Effect of triplet encapsulated atoms in [60] fullerenes: a theoretical analysis

The present investigation reports on the interaction of the C/O triplet atoms inside of the [60] fullerene (C60) species with small polar molecules (H²O, CH³OH, HF, NH³) using Density Functional Theory (DFT) calculations. The calculations show that in all the computed cases the encapuslated complexes with the molecules are more stable than without internal atoms.

Molecular modeling of asymmetric induction in heterogeneously catalyzed hydrogenation of the C=O bond

Modifiering av metallytor med starkt adsorberade kirala organiska molekyler är eventuellt den mest relevanta teknik man vet i dag för att skapa kirala ytor. Den kan utnyttjas i katalytisk produktion av enantiomeriskt rena kirala föreningar som behövs t.ex. som läkemedel och aromkemikalier. Trots många fördelar av asymmetrisk heterogen katalys jämfört med andra sätt för att få kirala föreningar, har den ändå inte blivit ett allmänt verktyg för storskaliga tillämpningar. Detta beror t.ex. på brist på djupare kunskaper i katalytiska reaktionsmekanismer och ursprunget för asymmetrisk induktion. I denna studie användes molekylmodelleringstekniker för att studera asymmetriska, heterogena katalytiska system, speciellt hydrering av prokirala karbonylföreningar till motsvarande kirala alkoholer på cinchona-alkaloidmodifierade Pt-katalysatorer. 1-Fenyl-1,2-propandion (PPD) och några andra föreningar, som innehåller en prokiral C=O-grupp, användes som reaktanter. Konformationer av reaktanter och cinchona-alkaloider (som kallas modifierare) samt vätebundna 1:1-komplex mellan dem studerades i gas- och lösningsfas med metoder som baserar sig på vågfunktionsteori och täthetsfunktionalteori (DFT). För beräkningen av protonaffiniteter användes också högst noggranna kombinationsmetoder såsom G2(MP2). Den relativa populationen av modifierarnas konformationer varierade som funktion av modifieraren, dess protonering och lösningsmedlet. Flera reaktant–modifierareinteraktionsgeometrier beaktades. Slutsatserna på riktning av stereoselektivitet baserade sig på den relativa termodynamiska stabiliteten av de diastereomeriska reaktant–modifierare-komplexen samt energierna hos π- och π*-orbitalerna i den reaktiva karbonylgruppen. Adsorption och reaktioner på Pt(111)-ytan betraktades med DFT. Regioselektivitet i hydreringen av PPD och 2,3-hexandion kunde förklaras med molekyl–yta-interaktioner. Storleken och formen av klustret använt för att beskriva Pt-ytan inverkade inte bara på adsorptionsenergierna utan också på de relativa stabiliteterna av olika adsorptionsstrukturer av en molekyl. Populationerna av modifierarnas konformationer i gas- och lösningsfas korrelerade inte med populationerna på Pt-ytan eller med enantioselektiviteten i hydreringen av PPD på Pt–cinchona-katalysatorer. Vissa modifierares konformationer och reaktant–modifierare-interaktionsgeometrier var stabila bara på metallytan. Teoretiskt beräknade potentialenergiprofiler för hydrering av kirala α-hydroxiketoner på Pt implicerade preferens för parvis additionsmekanism för väte och selektiviteter i harmoni med experimenten. De uppnådda resultaten ökar uppfattningen om kirala heterogena katalytiska system och kunde därför utnyttjas i utvecklingen av nya, mera aktiva och selektiva kirala katalysatorer.

Atomic level phenomena on transition metal surfaces

In this study we discuss the atomic level phenomena on transition metal surfaces. Transition metals are widely used as catalysts in industry. Therefore, reactions occuring on transition metal surfaces have large industrial intrest. This study addresses problems in very small size and time scales, which is an important part in the overall understanding of these phenomena. The publications of this study can be roughly divided into two categories: The adsorption of an O2 molecule to a surface, and surface structures of preadsorbed atoms. These two categories complement each other, because in the realistic case there are always some preadsorbed atoms at the catalytically active surfaces. However, all transition metals have an active d-band, and this study is also a study of the in uence of the active d-band on other atoms. At the rst part of this study we discuss the adsorption and dissociation of an O2 molecule on a clean stepped palladium surface and a smooth palladium surface precovered with sulphur and oxygen atoms. We show how the reactivity of the surface against the oxygen molecule varies due to the geometry of the surface and preadsorbed atoms. We also show how the molecular orbitals of the oxygen molecule evolve when it approaches the di erent sites on the surface. In the second part we discuss the surface structures of transition metal surfaces. We study the structures that are intresting on account of the Rashba e ect and charge density waves. We also study the adsorption of suphur on a gold surface, and surface structures of it. In this study we use ab-initio based density functional theory methods to simulate the results. We also compare the results of our methods to the results obtained with the Low-Energy-Electron-Difraction method.

Defects in Persistent Luminescence Materials

Persistent luminescence materials can store energy from solar radiation or artificial lighting and release it over a period of several hours without a continuous excitation source. These materials are widely used to improve human safety in emergency and traffic signalization. They can also be utilized in novel applications including solar cells, medical diagnostics, radiation detectors and structural damage sensors. The development of these materials is currently based on methods based on trial and error. The tailoring of new materials is also hindered by the lack of knowledge on the role of their intrinsic and extrinsic lattice defects in the appropriate mechanisms. The goal of this work was to clarify the persistent luminescence mechanisms by combining ab initio density functional theory (DFT) calculations with selected experimental methods. The DFT approach enables a full control of both the nature of the defects and their locations in the host lattice. The materials studied in the present work, the distrontium magnesium disilicate (Sr₂MgSi₂O₇) and strontium aluminate (SrAl₂O₄) are among the most efficient persistent luminescence hosts when doped with divalent europium Eu²⁺ and co-doped with trivalent rare earth ions R³⁺ (R: Y, La-Nd, Sm, Gd-Lu). The polycrystalline materials were prepared with the solid state method and their structural and phase purity was confirmed by X-ray powder diffraction. Their local crystal structure was studied by high-resolution transmission electron microscopy. The crystal and electronic structure of the nondoped as well as Eu²⁺, R^2+/3+ and other defect containing materials were studied using DFT calculations. The experimental trap depths were obtained using thermoluminescence (TL) spectroscopy. The emission and excitation of Sr₂MgSi₂O₇:Eu²+,Dy³⁺ were also studied. Significant modifications in the local crystal structure due to the Eu²⁺ ion and lattice defects were found by the experimental and DFT methods. The charge compensation effects induced by the R³⁺ co-doping further increased the number of defects and distortions in the host lattice. As for the electronic structure of Sr₂MgSi₂O₇ and SrAl₂O₄, the experimental band gap energy of the host materials was well reproduced by the calculations. The DFT calculated Eu²⁺ and R^2+/3+ 4fn as well as 4f^n-15d¹ ground states in the Sr₂MgSi₂O₇ band structure provide an independent verification for an empirical model which is constructed using rather sparse experimental data for the R³⁺ and especially the R²⁺ ions. The intrinsic and defect induced electron traps were found to act together as energy storage sites contributing to the materials’ efficient persistent luminescence. The calculated trap energy range agreed with the trap structure of Sr₂MgSi₂O₇ obtained using TL measurements. More experimental studies should be carried out for SrAl₂O₄ to compare with the DFT calculations. The calculated and experimental results show that the electron traps created by both the rare earth ions and vacancies are modified due to the defect aggregation and charge compensation effects. The relationships between this modification and the energy storage properties of the solid state materials are discussed.

The role of van der Waals interactions in the case of H2 adsorption on ruthenium (0001) surface

Computational material science with the Density Functional Theory (DFT) has recently gained a method for describing, for the first time the non local bonding i.e., van der Waals (vdW) bonding. The newly proposed van der Waals-Density Functional (vdW-DF) is employed here to address the role of non local interactions in the case of H2 adsorption on Ru(0001) surface. The later vdW-DF2 implementation with the DFT code VASP (Vienna Ab-initio Simulation Package) is used in this study. The motivation for studying H2 adsorption on ruthenium surface arose from the interest to hydrogenation processes. Potential energy surface (PES) plots are created for adsorption sites top, bridge, fcc and hcp, employing the vdW-DF2 functional. The vdW-DF yields 0.1 eV - 0.2 eV higher barriers for the dissociation of the H2 molecule; the vdW-DF seems to bind the H2 molecule more tightly together. Furthermore, at the top site, which is found to be the most reactive, the vdW functional suggests no entrance barrier or in any case smaller than 0.05 eV, whereas the corresponding calculation without the vdW-DF does. Ruthenium and H2 are found to have the opposite behaviors with the vdW-DF; Ru lattice constants are overestimated while H2 bond length is shorter. Also evaluation of the CPU time demand of the vdW-DF2 is done from the PES data. From top to fcc sites the vdW-DF computational time demand is larger by 4.77 % to 20.09 %, while at the hcp site it is slightly smaller. Also the behavior of a few exchange correlation functionals is investigated along addressing the role of vdW-DF. Behavior of the different functionals is not consistent between the Ru lattice constants and H2 bond lengths. It is thus difficult to determine the quality of a particular exchange correlation functional by comparing equilibrium separations of the different elements. By comparing PESs it would be computationally highly consuming.

Computational modeling of the properties of TiO2 nanoparticles

In this study we discuss the electronic, structural, and optical properties of titanium dioxide nanoparticles, and also the properties of Ni(II) diimine dithiolato complexes as dyes in dye-sensitized TiO2 based solar cells. The abovementioned properties have been modeled by using computational codes based on the density functional theory. The results achieved show slight evidence on the structure-dependent band gap broadening, and clear blue-shifts in absorption spectra and refractive index functions of ultra-small TiO2 particles. It is also shown that these properties are strongly dependent on the shape of the nanoparticles. Regarding the Ni(II) diimine dithiolato complexes as dyes in dye-sensitized TiO2 based solar cells, it is shown that based on the experimental electrochemical investigation and DFT studies all studied diimine derivatives could serve as potential candidates for the light harvesting, but the e ciencies of the dyes studied are not very promising.

Novel technology for preparation of optically active chemicals

Asymmetric synthesis using modified heterogeneous catalysts has gained lots of interest in the production of optically pure chemicals, such as pharmaceuticals, nutraceuticals, fragrances and agrochemicals. Heterogeneous modified catalysts capable of inducing high enantioselectivities are preferred in industrial scale due to their superior separation and handling properties. The topic has been intensively investigated both in industry and academia. The enantioselective hydrogenation of ethyl benzoylformate (EBF) to (R)-ethyl mandelate over (-)-cinchonidine (CD)-modified Pt/Al2O3 catalyst in a laboratory-scale semi-batch reactor was studied as a function of modifier concentration, reaction temperature, stirring rate and catalyst particle size. The main product was always (R)-ethyl mandelate while small amounts of (S)-ethyl mandelate were obtained as by product. The kinetic results showed higher enantioselectivity and lower initial rates approaching asymptotically to a constant value as the amount of modifier was increased. Additionally, catalyst deactivation due to presence of impurities in the feed was prominent in some cases; therefore activated carbon was used as a cleaning agent of the raw material to remove impurities prior to catalyst addition. Detailed characterizations methods (SEM, EDX, TPR, BET, chemisorption, particle size distribution) of the catalysts were carried out. Solvent effects were also studied in the semi-batch reactor. Solvents with dielectric constant (e) between 2 and 25 were applied. The enantiomeric excess (ee) increased with an increase of the dielectric coefficient up to a maximum followed by a nonlinear decrease. A kinetic model was proposed for the enantioselectivity dependence on the dielectric constant based on the Kirkwood treatment. The non-linear dependence of ee on (e) successfully described the variation of ee in different solvents. Systematic kinetic experiments were carried out in the semi-batch reactor. Toluene was used as a solvent. Based on these results, a kinetic model based on the assumption of different number of sites was developed. Density functional theory calculations were applied to study the energetics of the EBF adsorption on pure Pt(1 1 1). The hydrogenation rate constants were determined along with the adsorption parameters by non-linear regression analysis. A comparison between the model and the experimental data revealed a very good correspondence. Transient experiments in a fixed-bed reactor were also carried out in this work. The results demonstrated that continuous enantioselective hydrogenation of EBF in hexane/2-propanol 90/10 (v/v) is possible and that continuous feeding of (-)-cinchonidine is needed to maintain a high steady-state enantioselectivity. The catalyst showed a good stability and high enantioselectivity was achieved in the fixed-bed reactor. Chromatographic separation of (R)- and (S)-ethyl mandelate originating from the continuous reactor was investigated. A commercial column filled with a chiral resin was chosen as a perspective preparative-scale adsorbent. Since the adsorption equilibrium isotherms were linear within the entire investigated range of concentrations, they were determined by pulse experiments for the isomers present in a post-reaction mixture. Breakthrough curves were measured and described successfully by the dispersive plug flow model with a linear driving force approximation. The focus of this research project was the development of a new integrated production concept of optically active chemicals by combining heterogeneous catalysis and chromatographic separation technology. The proposed work is fundamental research in advanced process technology aiming to improve efficiency and enable clean and environmentally benign production of enantiomeric pure chemicals.

First-principles study on electronic and structural properties of Cu(In/Ga)Se alloys for solar cells

Thin-film photovoltaic solar cells based on the Cu(In1−xGax)Se2 (CIGS) alloys have attracted more and more attention due to their large optical absorption coefficient, long term stability, low cost, and high efficiency. Modern theoretical studies of this material with first-principles calculations can provide accurate description of the electronic structure and yield results in close agreement with experimental values, but takes a large amount of calculation time. In this work, we use first-principles calculations based on the computationally affordable meta- generalized gradient approximation of the density-functional theory to investigate electronic and structural properties of the CIGS alloys. We report on the simulation of the lattice parameters and band gaps, as a function of chemical composition. The obtained results were found to be in a good agreement with the available experimental data.

PREDICTING DIFFUSIVITIES IN DENSE FLUIDS

In this work the Weeks-Chandler-Andersen (WCA) perturbation theory coupled with the Enskog’s solution of the Boltzmann equation for dense hard-sphere fluids is employed for estimating diffusion coefficients in compressed pure liquids and fluids and dense fluid mixtures. The effect of density correction on the estimation of diffusivities is analyzed using the Carnahan-Starling pair correlation function and the correlation of Speedy and Harris which have been proposed as models of self-diffusion coefficient of hard-sphere fluids. The approach presented here is based on the smooth hard-sphere theory without any binary adjustable parameters and can be readily used for estimating diffusivities in multicomponent fluid mixtures. It is shown that the correlated and the predicted diffusivities are in good agreement with the experimental data and much better than estimates of Wilke-Chang equation.

Molecular dynamics calculation of mean square displacement in alkali metals and rare gas solids and comparison with lattice dynamics

Molec ul ar dynamics calculations of the mean sq ua re displacement have been carried out for the alkali metals Na, K and Cs and for an fcc nearest neighbour Lennard-Jones model applicable to rare gas solids. The computations for the alkalis were done for several temperatures for temperature vol ume a swell as for the the ze r 0 pressure ze ro zero pressure volume corresponding to each temperature. In the fcc case, results were obtained for a wide range of both the temperature and density. Lattice dynamics calculations of the harmonic and the lowe s t order anharmonic (cubic and quartic) contributions to the mean square displacement were performed for the same potential models as in the molecular dynamics calculations. The Brillouin zone sums arising in the harmonic and the quartic terms were computed for very large numbers of points in q-space, and were extrapolated to obtain results ful converged with respect to the number of points in the Brillouin zone.An excellent agreement between the lattice dynamics results was observed molecular dynamics and in the case of all the alkali metals, e~ept for the zero pressure case of CSt where the difference is about 15 % near the melting temperature. It was concluded that for the alkalis, the lowest order perturbation theory works well even at temperat ures close to the melting temperat ure. For the fcc nearest neighbour model it was found that the number of particles (256) used for the molecular dynamics calculations, produces a result which is somewhere between 10 and 20 % smaller than the value converged with respect to the number of particles. However, the general temperature dependence of the mean square displacement is the same in molecular dynamics and lattice dynamics for all temperatures at the highest densities examined, while at higher volumes and high temperatures the results diverge. This indicates the importance of the higher order (eg. ~* ) perturbation theory contributions in these cases.

Experimental and Computational Studies on Copper and Hydrobenzoin Derivatives in Catalytic Asymmetric Reactions

The use of theory to understand and facilitate catalytic enantioselective organic transformations involving copper and hydrobenzoin derivatives is reported. Section A details the use of theory to predict, facilitate, and understand a copper promoted amino oxygenation reaction reported by Chemler et al. Using Density Functional Theory (DFT), employing the hybrid B3LYP functional and a LanL2DZ/6-31G(d) basis set, the mechanistic details were studied on a N-tosyl-o-allylaniline and a [alpha]-methyl-[gamma]-alkenyl sulfonamide substrate. The results suggest the N-C bond formation proceeds via a cisaminocupration, and not through a radical-type mechanism. Additionally, the origin of diastereoselection observed with [alpha]-methyl-[gamma]-alkenyl sulfonamide arises from avoidance of unfavourable steric interactions between the methyl substituent and the N -protecting group. Section B details the computationally guided, experimental investigation of two hydrobenzoin derivatives as ligands/ catalysts, as well as the attempted synthesis of a third hydrobenzoin derivative. The bis-boronic acid derived from hydrobenzoin was successful as a Lewis acid catalyst in the Bignielli reaction and the Conia ene reaction, but provided only racemic products. The chiral diol derived from hydrobenzoin successfully increased the rate of the addition of diethyl zinc to benzaldehyde in the presence of titanium tetraisopropoxide, however poor enantioinduction was obseverved. Notably, the observed reactivity was successfully predicted by theoretical calculations.

A DFT Guided/Experimental Approach to Asymmetric Allylation and Phase-Transfer Catalysis

The Dudding group is interested in the application of Density Functional Theory (DFT) in developing asymmetric methodologies, and thus the focus of this dissertation will be on the integration of these approaches. Several interrelated subsets of computer aided design and implementation in catalysis have been addressed during the course of these studies. The first of the aims rested upon the advancement of methodologies for the synthesis of biological active C(1)-chiral 3-methylene-indan-1-ols, which in practice lead to the use of a sequential asymmetric Yamamoto-Sakurai-Hosomi allylation/Mizoroki Heck reaction sequence. An important aspect of this work was the utilization of ortho-substituted arylaldehyde reagents which are known to be a problematic class of substrates for existing asymmetric allylation approaches. The second phase of my research program lead to the further development of asymmetric allylation methods using o-arylaldehyde substrates for synthesis of chiral C(3)-substituted phthalides. Apart from the de novo design of these chemistries in silico, which notably utilized water-tolerant, inexpensive, and relatively environmental benign indium metal, this work represented the first computational study of a stereoselective indium-mediated process. Following from these discoveries was the advent of a related, yet catalytic, Ag(I)-catalyzed approach for preparing C(3)-substituted phthalides that from a practical standpoint was complementary in many ways. Not only did this new methodology build upon my earlier work with the integrated (experimental/computational) use of the Ag(I)-catalyzed asymmetric methods in synthesis, it provided fundamental insight arrived at through DFT calculations, regarding the Yamamoto-Sakurai-Hosomi allylation. The development of ligands for unprecedented asymmetric Lewis base catalysis, especially asymmetric allylations using silver and indium metals, followed as a natural extension from these earlier discoveries. To this end, forthcoming as well was the advancement of a family of disubstituted (N-cyclopropenium guanidine/N-imidazoliumyl substituted cyclopropenylimine) nitrogen adducts that has provided fundamental insight into chemical bonding and offered an unprecedented class of phase transfer catalysts (PTC) having far-reaching potential. Salient features of these disubstituted nitrogen species is unprecedented finding of a cyclopropenium based C-H•••πaryl interaction, as well, the presence of a highly dissociated anion projected them to serve as a catalyst promoting fluorination reactions. Attracted by the timely development of these disubstituted nitrogen adducts my last studies as a PhD scholar has addressed the utility of one of the synthesized disubstituted nitrogen adducts as a valuable catalyst for benzylation of the Schiff base N-diphenyl methylene glycine ethyl ester. Additionally, the catalyst was applied for benzylic fluorination, emerging from this exploration was successful fluorination of benzyl bromide and its derivatives in high yields. A notable feature of this protocol is column-free purification of the product and recovery of the catalyst to use in a further reaction sequence.

DFT Studies of the Organocatalytic Aldol Reaction and a Frustrated Lewis Pair

The computational study, and in particular the density functional theory (DFT) study of the organocatalytic α-chlorination-aldol reaction and the chiral backbone Frustrated Lewis Pair (FLP) system served as a valuable tool for experimental purposes. This thesis describes methods to consider different transition states of the proline- catalyzed α-chlorination aldol reaction to determine the reasonable transition state in the reaction between the enamine and α-chloro aldehydes. Moreover, the novel intramolecular Frustrated Lewis pair based on a chiral backbone for the asymmetric hydrogenation of imines and enamines was designed and the ability of hydrogen splitting by this new FLP system was examined by computational modeling and calculating the hydrogen activation energy barrier.

Mirroring Enzymes: The Role of H-Bonding In HQuin-BAM Catalyzed Asymmetric Aza-Henry Reactions: A DFT Study into the Reactivity, Mechanism, and Origins of Selectivity

The exact mechanistic understanding of various organocatalytic systems in asymmetric reactions such as Henry and aza-Henry transformations is important for developing and designing new synthetic organocatalysts. The focus of this dissertation will be on the use of density functional theory (DFT) for studying the asymmetric aza-Henry reaction. The first part of the thesis is a detailed mechanistic investigation of a poorly understood chiral bis(amidine) (BAM) Brønsted acid catalyzed aza-Henry reaction between nitromethane and N-Boc phenylaldimine. The catalyst, in addition to acting as a Brønsted base, serves to simultaneously activate both the electrophile and the nucleophile through dual H-bonding during C-C bond formation and is thus essential for both reaction rate and selectivity. Analysis of the H-bonding interactions revealed that there was a strong preference for the formation of a homonuclear positive charge-assisted H-bond, which in turn governed the relative orientation of substrate binding. Attracted by this well-defined mechanistic investigation, the other important aspect of my PhD research addressed a detailed theoretical analysis accounting for the observed selectivity in diastereoselective versions of this reaction. A detailed inspection of the stereodetermining C-C bond forming transition states for monoalkylated nitronate addition to a range of electronically different aldimines, revealed that the origins of stereoselectivity were controlled by a delicate balance of different factors such as steric, orbital interactions, and the extent of distortion in the catalyst and substrates. The structural analysis of different substituted transition states established an interesting dependency on matching the shape and size of the catalyst (host molecule) and substrates (guest molecules) upon binding, both being key factors governing selectivity, in essence, offering an analogy to positive cooperative binding effect of catalytic enzymes and substrates in Nature. In addition, both intra-molecular (intra-host) and inter-molecular (host-guest, guest-guest) stabilizing interactions play a key role to the high π-facial selectivity. The application of dispersion-corrected functionals (i.e., ωB97X-D and B3LYP-D3) was essential for accurately modeling these stabilizing interactions, indicating the importance of dispersion effects in enantioselectivity. As a brief prelude to more extensive future studies, the influence of a triflate counterion on both reactivity and selectivity in this reaction was also addressed.

Etude théorique des propriétés électroniques et optiques des super-réseaux de Si/SiO2

FRANCAIS: L'observation d'une intense luminescence dans les super-réseaux de Si/SiO2 a ouvert de nouvelles avenues en recherche théorique des matériaux à base de silicium, pour des applications éventuelles en optoélectronique. Le silicium dans sa phase cristalline possède un gap indirect, le rendant ainsi moins intéressant vis-à-vis d'autres matériaux luminescents. Concevoir des matériaux luminescents à base de silicium ouvrira donc la voie sur de multiples applications. Ce travail fait état de trois contributions au domaine. Premièrement, différents modèles de super-réseaux de Si/SiO2 ont été conçus et étudiés à l'aide de calculs ab initio afin d'en évaluer les propriétés structurales, électroniques et optiques. Les deux premiers modèles dérivés des structures cristallines du silicium et du dioxyde de silicium ont permis de démontrer l'importance du rôle de l'interface Si/SiO2 sur les propriétés optiques. De nouveaux modèles structurellement relaxés ont alors été construits afin de mieux caractériser les interfaces et ainsi mieux évaluer la portée du confinement sur les propriétés optiques. Deuxièmement, un gap direct dans les modèles structurellement relaxés a été obtenu. Le calcul de l'absorption (par l'application de la règle d'or de Fermi) a permis de confirmer que les propriétés d'absorption (et d'émission) du silicium cristallin sont améliorées lorsque celui-ci est confiné par le SiO2. Un décalage vers le bleu avec accroissement du confinement a aussi été observé. Une étude détaillée du rôle des atomes sous-oxydés aux interfaces a de plus été menée. Ces atomes ont le double effet d'accroître légèrement le gap d'énergie et d'aplanir la structure électronique près du niveau de Fermi. Troisièmement, une application directe de la théorique des transitions de Slater, une approche issue de la théorie de la fonctionnelle de la densité pour des ensembles, a été déterminée pour le silicium cristallin puis comparée aux mesures d'absorption par rayons X. Une très bonne correspondance entre cette théorie et l'expérience est observée. Ces calculs ont été appliqués aux super-réseaux afin d'estimer et caractériser leurs propriétés électroniques dans la zone de confinement, dans les bandes de conduction.