Vibrations of nuclei in crystals govern various properties such as thermal expansion, phase transitions, and elasticity, and the quasiharmonic approximation (QHA) is the simplest nontrivial approximation which includes the effects of vibrational anharmonicity into temperature dependent observables. Nonetheless, the QHA is often implemented with additional approximations due to the complexity of computing phonons under arbitrary strains, and the generalized QHA, which employs constant stress boundary conditions, has not been completely developed. Here we formulate the generalized QHA, providing a practical algorithm for computing the strain and other observables as a function of temperature and true stress. We circumvent the complexity of computing phonons under arbitrary strains by employing irreducible second order displacement derivatives of the Born-Oppenheimer potential and their strain dependence, which are efficiently and precisely computed using the lone irreducible derivative approach. We formulate two complementary strain parametrizations: a discretized strain grid interpolation and a Taylor series expansion in symmetrized strain. We illustrate the quasiharmonic approximation by evaluating the temperature and pressure dependence of select elastic constants and the thermal expansion in thoria (ThO₂) using density functional theory with three exchange-correlation functionals. The convergence of the two complementary strain parametrizations is evaluated for the computed thermal expansion. The temperature dependent lattice parameter and thermal expansion computed within the QHA is compared with experimental measurements. The QHA results are compared to measurements of the elastic constant tensor using time domain Brillouin scattering and inelastic neutron scattering. We then demonstrate the generalized quasiharmonic approximation in a non-cubic material, ferroelectric lead titanate, computing the temperature and stress dependence of the full elastic constant tensor. The irreducible derivative approach is employed for computing strain dependent phonons using finite difference, explicitly including dipole-quadrupole contributions. We use density functional theory, computing all independent elastic constants and piezoelectric strain coefficients at finite temperature and stress. There is good agreement between the quasiharmonic approximation and the experimentally measured lattice parameters close to 0 K. The quasiharmonic approximation overestimates the measured temperature dependence of the lattice parameters and elastic constant tensor, demonstrating that a higher level of strain dependent anharmonic vibrational theory is needed. The next material we study is zirconium nitride, employing the quasiharmonic approximation with the irreducible derivative approach to compute the phonons and thermal expansion. Density functional theory is used with two exchange-correlation functionals. We investigate the difference between the measured and computed optical phonon branches, showing that volume effects, two-phonon scattering, and nitrogen vacancies do not explain the discrepancy between the measurement and computation. The temperature dependent lattice parameter is computed within the QHA, where the thermal expansion is overestimated as compared with existing experimental measurements.

Quantum chemistry methodologies can be used to address a wide variety of chemical problems. Key to the success of quantum chemistry methodologies, however, is the selection of suitable methodologies for specific problems of interest, which often requires significant assessment. To gauge a number of methodologies, the utility of density functionals (BLYP, B97D, TPSS, M06L, PBE0, B3LYP, M06, and TPSSh) in predicting reaction energetics was examined for model studies of C-O bond activation of methoxyethane and methanol. These species provide excellent representative examples of lignin degradation via C-O bond cleavage. PBE0, which performed better than other considered DFT functionals, was used to investigate late 3d (Fe, Co, and Ni), 4d (Ru, Rh, and Pd), and 5d (Re, Os, and Ir) transition metal atom mediated Cβ -O bond activation of the β–O–4 linkage of lignin. Additionally, the impact of the choice of DFT functionals, basis sets, implicit solvation models, and layered quantum chemical methods (i.e., ONIOM, Our Own N-layered Integrated molecular Orbital and molecular Mechanics) was investigated for the prediction of pKa for a set of Ni-group metal hydrides (M = Ni, Pd, and Pt) in acetonitrile. These investigations have provided insight about the utility of a number of theoretical methods in the computation of thermodynamic properties of transition metal hydrides in solution. As single reference wavefunction methods commonly perform poorly in describing molecular systems that involve bond-breaking and forming or electronic near-degeneracies and are typically best described with computationally costly multireference wavefunction-based methods, it is imperative to a priori analyze the multireference character for molecular systems so that the proper methodology choice is applied. In this work, diagnostic criteria for assessing the multireference character of 4d transition metal-containing molecules was investigated. Four diagnostics were considered in this work, including the weight of the leading configuration of the CASSCF wavefunction, C02; T1, the Frobenius norm of the coupled cluster amplitude vector related to single excitations and D1, the matrix norm of the coupled cluster amplitude vector arising from coupled cluster calculations; and the percent total atomization energy, %TAE. This work demonstrated the need to have different diagnostic criteria for 4d molecules than for main group molecules.

No / In this paper we present a method for generating Bézier surfaces from the boundary information based on a general 4th-order PDE. This is a generalisation of our previous work on harmonic and biharmonic Bézier surfaces whereby we studied the Bézier solutions for Laplace and the standard biharmonic equation, respectively. Here we study the Bézier solutions of the Euler¿Lagrange equation associated with the most general quadratic functional. We show that there is a large class of fourth-order operators for which Bézier solutions exist and hence we show that such operators can be utilised to generate Bézier surfaces from the boundary information. As part of this work we present a general method for generating these Bézier surfaces. Furthermore, we show that some of the existing techniques for boundary based surface design, such as Coons patches and Bloor¿Wilson PDE method, are indeed particular cases of the generalised framework we present here.

Nuclear Magnetic Resonance (NMR) and computational methods increasingly play a predominant and indispensable role in modern chemical research. The insights into the local nuclear environment that NMR can provide is unique information which allows the structural characterization of novel materials, as well as the understanding and explanation of their relevant properties on an atomic scale. Computational methods, on the other hand, can be used to support experimental findings, providing a rigorous theoretical basis. Furthermore, when more complex chemical systems are considered, calculations can prove to be invaluable for the interpretation of experimental data and often allow an otherwise impossible spectral assignment. This thesis presents a series of studies in which NMR spectroscopy, in combination with computational methods, is utilized to investigate a variety of chemical systems both in solution and the solid state. An overview of the thesis and experimental and computational details are given in Chapter 1. In Chapter 2, the quantum mechanical basis necessary for the description of the NMR phenomenon is presented. Chapter 3 explores the main experimental techniques employed routinely for the acquisition of NMR spectra in both solution and the solid state. Chapter 4 describes the main features of density functional theory (DFT) and its implementation in computational methods for the calculation of relevant NMR parameters. Chapter 5 reports an experimental solution-phase NMR study and a parallel computational investigation of the poly(CTFE-co-EVE) fluoropolymer. In Chapter 6, the combination of [superscript(14/15)]N solution-phase NMR techniques and DFT methods for the study of alkylammonium cationic templates used in the synthesis of microporous materials is presented. The characterization of a boroxoaromatic compound in the solid state and the study of its reactivity are described in Chapter 7. In Chapter 8, two experimental NMR methods for the study of the anisotropic chemical shift interaction in the solid state are compared and used to characterize a range of materials. Cross-polarization and nutation of quadrupolar nuclei are computationally investigated under both static and spinning conditions in Chapter 9. A general conclusion and a summary are given in Chapter 10.

Thesis (PhD)--Stellenbosch University, 2013. / Please refer to full text to view abstract.

Identificação e predição do comportamento aeroelástico representa um grande desafio para a análise e controle de fenômenos aeroelásticos adversos. A modelagem aeroelástica requer informações tanto sobre a dinâmica estrutural quanto sobre o comportamento aerodinâmico não estacionário. No entanto, a maioria das metodologias disponíveis atualmente são baseadas no desacoplamento entre o modelo estrutural e o modelo aerodinâmico não estacionário. Conseqüentemente, métodos alternativos são bem vindos na área de pesquisa aerolástica. Entre os métodos alternativos está o funcional multicamada, que fornece uma rigorosa representação matemática apropriada para modelagem aeroelástica e pode ser obtido através de redes neurais artificiais. Esse trabalho apresenta uma aplicação desse método, consistindo de um procedimento de identificação baseado em redes neurais artificiais que representam o funcional da resposta aeroelástica. O modelo neural foi treinado usando o algoritmo de Levenberg-Marquardt, o qual tem sido considerado um método de otimização muito eficiente. Ele combina a garantia de convergência do método do gradiente e o alto desempenho do método de Newton, sem a necessidade de calcular as derivadas de segunda ordem. Um modelo de asa ensaiado em túnel de vento foi usado para fornecer a resposta aeroelástica. A asa foi fixada a uma mesa giratória e um motor elétrico lhe fornecia o movimento de incidência. Essa representação aeroelástica funcional foi testada para diversas condições operacionais do túnel de vento. Os resultados mostraram que o uso de redes neurais na identificação da resposta aeroelástica é um método alternativo promissor, o qual permite uma rápida avaliação da resposta aerolástica do modelo. / Identification and prediction of aeroelastic behavior presents a significant challenge for the analysis and control of adverse aeroelastic phenomena. Aeroelastic modeling requires information from both structural dynamics and unsteady aerodynamic behavior. However, the majority of methodologies available today are based on the decoupling of structural model from the unsteady aerodynamic model. Therefore, alternative methods are mostly welcome in the aeroelastic research field. Among the alternative methods there is the multi-layer functional (MLF), that allows a rigorous mathematical framework appropriate for aeroelastic modeling and can be realized by means of artificial neural networks. This work presents an identification procedure based on artificial neural networks to represent the motion-induced aeroelastic response functional. The neural network model has been trained using the Levenberg-Marquardt algorithm that has been considered a very efficient optimization method. It combines the guaranteed convergence of steepest descent and the higher performance of the Newton\'s method, without the necessity of second derivatives calculation. A wind tunnel aeroelastic wing model has been used to provide motion-induced aeroelastic responses. The wing has been fixed to a turntable, and an electrical motor provides the incidence motion to the wing. This aeroelastic functional representation is then tested for a range of the wind tunnel model operational boundaries. The results showed that the use of neural networks in the aeroelastic response identification is a promising alternative method, which allows fast evaluation of aeroelastic response model.

Des facteurs fondamentaux pour la performance de matériaux à haute permittivité basés sur des pérovskites sont étudiés par des techniques ab-initio. L’anomalie diélectrique géante à 0K des pérovskites est investiguée aux niveaux Hartree-Fock, Théorie de la Fonctionnelle de la Densité et méthodes hybrides, en termes de la stabilité thermodynamique des phases, des contributions structurales et vibrationnelles et des charges effectives de Born. Le mode mou actif en infra-rouge est responsable par l’anomalie et des méthodes hybrides sont nécessaires pour reproduire les données expérimentales. L’évolution de l’instabilité ferroélectrique dans les pérovskites ABO3 avec la substitution de l’ion A est reliée de façon systématique aux rayons ioniques ainsi qu’aux degrés d’hybridation dans les liaisons pour des tantalates, niobates et titanates. / Ab-initio techniques are used to investigate key factors influencing the dielectric performance of high permittivity materials based on perovskites. The pressure-induced giant dielectric anomaly at 0K of ABO3 perovskites is investigated at the Hartree-Fock, density-functional theory and hybrid levels. Its mechanism is analyzed in terms of thermodynamic phase stability, structural and phonon contributions and Born effective charges. It is shown that the IR-active soft phonon is responsible for the anomaly and the use of hybrid functionals is required for agreement with experimental data. The evolution of the ferroelectric instability in ABO3 perovskites with substitution of the ion in the A site is systematically investigated for tantalates, niobates and titanates and correlated with the ionic radii as well as the degree of hybridization in the bonds.

Thesis (Ph.D.); Submitted to Iowa State Univ., Ames, IA (US); 19 Dec 2004. / Published through the Information Bridge: DOE Scientific and Technical Information. "IS-T 2397" Seong Huh. US Department of Energy 12/19/2004. Report is also available in paper and microfiche from NTIS.

Thesis (Ph. D.)--Ohio State University, 2006. / Title from first page of PDF file. Includes bibliographical references (p. 355-382).

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