We studied the structural instabilities of one-dimensional (1D) and quasi-one-dimensional (Q1D) electron-phonon systems at low temperature through two models, SuSchrieffer-Heeger (SSH) and molecular crystal (CM) with and without spin. The phase diagrams are obtained using a Kadanoff-Wilson renormalization group approach (GR). For the 1D half-filled system the study of the frequency dependence of the electronic gap allowed us to connect continuously the two limits, adiabatic and non-adiabatic. The Peierls and Cooper channels interference and the quantum fluctuations reduce the gap. A regime change occurs when the frequency becomes of the order of mean field gap, marking a quantum-classical crossover that is the Kosterlitz-Thouless type. At this level, the effective coupling behaves in power law function on frequency. For the case with spin, a gapped Peierls state is maintained in the non-adiabatic limit, while for the case without spin, the system transits to ungapped disordered state, namely the Luttinger liquid stat (LL). For the SSH model without spin, the GR confirms the existence of a threshold phonon coupling beyond which the gap is restored. The study of the rigidities of the two models without spin allowed us to trace the main features of the LL state predicted by the bosonization method. The study of the Holstein-Hubbard model has allowed us not only to reproduce the phase diagrams already obtained by the Monte Carlo method, but to highlight two additional phases, namely, free fermions phase and the bond charge-density-wave phase. We have extended this study to the quarter-filled Q1D Peierls systems at finite temperature. Within the SSH model, an unconventional superconducting phase with spin singlet symmetry SS-s emerges at low temperature when the deviation to the perfect nesting of the Fermi surface is strong enough. Peierls-SS transition is characterized by the presence of a quantum critical point at low frequency and by a power law behavior of the transition temperature as a function of frequency with an exponent identical to one of 1D system. This exponent which universality has been verified contrasts with the BCS result. Coulomb interactions have been introduced through the study of the extended SSH-Hubbard model. The extension of this work to half-filled SSH and CM cases was also performed.

Die Arbeit untersucht den Anregungsenergietransfer in supramolekularen Phäophorbid-a-Komplexen. Das P4- und das P16-Molekül bestehen aus vier bzw. sechzehn Phäophorbid-a-Molekülen. Die Komplexe werden in explizitem Lösungsmittel im Rahmen einer gemischt quanten-klassischen Methode untersucht. Klassische Molekulardynamik-Simulationen werden durchgeführt. Die zeitabhängige Schrödingergleichung wird gelöst, der entsprechende Hamiltonoperator hängt parametrisch von den Kernkoordinaten ab. Es wird eine Methode vorgestellt, die die Berechnung des Schwingungsbeitrags der Koordinatenabhängigkeit in harmonischer Näherung ermöglicht. Die Qualität der Methode wird bewiesen. Es werden drei verschiedene Ansätze benutzt, um das Zeitverhalten des Anregungsenergietransfers innerhalb der Chromophorkomplexe zu charakterisieren. Es werden zunächst Transferraten berechnet und entsprechende Ratengleichungen gelöst. Desweiteren werden gemittelte zeitabhängige Populationen aus der Lösung der Schrödingergleichung bestimmt. Zudem wird die Zeitskala des Anregungsenergietransfers aus der Anisotropie erhalten. Die Berechnung der Anisotropie beruht auf der Lösung einer Schrödingergleichung, welche das elektromagnetischen Feldes explizit enthält. Für alle drei Ansätze ergibt sich die gleiche Dynamik des Anregungsenergietransfers. Es werden zudem lineare und transiente Spektren der Qy-Banden der Chromophorkomplexe berechnet. Für ein einzelnes Phäophorbid-a-Molekül in Ethanol werden zusätzlich die Qx-Bande und die Schwingungsprogression bestimmt. Außerdem wird die lineare Absorption von Phäophorbid a und P16 neben einem Gold-Nanopartikel untersucht, die erwartete Verstärkung des Absorptionssignals durch die Präsenz des Nanoteilchens wird gezeigt. Abschließend wird eine neue Methode vorgestellt, die es erlaubt, die abstands- und orientierungsabhängige Abschirmung der exzitonischen Kopplung parametrisch in die gemischt quanten-klassische Methode zu integrieren. / This thesis investigates the excitation energy transfer in pheophorbide a complexes. The P4 and the P16 molecule consist of four and sixteen pheophorbide a molecules, respectively. The complexes in explicit ethanol solution are investigated utilizing a mixed quantum-classical methodology. Classical molecular dynamics simulations are carried out. The time-dependent Schrödinger equation is solved for a Hamiltonian that depends parametrically on the classical nuclear coordinates. In this thesis a method is introduced which allows the computation of the vibrational contribution in harmonic approximation. The high quality of the method is proven. Three different ansatzes were utilized to compute the time development of the excitation energy transfer within the chromophore complexes. The expansion coefficients that result from the solution of the time-dependent Schrödinger equation are utilized to compute averaged time-dependent populations. Also, the expansion coefficients are used to compute excitation energy transfer rates in second order of the excitonic coupling. Thirdly, the time scale of the excitation energy transfer is derived from the delay-time dependent transient anisotropy. In order to compute the anisotropy, the electromagnetic field is included directly in the Hamiltonian of the system. The excitation energy transfer dynamics is exactly the same for the three approaches. In addition, linear and transient spectra of the chromophor complexes Qy band are computed. For a single pheophorbide a in ethanol, the Qx band and the vibrational progression are calculated. Furthermore, the linear absorption of pheophorbide a and P16 next to a gold nanoparticle is studied. The amplification of the molecular absorption signal due to the presence of the nanoparticle is shown. Finally, a new method is introduced to treat distance and conformation dependent screening of the excitonic coupling parametrically within a mixed quantum-classical description.

En esta tesis desarrollamos métodos híbridos clásico-cuánticos para el estudio de la relajación vibracional de moléculas en disolución. En estos tratamientos se realiza una descripción cuántica de la vibración del soluto, mientras que el resto de grado de libertad se describen clásicamente. Estos métodos superan las limitaciones inherentes a los tratamientos clásicos y permiten el análisis del flujo de energía entre el soluto y el disolvente. Hemos aplicado estas metodologías al estudio de la relajación vibracional de la molécula de yodo en xenón líquido y del ión cianuro en agua, analizando el papel del disolvente en las transiciones vibracionales del soluto. Nuestros resultados para estos sistemas, de naturaleza tan diferente, concuerdan bien con las medidas experimentales, lo que en ausencia de resultados teóricos exactos supone una valiosa prueba de la capacidad de estos métodos para el estudio de los procesos de relajación vibracional en líquidos. / In this thesis we have developed hybrid quantum-classical methods to study vibrational relaxation of molecules in solution. In these treatments a quantum description of solute vibration is done, while the other degrees of freedom are classically described. These methods overcome the inherent limitations of classical treatments and let us the analysis of energy flux between solute and solvent. We have applied these methodologies to study vibrational relaxation of iodine molecule in liquid xenon and cyanide ion in water, analyzing the role of the solvent in the vibrational transitions of the solute. Our results for these systems, of so different kind, agree well with experimental measures, what in absence of exact theoric results is a valious proof of the ability of these methods to study the vibrational relaxation processes in liquids.

No description available.

Cette thèse présente le développement et les applications d'un formalisme hybride quantique-classique pour décrire la structure électronique d'un système actif avec un environnement cryogénique (agrégat ou matrice d'atomes de gaz rare). La description quantique de la structure électronique du système actif est faite dans le cadre d'une approximation de type Liaisons Fortes de la Théorie de la Fonctionnelle de la Densité, avec charges atomiques autocohérentes (SCC-DFTB). L'environnement de gaz rare est décrit par des potentiels classiques atome-atome (FF). L'interaction entre le sytème actif et les atomes de l'environnement cryogénique est représentée par des opérateurs matriciels locaux anisotropes électron-atome, ainsi que par des contributions de polarisation et de dispersion. La détermination des opérateurs et des paramètres d'interaction est extraite de calculs ab initio post Hartree-Fock (CCSD-T) sur les paires atome actif/atome d'argon. Les applications concernent les interactions entre hydrocarbures, agrégats d'eau isolés ou complexes hydrocarbures/eau avec des agrégats et ou des matrices d'argon. Le modèle est validé sur de petits systèmes (molécule C6H6 , molécule H2O) en interaction avec des atomes et agrégats d'argon. Nous avons ainsi déterminé les données structurales et énergétiques pour les agrégats (C6H6)Arn (n < 55) qui ont été comparées à des données ab initio (DFT, CCSD-T) pour les plus petits agrégats, ou à des calculs de champ de force publiés dans la littérature pour les agrégats de plus grande taille. Le modèle permet également un traitement unifié de différentes situations électroniques permettant ainsi la détermination de l'évolution des potentiels d'ionisation du système actif en fonction de la taille n de l'agrégat solvatant. Le modèle DFTB/FF a ensuite été appliqué à des molécules et nano-agrégats d'eau (H2O)n (n=2-6) insérés dans des matrices d'argon, représentées par des sous-ensembles finis du réseau cristallin cubique faces centrées. Des données structurales et énergétiques ont été obtenues. Des études de dynamique moléculaire ont permis la détermination de spectres infrarouges (IR) à température finie. La comparaison des spectres IR théoriques caractérisant une molécule d'eau en matrice avec les données expérimentales nous a permis de valider l'approche DFTB/FF. Le cas de l'hexamère (H2O)6, plus petit agrégat présentant une structure tri-dimensionnelle et caractérisé par plusieurs isomères stables, a été étudié de façon exhaustive : l'effet de la matrice sur les structures de certains de ces isomères a été mis en évidence, ainsi que des effets différentiels sur leur stabilités respectives. Une influence sur les positions des bandes IR des agrégats a également été montrée. Les résultats obtenus permettent une interprétation satisfaisante des données expérimentales existantes pour les plus petits agrégats. L'assignation des spectres expérimentaux de l'hexamère demeure incertaine. Enfin, des résultats préliminaires sur les structures, l'énergétique et les spectres IR à température finie ont été obtenus pour des complexes d'Hydrocarbures Aromatiques Polycycliques avec l'eau (HAP-H2O) en matrices d'argon. L'ensemble des données obtenues pour ces complexes est discuté en relation avec les résultats expérimentaux en environnement cryogénique obtenus dans l'équipe de Joëlle Mascetti de l'Institut des Sciences Moléculaires de l'Université Bordeaux I, dans le cadre d'une collaboration ANR (ANR PARCS no 13-BS08-0005). Ce travail a bénéficié d'une allocation de thèse co-financée par l'Institut de Physique du CNRS et le Conseil Régional de la région Midi-Pyrénées. / This thesis presents the development and applications of an hybrid quantum-classical formalism in order to describe the electronic structure of an active system in a cryogenic environment (cluster or rare gas matrix). The quantum description of the electronical structure of the active system is based on a a tight-binding approximation of the density functional theory, with self-consistency regarding the charges (SCC-DFTB). The rare gaz environment is described via classical atom-atom potential (FF). The interaction between the active system and the atoms of the cryogenic environment is represented by local anisotropic matricial electron-atom operators, as well as by polarisation and dispersion contributions. Operators and interaction parameters are extracted from post Hartree-Fock \textit{ab initio} calculations (CCSD-T) of active atom/argon atom pairs. The applications involve hydrocarbons, isolated water clusters or hydrocarbon/water complexes in interaction with argon clusters or matrices. The model has been validated on small systems (C6H6 molecule, H2O molecule) in interaction with argon atoms and clusters. We have been able to determine structural and energetic data for (C6H6)Arn (n < 55) clusters which are benchmarked against ab initio results (DFT,CCSD-T) for the smaller sizes, or with respect to FF calculations, available in the literature, for larger sized clusters. The model enables to treat various electronic situations, allows in particular to determine the evolution of the ionization potentials of the active system as a function of the inert cluster size. The SCC-DFTB/FF model has then been applied to water molecules and water nano-clusters (H2O)n (n=2-6) embedded in argon matrices, represented by finite size cristal pieces of the face centered cubic lattice. Structural and energetical data have been obtained. Molecular dynamics studies have enabled the determination of finite temperature infrared (IR) spectra. Comparison between the theoretical and experimental spectra of the water monomer embedded in the matrix validates the SCC-DFTB/FF approach. The case of the water hexamer (H2O)6, the smallest cluster presenting a three-dimensional structure and caracterized by several low-energy isomers, has been investigated exhaustively : the effect of the matrix on the structures of some isomers has been shown as well as differential effects on their respective stabilities. An influence on IR lines positions has also been highlighted. Our theoretical study allows for a satisfactory interpretation of the experimental data for the smallest clusters (n<4). The assignment of the experimental spectra of the hexamer remains in discussion. Finally, preliminary results on structures, energetics and finite temperature IR spectra have been obtained for Polycyclic Aromatic Hydrocarbons (PAH) /water complexes. The results for the complexes are discussed in relation with experimental data obtained in the team of Joëlle Mascetti at the Institute of Molecular Sciences (University of Bordeaux I), in the context of an ANR collaborative project (ANR PARCS no 13-BS08-0005). The thesis has been co-financed by the CNRS Institute of Physics and Conseil Regional of Region Midi-Pyrénées.

Thermostated time evolutions are on a firm ground and widely used in classical molecular dynamics (MD) simulations. Hamilton´s equations of motion are supplemented by time-dependent pseudofriction terms that convert the microcanonical isoenergetic time evolution into a canonical isothermal time evolution, thus permitting the calculation of canonical ensemble averages by time averaging. However, similar methods for quantum MD schemes are still lacking. Given the rich dynamical behavior of ultracold trapped quantum gases depending on the value of the s-wave scattering length, it is timely to investigate how classical thermostating methods can be combined with powerful approximate quantum dynamics schemes to deal with interacting quantum systems at finite temperature. In this work, the popular method of Nose and Hoover to create canonically distributed positions and momenta in classical MD simulations is generalized to a genuine quantum system of infinite dimensionality. We show that for the quantum harmonic oscillator, the equations of motion in terms of coherent states may be modified in a Nose-Hoover manner to mimic the coupling of the system to a thermal bath and create a quantum canonical ensemble. The method is developed initially for a single particle and then generalized to the case of an arbitrary number of identical quantum particles, involving entangled distribution functions. The resulting isothermal equations of motion for bosons and fermions contain additional terms leading to Bose-attraction and Pauli-blocking, respectively. Questions of ergodicity are discussed for different coupling schemes. In the many-particle case, the superiority of the Nose-Hoover technique to a Langevin approach is demonstrated. In addition, the work contains an investigation of the Grilli-Tosatti thermostating method applied to the harmonic oscillator, and calculations for quantum wavefunctions moving with a time-invariant shape in a harmonic potential.