288 research outputs found

    Accurate variational electronic structure calculations with the density matrix renormalization group

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    During the past 15 years, the density matrix renormalization group (DMRG) has become increasingly important for ab initio quantum chemistry. The underlying matrix product state (MPS) ansatz is a low-rank decomposition of the full configuration interaction tensor. The virtual dimension of the MPS controls the size of the corner of the many-body Hilbert space that can be reached. Whereas the MPS ansatz will only yield an efficient description for noncritical one-dimensional systems, it can still be used as a variational ansatz for other finite-size systems. Rather large virtual dimensions are then required. The two most important aspects to reduce the corresponding computational cost are a proper choice and ordering of the active space orbitals, and the exploitation of the symmetry group of the Hamiltonian. By taking care of both aspects, DMRG becomes an efficient replacement for exact diagonalization in quantum chemistry. DMRG and Hartree-Fock theory have an analogous structure. The former can be interpreted as a self-consistent mean-field theory in the DMRG lattice sites, and the latter in the particles. It is possible to build upon this analogy to introduce post-DMRG methods. Based on an approximate MPS, these methods provide improved ans\"atze for the ground state, as well as for excitations. Exponentiation of the single-particle (single-site) excitations for a Slater determinant (an MPS with open boundary conditions) leads to the Thouless theorem for Hartree-Fock theory (DMRG), an explicit nonredundant parameterization of the entire manifold of Slater determinants (MPS wavefunctions). This gives rise to the configuration interaction expansion for DMRG. The Hubbard-Stratonovich transformation lies at the basis of auxiliary field quantum Monte Carlo for Slater determinants. An analogous transformation for spin-lattice Hamiltonians allows to formulate a promising variant for MPSs.Comment: PhD thesis (225 pages). PhD thesis, Ghent University (2014), ISBN 978946197194

    Accurate variational electronic structure calculations with the density matrix renormalization group

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    During the past fifteen years, the density matrix renormalization group (DMRG) has become increasingly important for ab initio quantum chemistry. Its underlying wavefunction ansatz, the matrix product state (MPS), is a low­-rank decomposition of the full configuration interaction tensor. The virtual dimension of the MPS, the rank of the decomposition, controls the size of the corner of the many­-body Hilbert space that can be reached with the ansatz. This parameter can be systematically increased until numerical convergence is reached. Whereas the MPS ansatz can only capture exponentially decaying correlation functions in the thermodynamic limit, and will therefore only yield an efficient description for noncritical one-dimensional systems, it can still be used as a variational ansatz for finite­-size systems. Rather large virtual dimensions are then required. The two most important aspects to reduce the corresponding computational cost are a proper choice and ordering of the active space orbitals, and the exploitation of the symmetry group of the Hamiltonian. By taking care of both aspects, DMRG becomes an efficient replacement for exact diagonalization in quantum chemistry. For hydrogen chains, accurate longitudinal static hyperpolarizabilities were obtained in the thermodynamic limit. In addition, the low-lying states of the carbon dimer were accurately resolved. DMRG and Hartree-­Fock theory have an analogous structure. The former can be interpreted as a self­-consistent mean­-field theory in the DMRG lattice sites, and the latter in the particles. It is possible to build upon this analogy to introduce post-­DMRG methods. Based on an approximate MPS, these methods provide improved ansätze for the ground state, as well as for excitations. Exponentiation of the single­-particle excitations for a Slater determinant leads to the Thouless theorem for Hartree-­Fock theory, an explicit nonredundant parameterization of the entire manifold of Slater determinants. For an MPS with open boundary conditions, exponentiation of the single-site excitations leads to the Thouless theorem for DMRG, an explicit nonredundant parameterization of the entire manifold of MPS wavefunctions. This gives rise to the configuration interaction expansion for DMRG. The Hubbard-­Stratonovich transformation lies at the basis of auxiliary field quantum Monte Carlo for Slater determinants. An analogous transformation for spin-­lattice Hamiltonians allows to formulate a promising variant for matrix product states

    Chemical applications of electron localization-delocalization matrices (LDMs) with an emphasis on predicting molecular properties

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    ix, 123 leaves : col. ill. ; 29 cmIncludes abstract and appendices.Includes bibliographical references.A matrix is constructed where the vertices (atoms) are connected by edges (bonds) resulting in a square matrix that is symmetrical. The localization index (unshared electrons) occupies the long diagonal where the delocalization index (shared electrons between two di erent atoms divided by 2) represent the o -diagonal elements. Such a matrix is called a localization-delocalization matrix or LDM. These matrices have shown promise as a novel Quantitative Structure Activity Relationship (QSAR) method via the Frobenius Distance, a method to compare matrices of similar sizes that returns a Euclidean distance. Some notable results that will be expanded upon are that for a series of 14 para-substituted benzoic acids for pKa prediction (r2 = 0.986), and a series of 13 polycyclic benzenoid hydrocarbons (PBH) separated by inner and outer rings (r2= 0.97). A program (AIMLDM) was developed in Python 3.4.1 to construct these matrices and perform the required calculations

    CP2K: An electronic structure and molecular dynamics software package - Quickstep: Efficient and accurate electronic structure calculations

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    CP2K is an open source electronic structure and molecular dynamics software package to perform atomistic simulations of solid-state, liquid, molecular, and biological systems. It is especially aimed at massively parallel and linear-scaling electronic structure methods and state-of-the-art ab initio molecular dynamics simulations. Excellent performance for electronic structure calculations is achieved using novel algorithms implemented for modern high-performance computing systems. This review revisits the main capabilities of CP2K to perform efficient and accurate electronic structure simulations. The emphasis is put on density functional theory and multiple post–Hartree–Fock methods using the Gaussian and plane wave approach and its augmented all-electron extension

    Computational studies on photophysical properties of molecular aggregates

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    179 p.The present project is devoted to analyze the electronic structure of the ground and excited electronic states and the associated optical properties of organic dyes and supramolecular assemblies of potential interest for optical applications. Following these points, the project has been classified in three interrelated research lines. First, we report a join experimental and computational investigation at the DFT level on monomers and covalently-linked dimers of borondifluoride complexes of curcuminoid derivatives, a prototype example of conjugated organic dyes. The nature of the electronic states was analyzed by employing an effective approach based on the development of the electronic wave functions in terms of diabatic basis states. A similar approach was used in a second study for rationalizing the absorption and fluorescence emission properties of conjugated dyes composed of dimethylamino flavylium heterocycles linked by a polymethine chain, which were recently reported to act as efficient shortwave infrared emitters. Finally, a third study focused on the development of a new theoretical approach allowing the precise characterization of electronic excited states resulting from the interaction between chromophoric units in model molecular aggregates. Theoretical descriptions of such systems are usually achieved by means of excitonic models, using effective Hamiltonians built on a basis of diabatic states that enable physical interpretations in terms of local excitations, charge transfer, or multiexcitonic configurations. The alternative approach that has been developed is based on a diabatization scheme, which allows the decomposition of the adiabatic excited state energies of molecular aggregates into contributions issued from intermolecular couplings, without requiring any a priori definition of diabatic states. This methodology constitutes a promising tool to extract accurate ab initio diabatic state energies and interstate couplings for eventual derivation of model excitonic Hamiltonians

    Development of Quantum-Crystallographic Methods for Chemical and Biochemical Applications

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    The field of crystallography is a key branch of natural sciences, important not only for physics, geology, biology or chemistry, but it also provides crucial information for life sciences and materials science. It laid the foundations of our textbook knowledge of matter in general. In this thesis, the field of quantum crystallography – a synergistic approach of crystallography and quantum mechanics – is used as a tool to predict and understand processes of molecules and their interactions. New methods are proposed and used that provide deeper insight into the influence of local molecular environments on molecules and allows advanced predictions of the biochemical effect of drugs. Ultimately, this means that we can now understand interactions between molecules in crystal structures more completely that were long thought to be fully characterized. As part of this work, new software was developed to handle theoretical simulations as well as experimental data – and also both of them together at the same time. The introduction of non-spherical refinements in standard software for crystallography opens the field of quantum crystallography to a wide audience and will hopefully strengthen the mutual ground between experimentalists and theoreticians. Specifically, we created a new native interface between Olex2 and non-spherical refinement techniques, which we called NoSpherA2. This interface has been designed in such a way that it can be used for any kind of non-spherical atom descriptions. This will allow refinement of modern diffraction data employing modern quantum crystallographic models, leaving behind the century old Independent Atom Model (IAM). New software was also developed to provide novel models and descriptors for understanding environmental effects on the electron density and electrostatic potential of a molecule. This so-called Quantum Crystallographic Toolbox (QCrT) provides a framework for the fast and easy implementation of various methods and descriptors. File conversion tools allow the interfacing with many existing software packages and might provide useful information for future method development, experimental setups and data evaluation, as well as chemical insight into intra- and intermolecular interactions. It is fully parallelized and portable to graphic card processors (GPUs), which provide extraordinary amounts of computational power with moderate resource requirements. Especially in the context of ultra-bright X-ray sources like X-ray free electron lasers and electron diffraction these new models become crucial to have a better description of experimental findings. In applying this new framework of quantum crystallographic methods, we analyze a type of bonding at the edge of conventional organic chemistry: The push-pull systems of ethylenes. We show how X-ray constrained bonding analysis leads to the unambiguous determination of the behavior and type of bonding present in a series of compounds which are contradicting the Lewis-picture of a double-bond. This new understanding has led to the development of a new potential drug, namely a silicon analogue of ibuprofen; one of the most important drugs known to humankind. We determined its physical properties, investigated its stability and potency as a more soluble and novel alternative of ibuprofen: While retaining the same pharmaceutical activity of ibuprofen, making it a bioisoster for ibuprofen, this material shows a better applicability in aqueous media

    Theoretical Investigations on the Electrochemical Fluorination Reaction in the Simons Process

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    Perfluorinated compounds are found in a wide array of technical applications associated with modern society. For instance, perfluorinated compounds are used as various surfactants, or as cooling agents in the production of electronics. The Simons process is applied in industry for the synthesis of such compounds. The experimental setup consists of a Ni anode, a cathode (often Ni or Fe) and anhydrous hydrogen fluoride (HF) as fluorine source and solvent, in which organic substrates are dissolved. A cell potential of around 4.5-6.0 V is applied, which drives the fluorination reaction. Despite the prevalence in industrial applications, the chemical mechanism of the Simons process has still not been fully understood. There is evidence that the electrochemistry only involves the oxidation of the Ni anode and subsequent binding of fluoride ions from the solvent, leading to a reactive nickel fluoride film (NixFy) forming at the anode. The film is of unknown structure and chemical composition, although it is believed to include highly oxidized Ni3+ or Ni4+ centers. In this thesis, the structure and formation of the NixFy film is considered. Using a model system involving Ni(111) surfaces and layers of explicit solvent molecules, results from DFT calculations indicate that a metallic Ni anode is easily oxidized at very low cell potentials. Furthermore, the work contains studies on the interface of a Ni(111) surface and a single HF molecule, in order to gain knowledge of the adsorption mechanism of the molecule in a non-electrochemical environment. A good starting point for models of NixFy films are the already known binary nickel fluorides. Particularly NiF3 is of interest because of its strongly oxidizing properties and proposed role in the Simons process. The series of magnetic 3d metal trifluorides from TiF3 to NiF3 is considered with hybrid DFT and DFT+U methods. NiF3 is characterized as an antiferromagnetic wide-bandgap (3.3 eV) semiconductor. Hence, the compound is expected to be less electrically insulating than the Mott-Hubbard insulator NiF2 (bandgap 5 eV). Anodes are typically passivized at cell potentials below ca. 3 V, due to the formation of an insulating NiF2 film. In this thesis, the anode is structurally modeled as different NiF2 surfaces. Using hybrid DFT calculations and thermodynamical considerations for the cell potential, the oxidation of surface Ni2+ to Ni3+ is calculated to proceed at potentials around 3.1 V, which is in good agreement with oxidation features in cyclic voltammetry experiments.Perfluorinierte Verbindungen kommen in vielen technischen Anwendungen vor, die mit unserer modernen Gesellschaft verbunden sind. Perfluorinierte Verbindungen werden zum Beispiel als Tenside verwendet, oder als Kühlmittel, die bei der Herstellung elektronischer Geräte notwendig sind. Der Simons-Prozess wird häufig in der Industrie benutzt, um solche Verbindungen zu synthetisieren. Die experimentelle Einrichtung besteht aus einer Ni-Anode, einer Kathode (typisch Ni oder Fe) und wasserfreiem Fluorwasserstoff (HF), der als Fluor-Quelle und Lösungsmittel dient, in das die organischen Reaktanten aufgelöst werden. Es wird eine Zellspannung von 4.5-6.0 V benutzt, um die Fluorierungsreaktion voranzutreiben. Trotz der Vielfalt an industriellen Anwendungen, ist der chemische Mechanismus des Simons-Prozesses nicht komplett aufgeklärt worden. Es ist bereits literaturbekannt, dass die elektrochemischen Schritte die Oxidation der Ni-Anode betreffen, mit folgendem Binden von Fluorid-Ionen aus dem Lösungsmittel, so dass ein reaktiver Nickel-Fluorid-Oberflächenfilm (NixFy) an der Anode gebildet wird. Die Struktur und chemische Zusammensetzung des Filmes sind immer noch unbekannt, obwohl hoch-oxidierte Ni3+- oder Ni4+-Stellen als mögliche Komponente des Filmes vorgeschlagen worden sind. Diese Dissertation behandelt die Struktur und Entstehungsmechanismen des NixFy-Films. Mittels eines Grenzflächenmodells bestehend aus Ni(111)-Oberflächen und Schichten explizierter Lösungsmittelmoleküle, wird durch DFT-Berechnungen indiziert, dass eine metallische Ni-Anode einfach oxidiert wird, auch bei sehr kleinen Zellspannungen. Auÿerdem wird das Gränzflächensystem einer Ni(111)-Oberfläche und eines einzelnen HF-Moleküls untersucht, um Einsichten zu erhalten, über den Adsorptionsmechanismus des Moleküls in einer nicht-elektrochemischen Umgebung. Ein guter Ansatzpunkt für NixFy-Modelle sind die schon bekannten binären Nickelfluoride. Besonders interessant ist NiF3, wegen seiner stark oxidierenden Eigenschaften und vorgeschlagenen Rolle im Simons-Prozess. Die Serie der magnetischen 3d-Übergangsmetalltrifluoride wird mit hybrid-DFT und DFT+U Methoden untersucht. NiF3 lässt sich als antiferromagnetischer Halbleiter mit einem breiten Bandabstand (3.3 eV) charakterisieren. Deswegen wird erwartet, dass NiF3 weniger elektrisch isolierend wirkt, im Vergleich zu dem Mott-Hubbard-Isolator NiF2 (Bandlücke 5 eV). Anoden werden typischerweise passiviert im Zellspannungsbereich bis zu etwa 3 V, wegen eines entstehenden isolierenden NiF2-Films. In dieser Dissertation wird die Anodenstruktur als verschiedene NiF2-Oberflächen dargestellt. Durch hybrid-DFT-Berechnungen und thermodynamische Modelle für die Zellspannung, wird berechnet, dass die Oxidation von Ni2+ an der Oberfläche zu Ni3+ bei der Zellspannung 3.1 V stattfindet, was gut mit Cyclovoltammetrieversuchen übereinstimmt

    A quantum crystallographic approach to study properties of molecules in crystals

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    In this dissertation, the behaviour of atoms, bonds, functional groups and molecules in vacuo but especially also in the crystal is studied using quantum crystallographic methods. The goal is to deepen the understanding of the properties of these building blocks as well as of the interactions among them, because good comprehension of the microscopic units and their interplay also enables us to explain the macroscopic properties of crystals. The first part (chapters 1-3) and second part (chapter 4) of this dissertation contain theoretical introductions about quantum crystallography. On the one hand, this expression contains the termquantum referring to quantumchemistry. Therefore, the very first chapter gives a brief overview about this field. The second chapter addresses different options to partition quantum chemical entities, such as the electron density or the bonding energy, into their components. On the other hand, quantumcrystallography consists obviously of the crystallographic part and chapter 3 covers these aspects focusing predominantly on X-ray diffraction. A more detailed introduction to quantum crystallography itself is presented in the second part (chapter 4). The third part (chapters 5-9) starts with an overview of the goals of this work followed by the results organized in four chapters. The goal is to deepen the understanding of properties of crystals by theoretically analysing their building block. It is for example studied how electrons and orbitals rearrange due to the electric field in a crystal or how high pressure leads to the formation of new bonds. Ultimately, these findings shall help to rationally design materials with desired properties such as high refractive index or semiconductivity.Mithilfe quantenkristallografischer Methoden werden Atome, Bindungen, funktionellen Gruppen und Moleküle in vacuo aber vor allem auch in Kristallen untersucht. Das Ziel ist es die Eigenschaften dieser Bestandteile zu verstehen und wie sie miteinander interagieren. Das Verständnis der Verhaltensweise der einzelnen Bausteine sowie deren Zusammenspiel auf mikroskopischer Ebene kann auch die makroskopischen Eigenschaften von Kristallen erklären. Der erste Teil dieser Doktorarbeit (Kapitel 1-3) beinhaltet eine theoretische Einleitung in die verschiedenen Bereiche der Quantenkristallografie. Wie der Name Quantenkristallografie besagt, besteht diese zum einen aus dem quantenchemischen Teil, weswegen das erste Kapitel eine kurze Einführung in die Quantenchemie gibt. Das zweite Kapitel widmet sich den verschiedenen Möglichkeiten quantenchemische Grössen wie zum Beispiel die Elektronendichte oder Bindungsenergien in Einzelteile zu zerlegen. Zum anderen trägt der kristallografische Teil zur Quantenkristallografie bei. Kapitel drei besteht daher aus einem kurzen Überblick über die Kristallografie mit Fokus auf der Röntgenbeugung. Anschliessend folgt im zweiten Teil (Kapitel 4) eine ausführlichere Einleitung in die Quantenkristallografie selbst. Der dritte Teil (Kapitel 5-9) beginnt mit einer kurzen Übersicht über die Ziele dieser Arbeit worauf die Resultate, gegliedert in vier verschiedene Kapitel, folgen. Das Ziel dieser Arbeit ist es die Eigenschaften von Kristallen besser zu verstehen, indem man ihre Einzelteile theoretisch analysiert und mit verschiedenen Methoden rationalisiert. Beispielsweise wird untersucht wie sich Elektronen und Orbitale aufgrund des elektrischen Feldes in Kristallen neu anordnen oder wie unter hohem Druck Bindungen neu geformt werden. Schlussendlich können all diese Erkenntnisse helfen, Materialien mit spezifischen gewünschten Eigenschaften herzustellen.Les atomes, les liaisons entre eux, les groupes fonctionnels et les molécules sont examinés en utilisant des méthodes de la cristallographie quantique. Le but est de comprendre les propriétés de ces composants et comment ils interagissent in vacuo mais surtout aussi dans les cristaux. En comprenant leurs caractéristiques et interactions au niveau microscopique, on peut aussi rationaliser les propriétés macroscopiques des cristaux. La première partie (chapitres 1-3) de cette thèse de doctorat contient une introduction brève à la cristallographie quantique. Comme le noml’indique, ce domaine de recherche est composé de la chimie quantique et la cristallographie. Pour cette raison le premier chapitre donne une introduction à la chimie quantique. Le deuxième chapitre présente quelques méthodes de décomposition des quantités de la chimie quantique comme la densité électronique ou l’énergie de liaison. Le troisième chapitre couvre la partie cristallographique. Ensuite dans la deuxième partie (chapitre 4) une introduction plus détaillée sur la cristallographie quantique elle-même est donnée. La troisième partie (chapitres 5-9) commence par un aperçu des objectives de cette dissertation suivis des résultats structurés en quatre chapitres. Le but est de comprendre les propriétés des cristaux en analysant leurs building blocks avec différentes méthodes théoriques. Il était par example examiné comment les électrons et les orbitales se réorganisent dans un cristal à cause du champ électrique ou comment des nouvelles liaisons sont formées sous pression. Finalement on peut utiliser ces conclusions pour modeler des matériaux avec des propriétés désirées
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