Kohn-Sham density functional theory (DFT) is the most widely used method in quantum chemistry. It has the potential to provide accurate results at low computational cost. The quality of a DFT calculation is determined by the exchange-correlation energy functional. Hybrid functionals, which contain a fraction of exact orbital exchange, are extensively used due to their accuracy in a variety of applications. However, as commonly implemented, these functionals are outside the Kohn-Sham scheme, since the exchange operator is not a local multiplicative potential. In order to handle orbital dependent functionals correctly, schemes which determine a local multiplicative potential must be employed. The implementation and application of several such methods is the focus of this thesis. In Chapter 1 we outline the Hartree-Fock scheme, which defines the exchange energy, and overview wavefunction based procedures that recover correlation energy. Alternative theories based on the electron density are then considered and the foundations of modern DFT are reviewed. The formalism of the optimized effective potential (OEP) method is introduced, which is the rigorous way to handle orbital dependent functionals. A number of approximations to the exchange only OEP method are outlined in Chapter 2 and their implementation is described. The methods are applied to the calculation of NMR shielding constants, highlighting differences between the approximations; their use in the construction of multiplicative hybrid functionals is also considered. In Chapter 3 these approximations are further investigated in the calculation of excited states and structural perturbations. In Chapter 4, the theory and implementation of a direct optimization procedure to determine OEPs is outlined, along with an implementation of the constrained search procedure, which allows the determination of the Kohn-Sham exchange-correlation potential from any input density. Chapter 5 compares the performance of the approximate exchange potentials with those of OEP, highlighting the presence of correlated character in some of the approximate methods. The OEP implementation is extended to include hybrid exchange-correlation functionals in Chapter 6. The performance of these methods for the calculation of NMR shielding constants, rotational g tensors and transition metal NMR chemical shifts is investigated. In all cases, substantial improvements over conventional results are obtained. In Chapter 7 DFT is used to investigate an interaction of relevance in organic chemistry. Concluding remarks are given in Chapter 8.

A number of SrTiO3(001) surface reconstructions have been studied using Plato, Package for Linear Combinations of Atomic Type Orbitals, a first principles density functional theory approach. Energy calculations have been performed for each surface reconstruction, and phase diagrams produced for a range of temperatures and pressures.

The evaluation of molecular integrals is a vital but computationally expensive part of electronic structure calculations. This computational expense is particularly problematic for the explicitly correlated methods, in which complicated and numerous integrals over more than two-electrons must be evaluated. The successful R12/F12 methods overcome this difficulty by decomposition of these many-electron integrals by means of approximate resolutions of the identity (RIs). To obtain accurate results with this approach, however, requires large auxiliary basis sets with high angular momentum functions. To address this issue, we present a new RI-free variant of MP2-F12 theory, which uses density fitting to approximate three-electron integrals, rather than RIs. This approach demonstrates improved convergence of calculated energies with respect to the size and maximum angular momentum of the auxiliary basis set compared to the standard RI-based approach. For the systems on which the method was tested, relatively small auxiliary basis sets were sufficient to reduce errors in the correlation energy to less than a millihartree. The software implementation of the three-electron integral types needed in the new MP2-F12 variant proved to be extremely time-consuming. This difficulty inspired us to develop "Intception", a code generator which generates code for molecular integral evaluation. Intception is capable of automatically implementing code for evaluating a wide range of molecular integral types, using a general theoretical framework based on Obara-Saika-type recurrence relations [1] . To flexibly express integral definitions for use in Intception, a new domain-specific language was created. Testing revealed that the generated code evaluated integrals to a high numerical accuracy and on a reasonable timescale, though somewhat slower than existing optimized implementations. A detailed analysis of the performance of the generated code was undertaken, which suggested some possible routes to improving the efficiency of the code.

This thesis explores Feynman’s idea of quantum simulations by using ultracold quantum gases. In the first part of the thesis we develop a general method applicable to atoms or molecules or even nanoparticles, to decelerate a hot fast gas beam to zero velocity by using an optical cavity. This deceleration method is based on a novel phase stability mechanism in the bad cavity regime, which is very different from the traditional cavity cooling studies where a good cavity is needed. We propose several schemes to decelerate the gas beam based on this new phase stability mechanism. Practical issues for realizing the proposals are also discussed in detail which show that the deceleration schemes are feasible using present experimental techniques. In the second part of this thesis, we show how the concept of quantum simulations is applied to multiple-layered Dirac cones and related phenomena by using multi-component ultracold fermionic atoms in optical lattices where the spin-dependent hopping and on-site spin flipping are both controlled by Raman lasers. By tuning the spin-dependent hopping according to the representations of su(2) algebra, we show that we can simulate the Dirac-Weyl fermions with any arbitrary spin beyond the spin ½ cases found in graphene and topological insulators. These high spin Dirac-Weyl fermions show rich anomalous quantum Hall effects and a remarkable Klein multi-refringent tunnelling. Moreover, when getting rid of the limitations of su(2) algebra and allowing for on-site spin flipping, we further investigate Modified Dispersion Relations (MDRs) and Neutrino Oscillations (NOs) as in Standard Model Extensions (SMEs) by virtue of an analogue between the three-family fermions in particle physics and a three-layered Dirac cones scheme. This thesis shows the important role ultracold quantum gases play in quantum simulations to address some of the most challenging topics in modern physics.

The research presented in this thesis focuses on the optical properties of InGaN/GaN, GaN/AIGaN, and InGaN/AllnGaN quantum well structures.

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Kohn-Sham density functional theory (DFT) is the most widely-used method for quantum chemical calculations. For most chemical properties it offers relatively accurate results for a relatively low computational cost. This accuracy is governed by the quality of the exchange-correlation functional used. The development and assessment of new functionals is a vital aspect of DFT research, and is the focus of this thesis. In Chapter 1, the theory of traditional wavefunction-based quantum chemistry methods and of DFT is outlined, and the two approaches compared and contrasted. Chapter 2 considers the relatively poor performance of conventional DFT functionals for NMR shielding constants. A simple generalised gradient approximation (GGA) functional, denoted KTl, is developed, which improves this performance significantly. A more flexible functional fitted to experimental energetic data, denoted KT2, is also presented. In Chapter 3, KTl and KT2 are assessed for other magnetic properties, such as chemical shifts, magnetisabilities, and indirect spin-spin coupling constants. Chapter 4 details the development of a third GGA denoted KT3, which is designed to address the shortcomings of KT2 for non-magnetic properties. In Chapter 5, the more flexible functional form of KT3 is shown to give results competitive with the best GGAs for a wide range of chemical properties and for solid state calculations. In Chapter 6, we attempt to improve performance for classical chemical reaction barriers, for which KT3 is relatively poor. This requires a more flexible form in the resulting GGA functional, denoted KT4. A hybrid functional, B97- 3, is also developed with a similar emphasis on reaction barriers. Chapter 7 presents an extensive chemical assessment for KT4 and B97-3. For the systems considered, B97-3 is shown to be the most accurate semi-empirical functional developed to date. Concluding remarks are presented in Chapter 8.

A particular emphasis of this thesis has been to provide insight into the underlying stability of these complexes and hence interpret experimental data, and to establish the development of solvation shell structure and its effect on reactivity and excited states. Energy decomposition analysis, fragment analysis and charge analysis has been used throughout to provide deeper insight into the nature of the bonding in these complexes. This has also been used successfully to explain observed preferential stability and dissociative loss products.

Resumo em portugues e ingles / Tese (doutorado)-Universidade Estadual de Campinas / Bibliografia: f. 80-83 / Made available in DSpace on 2018-07-13T20:06:34Z (GMT). No. of bitstreams: 1 Tostes_JoseGlaucoRibeiro_D.pdf: 3445029 bytes, checksum: 6608e72da8d21a432982425e8983105c (MD5) Previous issue date: 1983 / Doutorado

Kahn-Sham density functional theory (OFT) calculations yield reliable accuracy in a wide variety of molecules and materials. The advent of linear-scaling OFT methods, based on locality of the electronic matter, has enabled calculations on systems with tens of thousands of atoms. Localisation constraints are imposed by expanding the Kahn-Sham states in terms of a set of atom-centred, spherically-localised functions. Chemical accuracy is then achieved via a self-consistent optimisation using a high-resolution basis set. This formalism reduces the size of, and brings predictable sparsity patterns to, the matrices expressed in this representation, such as the Hamiltonian matrix. In this work, we used the ONETEP program for DFT calculations, which is based on the abovementioncd principles. The vision behind our research is to advance the method by developing new and robust algorithms to enable novel applications based on localised orbitals.