The non-linear Hartree-Fock (HF) equations are usually solved via the iterative self-consistent field method. However, there is no a priori guarantee of convergence, especially in systems with strong electron correlation where symmetry breaking occurs. This work focuses on closed- shell systems in the HF approximation and the (in)stability of the found solutions, and proposes new deterministic methods for the localization of both symmetry-adapted and broken symmetry solutions. We employ a perturbative method and show how one can always obtain a symmetry-adapted solution of the HF equations. We also determine the radius of convergence, related to the existence of at least one bound state, of the perturbative series. Next, we rederive the matrix of stability and adapt it to spin and orbital symmetry. Calculation of higher energy variations follows, first in terms of spin-orbitals and then orbitals. Motivated by the investigation of the structure of a broken-symmetry solution, we propose a new deterministic method for the localization of a broken-symmetry solution. The general expressions are verified by reformulating the stability conditions for simple cases. The proposed methods are successfully applied to helium-, beryllium- and neon-like systems.

A busca por um conjunto de bases de alta qualidade é feita por vários grupos, pois a utilização destes conjuntos é importante para a obtenção de resultados exatos, tanto para propriedades atômicas quanto para propriedades moleculares. Os conjuntos usados neste trabalho são constituídos através da utilização do Método da Coordenada Geradora Hartree-Fock em sua versão polinomial e foram construídos de forma a permitirem uma maior flexibilidade à camada de valência do átomo, flexibilidade esta que foi proporcionada pelo número de funções que descrevem a última camada do átomo. Uma nova metodologia para a construção de conjuntos de base foi proposta neste trabalho. Esta nova metodologia diminui a busca artesanal pela busca pelos conjuntos de base introduzindo o Método Simplex em nosso programa gerador de base GENBASIS minimizando o tempo de procura por essa bases de qualidade. A aplicação destes conjuntos para estimativa de propriedades atômicas e moleculares foi feita em comparação com conjuntos de base largamente utilizados na literatura, envolvendo cálculos com vários níveis de teoria, desde o método Hartree-Fock até a Teoria do Funcional Densidade. / The search for high quality basis set is made by several groups since the quality of the basis sets is a very important factor to obtain accurate results for atomic and molecular properties. The basis sets used in this work are designed by using the polynomial Generate Coordinate Method and were constructed with the aim to improve the flexibility of a basis sets to describe the valence shell. A new methodology for the search of this basis set is proposed in this work. This new methodology makes the search for this basis set less artisanal with the introduction of the Simplex Method in our basis generator program, GENBASIS. This introduction minimizes the time used in the search for these quality basis set. The application of our basis sets in atomic and molecular calculations were compared with the most used basis sets in the literature and were performed by using different level of calculations, namely, from Hartree-Fock to Density Functional Theory.

In this thesis, I present a theory of electron-electron interactions in optical properties of graphene and transition metal dichalcogenides (TMDCs), two dimensional nanostructures with a hexagonal lattice. We start our discussion with electron-electron interactions in artificial rings for which the strength of interactions can be varied and exact results can be obtained. The artificial rings are described by the extended Hubbard model and solved using an exact diagonalization method in real and Fourier space of configurations. Exact and analytical results for charged rings are obtained in the limit of very strong interactions. For the quadruple quantum dot ring and the artificial benzene ring, we find that chirality leads to the appearance of a topological phase and an effective gauge field that determines the ground state character with varied interaction strength. For the charged artificial benzene ring, our numerical results show a transition from a degenerate to a non-degenerate ground state with increasing strength of Coulomb interactions. We show that the artificial gauge and the transition in the ground state can be detected as changes in the optical absorption spectrum. In the second part of the thesis, the electronic and optical properties of colloidal graphene quantum dots (CGQD) consisting of many benzene rings are determined. The CGQDs are described by the combination of tight binding, mean field Hartree Fock (HF) and Configuration Interaction methods. The single particle properties are described through the tight binding method based on the pz carbon orbitals. Screened Coulomb interactions between electrons, including direct, exchange, and scattering matrix elements, are calculated using Slater pz orbitals. HF ground states corresponding to semiconductor, Mott-insulator, and spin-polarized phases are obtained as a function of the strength of the screened interaction versus the tunnelling matrix element. The many-body ground and excited states in the semiconducting phase are constructed as a linear combination of a finite number of electron-hole pair excitations from the HF ground state (GS). The Hamiltonian is constructed in the subspace of multi-pair HF excitations to obtain the low energy, many body states by exact diagonalization using the Lanczos method. The degeneracy of the valence- and conduction-band edges of 3-fold rotationally symmetric CGQDs is shown to lead to a characteristic exciton and bi-exciton spectrum. The low-energy exciton spectrum is predicted to consist of two bright-singlet exciton states corresponding to two circular polarizations of light and a lower-energy band of dark singlets and dark triplets. The robustness of the bright degenerate singlet pair against correlations in the many-body state is demonstrated as well as the breaking of the degeneracy by the lowering of symmetry of the CGQD. Band edge biexciton energies and binding energies are predicted, and two degenerate exciton (X) states and a corresponding biexciton (XX) state are identified for the generation of an XX-X cascade. The Auger coupling of XX and excited X states is determined and our theoretical results are compared with experimental absorption and non-linear transient absorption spectra. In the third and final part of the thesis, we replace the two non-equivalent carbon atoms of the graphene hexagonal lattice with a heavy transition-metal atom M, (e.g. Mo or W) and a dimer X2 (e.g. S). The bandstructure of a monolayer MX2 is calculated using density functional theory (DFT). It is shown that a direct gap opens up at all K points of the Brillouin zone and strong spin orbit coupling leads to spin splitting of the valence and conduction bands and emergence of valley dependent optical selection rules. Finally, the magnetoluminescence experiments on a monolayer WS2 emitting circularly polarized light upon its excitation by unpolarized light are described. The emission of polarized light in zero magnetic field is explained by the possibility of formation of a valley polarized 2D electron gas in unintentionally doped WS2.

A evolução continua dos computadores levou a várias modificações na maneira de fazer ciência, fazendo surgir uma infinidade de novas opções para resolvermos problemas científicos. A implementação computacional de métodos teóricos possibilitou a tratamento de sistemas grandes, complexos e em diferentes áreas da ciência.Uma área particularmente em destaque e a química de moléculas, atualmente podemos descrever sistemas moleculares relativamente complexos com extrema precisão. Os métodos teóricos em química molecular podem ser divididos basicamente em métodos clássicos ou quânticos, dependendo do que queremos estudar, podemos também utilizar métodos híbridos ou seqüenciais, contudo para uma descrição detalhada da estrutura eletrônica e de ligações químicas é necessária a utilização de métodos quânticos.Cálculos ab initio da estrutura eletrônica de átomos e especialmente moléculas foram realizados pela primeira vez utilizando-se o método de expansão de Roothaan na década de cinqüenta. Em 1986, uma versão integral das equações de Griffin-Wheele-Hartree-Fock (GW-HF) foi apresentada na literatura , inspirada no Método da Coordenada Geradora (MCG), introduzido por Griffin e Wheeler na década de cinqüenta. A versão integral das equações de Hartree-Fock foi denominada de Método da Coordenada Geradora Hartree-Fock (MCG-HF), e uma de suas primeiras aplicações foi na geração de bases atômicas universais . De fato, uma integração numérica cuidadosa das equações de GW-HF permite a geração de bases universais bem mais generalizadas do que as já publicadas na literatura.Recentemente, Barbosa e da Silva propuseram uma modificação na metodologia da discretização com o intuito de melhorar a obtenção de conjuntos de funções Gaussianas (GTF) por meio do MCG-HF, tornando possível a geração de GTF tão boas ou melhores quanto as até agora obtidas na literatura, porém mais compactas e precisas (acuradas). / The ongoing evolution of computers has led to several changes in the way of doing science, to create a multitude of new options for solving scientific problems. The implementation of computational methods allowed the theoretical treatment of large systems, complex and different areas of science. One area of particular focus and chemistry of molecules, now can describe relatively complex molecular systems with extreme precision. The theoretical methods in molecular chemistry can be basically divided into classical and quantum methods, depending on what we consider, we can also use sequential or hybrid methods, however for a detailed description of the electronic structure and chemical bonds is required the use of quantum methods. Ab initio calculations of the electronic structure of atoms and molecules have been specially made for the first time using the method of Roothaan expansion in the decade of the fifties . In 1986, a full version of the equations of Griffin-Wheeler-Hartree-Fock (HF-GW) was presented in the literature , inspired by the Method of Coordinate Generator (MCG), introduced by Griffin and Wheeler in the decade of fifty . The full equations of the Hartree-Fock method was called the Generator Coordinate Hartree-Fock (HF-MCG) and its first applications was the generation of atomic universal bases In fact, a careful numerical integration of equations of GW-HF allows the generation of universal bases and more widespread than those already published in the literature .Recently, Barbosa and Silva proposed a modification in the methodology of the discretization to improve the collection of sets of Gaussian functions (GTF) by means of MCG-HF, making possible the generation of GTF as good or better as the so far obtained in the literature, but more compact and precise (accurate). A polynomial expansion is proposed as a new way to discretize the Griffin-Wheeler-Hartree-Fock equations of the Generator Coordinate Hartree-Fock method. The implementation of the polynomial expansion in the Generator Coordinate Hartree-Fock method discretizes the Griffin-Wheeler-Hartree-Fock equations through a numerical mesh, which is not equally spaced. This procedure makes the optimization of Gaussian exponents in the Generator Coordinate Hartree-Fock method more flexible and more efficient. The results obtained with the polynomial expansion for atomic Hartree-Fock energies show this technique is very powerful when employed in the design of compact and high accurate Gaussian basis sets used in ab initio non-relativistic (Hartree-Fock) and relativistic (Dirac-Fock) calculations.

Inhalt dieser Arbeit ist die Untersuchung der Physik des ungeordneten wechselwirkenden Elektronenproblems auf der isolierenden Seite des Metall-Isolator-Uebergangs. Als Modellsystem dient dabei ein verallgemeinertes Coulomb-Glas-Modell mit Transfermatrixelementen zwischen verschiedenen Plaetzen, das Quanten-Coulomb-Glas. Ziel ist, herauszufinden, wie sich die Elektron-Elektron-Wechselwirkung auf die Lokalisierungs- und Transporteigenschaften des Modells auswirkt. Im ersten Teil wird das Quanten-Coulomb-Glas in Hartree-Fock-Naeherung behandelt. Da diese Naeherung eine effektive Einteilchentheorie ist, koennen die Lokalisierungs- und Transporteigenschaften mit denselben Methoden wie beim Anderson-Modell der Lokalisierung untersucht werden. Es erweist sich, dasz die Wechselwirkung im Rahmen einer Einteilchen-Naeherung immer zu einer staerkeren Lokalisierung der Zustaende an der Fermienergie und damit zu einer Verschlechterung des Transports im Vergleich zum nichtwechselwirkenden System fuehrt. Dieses Ergebnis laeszt sich auch gut physikalisch verstehen. Im zweiten Teil steht die Frage nach der Gueltigkeit der Hartree-Fock-Naeherung fuer das Quanten-Coulomb-Glas im Mittelpunkt. Dazu werden die Hartree-Fock-Resultate mit Ergebnissen aus der exakten Diagonalisierung sehr kleiner Gitter verglichen. Es werden Lokalisierungskriterien entwickelt, die einen direkten Vergleich mit den Einteilchenlokalisierungsmaszen gestatten. Zur Beurteilung der Transporteigenschaften dient der Gleichstromleitwert nach dem Kubo-Greenwood-Formalismus. Es zeigt sich, dasz die Hartree-Fock-Naeherung den Transport unterschaetzt und dasz die Wechselwirkung im Vergleich zum nichtwechselwirkenden System bei schwacher Unordnung eine Verringerung des Transports und bei groszer Unordnung eine Erhoehung des Transports bewirkt. In dritten Teil werden Idee und Realisierung einer neuen Naeherung, der Hartree-Fock-basierten Diagonalisierung, diskutiert. Ueberlegungen und Untersuchungen zur Konvergenz von Grundzustandsenergie, Energie der angeregten Zustaende, Einteilchenzustandsdichte, Rueckkehrwahrscheinlichkeit und Leitwert werden vorgenommen. Ergebnisse fuer zweidimensionale Systeme mit 12, 16 und 25 Gitterplaetzen bei Halbfuellung werden vorgestellt. Auszerdem erfolgen Untersuchungen mit verschiedenen Wechselwirkungsstarken fuer ein-, zwei und dreidimensionale Systeme mit 25*1, 5*5 und 3*3*3 Gitterplaetzen. Die Resultate aus dem zweiten Teil bestaetigen sich: Fuer genuegend starke Unordnung induziert Wechselwirkung immer eine staerkere Delokalisierung, fuer genuegend kleine Unordnung immer eine staerkere Lokalisierung. / This work investigates the physics of the disordered interacting electron problem on the isolating side of the metal-insulator-transition. A generalized Coulomb-Glass with transfermatrixelements between next neighbours - the Quantum-Coulomb-Glass - serves as model system. The goal is to find out how electron-electron interaction influences the localization and transport properties of the model. In the first part the Quantum-Coulomb-Glass is treated at Hartree-Fock level. Because this approximation is an effective one-particle theory localization and transport properties can be investigated with the same methods as in the Anderson-Model of localization. It ist found that interaction in the framework of an one-particle approximation always leads to an enhanced localization of the states near the Fermi-energy in comparison to the nonintercting system. This also can be well understood within different physically argumentations. The second part centers around the question how valid Hartree-Fock approximation is. Thus Hartree-Fock results are compared with results for exact diagonalization of small lattices. Criteria of localization are developed which allow a direct comparison to measures of single-particle localization. The transport-properties are measured by the zero frequency Kubo-conductance. It shows that Hartree-Fock approximation underestimates the transport and that interaction leads to a decrease of transport in the region of small disorder and to an increase for strong disorder. The third part discusses idea and realisation of a new approximation - the Hartree-Fock-based diagonalization. Aguments and investigations about convergence of ground-state-energy, excited-state-energy, single-particle density of states, return probability and conductance are shown. Results for systems in two dimensions with 12, 16 and 25 sites and half filling are presented. Additionally different interaction strenghts for one-, two- and three-dimensional systems with 25*1, 5*5 and 3*3*3 sites are investigated. The results from part two are hardened: Interaction always leads to enhanced delocalization if disorder is strong enough and always leads to enhanced localization if disorder is small enough.

Šiame baigiamajame magistro darbe nagrinėjamas alavo fosfido fotoelektroninis spektras. Tyrimo objektu pasirinktas Sn2P2S6 kristalas. Jis pasižymi pirmos rūšies faziniu virsmu. Kambario temperatūroje yra feroelektrikas, 360 K temperatūroje paraelektrikas. Darbe nagrinėjami kristalo fotoelektroninio spektro atlikto XPS metodu skitrumai po fazinio virsmo, bei atliktas lyginimas su teoriniu kristalo modeliu. Teorinis modelis remiasi Hartre-Foko-Rutano metodu. / In this graduating master`s work is researched photo electronis spectra of tin fosfydium crystal (Sn2P2S6). It is unique by ability to be feroelectric in ferophase (room temperature) and papaelectric in paraphase (360 K). In this work we are researching XPS differences of given crystal after the phasic transformation. Also we are comparing experimental XPS to theoretical crystal model, made by Hartree-Fock-Rutan method.

The Fast Multipole Method of Greengard and Rokhlin does the seemingly impossible: it approximates the quadratic scaling N-body problem in linear time. The key is to avoid explicitly computing the interactions between all pairs of N points. Instead, by organizing the data in a space-partitioning tree, distant interactions are quickly and efficiently approximated. Similarly, dual-tree algorithms, which approximate or eliminate parts of a computation using distance bounds, are the fastest algorithms for several fundamental problems in statistics and machine learning -- including all nearest neighbors, kernel density estimation, and Euclidean minimum spanning tree construction. We show that this overarching principle -- that by organizing points spatially, we can solve a seemingly quadratic problem in linear time -- can be generalized to problems involving interactions between sets of three or more points and can provide orders-of-magnitude speedups and guarantee runtimes that are asymptotically better than existing algorithms. We describe a family of algorithms, multi-tree algorithms, which can be viewed as generalizations of dual-tree algorithms. We support this thesis by developing and implementing multi-tree algorithms for two fundamental scientific applications: n-point correlation function estimation and Hartree-Fock theory. First, we demonstrate multi-tree algorithms for n-point correlation function estimation. The n-point correlation functions are a family of fundamental spatial statistics and are widely used for understanding large-scale astronomical surveys, characterizing the properties of new materials at the microscopic level, and for segmenting and processing images. We present three new algorithms which will reduce the dependence of the computation on the size of the data, increase the resolution in the result without additional time, and allow probabilistic estimates independent of the problem size through sampling. We provide both empirical evidence to support our claim of massive speedups and a theoretical analysis showing linear scaling in the fundamental computational task. We demonstrate the impact of a carefully optimized base case on this computation and describe our distributed, scalable, open-source implementation of our algorithms. Second, we explore multi-tree algorithms as a framework for understanding the bottleneck computation in Hartree-Fock theory, a fundamental model in computational chemistry. We analyze existing fast algorithms for this problem, and show how they fit in our multi-tree framework. We also show new multi-tree methods, demonstrate that they are competitive with existing methods, and provide the first rigorous guarantees for the runtimes of all of these methods. Our algorithms will appear as part of the PSI4 computational chemistry library.

Stuttgart, Univ., Diss., 2007.

MELO, Heitor Alves de. Propriedades eletrônicas de pontos quânticos contendo muitos elétrons. 2010. 75 f. : Dissertação (mestrado) - Universidade Federal do Ceará, Centro de Ciências, Departamento de Física, Fortaleza, 2010 . / Submitted by francisco lima (admir@ufc.br) on 2012-11-27T15:20:10Z No. of bitstreams: 1 2010_hadmelo.pdf: 2475149 bytes, checksum: f2b733568c55c95683fc14e493c5ab31 (MD5) / Approved for entry into archive by Nirlange Queiroz(nirlange@gmail.com) on 2015-09-18T12:10:21Z (GMT) No. of bitstreams: 1 2010_hadmelo.pdf: 2475149 bytes, checksum: f2b733568c55c95683fc14e493c5ab31 (MD5) / Made available in DSpace on 2015-09-18T12:10:21Z (GMT). No. of bitstreams: 1 2010_hadmelo.pdf: 2475149 bytes, checksum: f2b733568c55c95683fc14e493c5ab31 (MD5) / This work investigates the eletronic properties of semiconductor quantum dots in which there are many electrons con ned. In particular, we study Si and Ge quantum dots embedded in dielectric matrices (SiO2 e HfO2). The theoretical methos used to calculate the total energy of N electrons con ned in quantum dots is based on a simpli ed 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 ective mass in Ge, which raises the energies of the con ned states. As for the role of the dielectric matrix, the total energy is always larger for SiO2 than for HfO2. Physically, this e ect is caused by the fact that SiO2 has larger con nement barriers (3.2 eV) than HfO2 (1.5 eV). Smaller barriers favor larger spatial extent of the wavefunctions, decreasing the repulsion energy of the con ned electrons. The chemical potential and additional energy was also calculated as function of the number of con ned 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 enegy (of the order of 3=2kBT), this phenomena can only be observed for the case where there are only a few electrons con ned in the quantum dots. / Este trabalho dedica-se ao estudo das propriedades eletrônicas de pontos quânticos semicondutores contendo muitos el etrons con nados. Em particular, ser~ao investigados pontos quânticos de Si e Ge imersos em matrizes diel etricas (SiO2 e HfO2). O m etodo te orico utilizado para calcular a energia total de um sistema de N el etrons con nados baseia-se numa vers~ao simpli cada do m etodo de Hartree-Fock. Neste modelo a energia total e calculada a partir das fun ções de onda e estados de energia de uma unica part cula. Os resultados obtidos mostram que a energia total em pontos quânticos de Ge s~ao em geral maiores que em pontos quânticos de Si, independentemente do n umero de el etrons con nados. Isto acontece devido a massa efetiva menor dos el etrons no Ge que aumentam as energia de con namento. Em rela ção ao papel das barreiras diel etricas, a energia total e sempre maior nos casos em que o ponto quântico est a envolvido por SiO2. Fisicamente, isto se deve ao fato de que a barreira de con namento do SiO2 (3.2 eV) e 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 el etrons con nados. Calculouse tamb em o potencial quí mico dos pontos quânticos em fun ção do n umero de el etrons con nados, e a energia adicional necess aria para aprisionar mais um el etron nos pontos quânticos. Veri cou-se que o potencial qu mico dos pontos quânticos de Ge são sempre maiores que nos de Si, por em o potencial qu mico 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 e muito maior que a energia t ermica (da ordem de 3=2kBT), este fenômeno s o ser a observado quando houver poucos el etrons con nados nos pontos quânticos.

nÃo hà / Este trabalho dedica-se ao estudo das propriedades eletrÃnicas de pontos quÃnticos semicondutores contendo muitos elÃtrons confinados. Em particular, serÃo investigados semicondutores contendo muitos elÃtrons confinados. Em particular, serÃo investigados pontos quÃnticos de Si e Ge imersos em matrizes dielÃtricas (SiO2 e HfO2). O mÃtodo teÃrico utilizado para calcular a energia total de um sistema de N elÃtrons confinados baseia-se numa versÃo simplificada do mÃtodo de Hartree-Fock. Neste modelo a energia total e calculada a partir das funÃÃes de onda e estados de energia de uma Ãnica partÃcula Os resultados obtidos mostram que a energia total em pontos quÃnticos de Ge sÃo em geral maiores que em pontos quÃnticos de Si, independentemente do nÃmero de elÃtrons confinados. Isto acontece devido a massa efetiva menor dos elÃtrons no Ge que aumentam as energia de confinamento. Em relaÃÃo ao papel das barreiras dielÃtricas, a energia total à sempre maior nos casos em que o ponto quÃntico està envolvido por SiO2. Fisicamente, isto se deve ao fato de que a barreira de confinamento do SiO2 (3.2 eV) à maior que a do HfO2 (1.5 eV). Barreiras mais baixas favorecem o aumento da extensÃo espacial das funÃÃes de onda, reduzindo a repulsÃo coulombiana dos elÃtrons confinados. Calculou se tambÃm o potencial quÃmico dos pontos quÃnticos em funÃÃo do nÃmero de elÃtrons confinados, e a energia adicional necessÃria para aprisionar mais um elÃtron nos pontos quÃnticos. Verificou-se que o potencial quÃmico dos pontos quÃnticos de Ge sÃo sempre maiores que nos de Si, por em o potencial quÃmico para pontos quÃnticos envoltos em HfO2 sÃo sempre maiores que no caso do SiO2. Em relaÃÃo a energia adicional, observa-se que esta quantidade apresenta fortes oscilaÃÃes e que varia entre 0 e 0.4 eV para todos os casos estudados. Se levarmos em conta que o fenÃmeno conhecido como bloqueio de Coulomb acontece quando a energia adicional à muito maior que a energia tÃrmica (da ordem de 3=2kBT), este fenÃmeno sÃo serà observado quando houver poucos elÃtrons confinados nos pontos quÃnticos. / 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.