In Chapter 1, we present the background for transient absorption spectroscopy through the polarization response of a material to an electric field which gives rise to linear and non-linear processes. We then discuss a theoretical description of how vibrational coherences are formed via four-wave mixing and impulsive excitation. We also describe signatures of coherent wavepackets in transient absorption and the application of vibrational coherences, specifically to observe non-radiative processes. We then summarize two previous studies using impulsive transient absorption on cresyl violet, the differences in the coherent dynamics reported, and the motivations behind the experiments presented in this work. Chapter 2 pertains to the apparatus used to perform the transient absorption experiments. We detail the source for the generation of ultrashort laser pulses (durations of less than 10 fs) used for the pump and probe from an argon-based white-light filament and non-colinear optical parametric amplifier. Two-dimensional shearing interferometry, the method used to measure the ultrashort pulses across a large portion of the visible spectrum (500-750 nm), is discussed. The retrieved temporal, spectral, and phase profiles of the pump and probe pulses are presented. Finally, the sample preparation for cresyl violet is described as well as the detection method and data processing used to generate the figures throughout this work. In Chapter 3, we present the results of impulsive transient absorption spectroscopy of cresyl violet perchlorate under four pump conditions. First, we report a study on controlling the formation of vibrational coherences on the ground or excited electronic states of cresyl violet by tuning the pump conditions from an off-resonant to a resonant scheme. The decay of the electronic population and positions of the stimulated emission and excited-state absorption maximums shows a dependence on the pump wavelength. Higher excitation frequencies blueshifts the stimulated emission 18 meV and red shifts excited-state absorption by 4 meV at early times compared to only 13 meV and 2 meV when using lower excitation frequencies. Coherent vibrations are observed and persist for approximately 6 ps after excitation, with phase flips appearing at 593 nm, the absorption maximum, after off-resonant excitation and at the emission (619 nm) and excited-state absorption (500 nm) maximums after resonant excitation. The ground- and excited-state vibrational modes are characterized by Fourier transform Raman spectroscopy. The excited-state vibration spectrum is shown to share nearly identical features as the ground-state, with each vibration slightly red-shifted, 2-10 cm-1, from the corresponding mode in the ground-state, particularly a prominent peak appearing at 594 cm-1 in the ground-state and 589 cm-1 in the excited-state. Next, two additional pump conditions using broadband and partially resonant pump pulses are explored to replicate the conflicting reports of non-adiabatic crossings in cresyl violet. Constant phase-flips observed in the control studies are replaced with phase flips that appear and disappear over several picoseconds. The Fourier Raman spectrum of the coherent signal after broadband excitation displays a mix of ground- and excited-state features, particularly prominent peaks at both 589 cm-1 and 594 cm-1. In Chapter 4, we analyze the coherent signals after broadband excitation using a Fourier filtering technique to isolate the ground- or excited-state coherent dynamics by carefully selecting representative vibrational modes for each state. Using a narrow filter to isolate the 589 cm-1 and 595 cm-1 features in the broadband Fourier Raman spectrum successfully isolates coherent vibrations with phase flips at either the emission and excited-state absorption maximums or the ground-state absorption maximum, respectively. A filter that includes both features generates apparent phase-flips that only appear for ~1ps and at probe wavelengths that do not correspond to the emission or absorption maximums. In Chapter 5, we present a simulation of the coherent signals using a model of two wavepackets with carrier frequencies of 589 cm-1 and 595 cm-1 and dephasing rates of 2 and 3 ps, respectively. Comparison to the broadband pump conditions and Fourier filtered coherent oscillations shows that the complex temporal dynamics observed are adequately described by the linear interference of two vibrational coherences evolving on different electronic potential energy surfaces, without the need to invoke non-adiabatic dynamics. / Chemistry

No description available.

Thesis (PhD)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: The availability of laser systems capable of generating ultrashort optical pulses in the visible spectral range have made it possible to study molecular species with a temporal resolution in the order of intra-molecular dynamics which previously were not accessible. Henceforth, in this study a popular pump-probe technique called ultrafast transient absorption spectroscopy (UTAS) is employed to study the initial photochromic reaction of metal complex, dithizonatophenylmercury (II) (DPM) under various conditions. These conditions include the use of different solvents and electronically altering DPM by the addition of substituents with specific electron affinity properties. For this study the photochromic behaviour of DPM dissolved in methanol is used as standard. Using this standard, the initial photochromic reaction after ultrafast excitation within less than 100 fs caused a radiationless photoreaction with a time constant of about 2 ps, which is interpreted as C=N isomerization along the twist coordinate. It is found that during this isomerization reaction an orthogonally twisted intermediate state was formed and observed through its excited-state absorption, which funnels through a conical intersection onto the ground state potential. Once here, bifurcation along pathways towards the ground states of the reactant and product configurations occurs. This was the first observation of photochromism for DPM in a strong polar solvent such as methanol. From the results of the test compound in methanol, comparisons to the photo-behaviour of DPM dissolved in deuterated methanol and dichloromethane are made. What is established is that changing the solvent resulted in slightly different decay times as well as spectral shifts in the absorption profile which suggested that the potential energy surface of the excited state is modified. This is similar to the results found from the electronically altered DPM species. Here the entire photoreaction is found to either be sped up (1 ps) or slowed down (4 ps) depending on the sample investigated. Previous studies on the photochromicity of DPM like systems concluded that apart from the photo-activated forward reaction, a back reaction occurs in the absence of light. Therefore a detailed look at the back reaction of DPM and its derivatives are also studied. This is done by temporally monitoring the absorption change of the photo-product as it converts back to the reactant. In doing so the lifetime of the photo-product is determined and found to differ greatly depending on the solvent and substituent used. Lastly, in assuming that the back reaction follows first order kinetics, an Arrhenius type measurement on the photo-product of DPM is conducted. The result of this measurement is that a potential energy barrier of 64.8 kJ/mol is overcome in the back reaction. The measurements performed and the results obtained from the photochromicity of DPM contribute to the understanding of photo-induced cis-trans isomerization reactions about a C=N double bond. / AFRIKAANSE OPSOMMING: Die beskikbaarheid van laser sisteme in staat om ultrakort optiese pulse te genereer in die sigbare spektrale gebied, het die studie van molekulˆere spesies met ’n tydresolusie in die orde van intra-molekulˆere dinamika wat voorheen nie toeganklik was nie. Voortaan, in hierdie studie word ’n populˆere aktiveer-interogeer tegniek genaamd ultravinnige tydafhanklike absorpsie spektroskopie (UTAS) aangewend om die aanvanklike fotochromiese reaksie van die metaal kompleks, ditisoonfenielkwik (II) (DFK) onder verskillende kondisies te bestudeer. Hierdie kondisies sluit in die gebruik van verskillende oplosmiddels en die elektroniese verstelling van DFK deur die toevoeging van substituente met spesifieke elektron affiniteit eienskappe. Vir hierdie studie word die fotochromiese gedrag van DFK, opgelos in metanol, as standaard gebruik. Met hierdie standaard, word gevind dat die aanvanklike fotochroom reaksie na ultravinnige opwekking binne minder as 100 fs, ’n stralingslose fotoreaksie met ’n tydkonstante van 2 ps veroorsaak. Hierdie fotoreaksie word verklaar as die C=N isomerisasie met betrekking tot die draai ko¨ordinaat. Daar is ook gevind dat gedurende hierdie isomerisasie reaksie, ’n ortogonaal verdraaide oorgangstoestand gevorm word wat waargeneem is deur sy absorpsie in die opgewekte toestand wat tregter deur ’n koniese kruispunt na die potensiaal van die grondtoestand. By hierdie punt vurk die proses na die grondtoestande van die reaktant en die produk vorme. Di´e was die eerste waarneming van fotochromisme van DFK opgelos in ’n sterk polˆere oplosmiddel soos metanol. Vanuit die resultate vir die toets mengsel in metanol word vergelykings getrek tot die fotogedrag van DFK opgelos in gedeureriese metanol en dichlorometaan. Wat hieruit vasgestel is, is dat die verandering in oplosmiddel wel die fotoreaksie be¨ınvloed deurdat verskillende vervaltye en spekrale verskuiwings in die apsorpsie profiel waargeneem word. Hierdie verskille dui aan dat die potensie¨ele energie oppervlakte van die opgewekte toestand wel gemodifiseer word. Dit is ook soortgelyk aan die resultate vir die elektronies verstelde BFK spesies. Hier is gevind dat die tempo van die totale fotoreaksie `of toeneem (1 ps) `of afneem (4 ps) afhanklik van die spesifieke spesie wat bestudeer word. Vorige studies van die fotochromiese gedrag van sisteme soortgelyk aan DFK het gevind dat behalwe vir die fotogeaktiveerde voorwaartse reaksie, daar ook ’n keersy reaksie plaasvind in die afwesigheid van lig. Dus word die keersy reaksie vir DFK en sy derivate ook in detial bestudeer. In hierdie studie word die absorpsie verskille van die fotoproduk tydelik waargeneem soos dit terugkeer na die reaktant. Op hierdie manier word die leeftyd van die fotoproduk bepaal en gevind dat dit grootliks afhang van die tipe oplosmiddel en tipe substituent wat gebruik word. Ten slote, wanneer daar aanvaar word dat di´e keersy reaksie eerste orde kinetika volg, word ’n Arrhenius tipe meting op die fotoproduk uitgevoer. Die resultaat van hierdie meting is dat ’n potensie¨ele enrgie versperring van 64.8 kJ/mol oorkom word in die keersy reaksie. Die metings wat uitgevoer is en die resultate wat verkry is van die fotochromiese gedrag van DFK dra by tot die verstandhouding van lig-ge¨ınduseerde cis-trans isomerisasie reaksies rondom ’n C=N dubbelbinding.

In this thesis, we consider real matrix functions that depend on two parameters and study the problem of how to detect and approximate parameters' values where the singular values coalesce. We prove several results connecting the existence of coalescing points to the periodic structure of the smooth singular values decomposition computed around the boundary of a domain enclosing the points. This is further used to develop algorithms for the detection and approximation of coalescing points in planar regions. Finally, we present techniques for continuing curves of coalescing singular values of matrices depending on three parameters, and illustrate how these techniques can be used to locate coalescing singular values of complex-valued matrices depending on three parameters.

C’est dernières années, les progrès des techniques expérimentales combinées avec les simulations théoriques ont données un accès à l’étude et le contrôle des réactions photochimiques dans des systèmes moléculaires de grande taille. Ceci ouvre des portes à de nouvelles applications technologiques. Par exemple, les molécules de la famille du 3-hydroxychromone et de l’aminobenzonitrile sont des types de systèmes où les spectres de fluorescences vont présentés des différences importantes suivant l’environnement du système ou même suivant les substituants utilisés. Ce type de propriété est crucial dans le domaine des matériaux organique, afin de pouvoir comprendre et designer des matériaux qui présentent des propriétés optiques choisis tells que les marqueurs fluorescents dans le domaine médical par exemple.Notre stratégie pour étudier la réactivité photochimique est la suivante: *Explorer la surface d’énergie potentielle et optimiser les points spécifiques avec des calculs de chimie quantiques. Dans un premier temps, on a utilisé des méthodes CASSCF/CASPT2 et la méthode PCM pour décrire les effets de solvant. * Génération des surfaces d énergies potentielles exprimer sous la forme de fonctions analytiques des coordonnées nucléaires. * Résolution de l’équation de Schrödinger dépendant du temps pour les noyaux et pour tout les derges de libertés de la molécule. Cette étape est faite à l’aide de la méthode multilayer multiconfiguration time-dependent hartree (ML-MCTDH). / Over the last decades, progress in experimental techniques combined with theoretical simulations has given access to studying and controlling the photochemical reactivity of large molecular systems with numerous technological applications. 3-hydroxychromone and aminobenzonitrile-like molecules are an example where different fluorescence patterns are observed, depending of the solvent or its substituents. Such properties are crucial in the field of organic materials to understand and design materials with specific optical properties such as fluorescent markers.Our strategy to study the photochemistry reactivity is summarised as follows: * Exploring the potential energy surfaces and optimising specific points with quantum chemistry calculations. In a first stage, these are run at the CASSCF/CASPT2 level of theory with a polarised extended basis set, and the solvent effect is described implicitly with the PCM model. * Generating the full dimension potential energy surfaces as analytical functions of the nuclear coordinates.* Solving the nuclear time-dependent Schrödinger equation for all the degrees of freedom. This is achieved with the multilayer Multi-Configuration Time-Dependent Hartree method (ML-MCTDH).

No description available.

This work presents a new implementation of the QP algorithm, a computer method to diagonalize the extremely large matrices arising in multimode vibronic problems. Benchmark calculations are included, showing the accuracy of the program. The QP algorithm is extended to treat multiple electronic surfaces for competitive control and this is demonstrated with an Hamiltonian including three electronic states, a model of the benzene radical cation. Finally, the evolution of zeroth-order states in a simple two electronic states, two dimensional model with a conical intersection is explored, towards building a time-dependent view of overlapping resonances coherent control.

This work presents a new implementation of the QP algorithm, a computer method to diagonalize the extremely large matrices arising in multimode vibronic problems. Benchmark calculations are included, showing the accuracy of the program. The QP algorithm is extended to treat multiple electronic surfaces for competitive control and this is demonstrated with an Hamiltonian including three electronic states, a model of the benzene radical cation. Finally, the evolution of zeroth-order states in a simple two electronic states, two dimensional model with a conical intersection is explored, towards building a time-dependent view of overlapping resonances coherent control.

This thesis discusses the development and application of theoretical and computational methods to study three-body processes. The main focus is on the calculation of three-body resonances and bound states. This broadly includes the study of Efimov states and resonances, three-body shape resonances, three-body Feshbach resonances, three-body pre-dissociated states in systems with a conical intersection, and the calculation of three-body recombination rate coefficients. The method was applied to a number of systems. A chapter of the thesis is dedicated to the related study of deriving correlation diagrams for three-body states before and after a three-body collision. More specifically, the thesis discusses the calculation of the H+H+H three-body recombination rate coefficient using the developed method. Additionally, we discuss a conceptually simple and effective diabatization procedure for the calculation of pre-dissociated vibrational states for a system with a conical intersection. We apply the method to H_3, where the quantum molecular dynamics are notoriously difficult and where non-adiabatic couplings are important, and a correct description of the geometric phase associated with the diabatic representation is crucial for an accurate representation of these couplings. With our approach, we were also able to calculate Efimov-type resonances. The calculations of bound states and resonances were performed by formulating the problem in hyperspherical coordinates, and obtaining three-body eigenstates and eigen-energies by applying the hyperspherical adiabatic separation and the slow variable discretization. We employed the complex absorbing potential to calculate resonance energies and lifetimes, and introduce an uniquely defined diabatization procedure to treat X_3 molecules with a conical intersection. The proposed approach is general enough to be applied to problems in nuclear, atomic, molecular and astrophysics.

<p>The accurate description of ground and electronic excited states is an important and challenging topic in quantum chemistry. The pairing matrix fluctuation, as a counterpart of the density fluctuation, is applied to this topic. From the pairing matrix fluctuation, the exact electron correlation energy as well as two electron addition/removal energies can be extracted. Therefore, both ground state and excited states energies can be obtained and they are in principle exact with a complete knowledge of the pairing matrix fluctuation. In practice, considering the exact pairing matrix fluctuation is unknown, we adopt its simple approximation --- the particle-particle random phase approximation (pp-RPA) --- for ground and excited states calculations. The algorithms for accelerating the pp-RPA calculation, including spin separation, spin adaptation, as well as an iterative Davidson method, are developed. For ground states correlation descriptions, the results obtained from pp-RPA are usually comparable to and can be more accurate than those from traditional particle-hole random phase approximation (ph-RPA). For excited states, the pp-RPA is able to describe double, Rydberg, and charge transfer excitations, which are challenging for conventional time-dependent density functional theory (TDDFT). Although the pp-RPA intrinsically cannot describe those excitations excited from the orbitals below the highest occupied molecular orbital (HOMO), its performances on those single excitations that can be captured are comparable to TDDFT. The pp-RPA for excitation calculation is further applied to challenging diradical problems and is used to unveil the nature of the ground and electronic excited states of higher acenes. The pp-RPA and the corresponding Tamm-Dancoff approximation (pp-TDA) are also applied to conical intersections, an important concept in nonadiabatic dynamics. Their good description of the double-cone feature of conical intersections is in sharp contrast to the failure of TDDFT. All in all, the pairing matrix fluctuation opens up new channel of thinking for quantum chemistry, and the pp-RPA is a promising method in describing ground and electronic excited states.</p> / Dissertation