This thesis contains four articles related to mathematical aspects of Density Functional Theory. In Paper A, the theoretical justification of density methods formulated with current densities is addressed. It is shown that the set of ground-states is determined by the ensemble-representable particle and paramagnetic current density. Furthermore, it is demonstrated that the Schrödinger equation with a magnetic field is not uniquely determined by its ground-state solution. Thus, a wavefunction may be the ground-state of two different Hamiltonians, where the Hamiltonians differ by more than a gauge transformation. This implies that the particle and paramagnetic current density do not determine the potentials of the system and, consequently, no Hohenberg-Kohn theorem exists for Current Density Functional Theory formulated with the paramagnetic current density. On the other hand, by instead using the particle density as data, we show that the scalar potential in the system's Hamiltonian is determined for a fixed magnetic field. This means that the Hohenberg-Kohn theorem continues to hold in the presence of a magnetic field, if the magnetic field has been fixed. Paper B deals with N-representable density functionals that also depend on the paramagnetic current density. Here the Levy-Lieb density functional is generalized to include the paramagnetic current density. It is shown that a wavefunction exists that minimizes the "free" Hamiltonian subject to the constraints that the particle and paramagnetic current density are held fixed. Furthermore, a convex and universal current density functional is introduced and shown to equal the convex envelope of the generalized Levy-Lieb density functional. Since this functional is convex, the problem of finding the particle and paramagnetic current density that minimize the energy is related to a set of Euler-Lagrange equations. In Paper C, an N-representable Kohn-Sham approach is developed that also include the paramagnetic current density. It is demonstrated that a wavefunction exists that minimizes the kinetic energy subject to the constraint that only determinant wavefunctions are considered, as well as that the particle and paramagnetic current density are held fixed. Using this result, it is then shown that the ground-state energy can be obtained by minimizing an energy functional over all determinant wavefunctions that have finite kinetic energy. Moreover, the minimum is achieved and this determinant wavefunction gives the ground-state particle and paramagnetic current density. Lastly, Paper D addresses the issue of a Hohenberg-Kohn variational principle for Current Density Functional Theory formulated with the total current density. Under the assumption that a Hohenberg-Kohn theorem exists formulated with the total current density, it is shown that the map from particle and total current density to the vector potential enters explicitly in the energy functional to be minimized. Thus, no variational principle as that of Hohenberg and Kohn exists for density methods formulated with the total current density. / <p>QC 20140523</p>

This doctoral study consists of three parts. In the first part, structural and electronic properties of Al_kTi_lNi_m (k+l+m=2,3) microclusters have been investigated by performing density functional theory (DFT) calculations within the B3LYP [which comprises the Becke-88 exchange functional and the correlation functional of Lee, Yang, and Parr] and the effective core potential (ECP) level. Dimers and trimers of the elements aluminum, titanium, and nickel, and their binary and ternary combinations have been studied in their ground states. The optimum geometries, possible dissociation channels, vibrational properties, and electronic structure of the clusters under study have been obtained. In the second part, after an empirical potential energy function (PEF) has been parametrized for the AlTiNi ternary system, stable (minimum-energy) structures of Al_kTi_lNi_m (k+l+m=4) microclusters have been determined by molecular dynamics (MD) simulations. The energetics of the microclusters in 1K and 300 K have been discussed. By performing, again, DFT calculations (within the B3LYP and ECP level), the possible dissociation channels and electronic properties of the obtained clusters have been calculated. In the last part, using the empirical PEF parametrized previously for the AlTiNi ternary system, minimum-energy structures of Al_nTi_nNi_n (n= 1-16) ternary alloy nanoparticles have been determined by performing MD simulations. The structural and energetic features of the obtained nanoparticles have been investigated.

Thermodynamic stabilities of eighteen cyclic C5H6 isomers were explored computationally both on singlet and triplet state potential energy surfaces (PES). All isomers have singlet ground states except for bicyclo[2.1.0]pent-5-ylidene (B5) having no stable geometry on the singlet C5H6 PES. Cyclopenta-1,3-diene (M1) is the most stable cyclic C5H6 isomer while cyclopent-1,4-diylidene is the least stable one among all. Cyclopenta-1,2-diene (M2) and cyclopentyne (M3) have biradical characters of 46.9 and 21.5%, respectively. Seven unimolecular isomerization reactions occurring among several of these molecules were investigated by DFT and ab initio methods. The conversion of bicyclo[2.1.0]pent-2-ene (B1) and tricyclo[2.1.0.02,5]-pentane (T1) into 1,3-cyclopentadiene (M1) are shown to be concerted processes whose reaction paths pass through TSs with a high degree of biradical character. The reaction enthalpies (DH0) are predicted to be -47.7 kcal/mol for B1 and -63.8 kcal/mol for T1 at UB3LYP/6-31G(d) level. The activation enthalpy (DH0&sup1 / ) for the ring opening of B1 was calculated by the CR-CCSD(T) method to be 25.2 kcal/mol, in good agreement with experiment. Furthermore, the DH0&sup1 / for the ring opening of T1 was obtained by the CR-CCSD(T) method to be 48.2 kcal/mol. The self-conversion of M1 via 1,5-hydrogen shift is a facile and concerted reaction with aromatic TS. The DH0&sup1 / estimations of B3LYP and CC methods are 25.24 and 28.78 kcal/mol, respectively. For 1,2-hydrogen shift reactions of cyclopent-3-enylidene (M4) and cyclopenten-2-ylidene (M5), the single point CC calculations predicted the DH0&sup1 / values of 3.13 and 10.12 kcal/mol, as well as, the DH0 values of -71.28 and -64.05 kcal/mol, respectively. The reason of M5 being more stable than M4 is due to the conjugation of the carbene carbon and the double bond in M5. The reaction path of cyclobutylidene methylene to cyclopentyne rearrangement is found to be rather shallow. The DH0&sup1 / and DH0 values predicted by the RCCSD(T) method to be 3.65 and -5.72 kcal/mol, respectively. Finally, triplet state isomerization of bicyclo[2.1.0]pent-5-ylidene to cyclopenta-1,2-diene, as well as, its parent reaction, cyclopropylidene to 1,2-propadiene were investigated at several levels of theory including DFT, CASSCF and CC methods. The UCCSD(T) method estimated a moderate barrier whose value is 8.12 kcal/mol for the isomerization of 3B5 with the reaction enthalpy of -44.63 kcal/mol.

The nature of the ground state and the first (lowest) singlet excited state geometrical conformations and electronic transitions in the aromatic five-membered heterocyclic oligomers &ndash / oligothiophenes (nT), oligofurans (nF), and oligopyrroles (nP)- containing up to six monomer units (total of 18 molecules) were explored using several computational methodologies. Geometry optimizations were carried out at Austin Model 1 (AM1), Restricted Hartree-Fock (RHF/6-31G*), and Density Functional Theory (DFT, B3LYP/6-31G*) levels for the ground-state conformations of these structurally well-defined heterocyclic oligomers. The Configuration Interaction Singles (CIS) method with the 6-31G* basis set was chosen in computation of the optimal geometry of the lowest singlet excited state. Lowest singlet excitation S1&szlig / S0 energies were calculated using the Zerner&rsquo / s Intermediate Neglect of Differential Overlap for Spectroscopy (ZINDO/S), CIS (CIS/6-31G*), and Time-Dependent DFT (TDDFT/6-31G* and TDDFT/6-31+G*) methods. In computation of the emission S1&agrave / S0 energies, we have employed all methods above except ZINDO/S. In investigation of geometries of the ground and lowest singlet excited state, we compared the bond length alternation (BLA) parameters, Dri in the conjugated backbone of the oligomers. Saturation of the geometrical parameters at the center of oligomers was observed after a certain chain length. Among all methodologies used in computation of excitation (S1&szlig / S0) and emission (S1&agrave / S0) energies, TDDFT results showed the best agreement with experimental data. Fits of computed and experimental excitation energies to an exponential function using the least squares method enabled us to predict Effective Conjugation Length (ECL) values. We obtained the ECLs of 17 (17), 16 (15), and 14 (13) monomer units for polythiophene (PTh), polyfuran (PFu), and polypyrrole (PPr), which have very good agreement with the results obtained from the fits of experimental data (the values in parentheses).

The reaction mechanism for the selective catalytic reduction (SCR) of nitric oxide by ammonia on (010) V2O5 surface represented by a V2O9H8 cluster was simulated by density functional theory (DFT) calculations. The computations indicated that SCR reaction consisted of three main parts. In the first part ammonia activation on Br&oslash / nsted acidic V-OH site as NH4+ species by a nonactivated process takes place. The second part includes the interaction of NO with pre-adsorbed NH4 + species to eventually form nitrosamide (NH2NO). The rate limiting step for this part as well as for the total SCR reaction is identified as NH3NHO formation reaction. The last part consists of the decomposition of NH2NO on the cluster which takes advantage of a hydrogen transfer mechanism between the active V=O and V-OH groups. Water and ammonia adsorption and dissociation are investigated on (101) and (001) anatase surfaces both represented by totally fixed and partially relaxed Ti2O9H10 clusters. Adsorption of H2O and NH3 by H-bonding on previously H2O and NH3 dissociated systems are also considered. By use of a (001) relaxed Ti2O9H10 cluster, the role of anatase support on SCR reaction is investigated. Since NH2NO formation on Ti2O9H10 cluster requires lower activation barriers than on V2O5 surface, it is proposed that the role of titanium dioxide on SCR reaction could be forming NH2NO. The role of vanadium oxide is crucial in terms of dissociating this product into H2O and N2. Finally, NH3 adsorption is studied on a V2TiO14H14 cluster which represents a model for vanadia/titania surface.

Mit Hilfe der Dichtefunktionaltheorie wurden magnetische Eigenschaften an 3d Elementen und Legierungen und 5f Verbindungen untersucht. Dabei wurde auf die Wichtigkeit von Orbitalpolarisationskorrekturen eingegangen und diese näher erörtert. Im ersten Anwendungsteil wurden magnetische Momente und die Magnetokristalline Anisotropie Energie an 3d Elementen untersucht. Des Weiteren wurden FeCo Legierungen als mögliche Bestandteile in der Festplattenindustrie diskutiert. Im letzten Abschnitt wurden Uranverbindungen in Hinsicht auf Ihre Orbitalpolarisation untersucht.

In the first part of this work, the influence of hydrogen on the structural and magnetic properties of Fe/V(001) superlattices was studied. The local structure of the vanadium-hydride layers was determined by extended x-ray absorption fine structure (EXAFS) measurements. The magnetic ordering in a weakly coupled Fe/V(001) superlattice was investigated using the magneto-optical Kerr effect (MOKE). The interlayer exchange coupling is weakened upon alloying with hydrogen and a phase with short-range magnetic order was observed. The second part is concerned with first-principles calculations of magnetic materials, with a focus on magnetic recording applications. The uniaxial magnetic anisotropy energy (MAE) of Fe, Co, and Ni was calculated for tetragonal and trigonal structures. Based on an analysis of the electronic states of tetragonal Fe and Co at the center of the Brillouin zone, tetragonal Fe-Co alloys were proposed as a material that combines a large uniaxial MAE with a large saturation magnetization. This was confirmed by experimental studies on (Fe,Co)/Pt superlattices. The large uniaxial MAE of L10 FePt is caused by the large spin-orbit interaction on the Pt sites in connection with a strong hybridization between Fe and Pt. Furthermore, it was shown that the uniaxial MAE can be increased by alloying the Fe sublattice with Mn. The combination of the high-moment rare-earth (RE) metals with the high-TC 3d transition metals in RE/Cr/Fe multilayers (RE = Gd, Tb, Dy) gives rise to a strong ferromagnetic effective exchange interaction between the Fe layers and the RE layer. The MAE of hcp Gd was found to have two principal contributions, namely the dipole interaction of the large localized 4f spins and the band electron magnetic anisotropy due to the spin-orbit interaction. The peculiar temperature dependence of the easy axis of magnetization was reproduced on a qualitative level.

Molecular electronics is envisioned as a possible next step in device miniaturization. It is usually taken to mean the design and manufacturing of electronic devices and applications where organic molecules work as the fundamental functioning unit. It involves the measurement and manipulation of electronic response and transport in molecules attached to conducting leads. Organic molecules have the advantages over conventional solid state electronics of inherent small sizes, endless chemical diversity and ambient temperature low cost manufacturing. In this thesis we investigate the switching and conducting properties of photoswitching dithienylethene derivatives. Such molecules change their conformation in solution when acted upon by light. Photochromic molecules are attractive candidates for use in molecular electronics because of the switching between different states with different conducting properties. The possibility of optically controlling the conductance of the molecule attached to conducting leads may lead to new device implementations. The switching reaction is investigated with potential energy calculations for different values of the reaction coordinate between the closed and the open isomer. The electronic and atomic structure calculations are performed with Density Functional Theory (DFT). The potential energy barrier separating the open and closed isomer is investigated, as well as the nature of the excited states involved in the switching. The conducting properties of the molecule inserted between gold, silver and nickel leads is calculated within the Non Equilibrium Green Function theory (NEGF). The molecule is found to be a good conductor in both conformations, with the low-bias current for the closed one being about 20 times larger than that of the open in the case of gold contacts, and over 30 times larger in the case of silver contacts. For the Ni leads the current for the closed isomer is almost 40 times larger than that of the open. Importantly, the current-voltage characteristics away from the linear response is largely determined by molecular orbital re-hybridization in an electric field, in close analogy to what happens for Mn12 molecules. However in the case of dithienylethene attached to Au and Ag such a mechanism is effective also in conditions of strong electronic coupling to the electrodes. In reality these molecules are in constant motion, and the dynamical properties has to be considered. In this thesis such a line of work is initiated. In order to facilitate efficient and stable dynamical simulations of molecular systems the extended Lagrangian formulation of Born-Oppenheimer molecular dynamics have been implemented in two different codes. The extended Lagrangian framework enables the geometric integration of both the nuclear and electronic degrees of freedom. This provides highly efficient simulations that are stable and energy conserving even under incomplete and approximate self-consistent field (SCF) convergence. In the density functional theory code FreeON, different symplectic integrators up to the 6th order have been adapted and optimized. It is shown how the accuracy can be significantly improved compared to a conventional Verlet integration at the same level of computational cost, in particular for the case of very high accuracy requirements. Geometric integration schemes, including a weak dissipation to remove numerical noise, are developed and implemented in the self-consistent tight-binding code LATTE. We find that the inclusion of dissipation in the symplectic integration methods gives an efficient damping of numerical noise or perturbations that otherwise may accumulate from finite arithmetics in a perfect reversible dynamics. The modification of the integration breakes symplecticity and introduces a global energy drift. The systematic driftin energy and the broken symplecticity can be kept arbitrarily small without significant perturbations of the molecular trajectories. / QC 20101202

Recent carbon allotropes such as carbon nanotubes (CNTs), fullerenes (C60s) and graphene have attracted great interests in both science and engineering due to their unique properties such as excellent electrical and mechanical properties as well as its vast surface area, and have led to many commercial applications. Especially, CNTs have been considered to be one of the promising candidates in the Li ion battery system because of its outstanding properties. However, the experimental results in the pristine CNT system have shown just slight improvement than original graphitic carbon material, which has been attributed to the weak adsorption of Li on CNTs. In this study, we investigated two types of CNT-C60 hybrid system consisting of CNTs and C60s to improve Li adsorption capabilities and predict its performance through quantum mechanical (QM) computations. First, we investigated adsorption energy of lithium (Li) on dilute CNT-C60 hybrid and CNT-C60 nanobud system as well as various electronic properties such as band structure, density of states (DOS), molecular orbital and charge distribution. Then, we expanded our interest to the more realistic condensed structure of CNT-C60 hybrid and nanobud system to examine actual electrochemical characteristics. The study of the condensed structure has been expanded to the very unique CNT-C60 nano-network system and examined mechanical strength as well as electronic properties. Finally, Li adsorption on other carbon allotropes system such as graphene-C60 hybrid and graphene-C60 bud system was investigated in order to provide fundamental understanding of electronic interaction between carbon allotrope and effect of Li adsorption.

Partant des composés ATiO3 (A=Ba, Pb, Sr) bien connus pour leurs propriétés de type ferroélectriques, il est possible de concevoir des super-réseaux de basse dimensionnalité (multi-couches, phases de type ,…) où ces propriétés peuvent être modulées en fonction de la composition, de l'épaisseur des couches mises en jeu, des contraintes aux interfaces. Nous proposons ici d'étudier par calculs de premiers principes les instabilités structurales et la dynamique de réseau pour des systèmes simples dans cette famille. En définissant clairement les zones interfaciales et de cœur des couches, et en étudiant la convergence de leurs propriétés en fonction de l'épaisseur, ce travail vise à établir des potentiels interatomiques modèles, analytiques et transférables, pour la prédiction des propriétés dynamiques et des instabilités structurales de super-réseaux étendus et/ou complexes. / The aim of the present thesis is to investigate, from first-principles, the ferroelectricproperties and related phase transition behaviors in perovskite type compounds. Wewill not focus only on the bulk perovskite systems, but also on related layered superlatticeswhere the interface may play an important role and induce new phenomena.