The aim of this thesis was to find anomalies of elastic properties induced by topological changes of the Fermi surface. The latter are called "Lifshitz transitions". Lifshitz transitions are an interesting subject to study because a topological change of the Fermi surface results in a van Hove singularity of the density of states at the Fermi energy, which again induces an anomaly in the free energy and therefore yield anomalies of observable physical quantities. In all cases the question arose, if the corresponding van Hove singularities are large enough to cause anomalies in the elastic properties, which are measurable by nowadays experimental techniques and computable within the accuracy reachable in nowadays computer calculations. The calculations have been done with the Full-Potential nonorthogonal Local-Orbital minimum-basis band-structure code FPLO. To shift the van Hove singularities through the Fermi energy we used hydrostatic pressure, which is mimicked in the computations by decreasing the volume of the unit cell. The materials under consideration had been YCo5 and LaCo5 as examples for magnetic compounds and the element Osmium as an example for a non-magnetic material. All these materials exhibit hexagonal symmetry. In the case of YCo5 our calculations yield a first order Lifshitz transition. Here, an extraordinarily large peak in the spin-up part of the DOS, which is caused by a nearly dispersionless band in the hexagonal plane, crosses the Fermi level under a pressure of about 21 GPa. Thus, the spin-up 3d states become partly depopulated, which results in a drop of the total magnetic moment of 35%. Therefore the transition can be regarded as a transition from strong to weak ferromagnetism. Further, the transition results in a volume collapse of 1.4%. Though the volume collapse is isomorphic, it exhibits the following anisotropy: while the lattice constant in the hexagonal plane is almost smoothly contracting with increasing pressure, the lattice constant in c-direction collapses at the transition-pressure. This volume collapse has been verified in experiment. Analogous calculations have been performed for the compound LaCo5, which is isoelectronic to YCo5. Here as well we predict a first order Lifshitz transition, taking place at a pressure of about 23 GPa. The mechanism of the transition is the same than in YCo5. Again we find a volume collapse under pressure together with a decrease of the magnetic moment. The relative volume change amounts to 1.3%. Like in YCo5, the unit cell dimensions in the hexagonal plane are decreasing almost smoothly with pressure while in c-direction the lattice constant collapses at the transition-pressure. For LaCo5 there are no such experiments done so far to the best of our knowledge. For Osmium we found, that LDA reproduces the ground state volume very well. Furthermore, we could detect three Lifshitz transitions taking place at very high pressures of about 72 GPa, 81 GPa, and 122 GPa. At first, a hole ellipsoid appears at the Gamma-point (V=24.6Å^3, P=72 GPa), then a neck is created at the symmetry-line LH (V=24.2Å^3, P=81 GPa), and finally a hole ellipsoid appears at the L-point (V=23.2 Å^3, P=122 GPa). Due to a degeneracy in the band structure, the hole ellipsoid at the L-point appears at the same pressure when the necks, situated at the symmetry-lines LH merge at L. The corresponding van Hove singularities in the DOS are very tiny and thus no anomalies in the elastic properties could be detected. Furthermore, we showed that the kink in c/a at 25 GPa and at 27 GPa found by Occelli et al. [Occelli et al., Phys. Rev. Lett. 93, 095502 (2004)] and Ma et al. [Ma et al., Phys. Rev. B 72, 174103 (2005)], respectively, is not statistically significant and that (c/a)(P) can be fitted equally well by a smooth function as by piece-wise linear functions as proposed in these references. / Das Ziel dieser Arbeit war es, Anomalien in den elastischen Eigenschaften zu finden, die durch topologische Änderungen der Fermifläche - genannt "Lifschitz Übergänge" - hervorgerufen werden. Lifschitz Übergänge sind ein interessantes Forschungsgebiet, denn die topologische Änderung der Fermifläche führt zu einer van Hove Singularität in der Zustandsdichte, die an der Fermienergie liegt und eine Anomalie in der freien Energie hervorruft und deswegen zu Anomalien in beobachtbaren physikalischen Größen führt. In allen Fällen kam die Frage auf, ob die entsprechenden van Hove Singularitäten groß genug sind, um mit heutigen Methoden meßbare und berechenbare Anomalien in den elastischen Eigenschaften zu verursachen. Die Daten wurden mit dem Computerprogramm FPLO (Full-Potential nonorthogonal Local-Orbital minimum-basis band-structure scheme) berechnet. Um die van Hove Singularitäten durch die Fermienergie zu schieben, verkleinerten wir das Volumen der Einheitszelle, um hydrostatischen Druck zu simulieren. Als zu untersuchende Stoffe wurden YCo5 und LaCo5 als Beispiele für magnetische Verbindungen gewählt und Osmium als Beispiel für ein nicht magnetisches Element. Im Falle von YCo5 fanden wir einen Lifschitz Übergang erster Ordnung. Hier springt ein besonders großer Peak im Spin-auf Teil der Zustandsdichte unter einem Druck von ca. 21 GPa über die Fermienergie. Dadurch werden die Spin-auf 3d Zustände teilweise unbesetzt und das magnetische Moment verringert sich um 35%. Deswegen kann man den Übergang als einen Übergang von starkem Ferromagnetismus zu schwachem Ferromagnetismus bezeichnen. Das Volumen verkleinert sich hierbei um 1.4%. Obwohl dieser Volumenkollaps isomorph ist, zeigt er folgende Anisotropie: während die Gitterkonstante in der hexagonalen Ebene mit zunehmendem Druck mehr oder weniger glatt kontrahiert, kollabiert am Übergangsdruck die Gitterkonstante in c-Richtung. Dieser Volumenkollaps wurde vom Experiment verifiziert. Analoge Rechnungen wurden für die Verbindung LaCo5, die isoelektronisch zu YCo5 ist, durchgeführt. Auch hier sagen wir einen Lifschitz Übergang erster Ordnung voraus, der bei einem Druck von ca. 23 GPa stattfinden wird. Der Mechanismus dieses Übergangs ist der selbe wie in YCo5. Wiederum finden wir einen Volumenkollaps unter Druck zusammen mit einer Verringerung des magnetischen Moments. Die relative Volumenänderung beträgt hier 1.3%. Wie in YCo5 verläuft hier die Kontraktion der Gitterkonstante in der hexagonalen Ebene mehr oder weniger glatt, während die Gitterkonstante in c-Richtung am Übergang kollabiert. Für LaCo5 existieren unseres Wissens hierzu noch keine Experimente. Im Falle von Osmium fanden wir drei Lifschitz Übergänge bei sehr hohen Drücken von ca. 72 GPa, 81 GPa, und 122 GPa. Zuerst bildet sich ein Lochellipsoid am Gamma-Punkt (V=24.6Å^3, P=72 GPa), dann bildet sich ein Hals an der Symmetrielinie LH (V=24.2Å^3, P=81 GPa), und zum Schluß erscheint ein Lochellipsoid am L-Punkt (V=23.2 Å^3, P=122 GPa). Auf Grund einer Entartung in der Bandstruktur taucht das Lochellipsoid am L-Punkt an dem Druck auf, an dem sich auch die Hälse auf der Symmetrielinie LH bei L verbinden. Die entsprechenden van Hove Singularitäten in der Zustandsdichte sind jedoch extrem klein und deswegen können keine Anomalien in den elastischen Eigenschaften detektiert werden. Desweiteren zeigten wir, daß der Knick in c/a, den Occelli et al. [Occelli et al., Phys. Rev. Lett. 93, 095502 (2004)] bei 25 GPa und Ma et al. [Ma et al., Phys. Rev. B 72, 174103 (2005)] bei 27 GPa fanden, statistisch nicht relevant ist und daß (c/a)(P) genauso gut von einer glatten Funktion gefittet wird als von stückweise linearen Funktionen.

Measurements of iron at extreme pressures do not agree on the melting temperature for conditions comparable with those believed to hold at Earth's core. To attempt to determine the stability of relevant lattices, simulations involving a huge amount of particles are needed. In this thesis, a machine learned model is trained to yield results from density functional theory. Different machine learning models are compared. The trained model is then used in molecular dynamics simulations of relevant lattices at a scale too large for density functional theory. / Mätningar av järns smälttemperatur under påfrestningar jämförbara med desom tros gälla i jordens kärna överensstämmer ej. För att försöka bestämma stabiliteten av relevanta gitter krävs simulationer av enorma mängder partiklar. I denna tes tränas en maskininlärd modell att återge resultat från Täthetsfunktionalteori. Olika maskininlärningsmodeller jämförs. Den tränade modellen används sedan i Molekyldynamik-simulationer av relevanta gitter som är förstora för Täthetsfunktionalteori.

Title: Structure and dynamics of electronic defects in liquid water Author: Ondřej Maršálek Institute: Institute of Organic Chemistry and Biochemistry, Academy of Sciences of the Czech Republic Supervisor: prof. Mgr. Pavel Jungwirth, DSc. Supervisor's e-mail address: pavel.jungwirth@uochb.cas.cz Abstract: In this thesis we present ab inito molecular dynamics simulations of two different electronic defects in water. Photoionization of liquid water produces a cationic hole, which undergoes ultrafast dynamics and forms the hydrated proton and the hydroxyl radical as its products. We study both the dynamics and spectroscopy of this process. The hydrated electron is a key intermediate in radiation chemistry of aqueous systems. We simulate its equilibrium properties in anionic water clusters as well as the dynamics of vertical electron attachment to cold and warm clusters. The hydrated electron reacts with a hydrated proton to form a hydrogen atom. We examine this reaction at a finite temperature in a larger cluster as well as in more detail in a smaller cluster. Because both of the electronic defects studied here are challenging open-shell species, we put emphasis on benchmarking and testing our computational setup. Six published articles are attached to the thesis. Keywords: density functional theory,...

Materials play an important role in society. Historically, and even at present, materials have been discovered by trial and error, and many of the most useful materials have been discovered by chance. The high-throughput approach aims to remove (as much as possible) chance and guesswork at the experimental level by filtering out materials candidates that are not predicted to exist. Many successes have been recorded. In the high-throughput approach to materials discovery, machined-learned models of materials are created from databases of theoretical materials. These databases are the result of millions of density-functional-theory (DFT) simulations. The size and accuracy of the data in the databases (and, consequently, the predictions of machined-learned models) are most affected by the band energy calculation; most of the computation of a DFT simulation is computing the band energy in the self-consistency cycle, and most of the error in the simulation comes from band energy error. The band energy is obtained from a two-part multidimensional numerical integral over the Brillouin or irreducible Brillouin zone. A quadratic approximation and integration algorithm for computing the band energy in 2D and 3D is described. Analytic and semi-analytic integration of quadratic polynomials over simplices improves the accuracy and efficiency of the calculation. A method is proposed for estimating the error bounds of the quadratic approximation that does not require additional eigenvalues. Error propagation of approximation errors leads to an adaptive refinement approach that is driven by band energy error. Because adaptive meshes have little symmetry, integration is performed within the irreducible Brillouin zone, and a general algorithm for computing the irreducible Brillouin zone is described. The efficiency of quadratic integration is tested on realistic empirical pseudopotentials. When compared to current integration methods, uniform quadratic integration over the irreducible Brillouin zone sometimes results in fewer k-points for a given accuracy. Adaptive refinement fails to improve integration performance because band energy error bounds are inaccurate, especially at accidental crossings at the Fermi level.

Ce mémoire porte sur l’étude théorique d’une réaction permettant la formation de macrocycles via une alkynylation de thiol catalysée au cuivre(I) (macro-CGS). Ce type de réaction implique le couplage entre un thiol et un carbone C(sp). Bien que le volet synthétique associé à cette réaction soit complété, jusqu’à ce jour aucune information n’existe concernant le mécanisme réactionnel. Des outils théoriques tels que la théorie de la fonctionnelle de la densité (DFT), la théorie de l’état de transition (TST) et les orbitales des liens naturels (NBO) ont été utilisés afin de mener cette étude à terme. Le mémoire comporte aussi un volet expérimental associé à la synthèse totale du macrocycle utilisé dans la réaction modèle. Le mémoire débutera avec une introduction portant sur la liaison de type S-C(sp) et sur les macrocycles. Nous introduirons ensuite en quoi consiste une étude théorique de mécanisme réactionnel. L’objectif du projet et la stratégie de recherche seront ensuite établis. L’introduction sera suivie d’un chapitre sur la méthodologie, dans lequel nous ferons un survol des concepts théoriques importants concernant le calcul de la structure électronique et la détermination des propriétés thermodynamiques d’un système chimique. Nous verrons ensuite les concepts théoriques importants qui ont été utilisés concertant la cinétique chimique et la modélisation de l’environnement chimique. Ce chapitre sera suivi de la justification du choix de la méthode computationnelle. Pour ce faire, différentes propriétés chimiques ont été prédites et comparées avec les résultats expérimentaux en utilisant différentes méthodes de calculs de structure électronique. Finalement, nous passerons aux résultats de la recherche, ce qui impliquera une courte section concernant la synthèse totale du macrocycle, une section concernant le profil énergétique des mécanismes examinés et une dernière section où nous proposerons une description des mécanismes les plus probables en se basant sur une analyse des orbitales de liaison naturelles (NBO). Les résultats de l’étude favorisent un mécanisme d’α-addition, mais un mécanisme d’α-cuprathiolation et d’addition oxydante - élimination réductrice seraient aussi à prendre en considération. Une étude expérimentale approfondie serait nécessaire afin de pouvoir obtenir plus d’informations concernant le mécanisme le plus probable. / This thesis is about the theoretical study of a reaction allowing the formation of macrocycles via Cu(I) -catalyzed S-C(sp) coupling to form a macrocyclic alkynyl sulfide. This type of reaction involves the coupling between a thiol and a C(sp) carbon. Although the synthetic part of that reaction is complete, to date, no information exists regarding the reaction mechanism. Theoretical tools such as density functional theory (DFT), transition state theory (TST) and natural bond orbitals (NBO) were used in order to undertake this study. The thesis also includes an experimental part associated with the total synthesis of the macrocycle used in the model reaction. The thesis will begin with an introduction on the S-C(sp) bond and on macrocycles in general. Afterwards, we will introduce the concept of theoretical study applied to a reaction mechanism. The goal and strategy of the study will then be established. The introduction will be followed by a chapter on the methodology, in which we make an overview of important theoretical concepts concerning electronic structure calculations and thermodynamic properties of a chemical system. We will then discuss theoretical concepts that have been used in concert with chemical kinetics and chemical environment. This chapter will be followed by a discussion on the choice of the computational method. For that purpose, different chemical properties were predicted and compared with experimental results using different electronic structure calculation methods. Finally, we will discuss the results of the study on the reaction investigated, which include a short section concerning the total synthesis of the macrocycle, a section concerning the energy profile of the studied mechanisms and a section where we provide a description of the most probable mechanisms based on a natural bond orbital (NBO) analysis. The results of the study are in favor of the α-addition mechanism, but the α-cuprathiolation and oxidative addition - reductive elimination mechanism should also be considered. Nevertheless, a thorough experimental study would be necessary in order to be able to obtain more information about the mechanism.

A coupling-limited approach for the Ullmann reaction-like on-surface synthesis of a two-dimensional covalent organic network starting from a halogenated metallo-porphyrin is demonstrated. Copper-octabromo-tetraphenylporphyrin molecules can diffuse and self-assemble when adsorbed on the inert Au(111) surface. Splitting-off of bromine atoms bonded at the macrocyclic core of the porphyrin starts at room temperature after the deposition and is monitored by X-ray photoelectron spectroscopy for different annealing steps. Direct coupling between the reactive carbon sites of the molecules is, however, hindered by the molecular shape. This leads initially to an ordered non-covalently interconnected supramolecular structure. Further heating to 300 °C and an additional hydrogen dissociation step is required to link the molecular macrocycles via a phenyl group and form large ordered polymeric networks. This approach leads to a close-packed covalently bonded network of overall good quality. The structures are characterized using scanning tunneling microscopy. Different kinds of lattice defects and, furthermore, the impact of polymerization on the HOMO–LUMO gap are discussed. Density functional theory calculations corroborate the interpretations and give further insight into the adsorption of the debrominated molecule on the surface and the geometry and coupling reaction of the polymeric structure. / Dieser Beitrag ist aufgrund einer (DFG-geförderten) Allianz- bzw. Nationallizenz frei zugänglich.

In the first two chapters we presented the basics of density functional theory and semiempirical LSD+U approximation, which was implemented in the full-potential local-orbital (FPLO) minimal-basis calculation scheme. In the third chapter we tested the implemented version of LSDA+U on 3d transitional metal monoxides. Essential improvement of the spectroscopic properties was obtained. A simple model describing the value and direction of the magnetic moment of a transition metal ion was presented. The model visualizes the interplay of the spin-orbit coupling and crystal field splitting. In the fourth chapter we calculated the electronic spectrum of the single Zn impurity in CuO2 plane considered as a vacancy in Cu 3d states. The analytic solution for the states of different symmetry was obtained. Depending on the strength of perturbation induced by the impurity on the neighboring Cu ions, the states are either resonant or localized. The critical values of the perturbation were computed. In the fifth chapter we presented the calculations for three novel vanadates: MgVO3, Sb2O2VO3 and VOMoO4. The tight-binding parameters and the exchange integrals were computed. The magnesium and antimony vanadates appeared to be spin-½ one-dimensional systems, the latter having much stronger one-dimensional character and being probably the best realization of inorganic spin-Peierls system. The molybdenum vanadate was found to be two-dimensional spin-½ system. The Mo 4d orbitals play an important role in the electronic transfer.

In this project machine learning (ML) interatomic potentials are trained and used in molecular dynamics (MD) simulations to predict the physical properties of total energy, mean squared displacement (MSD) and specific heat capacity for systems of bulk Aluminium and Silicon. The interatomic potentials investigated are potentials trained using the ML models kernel ridge regression (KRR) and moment tensor potentials (MTPs). The simulations using these ML potentials are then compared with results obtained from ab-initio simulations using the gold standard method of density functional theory (DFT), as implemented in the Vienna ab-intio simulation package (VASP). The results show that the MTP simulations reach comparable accuracy compared to the DFT simulations for the properties total energy and MSD for Aluminium, with errors in the orders of magnitudes of meV and 10-5 Å2. Specific heat capacity is not reasonably replicated for Aluminium. The MTP simulations do not reasonably replicate the studied properties for the system of Silicon. The KRR models are implemented in the most direct way, and do not yield reasonably low errors even when trained on all available 10000 time steps of DFT training data. On the other hand, the MTPs require only to be trained on approximately 100 time steps to replicate the physical properties of Aluminium with accuracy comparable to DFT. After being trained on 100 time steps, the trained MTPs achieve mean absolute errors in the orders of magnitudes for the energy per atom and force magnitude predictions of 10-3 and 10-1 respectively for Aluminium, and 10-3 and 10-2 respectively for Silicon. At the same time, the MTP simulations require less core hours to simulate the same amount of time steps as the DFT simulations. In conclusion, MTPs could very likely play a role in accelerating both materials simulations themselves and subsequently the emergence of the data-driven materials design and informatics paradigm.

This master’s thesis focuses on investigating the electronic properties of the superconducting spinel compound LiTi2O4 by means of computational and experimental effort. The title compound has been extensively studied in the past years, being the only known superconducting spinel oxide with relatively high Tc = 11.5 K. Even so, the origin of its superconducting mechanism is under debate, and its anomalous superconductivity is still inquired. Thanks to the recently developed ability to produce high-quality epitaxial LiTi2O4 thin films, a renewed research interest in this compound has matured. With this work, we partake in this challenge and present combined experimental and computational results on the electronic band structure of the material. Density functional theory (DFT) has been employed for the first principle electronic structure calculations performed with the Quantum ESPRESSO software. Furthermore, thin-film samples were in-situ realized with the pulsed laser deposition (PLD) method and investigated through the angle-resolved photoemission spectroscopy (ARPES) technique conducted at the ULTRA end-station of the SLS synchrotron facility at PSI in Switzerland. Here, we report the computed electronic band structure of LiTi2O4, with a detailed investigation of its density of states and Fermi surface. Further, we compare these calculations with the obtained experimental ARPES data. Emerging from this study are results supporting the non-conventional superconducting nature of LiTi2O4, which presents coexisting correlation effects, such as electron-phonon coupling and enhanced electron-electron interactions. / Denna masteruppsats fokuserar på att undersöka de elektroniska egenskaperna hos det supraledande spinellmaterialet LiTi2O4 med hjälp av datorsimuleringar samt experimentella mätningar. LiTi2O4 har studerats omfattande under de senaste åren, eftersom den är den enda kända supraledande spinelloxiden med relativt hög Tc = 11.5 K. Trots det är ursprunget till dess supraledande mekanism debatterad, och meaknismen för dess okonventionella supraledning är fortfarande inte helt förstådd. Tack vare den nyligen utvecklade förmågan att producera tunna högkvalitativa epitaxiella LiTi2O4 filmer, har ett förnyat forskningsintresse för denna förening mognat. Med detta arbete deltar vi i denna utmaning och presenterar kombinerade experimentella och beräkningsresultat om materialets elektroniska bandstruktur. Densitetsfunktionsteori (DFT) har använts för principiella elektroniska strukturberäkningar utförda med Quantum ESPRESSO-mjukvaran. Vidare realiserades tunnfilmsprover in-situ med pulsed laser deposition (PLD) medoden och undersöktes experimentellt via vinkelupplöst fotoemissionsspektroskopi (ARPES) som utfördes vid ULTRA-ändstationen på SLS synkrotronanläggningen vid PSI i Schweiz. Här rapporterar vi den beräknade elektroniska bandstrukturen för LiTi2O4, med en detaljerad undersökning av dess tillståndstäthet och Fermi-yta. Vidare jämför vi dessa teoretiska beräkningar med de erhållna experimentella ARPES data. Resultat från denna studie stöder den icke-konventionella supraledande naturen hos LiTi2O4, som också uppvisare samexisterande korrelationseffekter, såsom elektron-fononkoppling samt starka elektron-elektron-interaktioner.

III-valent dopants have shown to be most effective in stabilizing the ferroelectric, crystalline phase in atomic layer deposited, polycrystalline HfO₂ thin films. On the other hand, such dopants are commonly used for tetragonal and cubic phase stabilization in ceramic HfO₂. This difference in the impact has not been elucidated so far. The prospect is a suitable doping to produce ferroelectric HfO₂ ceramics with a technological impact. In this paper, we investigate the impact of Al, Y, and La doping, which have experimentally proven to stabilize the ferroelectric Pca21 phase in HfO₂, in a comprehensive first-principles study. Density functional theory calculations reveal the structure, formation energy, and total energy of various defects in HfO₂. Most relevant are substitutional electronically compensated defects without oxygen vacancy, substitutional mixed compensated defects paired with a vacancy, and ionically compensated defect complexes containing two substitutional dopants paired with a vacancy. The ferroelectric phase is strongly favored with La and Y in the substitutional defect. The mixed compensated defect favors the ferroelectric phase as well, but the strongly favored cubic phase limits the concentration range for ferroelectricity. We conclude that a reduction of oxygen vacancies should significantly enhance this range in Y doped HfO₂ thin films. With Al, the substitutional defect hardly favors the ferroelectric phase before the tetragonal phase becomes strongly favored with the increasing concentration. This could explain the observed field induced ferroelectricity in Al-doped HfO₂. Further Al defects are investigated, but do not favor the f-phase such that the current explanation remains incomplete for Al doping. According to the simulation, doping alone shows clear trends, but is insufficient to replace the monoclinic phase as the ground state. To explain this fact, some other mechanism is needed.