photoelectrons corresponding to ionization to the vibrationless cation ground state; this beat pattern was obscured for photoelectron energies corresponding to ionization from the vibrationally excited CS2 cation. The TRPAD data was recorded for two general molecular ensemble cases: with and without a pre-excitation alignment laser pulse. It was found that in the case of ensemble alignment (Chapter 6), the “molecular frame” TRPAD (i.e. TRMFPAD) was able to image the purely valence electronic dynamics of the evolving CS2 C-state. The unaligned ensemble TRPAD observable suffers from excessive orientational averaging and was unable to observe the quantum beat. Engineering efforts were also undertaken to eliminate scattered light background signal (Chapter 7, Appendix A) and improve laser stability as a function of ambient pressure (Appendix B) for TRMFPAD experiments. / Thesis (Ph.D, Chemistry) -- Queen's University, 2012-09-11 22:18:20.89