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Aggregates of PCBM Molecules: A computational studyKaiser, Alexander, Probst, Michael, Stretz, Holly A., Hagelberg, Frank 15 May 2014 (has links)
Small clusters of [6,6] phenyl-C61-butyric acid methyl ester (PCBM) molecules are analyzed with respect to their equilibrium geometries and associated electronic as well as energetic properties. Plane wave density functional theory (PWDFT) computations, assisted by molecular dynamics (MD) simulations, are performed on systems of the form PCBMn (n = 1-5). The bonding operative in these units is described as a cooperation between HO bonding, involving the C5H9O2 groups of the PCBM molecule, and fullerene-fullerene attraction. The maximally stable structures identified tend to include a dimer motif that combines both interaction modes. The great importance of van-der-Waals effects in stabilizing the studied clusters is demonstrated by comparing the PCBM3 series with and without inclusion of a van-der-Waals term in the PWDFT procedure. The two approaches yield reverse orders of stability. A decreasing tendency in the Kohn-Sham HOMO-LUMO gaps of PCBMn with the cluster size may be used to monitor PCBM aggregation in the active layer of organic photovoltaic devices by optical spectroscopy.
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Investigating sub-10 nm-thick Cloaking Films on Sessile Water Droplets Placed on Slippery Lubricant-Infused Porous Surfaces (SLIPS)Ridwan, Muhammad Ghifari 04 1900 (has links)
Slippery liquid-infused porous surfaces (SLIPS) – a new class of bio-inspired liquid-repellent surfaces – comprise arbitrarily porous architectures filled with oils that exhibit high interfacial tensions to probe liquids and present ultralow contact angle hysteresis (<〖10〗^°). However, before practical technologies based on SLIPS can be designed at large-scale, a number of fundamental questions remain to be answered. For instance, depending on the sign of the spreading coefficient of the Vapor(V)-lubricant oil(O)-liquid(L) system, defined as S_(OL(V))=γ_LV-γ_LO-γ_OV>0, the lubricating layer forms a layer at the liquid-vapor interface (here, γ_LV is a liquid-vapor interfacial tension, γ_LO – liquid-oil, and γ_OV – oil-vapor). This “cloaking” of liquid drops can deplete SLIPS’ lubricant over time and contaminate the probed liquid. So far, cloaking has been investigated by contact angle goniometry and confocal microscopy, which cannot resolve films of molecular thickness and factors that govern the equilibrium thickness of those films are not entirely clear. Here, we report on the development and application of a reflective-mode SFA platform to characterize the cloaking of water droplets placed on SLIPS. A multilayer matrix method is utilized to analyze the interferometry data. Using this complementary experimental and analytical approach, we determined the thickness of the cloaking layer for the FDTS(solid)-VF-40(lubricant)-water(probe liquid)-air system to be z3= 7±1 nm. Towards deeper insights into the intermolecular and surface forces responsible for cloaking, we demonstrate that repulsive van der Waals interactions are responsible for stabilizing the cloaking film at the water-air interface. Our experimental platform and the analytical framework should facilitate investigations of other SLIPS and probe liquid systems down to the molecular-scale resolution. These findings might aid the rational design of SLIPS, e.g., for drag reduction, anti-biofouling, and anti-corrosion.
In addition to investigating SLIPS, We addressed the following questions with the help of atomic force microscopy (AFM): (i) how do zwitterionic osmolytes modulate electrostatic and hydrophobic interactions in nanoscale confinement, and (ii) is it possible to have two negatively charged surfaces attract each other? Our findings are presented as appendices in this thesis.
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Electronic Structure, Optical Properties and Long-Range-Interaction Driven Mesoscale AssemblyMa, Yingfang 07 September 2017 (has links)
No description available.
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Mesure de l’interaction de van der Waals entre deux atomes de Rydberg / Measurement of the van der Waals interaction between two Rydberg atomsBeguin, Lucas 13 December 2013 (has links)
Les atomes neutres sont des candidats prometteurs pour la réalisation et l’étude d’états intriqués à quelques dizaines de particules. Pour générer de tels états, une approche consiste à utiliser le mécanisme de blocage dipolaire résultant des fortes interactions dipôle-dipôle entre atomes de Rydberg.Suivant cette approche, cette thèse présente la conception et la caractérisation d’un dispositif expérimental permettant de manipuler des atomes de 87Rb individuels piégés dans des pinces op- tiques microscopiques, et à les exciter vers des états de Rydberg. Un environnement électrostatique stable et des électrodes de contrôle permettent une manipulation fine de ces états. Avec deux pinces optiques séparées de quelques microns, nous démontrons le blocage de Rydberg entre deux atomes, et nous observons leur excitation collective.Enfin, en opérant en régime de blocage partiel, nous développons une méthode permettant de mesurer l’interaction de van der Waals ∆E = C6 /R6 entre deux atomes séparés par une distance R contrôlée. Les coefficients C6 obtenus pour différents états de Rydberg sont en bon accord avec des calculs théoriques ab initio, et nous observons l’augmentation spectaculaire de l’interaction en fonction du nombre quantique principal n de l’état de Rydberg. / Neutral atoms are promising candidates for the realization of entangled states involving up to a few tens of particles. To generate such states, one approach consists in using the dipole blockade mechanism, which results from the strong dipole-dipole interactions between Rydberg atoms.Following this approach, this thesis describes the design and the characterization of an experimental apparatus allowing to manipulate single 87Rb atoms trapped in microscopic optical tweezers, and to excite them towards Rydberg states. A stable electrostatic environment and controlled electrodes enable the fine manipulation of these states. Using two optical tweezers separated by a few microns, we demonstrate the Rydberg blockade between two single atoms, and we observe their collective excitation.Finally, by operating in the partial blockade regime, we develop a method allowing to measure the van der Waals interaction ∆E = C6 /R6 between two atoms separated by a controlled distance R. The C6 coefficients obtained for various Rydberg states agree well with ab initio theoretical calculations, and we observe the dramatic increase of the interaction with the principal quantum number n of the Rydberg state.
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Sterically flexible molecules in the gas phaseErlekam, Undine 24 October 2008 (has links)
Für die makroskopischen Eigenschaften und Funktionen biologisch relevanter Materie spielen schwache, intra- und intermolekulare Wechselwirkungen dispersiver und elektrostatischer Natur auf molekularem Niveau eine große Rolle. Um diese schwachen Wechselwirkungen zu untersuchen, können Modellsysteme, isoliert in der Gasphase, herangezogen werden. Benzoldimer, ein schwach gebundener Van der Waals Komplex, kann beispielsweise als Modellsystem für dispersive Wechselwirkungen dienen. In der vorliegenden Arbeit werden die strukturellen Eigenschaften und die (interne) Dynamik des Benzoldimers mit Hilfe spektroskopischer Methoden in den Energiebereichen der Rotationen, Vibrationen und elektronischen Übergänge untersucht und im Kontext der Symmetrie diskutiert. Die in dieser Arbeit vorgestellten Experimente tragen zu einem tieferen Verständnis des Benzoldimers bei, jedoch zeigt das Experiment zur internen Dynamik auch, dass eine ausreichende theoretische Beschreibung des Benzoldimers nach wie vor eine Herausforderung darstellt. Schwingungsübergänge hochsymmetrischer Moleküle sind oft optisch inaktiv, können jedoch mit der hier vorgestellten Methode der Symmetrieerniedrigung durch Komplexierung zugänglich gemacht werden, wie am Beispiel des Benzols demonstriert wird. Außerdem wird ein Mechanismus vorgstellt, der kollisionsinduzierte Konformationsänderungen in einem Molekularstrahl beschreibt. Dieses Modell kann generell für Molekularstrahlexperimente an flexiblen Molekülen hilfreich sein, einerseits um die beobachtete Konformationsverteilung zu verstehen, andererseits um die experimentellen Parameter gezielt zu verändern und somit Konformerpopulationen zu manipulieren. Die in dieser Dissertation vorgestellten spektroskopischen Experimente liefern einerseits molekülspezifische Informationen und ermöglichen andererseits, Modelle, die von allgemeiner Bedeutung sind, zu entwickeln. / The macroscopically observable properties and functionalities of biological matter are often determined by weak intra- and intermolecular interactions on the microscopic level. Such weak interactions are for example hydrogen bonding and van der Waals interactions and can be investigated best on isolated model systems in the gas phase. The benzene dimer, for example, is a prototype system to investgate dispersive interactions. The spectroscopic experiments, covering the energy ranges of rotations, vibrations and electronic transitions, presented in this thesis, contribute to a deeper understanding of the benzene dimer. However, from the experiments investigating the internal dynamics it becomes clear that an appropriate theoretical description of the benzene dimer is still a challenge. Vibrational transitions of highly symmetric molecules, as for example of the benzene, are often optically inactive. Here, a method is presented, which exploits symmetry reduction upon complexation and thus allows one to access such modes. Furthermore, a model is proposed describing collision induced conformational interconversion in a molecular beam. This model can be helpful for molecular beam experiments of flexible molecules to understand the observed relative conformational population and to adapt the experimental conditions allowing for the manipulation of the relative conformer abundances. In this thesis, results are presented that allow one on the one hand to deduce molecular specific information and that on the other hand also give a broader insight into phenomena of general importance.
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Force measurements using scanning probe microscopy : Applications to advanced powder processingMeurk, Anders January 2000 (has links)
The object of this thesis is to apply scanning probemicroscopy (SPM) to the field of advanced powder processing.Measurement of interparticle surface forces at conditionsrelevant to ceramic processing has been performed together withthorough studies of powder friction. Surface force measurements between silicon nitride andsilica surfaces in 1-bromonaphtalene and diiodomethane resultedin an attractive van der Waals force in both media for thesymmetric systems and a repulsive van der Waals force for theasymmetric systems. This agreed well with theoreticalpredictions from Lifshitz theory. Measurements in electrolytesolutions between silicon nitride surfaces with a varyingdegree of oxidation showed that silanol groups dominated theinteractions at a high degree of oxidation, whereas theinfluence of amine species became stronger after surfaceetching. Surface charge, surface potential and density ofsurface groups have been extracted from DLVO computer modellingof the experimental force curves. Surface force measurementshave been carried out using a nitrided silica sphere as acolloidal probe, representative for commercial silicon nitridepowders. Adsorption of poly(acrylic acid) above the isoelectricpoint generated a thin polymer layer of an essentially flatconformation. Friction force measurements were attainable via novelcalibration procedures of both the lateral photodetectorresponse and the cantilever torsional spring constant.Combining the method for detector calibration with evaluationof static friction slopes simplified the choice of appropriatecontact mechanics theory to evaluate the friction measurements.Applying the method on friction measurements between ironsurfaces coated with commercial lubricants showed a substantialsurface deformation not seen from the friction force alone. Thenanorheological properties of silica surfaces coated with twodifferent stearic acids have been evaluated from friction forcemeasurements. Steady sliding motion was replaced by highlyregular stick-slip motion at a critical load and velocity. Thestick-slip motion was successfully described and fitted to aphenomenological model. The contact area evaluated fromMaugis-Dugdale theory revealed the contact diameter to be veryclose to the stick-slip periodicity. Friction measurements were carried out between individualspray-dried ceramic granules as a function of binderconcentration and relative humidity. The hygroscopic nature ofthe binder resulted in a higher adhesion force but lowerfriction coefficient with increasing humidity. This effect wasascribed to softening of the binder and a lowering of the shearstrength of the binder rich surface layer on the granules.Comparison of the friction force between two granules and agranule and a hard metal surface confirmed that resistance toflow during the initial stages of powder pressing is dominatedby granule-wall friction and adhesion. Keywords: Atomic force microscope, AFM, SPM, van der Waalsinteraction, DLVO-theory, surface forces, colloidal probe,force curve, friction, adhesion, stick-slip, cantilever,calibration, spring constant, silicon nitride, iron,silica.
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Rotational Spectroscopic And Ab Initio Studies On The Weakly Bound Complexes Containing 0-H...π And S-H...π InteractionsGoswami, Mausumi 07 1900 (has links)
Work reported in this thesis mainly comprises of the assignments and analysis of the rotational spectra and structures of three weakly bound complexes: C2H4•••H2S, C6H5CCH•••H2O and C6H5CCH•••H2S. All the data have been collected using a home built Pulsed Nozzle Fourier Transform Microwave Spectrometer. Apart from this, the thesis also deals with a criterion of classifying a weakly bound complex to a ‘hydrogen-bonded’ one.
First chapter of the thesis gives a brief intermolecular interactions and molecular clusters of π system. It also briefly touches on the structural determination by rotational spectroscopy and the basic information one can gain from the rotational spectrum. Second chapter of the thesis gives a brief introduction to the experimental and theoretical methodology. It also gives a description of the software used in the FTMW spectrometer which was rebuilt using Labview 7.1. Third chapter of the thesis deals with the rotational spectra and structure of eight isotopologoues of C2H4•••H2S complex. The lines are split into four components for the parent isotopologue due to the presence of large amplitude motion. The smaller splitting is 0.14 MHz and the higher splitting is 1.67 MHz in (B+C)/2 for the parent isotopologue. Spectral splitting pattern of the isotopologues confirmed that smaller splitting is due to the rotation of ethylene about its C-C bond axis along with the contraction of S-H bond whereas the larger motion arises due to the interchange of equivalent hydrogens of H2S in the complex. A detailed spectral analysis and ab initio calculation for this system have been described in chapter III. The fourth chapter of the thesis describes the rotational spectroscopic studies of five isotopologues of C6H5CCH•••H2O complex. Rotational spectra unequivocally confirm the structure of the complex to be a one where H2O is donating one of its hydrogen to the acetylenic π cloud forming a O-H••• π bond whereas the ring ortho C-H bond forms C-H•••O bond with the water oxygen. For theparent isotopomer the lines are split into two components due to the rotation of H2O about its C2 symmetric axis. The fifth chapter of thesis describes the rotational spectroscopic and ab initio studies of five isotopologues of C6H5CCH•••H2S complex. Rotational spectra indicate the structure to be the one where H2S is sitting on the top of the phenyl ring and shifted towards the acetylenic group. The sixth chapter of the thesis describes a criterion for calling a complex to be hydrogen bonded based on the dynamic structure rather than the static structure of the complex. The question asked is if the anisotropy of the interaction is strong enough to hold the ‘hydrogen bond’ when one takes dynamics into account. The proposed criterion is that the zero point energy of the motion which takes the hydrogen away from the acceptor should be much less than the barrier height of the respective motion supporting at least one bound level below the barrier. Ab initio calculations have been done on four model systems Ar2•••H2O, Ar2•••H2S, C2H4••• H2O and C2H4••• H2S to emphasize this criterion.
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Force measurements using scanning probe microscopy : Applications to advanced powder processingMeurk, Anders January 2000 (has links)
<p>The object of this thesis is to apply scanning probemicroscopy (SPM) to the field of advanced powder processing.Measurement of interparticle surface forces at conditionsrelevant to ceramic processing has been performed together withthorough studies of powder friction.</p><p>Surface force measurements between silicon nitride andsilica surfaces in 1-bromonaphtalene and diiodomethane resultedin an attractive van der Waals force in both media for thesymmetric systems and a repulsive van der Waals force for theasymmetric systems. This agreed well with theoreticalpredictions from Lifshitz theory. Measurements in electrolytesolutions between silicon nitride surfaces with a varyingdegree of oxidation showed that silanol groups dominated theinteractions at a high degree of oxidation, whereas theinfluence of amine species became stronger after surfaceetching. Surface charge, surface potential and density ofsurface groups have been extracted from DLVO computer modellingof the experimental force curves. Surface force measurementshave been carried out using a nitrided silica sphere as acolloidal probe, representative for commercial silicon nitridepowders. Adsorption of poly(acrylic acid) above the isoelectricpoint generated a thin polymer layer of an essentially flatconformation.</p><p>Friction force measurements were attainable via novelcalibration procedures of both the lateral photodetectorresponse and the cantilever torsional spring constant.Combining the method for detector calibration with evaluationof static friction slopes simplified the choice of appropriatecontact mechanics theory to evaluate the friction measurements.Applying the method on friction measurements between ironsurfaces coated with commercial lubricants showed a substantialsurface deformation not seen from the friction force alone. Thenanorheological properties of silica surfaces coated with twodifferent stearic acids have been evaluated from friction forcemeasurements. Steady sliding motion was replaced by highlyregular stick-slip motion at a critical load and velocity. Thestick-slip motion was successfully described and fitted to aphenomenological model. The contact area evaluated fromMaugis-Dugdale theory revealed the contact diameter to be veryclose to the stick-slip periodicity.</p><p>Friction measurements were carried out between individualspray-dried ceramic granules as a function of binderconcentration and relative humidity. The hygroscopic nature ofthe binder resulted in a higher adhesion force but lowerfriction coefficient with increasing humidity. This effect wasascribed to softening of the binder and a lowering of the shearstrength of the binder rich surface layer on the granules.Comparison of the friction force between two granules and agranule and a hard metal surface confirmed that resistance toflow during the initial stages of powder pressing is dominatedby granule-wall friction and adhesion.</p><p>Keywords: Atomic force microscope, AFM, SPM, van der Waalsinteraction, DLVO-theory, surface forces, colloidal probe,force curve, friction, adhesion, stick-slip, cantilever,calibration, spring constant, silicon nitride, iron,silica.</p>
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Coalescence de gouttes dans l'air : du millimètre au nanomètre / Coalescence of drops in air : from millimeter to nanometerIncerti, Véronique 14 December 2017 (has links)
La coalescence intervient dans de nombreuses situations physiques, naturelles ou industrielles, de la microphysique des nuages à la stabilité des émulsions ou l’assèchement des pétroles. Dans toutes ces situations, il est crucial de comprendre les mécanismes physiques en jeu, de manière pouvoir influencer la coalescence, la favoriser ou au contraire l’inhiber, selon les besoins. Dans cette thèse, nous étudions la coalescence dans l’air entre deux gouttes attachées et décomposons le processus global en quatre étapes : l’approche avec drainage du film d’air entre les gouttes, le perçage des interfaces, l’ouverture du pont résultant de ce perçage, les oscillations amorties conduisant à l’équilibre de la goutte résultante. Les théories décrivant les étapes 1, 2 et 4 font intervenir des modèles hydrodynamiques continus, se plaçant à une échelle macroscopique. Cependant, à l’articulation entre les deux premières étapes, intervient le perçage des interfaces, processus gouverné par des forces dont la portée correspond à une échelle de quelques dizaines de nanomètres. Une des difficultés les plus importantes dans l’étude de la coalescence est celle de l’intégration des processus ayant lieu à un niveau moléculaire, dans une théorie du continuum dont l’échelle caractéristique est bien supérieure. L’objectif est de faire le lien entre les différentes échelles : y a-t-il des interactions entre les processus se produisant à ces différentes échelles ? Pour répondre à cette question, nous développons trois axes de travail, engageant chacun une échelle caractéristique. L’un est l’étude, au niveau macroscopique du micromètre, de l’ouverture du pont liquide. Grâce à une caméra rapide, plusieurs régimes d’écoulement sont mis en évidence. Les modèles théoriques existants concernent essentiellement le régime visqueux, et aucun modèle complet ne décrit le régime purement inertiel. Nous explorons expérimentalement ce régime et décrivons la forme et la longueur du pont, à l’aide d’ondes capillaires. Nous mettons en évidence l’existence de deux lignes de très forte courbure, que nous appelons singularités, qui naissent sur le lieu de perçage des interfaces et se propagent presque sans déformation de part et d’autre. Ces singularités, conditionnées par la tension superficielle, moteur de la coalescence, façonnent la forme du pont liquide et donc l’écoulement dans ce dernier. Nous proposons un modèle simple d’écoulement inertiel, basé sur la forme du pont liée à ces singularités. Ce modèle permet de mieux comprendre les rôles des forces hydrodynamiques et de la courbure dans l’évolution temporelle de la largeur du pont. Un autre axe est une étude expérimentale par Microscope à Force Atomique, qui permet de décrire les forces responsables de la coalescence à l’échelle nanométrique, les déformations des gouttes intervenant à cette échelle et leur rôle dans la rupture des interfaces. Les mesures de forces entre goutte et flaque, puis entre deux gouttes sont effectuées avec un AFM principalement en mode dynamique de Modulation de Fréquence. Elles permettent de mettre en évidence une distance seuil de déclenchement de l’instabilité hydrodynamique responsable de la coalescence et de mesurer cette distance en fonction des propriétés physiques du liquide et du rayon des gouttes. Un diagramme de coalescence est proposé, qui permet de prévoir la valeur de la distance de déclenchement de la coalescence et le rôle des déformations d’interfaces à l’échelle nanométrique. Enfin, les oscillations du pont liquide, générées par la coalescence, sont étudiées, les modes et fréquences propres sont calculés numériquement par la méthode des éléments finis, puis comparés aux valeurs expérimentales mesurées à partir des films acquis par caméra rapide. / Coalescence is involved in numerous natural or man-made processes, from microphysics of clouds to emulsions stability, or water-crude oil separation processes. In these situations, it is crucial to understand the physics of coalescence of drops or bubbles, in order to influence the phenomenon, to enhance or inhibit the coalescence rate, depending on the needs. In this thesis, we study coalescence in air of two attached drops. We separate the coalescence process into four stages : the approach and drainage of the film between coalescing bodies, the interfaces breaking, the opening of the bridge resulting from this breaking, and the damped oscillations, generated by coalescence, leading to the equilibrium state of the resulting drop. The theoretical description of the stages 1, 2 and 4 are based on continuous hydrodynamic models, at a macroscopic scale. However, the transition between the first two stages is the interfaces break-up, controlled by short range interactions, at a nanometer scale. One of the most difficult issues is the integration of these nanoscale processes into a continuum hydrodynamic theory which length scale is much bigger. The purpose of this work is understand how the phenomenons occurring at the different scales are linked. We first study, at a macroscopic scale, the opening of the liquid bridge between the drops. Thanks to the experimental set-up, involving a high-speed camera, we explore different regimes of flow, by studying the shape and dimensions of the bridge. The existing hydrodynamic models mostly describe the viscous regime, and there exist no complete modeling of the inertial regime. We explore specifically this regime. The bridge shape is described by the mean of capillary waves. We focus on two lines of extremely high curvature on the free surface, that we call singularities, generated in the initial site of interfaces break-up, and propagating merely without deformation towards the extremities of the drops. We propose a model of inertial flow in the opening bridge, whose shape is linked to these "singularities", due to surface tension. This model allows to have a better understanding of the contribution of the hydrodynamic forces and surface tension regarding the time evolution of the length and radius of the bridge. The second area of investigation is a study at a nanometer scale. Atomic Force Microscopy (AFM) is used to measure van der Waals forces between the coalescing bodies and the nanoscale deformations leading to coalescence. We perform force measurements with an AFM, essentially in the Frequency Modulation Mode. Studying the interaction, first between a droplet and a bulk, then between two droplets, we measure the threshold distance below which the coalescence occurs, varying the physical properties of liquids and the drops radius. A coalescence diagram can be built, allowing to predict the threshold distance of coalescence and the part played by the nanoscale deformations in the process. The third point is the study of the weakly damped oscillations of the whole body, induced y coalescence. The eigen frequencies and modes are calculated using the finite elements method, and compared to the experimental results, measured by the mean of the high speed camera.
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Modélisation quantochimiques des forces de dispersion de London par la méthode des phases aléatoires (RPA) : développements méthodologiques / Quantum chemical studies of London dispersion forces by the random phase approximation (RPA) : methodological developments.Mussard, Bastien 13 December 2013 (has links)
Dans cette thèse sont montrés des développements de l'approximation de la phase aléatoire (RPA) dans le contexte de théories à séparation de portée. On présente des travaux sur le formalisme de la RPA en général, et en particulier sur le formalisme "matrice diélectrique" qui est exploré de manière systématique. On montre un résumé d'un travail sur les équations RPA dans le contexte d'orbitales localisées, notamment des développements des orbitales virtuelles localisées que sont les "orbitales oscillantes projetées" (POO). Un programme a été écrit pour calculer des fonctions telles que le trou de d'échange, la fonction de réponse, etc... sur des grilles de l'espace réel (grilles parallélépipédiques ou de type "DFT"). On montre certaines de ces visualisations. Dans l'espace réel, on expose une adaptation de l'approximation du dénominateur effectif (EED), développée originellement dans l'espace réciproque en physique du solide. Également, les gradients analytiques des énergies de corrélation RPA dans le contexte de la séparation de portée sont dérivés. Le formalisme développé ici à l'aide d'un lagrangien permet une dérivation tout-en-un des termes courte- et longue-portée qui émergent dans les expressions du gradient, et qui montrent un parallèle intéressant. Des applications sont montrées, telles que des optimisations de géométries aux niveaux RSH-dRPA-I et RSH-SOSEX d'un ensemble de 16 petites molécules, ou encore le calcul et la visualisation des densités corrélées au niveau RSH-dRPA-I / In this thesis are shown developments in the random phase approximation (RPA) in the context of range-separated theories. We present advances in the formalism of the RPA in general, and particularly in the "dielectric matrix" formulation of RPA, which is explored in details. We show a summary of a work on the RPA equations with localized orbitals, especially developments of the virtual localized orbitals that are the "projected oscillatory orbitals" (POO). A program has been written to calculate functions such as the exchange hole, the response function, etc... on real space grid (parallelepipedic or of the "DFT" type) ; some of those visualizations are shown here. In the real space, we offer an adaptation of the effective energy denominator approximation (EED), originally developed in the reciprocal space in solid physics. The analytical gradients of the RPA correlation energies in the context of range separation has been derived. The formalism developed here with a Lagrangian allows an all-in-one derivation of the short- and long-range terms that emerge in the expressions of the gradient. These terms show interesting parallels. Geometry optimizations at the RSH-dRPA-I and RSH-SOSEX levels on a set of 16 molecules are shown, as well as calculations and visualizations of correlated densities at the RSH-dRPA-I level
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