<p>This thesis is part of an effort to enable large-scale Hartree-Fock/Kohn-Sham (HF/KS) calculations. The objective is to model molecules and materials containing thousands of atoms at the quantum mechanical level. HF/KS calculations are usually performed with the Self-Consistent Field (SCF) method. This method involves two computationally intensive steps. These steps are the construction of the Fock/Kohn-Sham potential matrix from a given electron density and the subsequent update of the electron density usually represented by the so-called density matrix. In this thesis the focus lies on the representation of potentials and electron density and on the density matrix construction step in the SCF method. Traditionally a diagonalization has been used for the construction of the density matrix. This diagonalization method is, however, not appropriate for large systems since the time complexity for this operation is σ(n³). Three types of alternative methods are described in this thesis; energy minimization, Chebyshev expansion, and density matrix purification. The efficiency of these methods relies on fast matrix-matrix multiplication. Since the occurring matrices become sparse when the separation between atoms exceeds some value, the matrix-matrix multiplication can be performed with complexity σ(n).</p><p>A hierarchic sparse matrix data structure is proposed for the storage and manipulation of matrices. This data structure allows for easy development and implementation of algebraic matrix operations, particularly needed for the density matrix construction, but also for other parts of the SCF calculation. The thesis addresses also truncation of small elements to enforce sparsity, permutation and blocking of matrices, and furthermore calculation of the HOMO-LUMO gap and a few surrounding eigenpairs when density matrix purification is used instead of the traditional diagonalization method.</p>

Polymer Nanocomposites (PNC) are a new class of materials characterized by their large interfacial areas between the host polymer and nanofiller. This unique feature, due to the size of the nanofiller, is understood to be the cause of enhanced mechanical, electrical, optical, and barrier properties observed of PNCs, relative to the properties of the unfilled polymer. This interface can determine the miscibility of the nanofiller in the polymer, which, in turn, influences the PNC's properties. In addition, this interface alters the polymer's structure near the surface of the nanofiller resulting in heterogeneity of local properties that can be expressed at the macroscopic level. Considering the polymer-nanoparticle interface significantly influences PNC properties, it is apparent that some atomistic level of detail is required to accurately predict the behavior of PNCs. Though an all-atom simulation of a PNC would be able to accomplish the latter, it is an impractical approach to pursue even with the most advanced computational resources currently available. In this contribution, we develop (1) an equilibrium coarse-graining method to predict nanoparticle dispersion in a polymer melt, (2) a dynamic coarse-graining method to predict rheological properties of polymer-nanoparticle melt mixtures, and (3) a numerical approach that includes interfacial layer effects and polymer rigidity when predicting barrier properties of PNCs. In addition to the above, we study how particle and polymer characteristics affect the interfacial layer thickness as well as how the polymer-nanoparticle interface may influence the entanglement network in a polymer melt. More specifically, we use a mean-field theory approach to discern how the concentration of a semiflexible polymer, its rigidity and the particle's size determine the interfacial layer thickness, and the scaling laws to describe this dependency. We also utilize molecular dynamics and simulation techniques on a model PNC to determine if the polymer-nanoparticle interaction can influence the entanglement network of a polymer melt. / text

A polymer brush is formed by densely grafting the chain ends of polymers onto a surface. This tethering of the long macromolecules has considerable influence on the surface properties, which can be additionally modified by changing the environmental conditions. In this context it is of special interest to understand and control the behavior of the grafted layer and to create surfaces that display a desired response to external stimulation. The present work studies densely grafted polymer brushes and the effects that such an environment imposes on an individual chain molecule in the grafted layer. For this purpose we developed a new self-consistent field approach to describe mixtures of heterogeneous chains comprised of differently sized hard spheres. Applying this method to the case of polymer brushes we consider a fraction of grafted molecules to be different from the majority brush chains. The modification of these chains includes a variation in the degree of polymerization, a different solvent selectivity behavior and a variable size of the free end-monomer. Due to the computational efficiency of the present approach, as compared for example to direct simulation methods, we can study the conformations of the modified 'guest' chains systematically in dependence of the relevant parameters. With respect to brush profile and the distribution of the free chain ends the new method shows very good quantitative agreement with corresponding simulation results. We also confirm the observation that these 'guest' chains can undergo a conformational transition depending on the type of modification and the solvent quality. For the cases studied in the present work we analyze the conditions to achieve a most sensitive behavior of this conformational switching. In addition, an analytical model is proposed to describe this effect. We compare its predictions to the numerical results and find good agreement.

Alors que les approches standards de résolution de la structure électronique présentent un coût de calcul à la puissance 3 par rapport à la complexité du problème, des solutions permettant d’atteindre un régime asymptotique linéaire,O(N), sont maintenant bien connues pour le calcul de l'état fondamental. Ces solutions sont basées sur la "myopie" de la matrice densité et le développement d'un cadre théorique permettant de contourner le problème aux valeurs propres. La théorie des purifications de la matrice densité constitue une branche de ce cadre théorique. Comme pour les approches de type O(N) appliquées à l'état fondamental,la théorie des perturbations nécessaire aux calculs des fonctions de réponse électronique doit être révisée pour contourner l'utilisation des routines coûteuses.L'objectif est de développer une méthode robuste basée uniquement sur la recherche de la matrice densité perturbée, pour laquelle seulement des multiplications de matrices creuses sont nécessaires. Dans une première partie,nous dérivons une méthode de purification canonique qui respecte les conditions de N-representabilité de la matrice densité à une particule. Nous montrons que le polynôme de purification obtenu est auto-cohérent et converge systématiquement vers la bonne solution. Dans une seconde partie, en utilisant une approche de type Hartree-Fock, nous appliquons cette méthode aux calculs des tenseurs de réponses statiques non-linéaires pouvant être déterminés par spectroscopie optique. Au delà des calculs à croissance linéaire réalisés, nous démontrons que les conditions N-representabilité constituent un prérequis pour garantir la fiabilité des résultats. / Whereas standard approaches for solving the electronic structures present acomputer effort scaling with the cube of the number of atoms, solutions to overcomethis cubic wall are now well established for the ground state properties, and allow toreach the asymptotic linear-scaling, O(N). These solutions are based on thenearsightedness of the density matrix and the development of a theoreticalframework allowing bypassing the standard eigenvalue problem to directly solve thedensity matrix. The density matrix purification theory constitutes a branch of such atheoretical framework. Similarly to earlier developments of O(N) methodology appliedto the ground state, the perturbation theory necessary for the calculation of responsefunctions must be revised to circumvent the use of expensive routines, such asmatrix diagonalization and sum-over-states. The key point is to develop a robustmethod based only on the search of the perturbed density matrix, for which, ideally,only sparse matrix multiplications are required. In the first part of this work, we derivea canonical purification, which respects the N-representability conditions of the oneparticledensity matrix for both unperturbed and perturbed electronic structurecalculations. We show that this purification polynomial is self-consistent andconverges systematically to the right solution. As a second part of this work, we applythe method to the computation of static non-linear response tensors as measured inoptical spectroscopy. Beyond the possibility of achieving linear-scaling calculations,we demonstrate that the N-representability conditions are a prerequisite to ensurereliability of the results.

Scope and Content stated in the place of the abstract. / The principal methods of calculating nuclear spin coupling constants by applying perturbation theory to molecular orbital wavefunctions for the electronic structure of molecules are discussed. A new method employing a self-consistent-field perturbation theory (SCFPT) is then presented and compared with the earlier methods. In self-consistent-field (SCF) methods, the interaction of an electron with other electrons in a molecule is accounted for by treating the other electrons as an average distribution of negative charge. However, this charge distribution cannot be calculated until the electron-electron interactions themselves are known. In the SCF method, an initial charge distribution is assumed and then modified in an iterative calculation until the desired degree of self-consistency is attained. In most previous perturbation methods, these electron interactions are not taken into account in a self consistent manner in calculating the perturbed wavefunction even when SCF wavefunctions are used to describe the unperturbed molecule. The main advantage of the new SCFPT approach is that it treats the interactions between electrons with the same degree of self-consistency in the perturbed wavefunction as in the unperturbed wavefunction. The SCFPT method offers additional advantages due to its computational efficiency and the direct manner in which it treats the perturbations. This permits the theory to be developed for the orbital and dipolar contributions to nuclear spin coupling as well as for the more commonly treated contact interaction. In this study, the SCFPT theory is used with the Intermediate Neglect of Differential Overlap (INDO) molecular orbital approximation to calculate a number of coupling constants involving 13c and 19F. The usually neglected orbital and dipolar terms are found to be very important in FF and CF coupling. They can play a decisive role in explaining the experimental trend of JCF among a series of compounds. The orbital interaction is found to play a significant role in certain CC couplings. Generally good agreement is obtained between theory and experiment except for JCF and JFF in oxalyl fluoride and the incorrect signs obtained for cis JFF in fluorinated ethylenes. The nature of the theory permits the latter discrepancy to be rationalized in terms of computational details. The value of JFF in difluoracetjc acid is predicted to be -235 Hz. The SCFPT method is used with a theory of dπ - pπ bonding to predict in agreement with experiment that JCH in acetylene will decrease when that molecule is bound in a transition metal complex. / Thesis / Doctor of Philosophy (PhD)

This thesis is part of an effort to enable large-scale Hartree-Fock/Kohn-Sham (HF/KS) calculations. The objective is to model molecules and materials containing thousands of atoms at the quantum mechanical level. HF/KS calculations are usually performed with the Self-Consistent Field (SCF) method. This method involves two computationally intensive steps. These steps are the construction of the Fock/Kohn-Sham potential matrix from a given electron density and the subsequent update of the electron density usually represented by the so-called density matrix. In this thesis the focus lies on the representation of potentials and electron density and on the density matrix construction step in the SCF method. Traditionally a diagonalization has been used for the construction of the density matrix. This diagonalization method is, however, not appropriate for large systems since the time complexity for this operation is σ(n3). Three types of alternative methods are described in this thesis; energy minimization, Chebyshev expansion, and density matrix purification. The efficiency of these methods relies on fast matrix-matrix multiplication. Since the occurring matrices become sparse when the separation between atoms exceeds some value, the matrix-matrix multiplication can be performed with complexity σ(n). A hierarchic sparse matrix data structure is proposed for the storage and manipulation of matrices. This data structure allows for easy development and implementation of algebraic matrix operations, particularly needed for the density matrix construction, but also for other parts of the SCF calculation. The thesis addresses also truncation of small elements to enforce sparsity, permutation and blocking of matrices, and furthermore calculation of the HOMO-LUMO gap and a few surrounding eigenpairs when density matrix purification is used instead of the traditional diagonalization method. / <p>QC 20101123</p>

No description available.

While the spin trapping properties of thiols have been investigated through EPR analysis and kinetics studies, few groups have studied these properties using strictly computational methods. In particular, α-lipoic acid (ALA) and its reduced form, dihydrolipoic acid (DHLA), one of the strongest endogenously produced antioxidants, show potential for being effective, naturally occurring spin traps for the trapping of reactive oxygen species. This research covers electronic structure calculations of ALA, DHLA, and their corresponding hydroxyl radical spin adducts, performed at the cc-pVDZ/B3LYP/DFT level of theory. The effects on DHLA introduced by other radicals such as ·OOH, ·OCH3, and ·OOCH3 are reported. Explicit solvation was carried out using open-source molecular packing software and was studied using MOPAC PM6 semi-empirical geometry optimizations. Complete Basis Set (CBS) limit extrapolations were performed using cc-pVXZ (X = D, T, Q) Dunning basis sets under the DFT/B3LYP level of theory, and results are compared to the literature.

A polymer brush is formed by densely grafting the chain ends of polymers onto a surface. This tethering of the long macromolecules has considerable influence on the surface properties, which can be additionally modified by changing the environmental conditions. In this context it is of special interest to understand and control the behavior of the grafted layer and to create surfaces that display a desired response to external stimulation. The present work studies densely grafted polymer brushes and the effects that such an environment imposes on an individual chain molecule in the grafted layer. For this purpose we developed a new self-consistent field approach to describe mixtures of heterogeneous chains comprised of differently sized hard spheres. Applying this method to the case of polymer brushes we consider a fraction of grafted molecules to be different from the majority brush chains. The modification of these chains includes a variation in the degree of polymerization, a different solvent selectivity behavior and a variable size of the free end-monomer. Due to the computational efficiency of the present approach, as compared for example to direct simulation methods, we can study the conformations of the modified 'guest' chains systematically in dependence of the relevant parameters. With respect to brush profile and the distribution of the free chain ends the new method shows very good quantitative agreement with corresponding simulation results. We also confirm the observation that these 'guest' chains can undergo a conformational transition depending on the type of modification and the solvent quality. For the cases studied in the present work we analyze the conditions to achieve a most sensitive behavior of this conformational switching. In addition, an analytical model is proposed to describe this effect. We compare its predictions to the numerical results and find good agreement.

This thesis presents a means of enhancing the iterative calculation techniques used in electronic structure calculations, particularly Kohn-Sham DFT. Based on the subspace iteration method of the FEAST eigenvalue solving algorithm, this nonlinear FEAST algorithm (NLFEAST) improves the convergence rate of traditional iterative methods and dramatically improves their robustness. A description of the algorithm is given, along with the results of numerical experiments that demonstrate its effectiveness and offer insight into the factors that determine how well it performs.