Dissertations / Theses on the topic 'Electronic Structure Calculations - Computational Methods'

Le problème de la métallisation de l'hydrogène, posé il y a près de 80 ans, a été désigné comme la troisième question ouverte en physique du XXIe siècle. En effet, en raison de sa légèreté et de sa réactivité, les informations expérimentales sur l'hydrogène à haute pression sont limitées et extrêmement difficiles à obtenir. Il est donc essentiel de mettre au point des méthodes précises pour guider les expériences. Dans cette thèse, nous nous concentrons sur l'étude de la structure électronique, y compris les phénomènes d'état excité, en utilisant les techniques de Monte Carlo quantique (QMC). En particulier, nous développons une nouvelle méthode de calcul pour le gap accompagnée d'un traitement précis de l'erreur induit par la taille finie de la cellule de simulation. Nous établissons un lien formel entre l'erreur de la taille finie et la constante diélectrique du matériau. Avant d'étudier l'hydrogène, la nouvelle méthode est testée sur du silicium cristallin et du carbone de diamant, pour lesquels des informations expérimentales sur l'écart sont disponibles. Nos résultats montrent que le biais dû à la supercellule de taille finie peut être corrigé, de sorte que des valeurs précises dans la limite thermodynamique peuvent être obtenues pour les petites supercellules sans avoir besoin d'une extrapolation numérique. Comme l'hydrogène est un matériau très léger, les effets quantiques nucléaires sont importants. Une description précise des effets nucléaires peut être réalisée par la méthode de Monte Carlo à ions et électrons couplés (CEIMC), une méthode de simulation des premiers principes basée sur le QMC. Nous utilisons les résultats de la méthode CEIMC pour discuter les effets quantiques et thermiques des nuclei sur des propriétés électroniques. Nous introduisons une méthode formelle de traitement du gap électronique et de la structure des bandes à température finie dans l'approximation adiabatique et discutons des approximations qui doivent être faites. Nous proposons également une nouvelle méthode pour calculer des propriétés optiques à basse température, qui constituera une amélioration par rapport à l'approximation semi-classique couramment utilisée. Enfin, nous appliquons tout le développement méthodologique de cette thèse pour étudier la métallisation de l'hydrogène solide et liquide. Nous constatons que pour l'hydrogène moléculaire dans sa structure cristalline parfaite, le gap QMC est en accord avec les calculs précédents de GW. Le traitement des effets quantiques nucléaires entraîne une forte réduction du gap (2 eV). Selon la structure, le gap indirect fondamental se ferme entre 380 et 530 GPa pour les cristaux idéaux et 330-380 GPa pour les cristaux quantiques, ce qui dépend moins de la symétrie cristalline. Au-delà de cette pression, le système entre dans une phase de mauvais métal où la densité des états au niveau de Fermi augmente avec la pression jusqu'à 450-500 GPa lorsque l'écart direct se ferme. Notre travail soutient en partie l'interprétation des récentes expériences sur l'hydrogène à haute pression. Nous explorons également la possibilité d'utiliser une représentation multidéterminante des états excités pour modéliser les excitations neutres et calculer la conductivité via la formule de Kubo. Nous avons appliqué cette méthodologie à l'hydrogène cristallin idéal et limité au niveau de Monte Carlo variationnel de la théorie. Pour l'hydrogène liquide, la principale conclusion est que la fermeture du gap est continue et coïncide avec la transition de dissociation moléculaire. Nous avons été en mesure d'étalonner les fonctions de la théorie fonctionnelle de la densité (DFT) en nous basant sur la densité QMC des états. En utilisant les valeurs propres des calculs Kohn-Sham corrigé par QMC pour calculer les propriétés optiques dans le cadre de la théorie de Kubo-Greenwood , nous avons constaté que l'absorption optique théorique calculée précédemment s'est déplacée vers des énergies plus faibles
The hydrogen metallization problem posed almost 80 years ago, was named as the third open question in physics of the XXI century. Indeed, due to its lightness and reactivity, experimental information on high pressure hydrogen is limited and extremely difficult to obtain. Therefore, the development of accurate methods to guide experiments is essential. In this thesis, we focus on studying the electronic structure, including excited state phenomena, using quantum Monte Carlo (QMC) techniques. In particular, we develop a new method of computing energy gaps accompanied by an accurate treatment of the finite simulation cell error. We formally relate finite size error to the dielectric constant of the material. Before studying hydrogen, the new method is tested on crystalline silicon and carbon diamond, systems for which experimental information on the gap is available. Although finite-size corrected gap values for carbon and silicon are larger than the experimental ones, our results demonstrate that the bias due to the finite size supercell can be corrected for, so precise values in the thermodynamic limit can be obtained for small supercells without need for numerical extrapolation. As hydrogen is a very light material, the nuclear quantum effects are important. An accurate capturing of nuclear effects can be done within the Coupled Electron Ion Monte Carlo (CEIMC) method, a QMC-based first-principles simulation method. We use the results of CEIMC to discuss the thermal renormalization of electronic properties. We introduce a formal way of treating the electronic gap and band structure at a finite temperature within the adiabatic approximation and discuss the approximations that have to be made. We propose as well a novel way of renormalizing the optical properties at low temperature, which will be an improvement upon the commonly used semiclassical approximation. Finally, we apply all the methodological development of this thesis to study the metallization of solid and liquid hydrogen. We find that for ideal crystalline molecular hydrogen the QMC gap is in agreement with previous GW calculations. Treating nuclear zero point effects cause a large reduction in the gap (2 eV). Determining the crystalline structure of solid hydrogen is still an open problem. Depending on the structure, the fundamental indirect gap closes between 380 and 530 GPa for ideal crystals and 330–380 GPa for quantum crystals, which depends less on the crystalline symmetry. Beyond this pressure, the system enters into a bad metal phase where the density of states at the Fermi level increases with pressure up to 450–500 GPa when the direct gap closes. Our work partially supports the interpretation of recent experiments in high pressure hydrogen. However, the scenario where solid hydrogen metallization is accompanied by the structural change, for example, a molecular dissociation, can not be disproved. We also explore the possibility to use a multideterminant representation of excited states to model neutral excitations and compute the conductivity via the Kubo formula. We applied this methodology to ideal crystalline hydrogen and limited to the variational Monte Carlo level of the theory. For liquid hydrogen, the main finding is that the gap closure is continuous and coincides with the molecular dissociation transition. We were able to benchmark density functional theory (DFT) functionals based on the QMC density of states. When using the QMC renormalized Kohn-Sham eigenvalues to compute optical properties within the Kubo-Greenwood theory, we found that previously calculated theoretical optical absorption has a shift towards lower energies

Computational chemistry has led to the greater understanding of the molecular world, from the interaction of molecules, to the composition of molecular species and materials. Of the families of computational chemistry approaches available, the main families of electronic structure methods that are capable of accurate and/or reliable predictions of energetic, structural, and spectroscopic properties are ab initio methods and density functional theory (DFT). The focus of this dissertation is to improve the accuracy of predictions and computational efficiency (with respect to memory, disk space, and computer processing time) of some computational chemistry methods, which, in turn, can extend the size of molecule that can be addressed, and, for other methods, DFT, in particular, gain greater insight into which DFT methods are more reliable than others. Much, though not all, of the focus of this dissertation is upon transition metal species – species for which much less method development has been targeted or insight about method performance has been well established. The ab initio approach that has been targeted in this work is the correlation consistent composite approach (ccCA), which has proven to be a robust, ab initio computational method for main group and first row transition metal-containing molecules yielding, on average, accurate thermodynamic properties, i.e., within 1 kcal/mol of experiment for main group species and within 3 kcal/mol of experiment for first row transition metal molecules. In order to make ccCA applicable to systems containing any element from the periodic table, development of the method for second row transition metals and heavier elements, including lower p-block (5p and 6p) elements was pursued. The resulting method, the relativistic pseudopotential variant of ccCA (rp-ccCA), and its application are detailed for second row transition metals and lower p-block elements. Because of the computational cost of ab initio methods, DFT is a popular choice for the study of transition metals. Despite this, the most reliable density functionals for the prediction of energetic properties (e.g. enthalpy of formation, ionization potential, electron affinity, dissociation energy) of transition metal species, have not been clearly identified. The examination of DFT performance for first and second row transition metal thermochemistry (i.e., enthalpies of formation) was conducted and density functionals for the study of these species were identified. And, finally, to address the accuracy of spectroscopic and energetic properties, improvements for a series of density functionals have been established. In both DFT and ab initio methods, the harmonic approximation is typically employed. This neglect of anharmonic effects, such as those related to vibrational properties (e.g. zero-point vibrational energies, thermal contributions to enthalpy and entropy) of molecules, generally results in computational predictions that are not in agreement with experiment. To correct for the neglect of anharmonicity, scale factors can be applied to these vibrational properties, resulting in better alignment with experimental observations. Scale factors for DFT in conjunction with both the correlation and polarization consistent basis sets have been developed in this work.

Developments are made on the quantum Monte Carlo methods towards increasing the precision and the stability of the non fixed-node projector calculations of fermions. In the first part of the developments, the wavefunction correction scheme, which was developed to increase the precision of the diusion Monte Carlo (DMC) method, is applied to non fixed-node DMC to increase the precision of such fermion calculations which do not have nodal error. The benchmark calculations indicate a significant decrease of statistical error due to the usage of the correction scheme in such non fixed-node calculations. The second part of the developments is about the modifications of the wavefunction correction scheme for having a stable non fixed-node DMC algorithm for fermions. The minus signed walkers of the non fixed-node calculations are avoided by these modifications in the developed stable algorithm. However, the accuracy of the method decreases, especially for larger systems, as a result of the discussed modifications to overcome the sign instability.

Nous présentons des études expérimentales et théoriques de disiliciures alcalino-terreux, le disilane (Si2H6) et du carbone à haute pression. Nous étudions les disiliciures et en particulier le cas d’une phase plane de BaSI2 qui a une structure hexagonale avec des liaisons sp3 entre les atomes de silicium. Cet environnement électronique conduit à un gaufrage de feuilles du silicium. Nous démontrons alors une amélioration de la température de transition supraconductrice de 6 à 8.9 K lorsque les couches de silicium s’aplanissent dans cette structure. Des calculs ab initio basés sur DFT ont guidé la recherche expérimentale et permettent d’expliquer comment les propriétés électroniques et des phonons sont fortement affectés par les fluctuations du flambage des plans de silicium. Nous avons aussi étudié les phases cristallines de disilane à très haute pression et une nouvelle phase métallique est proposé en utilisant les méthodes de prédiction de structure cristalline. Les températures de transition calculées donnant un supraconducteur autour de 20 K à 100 GPa. Ces valeurs sont significativement plus faibles comparées à celles avancées dans la littérature. Finalement, nous présentons des études de structures de carbone à haute pression à travers une recherche de structure systématique. Nous avons trouvé une nouvelle forme allotropique du carbone avec une symétrie Cmmm que nous appelons Z-carbone. Cette phase est prévue pour être plus stable que le graphite pour des pressions supérieures à 10 GPa. Des expériences et simulation de rayon-X et spectre Raman sugèrent l’existence de Z-carbone dans des micro-domaines de graphite sous pression
We present experimental and theoretical studies of sp3 materials, alkaline-earth-metal (AEM) disilicides, disilane (Si2H6) and carbon at high pressure. First, we study the AEM disilicides and in particular the case of a layered phase of BaSi2 which has an hexagonal structure with sp3 bonding of the silicon atoms. This electronic environment leads to a natural corrugated Si-sheets. Extensive ab initio calculations based on DFT guided the experimental research and permit explain how electronic and phonon properties are strongly affected by changes in the buckling of the silicon plans. We demonstrate experimentally and theoretically an enhancement of superconducting transition temperatures from 6 to 8.9 K when silicon planes flatten out in this structure. Second, we investigated the crystal phases of disilane at the megabar range of pressure. A novel metallic phase of disilane is proposed by using crystal structure prediction methods. The calculated transition temperatures yielding a superconducting Tc of around 20 K at 100 GPa and decreasing to 13 K at 220 GPa. These values are significantly smaller than previously predicted Tc’s and put serious drawbacks in the possibility of high-Tc superconductivity based on silicon-hydrogen systems. Third, we studied the sp3-carbon structures at high pressure through a systematic structure search. We found a new allotrope of carbon with Cmmm symmetry which we refer to as Z-carbon. This phase is predicted to be more stable than graphite for pressures above 10 GPa and is formed by sp3-bonds. Experimental and simulated XRD, Raman spectra suggest the existence of Z-carbon in micro-domains of graphite under pressure

First principles calculations can be a computationally intensive task when studying large systems. Linear-scaling methods must be employed to find the electronic structure of systems consisting of thousands of atoms and greater. The goal of this thesis is to combine the linear-scaling divide-and-conquer (D&C) method with the linear-scaling capabilities of the SIESTA (Spanish Initiative for Electronic Simulations with Thousands of Atoms) density functional theory (DFT) methodology and present this union as a viable approach to large-scale first principles calculations. In particular, the density matrix version of the D&C method is implemented into the SIESTA package. This implementation can accommodate high quality calculations consisting of atom numbers in the tens of thousands using moderate computing resources. Low quality calculations have been tested up to half million atoms using reasonably sized computing resources.The D&C method is extended to better handle atomic dynamics simulations. First, by alleviating issues caused by discontinuities in the potential energy surface, with the application of a switching function on the Hamiltonian and overlap matrices. This allows for a smooth potential energy surface to be generated. The switching function has the additional benefit of accelerating the self-consistent field (SCF) process. Secondly, the D&C frozen density matrix (FDM) is modified to allow for improved charge transfer between the active and constrained regions of the system. This modification is found to reduce both the number of SCF iterations required for self-consistency and the number of relaxation steps in a local geometry optimisation. The D&C paradigm is applied to the real-time approach of time-dependent density functional theory (TDDFT). The method is tested on a linear alkane molecule with varying levels of success.Divergences in the induced dipole moment occur when the external excitation field is aligned parallel to the axis of the molecule. The method succeeds in producing accurate dipole moments when the external field is aligned perpendicular to the molecule. Various techniques are tested to improve the proposed method. Finally, the performance and effectiveness of the current D&C implementation is evaluated by studying three current systems. The first two systems consist of two different DNA sequences and the last system is the large ZIF-100 zeolitic imidazolate framework (ZIF).

Quantum Monte Carlo (QMC) methods are a class of stochastic techniques that can be used to compute the properties of electronic systems accurately from first principles. This thesis is mainly concerned with the development of trial wave functions for QMC. An extension of the backflow transformation to inhomogeneous electronic systems is presented and applied to atoms, molecules and extended systems. The backflow transformation I have developed typically retrieves an additional 50% of the remaining correlation energy at the variational Monte Carlo level, and 30% at the diffusion Monte Carlo level; the number of parameters required to achieve a given fraction of the correlation energy does not appear to increase with system size. The expense incurred by the use of backflow transformations is investigated, and it is found to scale favourably with system size. Additionally, I propose a single wave function form for studying the electron-hole system which includes pairing effects and is capable of describing all of the relevant phases of this system. The effectiveness of this general wave function is demonstrated by applying it to a particular transition between two phases of the symmetric electron-hole bilayer, and it is found that using a single wave function form gives a more accurate physical description of the system than using a different wave function to describe each phase. Both of these developments are new, and they provide a powerful set of tools for designing accurate wave functions. Backflow transformations are particularly important for systems with repulsive interactions, while pairing wave functions are important for attractive interactions. It is possible to combine backflow and pairing to further increase the accuracy of the wave function. The wave function technology that I have developed should therefore be useful across a very wide range of problems.

La caractérisation complète d’intermédiaires réactionnels intervenants dans des procédés de catalyse homogène est une tâche ardue en raison de leur réactivité et de leur faible concentration. Ceci est particulièrement vrai pour les espèces radicalaires telles que les complexes organométalliques réduits, qui sont des intermédiaires en photocatalyse ou lorsque ces complexes possèdent des ligands non-innocents. Par conséquent, leur structure électronique est encore mal comprise, sachant que l'électron ajouté peut être situé sur différents sites de la molécule.Dans ce contexte, nous avons développé une méthode d'analyse pour étudier en phase gazeuse des complexes organométalliques radicalaires. Des complexes organométalliques multichargés du zinc et du ruthénium avec des ligands bidentes de type bipyridine ou tridente de type bis(imino)pyridine ont d’abord été obtenus et isolés en phase gazeuse. Ils sont ensuite réduits avec les méthodes d’activation par un électron spécifiques à la spectrométrie de masse, la dissociation par capture ou transfert d’électron (ECD/ETD), permettant de former des espèces métalliques radicalaires monochargées. Celles-ci sont enfin isolés et leur spectre infrarouge est obtenu à l’aide de la spectroscopie d’action basée sur la dissociation induite par l’absorption de plusieurs photons dans l’infrarouge (IRMPD). Les méthodes DFT fournissent un complément pour modéliser la structure électronique et le spectre IR de ces espèces.Les challenges à relever pour développer ce nouvel outil d'analyse étaient de deux ordres. Tout d'abord, nous devions être en mesure d'obtenir les complexes souhaités en phase gazeuse. Ceci nous a conduit à examiner de multiples paramètres, tels que la nature des ligands ou l’énergie interne déposée lors de l’étape de réduction. Le deuxième défi portait sur l'utilisation des méthodes de modélisation. Nous avons montré l’absence de fiabilité des méthodes standards de modélisation pour décrire à la fois la structure électronique et le spectre infrarouge des complexes réduits. Les données expérimentales obtenues durant ce travail ont donc été utilisées comme références pour identifier les fonctionnelles DFT les plus appropriées pour l’étude de ces complexes radicalaires
The complete characterization of reaction intermediates in homogeneous catalytic processes is often a difficult task owing to their reactivity and low concentration. This is particularly true for radical species such as reduced organometallic complexes, which are intermediates in photocatalysis, or when these complexes included non-innocent ligands. Consequently, their electronic structure in the ground state is still poorly understood, knowing that the added electron can be located on different sites of the molecule.In this contect, we developed an analytical method to study radical organometallic complexes in the gas phase. We started with formation of suitable multi-charged zinc organometallic complexes in the gas phase from mixture of zinc metal cation and bipyridine-type bidentate or bis(imino)pyridine tridentate ligands. Multicharged ruthenium complexes with similar ligands have also been studied. Under ideal circumstances these complexes were isolated and reduced in the gas phase to form monocationic metal species. Electron activated methods such as electron capture dissociation (ECD) and electron transferred dissociation (ETD) techniques, available in FT-ICR mass spectrometers, have been used to that end. The resulting Zn and Ru radical cation complexes are then isolated in the gas phase and probed via infrared multi photon dissociation (IRMPD) action spectroscopy. In support, DFT theoretical calculations were performed to model their electronic structure and IR spectra.Two main issues were faced during the development of this new analytical tool. First, we had to be able to obtain the desired complexes in the gas phase. This has lead to monitor various parameters, such as the nature of the ligands or the internal energy provided by the reduction step. The second challenge dealt with the use of modeling methods. We have shown that standard modelling tools lack the accuracy to predict both electronic structure and spectral signatures of reduced complexes. The experimental data gathered in this work have therefore been used as benchmarks for the identification of DFT functionals that are most appropriate for the study of these radical complexes

This dissertation covers a series of related topics in the mathematical modelling of mass spectrometry data. The dissertation opens with a presentation of an optimal algorithm for the generation of the fine isotopic structure. We further show the applications of that algorithm to the problem of deconvoluting mixed isotopic signals, in two different ways. We also approach the problem of estimating the deep parameters of mass detectors, estimating the parameters of a function that relates the instrument-generated intensities to the numbers of ions. These solutions are applied to the problem of understanding Electron Driven reactions, whose principal aim is to induce ion fragmentation and, in that way, enhance the instrument’s identification capabilities. Finally, we show how to apply the mathematical theory of reaction kinetics to estimate the reaction rates of the electron transfer reactions.
Niniejsza rozprawa doktorska dotyczy szeregu tematyk z zakresu matematycznego modelowanie widm masowych. W pracy przedstawiam algorytm służący obliczeniom związanym z rozkładami izotopowymi cząsteczek. Algorytm ów wykorzystuję w problemie dekonwolucji mieszanek sygnałów ze znanych źródeł molekularnych, na dwa różne sposoby. Przedstawiam również sposób na wyznaczenie zależności pomiędzy zarejestrowanym sygnałem a liczbą jonów dla różnych detektorów jonów. Powyższe rozwiązania zostają również wykorzystane w celu dokładniejszego zrozumienia za- sad działania fragmentacji jonów za pomocą transferu elektronu, która znacząco poszerza możliwości identyfikacji substancji. Pokazuję również sposób na wyestymowanie parametrów tych reakcji, wykorzystując w tym celu matematyczny model kinetyki reakcji.

We report a performance comparison of two linear-scaling methods which avoid the diagonalization bottleneck of traditional electronic structure algorithms. The Chebyshev expansion method (CEWI) is implemented for carbon tight-binding calculations of large systems and its memory and timing requirements compared to those of our previously implemented conjugate gradient density matrix search (CG-DMS). Benchmark calculations are carried out on icosahedral fullerenes from C60 to C8640 and the linear scaling memory and CPU requirements of CEM demonstrated. We show that the CPU requisites of CEM and CG-DMS are similar for calculations with comparable accuracy.

Computational approaches play an important role in today's materials science owing to the remarkable advances in modern supercomputing architecture and algorithms. Ab initio simulations solely based on a quantum description of matter are now very able to tackle materials problems in which the system contains up to a few thousands atoms. This dissertation aims to address the modern electronic structure calculation methods applied to a range of various materials such as liquid and amorphous phase materials, nanostructures, and small organic molecules. Our simulations were performed within the density functional theory framework, emphasizing the use of real-space ab initio pseudopotentials. On the first part of our study, we performed liquid and amorphous phase simulations by employing a molecular dynamics technique accelerated by a Chebyshev-subspace filtering algorithm. We applied this technique to find l- and a- SiO₂ structural properties that were in a good agreement with experiments. On the second part, we studied nanostructured semiconducting oxide materials, i.e., SnO₂ and TiO₂, focusing on the electronic structures and optical properties. Lastly, we developed an efficient simulation method for non-contact atomic force microscopy. This fast and simple method was found to be a very powerful tool for predicting AFM images for many surface and molecular systems.
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