abstract: In this dissertation two kinds of strongly interacting fermionic systems were studied: cold atomic gases and nucleon systems. In the first part I report T=0 diffusion Monte Carlo results for the ground-state and vortex excitation of unpolarized spin-1/2 fermions in a two-dimensional disk. I investigate how vortex core structure properties behave over the BEC-BCS crossover. The vortex excitation energy, density profiles, and vortex core properties related to the current are calculated. A density suppression at the vortex core on the BCS side of the crossover and a depleted core on the BEC limit is found. Size-effect dependencies in the disk geometry were carefully studied. In the second part of this dissertation I turn my attention to a very interesting problem in nuclear physics. In most simulations of nonrelativistic nuclear systems, the wave functions are found by solving the many-body Schrödinger equations, and they describe the quantum-mechanical amplitudes of the nucleonic degrees of freedom. In those simulations the pionic contributions are encoded in nuclear potentials and electroweak currents, and they determine the low-momentum behavior. By contrast, in this work I present a novel quantum Monte Carlo formalism in which both relativistic pions and nonrelativistic nucleons are explicitly included in the quantum-mechanical states of the system. I report the renormalization of the nucleon mass as a function of the momentum cutoff, an Euclidean time density correlation function that deals with the short-time nucleon diffusion, and the pion cloud density and momentum distributions. In the two nucleon sector the interaction of two static nucleons at large distances reduces to the one-pion exchange potential, and I fit the low-energy constants of the contact interactions to reproduce the binding energy of the deuteron and two neutrons in finite volumes. I conclude by showing that the method can be readily applied to light-nuclei. / Dissertation/Thesis / Doctoral Dissertation Physics 2018

Orientador: Rogerio Custodio / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Quimica / Made available in DSpace on 2018-08-14T02:16:55Z (GMT). No. of bitstreams: 1 Streit_Livia_M.pdf: 2107026 bytes, checksum: 23d8f89115d585808f6950c1959f329b (MD5) Previous issue date: 2009 / Resumo: Os métodos Monte Carlo Quântico (MCQ) são métodos estocásticos de resolução da equação de Schrödinger que vêm se mostrando como uma alternativa recente e promissora para o cálculo de propriedades eletrônicas. Dentre esses métodos, o Monte Carlo Quântico de Difusão (MCQD) é um dos mais utilizados e baseia-se na solução da equação de Schrödinger dependente do tempo através de um processo de difusão. Neste trabalho investigamos a aplicabilidade do método Monte Carlo Quântico de Difusão no cálculo de energias de ionização de valência e camada interna para moléculas simples, com o intuito de desenvolver uma metodologia simples e segura para a obtenção de valores precisos. Para tanto, foram estudadas as energias de ionização simples e duplas, além das energias de transição Auger das moléculas CH4, NH3, H2O e HF. Ainda, foram estudadas as energias de ionização simples das moléculas OH, NH, CH, BH, BeH e LiH. As energias de ionização foram calculadas por diferença de energia entre os sistemas neutro e ionizado. Estudos preliminares envolvendo as energias de ionização sucessivas dos átomos do He ao Ne também foram realizados, bem como estudos complementares das energias de ionização simples de moléculas mais complexas, CO, NO e H2CO. As principais avaliações do método para o cálculo de energias de ionização dizem respeito à função de onda, especialmente à inclusão de funções de correlação eletrônica explícita, e à escolha de funções de base simples. Os resultados obtidos podem ser considerados excelentes, visto que apresentam desvios em relação aos dados experimentais aceitáveis, menores que a incerteza experimental. Desvios absolutos médios de 0,05 a 0,5 eV foram obtidos para as ionizações sucessivas dos átomos, de 0,04 a 1,5 eV para as ionizações simples, e de 1,1 a 2,3 eV para duplas e de transição Auger. Na maioria dos casos os desvios são menores ou da mesma ordem que os apresentados por métodos de cálculo de estrutura eletrônica de alto nível. Os resultados obtidos neste trabalho são confiáveis e podem ser usados como uma ferramenta auxiliar e determinante na interpretação de espectros fotoeletrônicos, o que evidencia a eficiência do método Monte Carlo Quântico de Difusão no cálculo de energias de ionização para as moléculas estudadas. Assim, pode-se vislumbrar o uso do MCQD em sistemas mais complexos e a obtenção de excelentes resultados / Abstract: The Quantum Monte Carlo Methods (QMC) are stochastic methods that solve the Schrödinger equation and emerge as a recent and promising alternative for the calculation of electronic properties. The most common QMC method is the Diffusion Quantum Monte Carlo (DQMC) and is based on the solution of the time dependent Schrödinger equation by a diffusion process. In this work we investigate the applicability of DQMC to calculate inner and valence shells ionization energies in simple molecules seeking a simple and safe procedure where accurate results are obtained. For this purpose, we studied single and double ionization energies and also Auger transition energies for CH4, NH3, H2O and HF molecules. The single ionization energies for OH, NH, CH, BH, BeH and LiH molecules were also investigated. The ionization energies were calculated as the difference between the ionized species and the neutral one. Studies about successive ionization from He to Ne and about single ionization for more complex molecules CO, NO and H2CO were also carried out. The main goal is to investigate the application of DQMC method using simple guide wave functions and modest electronic correlation factor. The obtained results are in good agreement with the experimental spectra. The average absolute error with respect to the experimental data are admissible, lower than experimental uncertainty. Average absolute errors from 0.04 to 0.5 eV were obtained for successive ionization energies for atoms, 0.05 to 1.5 eV for single ionizations, and from 1.1 to 2.3 eV for double and Auger ionizations energies. In most of the cases, the deviations are lower than or have the same order of magnitude of the deviations presented by other compared methods. The obtained results are reliable and may be used as an auxiliary and reliable tool in photoelectron spectra elucidation. Therefore, even using simple guide wave functions and modest explicit electronic correlation function, the DQMC method revealed significant efficiency in the calculation of single, double and Auger ionization energies for simple molecules. The present applications suggest that DQMC may be an excellent alternative for the calculation of ionization energies for more complex systems / Mestrado / Físico-Química / Mestre em Química

Submitted by Cláudia Bueno (claudiamoura18@gmail.com) on 2015-11-19T20:36:26Z No. of bitstreams: 2 Dissetação_Victor Giovanni Pina de Mello: 821688 bytes, checksum: 4dc42f6aa6afe5f8bc23a472087baf41 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2015-11-20T12:53:16Z (GMT) No. of bitstreams: 2 Dissetação_Victor Giovanni Pina de Mello: 821688 bytes, checksum: 4dc42f6aa6afe5f8bc23a472087baf41 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Made available in DSpace on 2015-11-20T12:53:16Z (GMT). No. of bitstreams: 2 Dissetação_Victor Giovanni Pina de Mello: 821688 bytes, checksum: 4dc42f6aa6afe5f8bc23a472087baf41 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2015-07-24 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this dissertation, we use the information theory to obtain the correlation energy of small lithium clusters. Unlike conventional methods for calculation of the correlation energy, the method used here requires only a single calculation in a Hartree-Fock level. With this calculation we obtain a total information energy of the clusters, through the addition of information energy of each atom of the cluster. The correlation energy is a bilinear function of the information energy and number of electrons in the cluster. In order to obtain a general equation for the correlation energy, we use the correlation energy expression that has been obtained through the information theory to t the exact energy of the system using a Monte Carlo quantum simulation of clusters ranging from 1 to 8 lithium atoms. The e ciency of the general equation for the correlation energy has been veri ed through the calculation of the binding energy for clusters of up to 9 and 10 atoms which have not been used in the obtained t. The obtained values for the binding energies are in good agreement with the experimental measurements using photoelectron spectroscopy. / Nesta dissertação obtemos a energia de correlação de pequenos clusters formados por átomos de Lí tio via teoria da informa ção. Diferentemente dos m étodos usuais para o c álculo da energia de correlação, o m étodo aqui utilizado requer somente um c álculo no n ível Hartree-Fock. Deste c álculo se obt em a energia de informação do cluster atráv es da soma das energias de informação dos átomos individuais do cluster. A energia de correlação e uma função bilinear da energia de informa ção e do n úmero de el étrons no cluster. A m de obter uma expressão geral para a energia de correla ção dos clusters de L tio, n os ajustamos a expressão obtida com seus respectivos coe cientes a energia exata deste sistema, calculada usando a simula ção de Monte Carlo quântico para clusters variando de 1 a 8 atomos. A veri cação dessa expressão para a energia de correla ção foi avaliada para clusters maiores não usados no ajuste atrav es do c álculo da energia de liga ção (para cluster de 9 e 10 átomos), os resultados indicam valores em bom acordo com as medidas experimentais usando espectroscopia de fotoel etrons.

Submitted by Cláudia Bueno (claudiamoura18@gmail.com) on 2016-01-13T15:36:07Z No. of bitstreams: 2 Dissertação - Emanuel Melo Isaac Moreira - 2015.pdf: 656931 bytes, checksum: 8e949a592f6171db8c2e771edb7895e2 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2016-01-14T11:04:15Z (GMT) No. of bitstreams: 2 Dissertação - Emanuel Melo Isaac Moreira - 2015.pdf: 656931 bytes, checksum: 8e949a592f6171db8c2e771edb7895e2 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Made available in DSpace on 2016-01-14T11:04:15Z (GMT). No. of bitstreams: 2 Dissertação - Emanuel Melo Isaac Moreira - 2015.pdf: 656931 bytes, checksum: 8e949a592f6171db8c2e771edb7895e2 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2015-04-08 / Conselho Nacional de Pesquisa e Desenvolvimento Científico e Tecnológico - CNPq / In this work we used a combination of density functional theory and quantum Monte Carlo methods to study the effect of electron correlation on stability and aromaticity of anionic Boron clusters (B− 3 and B− 4 ). We found that, in general, the cyclic isomer is energetically more stable than its open linear counterpart. Based on principles of minimum energy and electrophilicity, and maximum hardness, diffusion Monte Carlo indicates that B− 3 cluster is aromatic, however, the results are not conclusive with respect to the B− 4 cluster. Calculations were also performed within the Hartree–Fock approximation. From the obtained results, we analysed the impact of the electron correlation effects in these clusters and found that the correlation of the electrons contributes significantly to the ionization potential and electron affinities varying between 31% and 66% of their total values. / Neste trabalho combinamos a teoria do funcional da densidade com o método de Monte Carlo quântico para estudar o efeito da correlação eletrônica na estabilidade e na aromaticidade de clusters de boro aniônicos (B− 3 e B− 4 ). Verificamos que, em geral, o isômero cíclico é energeticamente mais estável que sua respectiva estrutura linear. Com base no princípio da mínima energia e eletrofilicidade, e máxima dureza, o método Monte Carlo por difusão indicou que o cluster B− 3 é aromático, porém, os resultados para o cluster B− 4 ainda não são conclusivos. Realizamos também cálculos com a aproximação de Hartree-Fock. Dos resultados obtidos, analisamos o impacto do efeito da correlação nesses clusters e verificamos que a correlação dos elétrons contribuem significativamente para o potencial

L'objectif de ce travail de thèse est double : - Le développement et application de méthodes originales pour la chimie quantique ; - La mise au point de stratégies informatiques variées permettant la réalisation de simulations à grande échelle. Dans la première partie, les méthodes d'integration de configuration (IC) et monte carlo quantique (QMC) utilisées dans ce travail pour le calcul des propriétés quantiques sont présentées. Nous détaillerons en particulier la méthode d'\IC sélectionnée perturbativement (CISPI) que nous avons utilisée pour construire des fonctions d'onde d'essai pour le QMC. La première application concerne le calcul des énergies totales non-relativistes des atomes de transition de la série 3d ; ceci a nécessité l'implémentation de fonctions de base de type Slater et a permis d'obtenir les meilleures valeurs publiées à ce jour. La deuxième application concerne l'implémentation de pseudo-potentiels adaptés à notre approche QMC, avec pour application une étude concernant le calcul des énergies d'atomisation d'un ensemble de 55 molécules. La seconde partie traite des aspects calcule haute performance (HPC) avec pour objectif l'aide au déploiement des simulations à très grande échelle, aussi bien sous l'aspect informatique proprement dit - utilisation de paradigmes de programmation originaux, optimisation des processus monocœurs, calculs massivement parallèles sur grilles de calcul (supercalculateur et Cloud), outils d'aide au développement collaboratif \textit{et cætera} -, que sous l'aspect \emph{utilisateur} - installation, gestion des paramètres d'entrée et de sortie, interface graphique, interfaçage avec d'autres codes. L'implémentation de ces différents aspects dans nos codes-maison quantum pakcage et qmc=chem est également présentée. / This thesis work has two main objectives: 1. To develop and apply original electronic structure methods for quantum chemistry 2. To implement several computational strategies to achieve efficient large-scale computer simulations. In the first part, both the Configuration Interaction (CI) and the Quantum Monte Carlo (QMC) methods used in this work for calculating quantum properties are presented. We then describe more specifically the selected CI approach (so-called CIPSI approach, Configuration Interaction using a Perturbative Selection done Iteratively) that we used for building trial wavefunctions for QMC simulations. As a first application, we present the QMC calculation of the total non-relativistic energies of transition metal atoms of the 3d series. This work, which has required the implementation of Slater type basis functions in our codes, has led to the best values ever published for these atoms. We then present our original implementation of the pseudo-potentials for QMC and discuss the calculation of atomization energies for a benchmark set of 55 organic molecules. The second part is devoted to the Hight Performance Computing (HPC) aspects. The objective is to make possible and/or facilitate the deployment of very large-scale simulations. From the point of view of the developer it includes: The use of original programming paradigms, single-core optimization process, massively parallel calculations on grids (supercomputer and Cloud), development of collaborative tools , etc - and from the user's point of view: Improved code installation, management of the input/output parameters, GUI, interfacing with other codes, etc.

Full Configuration Interaction Quantum Monte–Carlo (FCIQMC) al- lows for exact results to be obtained for the ground state of a system within a finite-basis approximation of the Schrödinger equation. Work- ing within imposed symmetry constraints permits dramatic reductions in the size and internal connectivity of the Hilbert space considered, with associated reductions in the computational cost involved, as well as permitting exclusion of the natural ground state to extract a se- ries of excited states of the system. As all converged solutions are ˆ eigenfunctions of the square of the total spin operator, S 2 , as well as the Hamiltonian and the projected spin, imposing spin-purity as an additional ‘symmetry’ is a natural extension. In this thesis, the use of various spin-pure spaces is compared to the previously used determinental spaces. Variations on the FCIQMC al- gorithm which work in non-orthogonal (and non-normalised) basis sets, and with the arbitrary discretisation of imaginary time removed, are considered along with the implications of the differences to the normal FCIQMC algorithm.

Fermionic matter is ubiquitous in nature, from the electrons in metals and semiconductors or the neutrons in the inner crust of neutron stars, to gases of fermionic atoms, like 40K or 6Li that can be created and studied under laboratory conditions. It is especially interesting to study these systems at very low temperatures, where we enter the world of quantum mechanical phenomena. Due to the Fermi-Dirac statistics, a dilute system of spin-polarised fermions exhibits no interactions and can be viewed as an ideal Fermi gas. However, interactions play a crucial role for fermions of several spin species. This thesis addresses several questions concerning interacting Fermi gases, in particular the transition between the normal and the superfluid phase and dynamical properties at higher temperatures. First we will look at the unitary Fermi gas: a two-component system of fermions interacting with divergent scattering length. This system is particularly interesting as it exhibits universal behaviour. Due to the strong interactions perturbation theory is inapplicable and no exact theoretical description is available. I will describe the Determinant Diagrammatic Monte Carlo algorithm with which the unitary Fermi gas can be studied from first principles. This algorithm fails in the presence of a spin imbalance (unequal number of particles in the two components) due to a sign problem. I will show how to apply reweighting techniques to generalise the algorithm to the imbalanced case, and present results for the critical temperature and other thermodynamic observables at the critical point, namely the chemical potential, the energy per particle and the contact density. These are the first numerical results for the imbalanced unitary Fermi gas at finite temperature. I will also show how temperatures beyond the critical point can be accessed and present results for the equation of state and the temperature dependence of the contact density. At sufficiently high temperatures a semiclassical description captures all relevant physical features of the system. The dynamics of an interacting Fermi gas can then be studied via a numerical simulation of the Boltzmann equation. I will describe such a numerical setup and apply it to study the collision of two spin-polarised fermionic clouds. When the two components are separated in an elongated harmonic trap and then released, they collide and for sufficiently strong interactions can bounce off each other several times. I will discuss the different types of the qualitative behaviour, show how they can be interpreted in terms of the equilibrium properties of the system, and explain how they relate to the coupling between different excitation modes. I will also demonstrate how transport coefficients, for instance the spin drag, can be extracted from the numerical data.

abstract: Quantum Monte Carlo is one of the most accurate ab initio methods used to study nuclear physics. The accuracy and efficiency depend heavily on the trial wave function, especially in Auxiliary Field Diffusion Monte Carlo (AFDMC), where a simplified wave function is often used to allow calculations of larger systems. The simple wave functions used with AFDMC contain short range correlations that come from an expansion of the full correlations truncated to linear order. I have extended that expansion to quadratic order in the pair correlations. I have investigated this expansion by keeping the full set of quadratic correlations as well an expansion that keeps only independent pair quadratic correlations. To test these new wave functions I have calculated ground state energies of 4He, 16O, 40Ca and symmetric nuclear matter at saturation density ρ = 0.16 fm−3 with 28 particles in a periodic box. The ground state energies calculated with both wave functions decrease with respect to the simpler wave function with linear correlations only for all systems except 4He for both variational and AFDMC calculations. It was not expected that the ground state energy of 4He would decrease due to the simplicity of the alpha particle wave function. These correlations have also been applied to study alpha particle formation in neutron rich matter, with applications to neutron star crusts and neutron rich nuclei. I have been able to show that this method can be used to study small clusters as well as the effect of external nucleons on these clusters. / Dissertation/Thesis / Doctoral Dissertation Physics 2019

Computational methods for predicting the binding affinity of small organic molecules tobiological macromolecules cover a vast range of theoretical and physical complexity. Generally, as the required accuracy increases so does the computational cost, thereby making the user choose a method that suits their needs within the parameters of the project. We present how WScore, a rigid-receptor docking program normally consigned to structure-based hit discovery in drug design projects, is systematically ameliorated to perform accurately enough for lead optimization with a set of ROCK1 complexes and congeneric ligands from a structure-activity relationship study. Initial WScore results from the Schrödinger 2019-3 release show poor correlation (R² ∼0.0), large errors in predicted binding affinity (RMSE = 2.30 kcal/mol), and bad native pose prediction (two RMSD > 4Å) for the six ROCK1 crystal structures and associated active congeneric ligands. Improvements to WScore’s treatment of desolvation, myriad code fixes, and a simple ensemble consensus scoring protocol improved the correlation (R² = 0.613), the predicted affinity accuracy (RMSE = 1.34 kcal/mol), and native pose prediction (one RMSD > 1.5Å). Then we evaluate a physically and thermodynamically rigorous free energy perturbation (FEP) method, FEP+, against CryoEM structures of the Machilis hrabei olfactory receptor, MhOR5, and associated dose-response assays of a panel of small molecules with the wild-type and mutants. Augmented with an induced-fit docking method, IFD-MD, FEP+ performs well for ligand mutating relative binding FEP (RBFEP) calculations which correlate with experimental log(EC50)with an R² = 0.551. Ligand absolute binding FEP (ABFEP) on a set of disparate ligands from the MhOR5 panel has poor correlation (R² = 0.106) for ligands with log(EC50) within the assay range. But qualitative predictions correctly identify the ligands with the lowest potency. Protein mutation calculations have no log(EC50) correlation and consistently fail to predict the loss of potency for a majority of MhOR5 single point mutations. Prediction of ligand efficacy (the magnitude of receptor response) is also an unsolved problem as the canonical active and inactive conformations of the receptor are absent in the FEP simulations. We believe that structural insights of the mutants for both bound and unbound (apo) states are required to better understand the shortcomings of the current FEP+ methods for protein mutation RBFEP. Finally, improvements to GPU-accelerated linear algebra functions in an Auxiliary-Field Quantum Monte Carlo (AFQMC) program effect an average 50-fold reduction in GPU kernel compute time using optimized GPU library routines instead of custom made GPU kernels. Also MPI parallelization of the population control algorithm that destroys low-weight walkers has a bottleneck removed in large, multi-node AFQMC calculations.Computational methods for predicting the binding affinity of small organic molecules tobiological macromolecules cover a vast range of theoretical and physical complexity. Generally, as the required accuracy increases so does the computational cost, thereby making the user choose a method that suits their needs within the parameters of the project. We present how WScore, a rigid-receptor docking program normally consigned to structure-based hit discovery in drug design projects, is systematically ameliorated to perform accurately enough for lead optimization with a set of ROCK1 complexes and congeneric ligands from a structure-activity relationship study. Initial WScore results from the Schrödinger 2019-3 release show poor correlation (R² ∼0.0), large errors in predicted binding affinity (RMSE = 2.30 kcal/mol), and bad native pose prediction (two RMSD > 4Å) for the six ROCK1 crystal structures and associated active congeneric ligands. Improvements to WScore’s treatment of desolvation, myriad code fixes, and a simple ensemble consensus scoring protocol improved the correlation (R² = 0.613), the predicted affinity accuracy (RMSE = 1.34 kcal/mol), and native pose prediction (one RMSD > 1.5Å). Then we evaluate a physically and thermodynamically rigorous free energy perturbation (FEP) method, FEP+, against CryoEM structures of the Machilis hrabei olfactory receptor, MhOR5, and associated dose-response assays of a panel of small molecules with the wild-type and mutants. Augmented with an induced-fit docking method, IFD-MD, FEP+ performs well for ligand mutating relative binding FEP (RBFEP) calculations which correlate with experimental log(EC50)with an R² = 0.551. Ligand absolute binding FEP (ABFEP) on a set of disparate ligands from the MhOR5 panel has poor correlation (R² = 0.106) for ligands with log(EC50) within the assay range. But qualitative predictions correctly identify the ligands with the lowest potency. Protein mutation calculations have no log(EC50) correlation and consistently fail to predict the loss of potency for a majority of MhOR5 single point mutations. Prediction of ligand efficacy (the magnitude of receptor response) is also an unsolved problem as the canonical active and inactive conformations of the receptor are absent in the FEP simulations. We believe that structural insights of the mutants for both bound and unbound (apo) states are required to better understand the shortcomings of the current FEP+ methods for protein mutation RBFEP. Finally, improvements to GPU-accelerated linear algebra functions in an Auxiliary-Field Quantum Monte Carlo (AFQMC) program effect an average 50-fold reduction in GPU kernel compute time using optimized GPU library routines instead of custom made GPU kernels. Also MPI parallelization of the population control algorithm that destroys low-weight walkers has a bottleneck removed in large, multi-node AFQMC calculations.

No description available.