Made available in DSpace on 2018-08-01T22:30:01Z (GMT). No. of bitstreams: 1 tese_8896_Tese final Fernando Néspoli.pdf: 1384436 bytes, checksum: f3462b5c8d9880e7dec5565dd15bafb3 (MD5) Previous issue date: 2015-05-06 / Um método sugerido previamente para calcular a energia de correlação no limite do conjunto de base completo pela redesignação dos números hierárquicos, e o uso do esquema de extrapolação unified singlet- and triplet-pair é aplicado a um conjunto de prova de 106 sistemas. A aproximação é utilizada para obter os valores extrapolados para energia de correlação, energia de atomização, anisotropia e polarizabilidade média no limite do conjunto de base completo, através de teoria de perturbação de segunda ordem de Møller-Plesset, método de coupled-cluster com excitações simples e duplas e coupled-cluster com excitações simples e duplas com correções triplas perturbativas. Uma boa concordância com as melhores estimativas disponíveis é obtida, mesmo quando o par de números hierárquicos (d, t) é usado para realizar a extrapolação. Com isso, é concebível justificar que não há razão física forte para excluir as energias dulpa-zeta em extrapolações, especialmente se a base é calibrada para obedecer ao modelo teórico. Além disso, um esquema simples de extrapolação unificado de um parâmetro é sugerido para extrapolar a energia de correlação de valência para o conjunto de base completo em espécies formadas por átomos de H até Ne. A performance do novo modelo é avaliada para a energia de correlação com um conjunto de de dados de 106 sistemas e, para polarizabilidade média, em um conjunto de 8 moléculas. Para as energias de correlação, os resultados são excelentes, na maioria das vezes melhores do que quando extrapolado com os mais populares protocolos de dois parâmetros disponíveis na literatura. Para a polarizabilidade, os resultados mostram uma melhora em relação aos valores ab initio, e uma boa concordância com os dados experimentais.

Orientador: Rogerio Custodio / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Quimica / Made available in DSpace on 2018-07-27T23:20:45Z (GMT). No. of bitstreams: 1 Gomes_AndreSeveroPereira_M.pdf: 1027128 bytes, checksum: f1b7d5eb3ae118af8a885c862f1ea2a2 (MD5) Previous issue date: 2001 / Mestrado

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Physics, 1982. / Includes bibliographical references. / by Thierry Troudet. / Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Physics, 1982.

Strong electron correlations in electronic structure theory are purely quantum effects arising as a result of degeneracies in molecules and materials, and exhibit significantly different yet interesting characters than do weak correlations. Although weak correlations have recently been able to be described very efficiently and accurately within single particle pictures, less known are good prescriptions for treating strong correlations efficiently. Brute-force calculations of strong correlations in wave function theories tend to be very computationally-intensive, and are usually limited to small molecules for applications. Breaking symmetry in a mean-field approximation is an efficient alternative to acquire strong correlations with, in many cases, qualitatively accurate results. The symmetry broken in quantum chemistry has been traditionally of spin, in so-called unrestricted methods, which typically break spatial symmetry as a consequence, and vice versa, in most situations. In this work, we present a novel approach to accurately describing strong correlations with a mean-field cost by means of Hartree- Fock-Bogoliubov (HFB) theory. We are inspired by the number-symmetry-breaking in HFB, which, with an attractive particle interaction, accounts for strong correlations, while maintaining spin and spatial symmetry. We show that this attractive interaction must be restricted to the chemically-relevant orbitals in an active space to obtain physically meaningful results. With such constraints, our constrained pairing mean-field theory (CPMFT) can accurately describe potential energy curves of various strongly-correlated molecular systems, by cleanly separating strong and weak correlations. To achieve the correct dissociation limits in hetero-atomic molecules, we have modified our CPMFT functional by adding asymptotic constraints. We also include weak correlations by combining CPMFT with density functional theory for chemically accurate results, and reveal the connection between CPMFT and traditional unrestricted methods. The similarity between CPMFT and unrestricted methods leads us to the idea of constrained active space unrestricted mean-field approaches. Motivated by CPMFT, we partially retrieve spin-symmetry that has been fully broken in unrestricted methods. We allow symmetry breaking only in an active space. This constrained unrestricted Hartree-Fock (CUHF) is an interpolation between two extrema: the fully broken-symmetry solution and the symmetry preserved solution. This thesis defines the theory behind and reports the results of CUHF. We first show that, if an active space is chosen to include only open-shell electrons, CUHF reduces to restricted open-shell Hartree-Fock (ROHF), and such CUHF proves in many ways significantly

Tez (Yüksek Lisans) - Süleyman Demirel Üniversitesi, Fen Bilimleri Enstitüsü, Fizik Anabilim Dalı, 2008. / Kaynakça var.

Cette thèse est consacrée à l'étude mathématique et numérique du modèle de Hartree-Fock-Bogoliubov (HFB) pour les systèmes quantiques attractifs, qui est abondamment utilisé en physique nucléaire. Après avoir présenté le modèle et ses principales caractéristiques, nous expliquons comment le discrétiser et nous montrons des résultats de convergence. Nous examinons tout particulièrement l'algorithme de point fixe (parfois appelé Roothaan) et montrons qu'il converge ou alors oscille entre deux états dont aucun n'est solution du problème. Ceci généralise au cadre HFB des résultats de Cancès et Le Bris pour le modèle plus simple de Hartree-Fock dans le cas répulsif. Suivant ces mêmes auteurs, nous proposons un algorithme basé sur la contrainte relachée et pour lequel la convergence est garantie. Dans dernière partie de la thèse, nous illustrons le comportement de ces algorithmes par des simulations numériques pour plusieurs modèles. Dans un premier temps nous considérons un système purement gravitationnel où les particules interagissent avec le potentiel de Newton. Nos simulations montrent que la matrice d'appariement est toujours non nulle, un fait qui n'a pas encore pu être démontré rigoureusement. Nous étudions ensuite un modèle très simplifié pour la description de protons et neutrons dans le noyau atomique. / This work is devoted to the theoretical and numerical study of Hartree-Fock-Bogoliubov (HFB) theory for attractive quantum systems, which is one of the main methods in nuclear physics. We first present the model and its main properties, and then explain how to discretize it. We prove some convergence results, in particular for the simple fixed point algorithm (sometimes called Roothaan). We show that it converges, or oscillates between two states, none of them being a solution. This generalizes to the HFB case previous results of Cancès and Le Bris for the simpler Hartree-Fock model in the repulsive case. Following these authors, we also propose a relaxed constraint algorithm for which convergence is guaranteed. In the last part of the thesis, we illustrate the behavior of these algorithms by some numerical experiments. We first consider a system where the particles only interact through the Newton potential. Our numerical results show that the pairing matrix never vanishes, a fact that has not yet been proved rigorously. We then study a very simplified model for protons and neutrons in a nucleus.

MELO, Heitor Alves de. Propriedades eletrônicas de pontos quânticos contendo muitos elétrons. 2010. 75 f. Dissertação (Mestrado em Física) - Programa de Pós-Graduação em Física, Departamento de Física, Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2010. / Submitted by Edvander Pires (edvanderpires@gmail.com) on 2015-05-04T17:47:42Z No. of bitstreams: 1 2010_dis_hamelo.pdf: 2475149 bytes, checksum: f2b733568c55c95683fc14e493c5ab31 (MD5) / Approved for entry into archive by Edvander Pires(edvanderpires@gmail.com) on 2015-05-07T14:29:38Z (GMT) No. of bitstreams: 1 2010_dis_hamelo.pdf: 2475149 bytes, checksum: f2b733568c55c95683fc14e493c5ab31 (MD5) / Made available in DSpace on 2015-05-07T14:29:38Z (GMT). No. of bitstreams: 1 2010_dis_hamelo.pdf: 2475149 bytes, checksum: f2b733568c55c95683fc14e493c5ab31 (MD5) Previous issue date: 2010 / This work investigates the electronic properties of semiconductor quantum dots in which there are many electrons confined. In particular, we study Si and Ge quantum dots embedded in dielectric matrices (SiO2 e HfO2). The theoretical method used to calculate the total energy of N electrons confined in quantum dots is based on a simplified version of the Hartree-Fock method. In this model, the total energy is obtained from single-particle wavefunctions and eigen-energies. The obtained results show that the total energy in Ge quantum dots are always larger than in Si ones. The reason is the smaller electron e effective mass in Ge, which raises the energies of the confined states. As for the role of the dielectric matrix, the total energy is always larger for SiO2 than for HfO2. Physically, this e effect is caused by the fact that SiO2 has larger confinement barriers (3.2 eV) than HfO2(1.5 eV). Smaller barriers favor larger spatial extent of the wavefunctions, decreasing the repulsion energy of the confined electrons. The chemical potential and additional energy was also calculated as function of the number of confined electrons. It was observed that the chemical potential of Ge quantum dots are always larger than Si ones, but the role of the dielectric matrix is inverted. The chemical potential for HfO2 is larger than for SiO2. With respect to the additional energy, we observed that this quantity strongly oscillates within the range 0 to 0.4 eV for cases. If one takes into account that the Coulomb blockade phenomena is only observed for additional energies much larger the thermal energy (of the order of 3/2kBT), this phenomena can only be observed for the case where there are only a few electrons confined in the quantum dots. / Este trabalho dedica-se ao estudo das propriedades eletrônicas de pontos quânticos semicondutores contendo muitos elétrons confinados. Em particular, serão investigados semicondutores contendo muitos elétrons confinados. Em particular, serão investigados pontos quânticos de Si e Ge imersos em matrizes dielétricas (SiO2 e HfO2). O método teórico utilizado para calcular a energia total de um sistema de N elétrons confinados baseia-se numa versão simplificada do método de Hartree-Fock. Neste modelo a energia total e calculada a partir das funções de onda e estados de energia de uma única partícula Os resultados obtidos mostram que a energia total em pontos quânticos de Ge são em geral maiores que em pontos quânticos de Si, independentemente do número de elétrons confinados. Isto acontece devido a massa efetiva menor dos elétrons no Ge que aumentam as energia de confinamento. Em relação ao papel das barreiras dielétricas, a energia total é sempre maior nos casos em que o ponto quântico está envolvido por SiO2. Fisicamente, isto se deve ao fato de que a barreira de confinamento do SiO2 (3.2 eV) é maior que a do HfO2 (1.5 eV). Barreiras mais baixas favorecem o aumento da extensão espacial das funções de onda, reduzindo a repulsão coulombiana dos elétrons confinados. Calculou se também o potencial químico dos pontos quânticos em função do número de elétrons confinados, e a energia adicional necessária para aprisionar mais um elétron nos pontos quânticos. Verificou-se que o potencial químico dos pontos quânticos de Ge são sempre maiores que nos de Si, por em o potencial químico para pontos quânticos envoltos em HfO2 são sempre maiores que no caso do SiO2. Em relação a energia adicional, observa-se que esta quantidade apresenta fortes oscilações e que varia entre 0 e 0.4 eV para todos os casos estudados. Se levarmos em conta que o fenômeno conhecido como bloqueio de Coulomb acontece quando a energia adicional é muito maior que a energia térmica (da ordem de 3=2kBT), este fenômeno são será observado quando houver poucos elétrons confinados nos pontos quânticos.

No description available.

The development of time-dependent mean-field theory (TDMF) for the treatment of ion-metal interactions is detailed. By allowing for the time-dependent, nonlinear response of the conduction electrons, TDMF provides a self-consistent description that is free of the adiabatic and linear response approximations that have conventionally been used to treat dynamical processes in simple metals. We present the first results of three-dimensional simulations of a bare proton passing through a thin metallic foil. The nonlinear-induced electron density, dynamical screening potential, and electronic stopping power are all displayed as functions of time for several proton velocities ranging from one-half to eight times the Fermi velocity of a simple metal (sodium). We find that a sizable induced density forms behind the proton and that this density is carried along in the wake of the proton with very little dispersion as it traverses the foil. At proton velocities comparable to or above the Fermi velocity, these wake-riding electrons are shaken off as the proton passes through the rear surface of the foil. We find no evidence that the proton forms a stable hydrogen atom as it traverses the foil. At the velocities studied, the conduction electrons provide a weak, asymmetric screening of the proton, with some regions behind the proton actually being overscreened at the higher velocities. A comparison of our results with a standard linear response treatment of the problem reveals both qualitative and quantitative differences in the calculated time-dependent electron density and screening length. We find that the basic assumption underlying the linear response approximation is not justified in this case, due to the strongly nonlinear nature of the conduction electrons' response. These results are illustrative of the kinds of calculations that can be carried out with the simulation package that we have developed and we describe several applications that are planned for the near future. Several innovations in numerical technique, developed in the course of this work, are also detailed.

The exact scalar wave solution for light scattering from a general dielectric disk array is found. The exact solution as well as a numerical solution is also given for an array of three dielectric disks, whose centers are placed on the vertices of an equilateral triangle. The various (differential, total and averaged total) cross sections and the poles of the scattering matrix are given. These results are analyzed in part by considering the effects which arise from the geometry of the system, and in part by comparison with the results (cross sections and poles) for a system with an identical arrangement of three hard (perfectly conducting) disks and with a system of one dielectric disk. This analysis helps rule out structure that arise from the chaos, which is very likely to exist, in the classical (geometric) limit of the three (or more) dielectric disk system. In the future after I study the geometric (classical) and physics (semiclassical) regimes of this system, I plan to reanalyse the exact wave solution in an attempt to discover the traces of the chaos present in the system. Time dependent Hartree-Fock theory (TDHF), with improved formulation and improved computer capabilities, is used to repeat the calculations of charge capture for the He²⁺ on He collision. The results of these calculations allow us to discuss the effects of various numerical truncations and to establish with certainty the viability and the accuracy of TDHF in its application to ion-atom collisions. Initially, we had hoped to find chaos in the TDHF problem, as it is nonlinear. However, due to the complexity and computational difficulties present in the TDHF problem, a simpler scattering system of light scattering from dielectric disk arrays was chosen for study.