We introduce a perturbative method for studying photoinduced electronic transitions through conical intersections. Our approach uses a quadratic vibronic coupling Hamiltonian and second order cumulant approximation for the diabatic coupling to derive an analytical expression for time evolution of electronic populations at given temperatures. The formalism is an extension of a previous method called the non-equilibrium Fermi golden rule approach which used the linear vibronic coupling Hamiltonian with the same cumulant treatment for diabatic coupling. The advantage of the quadratic Hamiltonian is that it can include electronic states with different frequencies and normal modes. We explore these advantages with 2D models showing the improved accuracy of the new quadratic method over the linear method. We then apply our formalism to some real molecules, 2,6-bis(methylene) adamantyl cation, and its dimethyl derivative, with parameters obtained from electronic structure calculations followed by diabatization. The results show good agreement with quantum dynamics techniques.

We introduce a perturbative method for studying photoinduced electronic transitions through conical intersections. Our approach uses a quadratic vibronic coupling Hamiltonian and second order cumulant approximation for the diabatic coupling to derive an analytical expression for time evolution of electronic populations at given temperatures. The formalism is an extension of a previous method called the non-equilibrium Fermi golden rule approach which used the linear vibronic coupling Hamiltonian with the same cumulant treatment for diabatic coupling. The advantage of the quadratic Hamiltonian is that it can include electronic states with different frequencies and normal modes. We explore these advantages with 2D models showing the improved accuracy of the new quadratic method over the linear method. We then apply our formalism to some real molecules, 2,6-bis(methylene) adamantyl cation, and its dimethyl derivative, with parameters obtained from electronic structure calculations followed by diabatization. The results show good agreement with quantum dynamics techniques.

No description available.

We study the unique phenomena which occur in certain systems characterized by the crossing or avoided crossing of two electronic eigenvalues. First, an example problem will be investigated for a given Hamiltonian resulting in a codimension 1 crossing by implementing results by Hagedorn from 1994. Then we perturb the Hamiltonian to study the system for the corresponding avoided crossing by implementing results by Hagedorn and Joye from 1998. The results from these demonstrate the behavior which occurs at a codimension 1 crossing and avoided crossing and illustrates the differences. These solutions may also be used in further studies with Herman-Kluk propagation and more. Secondly, we study codimension 2 crossings by considering a more general type of wave packet. We focus on the case of Schrödinger equation but our methods are general enough to be adapted to other systems with the geometric conditions therein. The motivation comes from the construction of surface hopping algorithms giving an approximation of the solution of a system of Schrödinger equations coupled by a potential admitting a conical intersection, in the spirit of Herman-Kluk approximation (in close relation with frozen/thawed approximations). Our main Theorem gives explicit transition formulas for the profiles when passing through a conical crossing point, including precise computation of the transformation of the phase and its proof is based on a normal form approach. / Doctor of Philosophy / We study energies of molecular systems in which special circumstances occur. In particular, when these energies intersect, or come close to intersecting. These phenomena give rise to unique physics which allows special reactions to occur and are thus of interest to study. We study one example of a more specific type of energy level crossing and avoided crossing, and then consider another type of crossing in a more general setting. We find solutions for these systems to draw our results from.

Light or photons can excite electrons in a molecule, leading to creation of electronically excited states. Such processes are ubiquitous in nature, such as, vision, photo-protection of DNA/RNA nucleobases, light harvesting, energy and charger transfer etc. This photoexcitation induces nuclear motion on the excited states, leading the excess energy to dissipate either non-radiatively via internal conversion back down to the ground state, isomerization, and dissociation, or radiatively via fluorescence and phosphorescence. In this dissertation, we investigate the non-radiative processes in organic chromophores that ensue in an ultrafast manner, mediated via conical intersections (CoIn). Description of such excited state processes generally require multi-reference treatment because of quasi-degeneracy near CoIns. Hence, most insight about these processes is typically gained by constructing potential energy surface (PES) using multi-reference electronic structure methods along important reaction coordinates. Nonetheless, the aforementioned static treatment fails to provide any dynamical information, such as, excited state lifetime, state populations, branching ratio, quantum yield etc. In this dissertation, we have gone beyond the static treatment by undertaking computationally expensive non-adiabatic excited state molecular dynamics simulations employing trajectory surface hopping (TSH) methodology on PESs created on-the-fly using multi-reference electronic structure methods. This allows us to compare theoretical results to experimental observables, when possible, strengthening the explanations underlying those processes. Our goal is to examine the effect of structure, and of electronic structure methods on the excited state dynamics. We have examined the non-adiabatic excited state dynamics of cis,cis-1,3-cyclooctadiene (cc-COD), a cyclic diene, in an effort to systematically compare and contrast the dynamics of cc-COD to that of other well studied conjugated molecules. Such exploration is very significant, since the majority of the molecules involved in natural photoexcited processes, include an ethylenic double bond or alternating double bonds creating conjugation. Our calculations have revealed ultrafast sub-ps decay for cc-COD, and have illustrated that the internal conversion dynamics is facilitated by CoIns, dominated by twisting of one of the double bonds and pyramidalization of one of the carbons of that double bond, similar to trans-1,3-butadiene and unlike 1,3-cyclohexadiene (CHD). Our high-level electronic structure calculations have also explained the features in the experimental time-resolved photoelectron spectrum of cc-COD. Another molecule of biological importance, uracil, was also investigated using TSH simulations, by systematically increasing dynamical correlation. We have found that the inclusion of dynamical correlation for uracil leads to an almost barrierless PES on S2, leading to a faster decay and no population trap on this state. Uracil also contains a double bond and the simulations have revealed that the ultrafast relaxation is dominated by an ethylenic twist and pyramidalization of a carbon of that bond, increasing importance of such nuclear motion in photoexcited molecular dynamics. A comparison of the molecules studied have illustrated that the rigid molecules, such as uracil, CHD, have a very local CoIn seam space, whereas cc-COD, which is flexible having many low frequency degrees of freedom, has a non-local or extended CoIn seam space. Overall, the work performed in this dissertation, elucidates the significance of structure and conjugation, in the photoinduced coupled electron-nuclear dynamics in organic molecules. / Chemistry

La photo-isomérisation par ouverture de cycle du benzopyrane a été étudiée à l'aide de la méthode MCTDH (Multi-Configuration Time-Dependent Hartree). Nous avons introduit différentes stratégies pour contrôler la conversion du benzopyrane en mérocyanine à l'aide d'impulsions laser. Nous avons utilisé un modèle pour le potentiel électronique à six dimensions développé dans le cadre d'un travail antérieur. Le modèle repose sur une généralisation des Hamiltoniens modèles standards pour les couplages vibroniques et utilise les six coordonnées les plus importantes pour le processus. Le principal objectif est de fournir des stratégies de contrôle qui pourront être utilisées par les expérimentateurs par la suite. Plus précisément, nous avons proposé: (i) une technique de type pompe-sonde pour contrôler la photostabilité, (ii) une stratégie en deux étape avec une préexcitation vibrationnel du système,(iii) une stratégie reposant sur un contrôle par effet Stark induit par un laser non-résonant. / The ring-opening photoisomerization of benzopyran, which occurs via a photochemical route involving a conical intersection,has been studied with quantum dynamics calculations using the multi-configuration time-dependent Hartree method (MCTDH). We introduce a mechanistic strategy to control the conversion of benzopyran to merocyanine with laser pulses. We use asix-dimensional model developed in a previous work for the potential energy surfaces (PES) based on an extension of thevibronic-coupling Hamiltonian model (diabatization method by ansatz), which depends on the most active degrees of freedom. The main objective of these quantum dynamics simulations is to provide a set of strategies that could help experimentalists tocontrol the photoreactivity vs. photostability ratio (selectivity). In this work we present:(i) a pump-dump technique used tocontrol the photostability, (ii) a two-step strategy to enhance the reactivity of the system: first, a pure vibrational excitation inthe electronic ground state that prepares the system and, second, an ultraviolet excitation that brings the system to the firstadiabatic electronic state; (iii) finally the effect of a non-resonant pulse (Stark effect) on the dynamics.

This thesis describes the development of several spectroscopic methods based on impulsive vibrational spectroscopy as well as of the technique itself. The first chapter describes the ultrafast time domain Raman spectrometer including the development of two noncollinear optical parametric amplifiers for sub-10 fs pulse generation with 343 or 515 nm pumping. In the first spectroscopic study we demonstrate, for the first time, that impulsive vibrational spectroscopy can be used for recording transient Raman spectra of molecules in excited electronic states. We obtain spectra of beta-carotene with comparable, or better, quality than established frequency domain based nonlinear Raman techniques. The following two chapters address the questions on the fate of vibrational coherences when generated on a reactive potential energy surface. We photoexcite bacteriorhodopsin and observe anharmonic coupling mediated vibrational coherence transfer to initially silent vibrational modes. Additionally, we are able to correlate the vibrational coherence activation with the efficiency of the isomerisation reaction in bR. Upon generation of vibrational coherence in the second excited electronic state of beta-carotene, by excitation from the ground electronic state, we are able to follow the wavepacket motion out of the Franck-Condon region. We observe vibrationally coherent internal conversion, through a conical intersection, into the first excited electronic state and are hence able to demonstrate that electronic surface crossings can occur in a vibrationally coherent fashion. Additionally, we find strong evidence for vibronic coupling mediated back and forth crossing between the two electronic states. As a combination of this work we develop a IVS based technique that allows for the direct recording of background and baseline free Raman spectra in the time domain. Several proof of principle experiments highlight the capabilities of this technique for time resolved Raman spectroscopy. In the final chapter we present work on weak-field coherent control. Here, we address the question of whether a photochemical reaction can be controlled by the phase term of an electric excitation field, in the one photon excitation limit. We study the systems rhodamine 101, bacteriorhodopsin, rhodopsin and isorhodopsin and, contrary to previous reports, find no evidence for one photon control.

Cette thèse a pour objet l’étude et le contrôle de la photo-réactivité d’interrupteurs moléculaires, en particulier la photo-isomérisation des spiropyranes. Ce travail théorique a été réalisé en collaboration étroite avec l’équipe expérimentale PFL de l’ICB à Dijon. Des simulations de dynamique quantique non-adiabatique ont été réalisées afin de reproduire et rationaliser les résultats expérimentaux de spectroscopie d’absorption transitoire résolue en temps. Ces expériences ont montré une photo-réactivité ultra-rapide (~ 100 fs) suite à une excitation par une pulse LASER ultra-court. Celle-ci est interprétée comme un mécanisme de conversion interne entre le premier état électronique excité singulet et l’état fondamental via une intersection conique. L’étude théorique a utilisé la réaction d’ouverture de cycle du benzopyrane comme modèle. Les développements réalisés ont porté sur : (1) L’exploration du mécanisme réactionnel et le calcul de surfaces d’énergie potentielle via des méthodes de chimie quantique post-CASSCF perturbatives (XMCQDPT2). Cette analyse a montré des résultats variant fortement par rapport à ceux relevés dans la littérature à des niveaux de calcul moins élevés. (2) Le développement d’un modèle de surfaces d’énergie potentielle électronique par la construction d’un hamiltonien diabatique à partir de données ab initio XMCQDPT2. Du fait de l’importante anharmonicité de l’état électronique fondamental, nous avons mis en place une approche effective en rupture avec les études antérieures. (3) La réalisation de simulations de dynamique quantique non-adiabatique par la méthode MCTDH. Les résultats obtenus sont en très bon accord avec les résultats expérimentaux. L’inclusion explicite du pulse LASER a permis de reproduire et de rationaliser l’effet de contrôle par mise en forme d’impulsion observé expérimentalement. Ce travail a ainsi permis la mise en place d’une collaboration et d’un dialogue théorie/expérience effectifs. / This thesis adresses the study and control of the photo-reactivity of molecular switches, here the photo-isomerisation of spiropyrans. This theoretical work has been achieved in close collaboration with the experimental team PFL within the ICB in Dijon. Non-adiabatic quantum dynamics simulations were carried out so as to reproduce and rationalise the experimental results from time-resolved transient absorption spectroscopy. Such experiments have demonstrated ultra-fast photo-reactivity (~ 100 fs) following excitation by an ultra-short LASER pulse. It is interpreted as an internal conversion mechanism between the first singlet excited eletronic state and the ground state via a conical intersection. The theoretical study used the ring-opening reaction of benzopyran as a model. Developments were made regarding: (1) The exploration of the reaction mechanism and the computation of potential energy surfaces with perturbative, post-CASSCF quantum chemistry methods (XMCQDPT2). This investigation showed that results changed significantly compared to those reported in the literature with lower-level calculations. (2) The generation of a diabatic Hamiltonian based on ab initio XMCQDPT2 data. Owing to the significant anharmonicity in the ground electronic state, we designed a new effective approach, quite different from the previous studies. (3) The production of non-adiabatic quantum dynamics simulations using the MCTDH method. The results thus obtained are in excellent agreement with the experimental ones. Including explicitly the LASER pulse allowed us to reproduce and rationalise the action of pulse shaping on control observed in experiments. The present work thus made possible the succesful implementation of a theoretical/experimental collaboration.

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

Cette thèse porte sur la description théorique de processus dynamiques ultra-rapides de molécules polyatomiques et de leur contrôle par impulsions laser. Nous avons d’abord étudié la photochimie de l’aniline à l’aide de calculs de structure électronique. Nous avons d´écrit plusieurs régions clé des surfaces d’énergie potentielle et analysé ces résultats en relation avec les données expérimentales existantes. La photochimie de la pyrazine a été étudiée par des calculs de dynamiques quantique basés sur un Hamiltonien modèle incluant les quatre états électroniques excités de plus basse énergie et seize modes de vibration. Nous montrons que l’état sombre Au(nπ∗) joue un rôle important dans la dynamique de la molécule après photo-excitation. Un modèle simplifié à deux états et quatre modes a été utilisé pour étudier le contrôle par laser de la dynamique de la pyrazine photo-excitée. Nous proposons un mécanisme visant à augmenter la durée de vie de l’état B2u(ππ∗) en utilisant l’effet Stark induit par une impulsion laser intense non-résonante. / The central subject of this thesis is the theoretical description of ultrafast dynamical processes in molecular systems of chemical interest and of their control by laser pulses. We first use electronic structure calculations to study the photochemistry of aniline. A umber of previously unknown features of the potential energy surfaces of the low-lying elec-tronic states are reported, and analyzed in relation with the experimental results available. We use quantum dynamics simulations, based on a model Hamiltonian including the four lowest excited electronic states and sixteen vibrational modes, to investigate the photochem-istry of pyrazine. We show that the dark Au(nπ∗) state plays an important role in the ultrafast dynamics of the molecule after photoexcitation. The laser control of the excited state dynamics of pyrazine is studied using a simplified two-state four-mode model Hamiltonian. We propose a control mechanism to enhance the lifetime of the bright B2u(ππ∗) state using the Stark effect induced by a strong non-resonant laser pulse. We finally focus on the laser control of the tunneling dynamics of the NHD2 molecule, using accurate full-dimensional potential energy and dipole moment surfaces. We use simple effective Hamiltonians to explore the effect of the laser parameters on the dynamics and design suitable laser fields to achieve the control. These laser fields are then used in MCTDH quantum dynamics simulations. Both enhancement and suppression of tunneling are achieved in our model.