Heterogenní katalýza hraje významnou roli pro zvy¹ování efektivity rùzných procesù. Vysokou katalytickou aktivitu vykazují oxidy ceru patøící k tzv. reducibilním oxidùm, je¾ snadno uvolòují èi (zpìtnì) pøijímají atomy kyslíku prostøednictvím procesù redukce a oxidace. Zámìrem pøedlo¾ené práce je vypoèítat pásové struktury a øezy plochami konstantní energie objemových a povrchových systémù oxidu ceru pomocí kvantovì-mechanické "ab initio"metody Teorie hustotního funkcionálu. Numerické simulace jsou provádìny pomocí programového balíèku Quantum ESPRESSO za u¾ití metod rovinných vln a pseudopotenciálu. Silná korelace elektronù v pøípadì atomù ceru je modelována pøidáním Hubbardova U-èlenu. Hlavní dùraz je kladen na mo¾nost porovnávání teoretických výsledkù s tìmi získanými pomocí experimentální metody úhlovì-rozli¹ené fotoelektronové spektroskopie umo¾òující pøímý zisk jak pásových struktur, tak øezù plochami konstantní energie zkoumaného materiálu. Porovnání pomù¾e jak poznat mo¾nosti a mo¾né hranice zmínìné experimentální metody, tak i roz¹íøit její teoretické zázemí vedoucí k prohloubení znalostí materiálù perspektivních pro katalýzu. Klíèová slova: Teorie hustotního funkcionálu, Hubbardùv U-èlen, pásová struktura, plocha konstantní energie, Brillouinova zóna 1

Certain types of porphyrins can be used as achiral agent for determination of enantiomeric excess (ee) of chiral molecules. Particular organic chiral molecule (guest) and porphyrin (host) form host-guest complex while inducing nonequiv- alency of particular proton resonances in symmetrical host. It causes splitting of NMR signals linearly dependent on ee of guest. In this work we investigated com- plexation of di-brombenzylated oxoporphyrin with chiral camphorsulfonic acid. NMR titration revealed that they form complex with 1:1 stoichiometry with as- sociation constant K ≈ 5 × 104 l/mol. We confirmed linear dependence of split- ting of host β-protons on ee of guest. Low temperature measurements revealed two conformations of host-guest complex with population around 0.7:0.3 (at −60 ◦ C). DFT quantum mechanical computations at BLYP/3-21G* level revealed also two conformations with population 0.79:0.21. NMR shifts were computed on this geometries with method GIAO/PBE1PBE/6-31G(2df,2pd) and compared to experimental values. 1

Two dimensional (2D) materials, such as graphene, phosphorene and transition metal chalcogenides, have received a great attention in recent years due to their unique physical and chemical properties. A majority of 2D materials is intrinsically non-magnetic, therefore, their applications in spintronics are limited. The design and synthesis of new 2D materials with intrinsic magnetism and high spin-polarization remains a challenge. Computational discovery of new 2D materials with desired magnetic and electronic properties is the subject of this thesis. Using density functional theory with PBE, PBE+U and HSE06 functionals, we have systematically investigated the structure, electronic, magnetic and topological properties of novel 2D materials. Investigated materials include MXenes and layered transition-metal trihalides, both with great potential applications in spintronic devices. Four different classes of materials showing unique magnetic properties were investigated and reported in this thesis. (1) Asymmetrically functionalized MXenes were studied. The coexistence of the fully compensated antiferromagnetic order (zero magnetization) and completely spin-polarized semiconductivity was found for the first time. Moreover, the spin carrier orientation and induced transition from bipolar antiferromagnetic...

Electron confinement due to the two-dimensional (2D) nature of layered materials accounts for their fascinating electronic properties and for their applications in new-generation electronic devices. Moreover, the large specific surface area of 2D materials also enables their use in surface-related applications, such as catalysis and adsorption. In addition, these 2D materials are promising photocatalysts thanks to the shorter migration distance of photogenerated electrons and of electron holes. The research reported in this thesis aimed to provide atomistic insight into 2D layered materials, particularly into their structures, electronic properties and potential applications in the field of catalysis, photocatalysis and alkali metal ion batteries. Our findings are not only theoretically relevant but also open new research avenues for our experimental collaborators to improve specific properties and activities of their materials. The main results from this thesis, for five different classes of 2D materials, are summarized below. 2D covalent organic frameworks (COFs). CTF-type COFs with similar topology but different nitrogen-to-carbon ratios were investigated for their potential in photocatalytic water splitting. More specifically, torsion and bending effects on structure stability were investigated in...

The development of materials with tailored functionalities and with continuously shrinking linear dimensions towards (and below) the nanoscale is not only going to revolutionize state of the art fabrication technologies, but also the computational methodologies used to model the materials properties. Specifically, atomistic methodologies are becoming increasingly relevant in the field of materials science as a fundamental tool in gaining understanding on as well as for pre-designing (in silico material design) the behavior of nanoscale materials in response to external stimuli. The major long-term goal of atomistic modelling is to obtain structure-function relationships at the nanoscale, i.e. to correlate a definite response of a given physical system with its specific atomic conformation and ultimately, with its chemical composition and electronic structure. This has clearly its pendant in the development of bottom-up fabrication technologies, which also require a detailed control and fine tuning of physical and chemical properties at sub-nanometer and nanometer length scales. The current work provides an overview of different applications of atomistic approaches to the study of nanoscale materials. We illustrate how the use of first-principle based electronic structure methodologies, quantum mechanical based molecular dynamics, and appropriate methods to model the electrical and thermal response of nanoscale materials, provides a solid starting point to shed light on the way such systems can be manipulated to control their electrical, mechanical, or thermal behavior. Thus, some typical topics addressed here include the interplay between mechanical and electronic degrees of freedom in carbon based nanoscale materials with potential relevance for designing nanoscale switches, thermoelectric properties at the single-molecule level and their control via specific chemical functionalization, and electrical and spin-dependent properties in biomaterials. We will further show how phenomenological models can be efficiently applied to get a first insight in the behavior of complex nanoscale systems, for which first principle electronic structure calculations become computationally expensive. This will become especially clear in the case of biomolecular systems and organic semiconductors.

Title: Magnetic circular dichroism and aromatic compounds Author: Petr Štěpánek Department/Institute: Institute of Organic Chemistry and Biochemistry AS CR, v.v.i. Supervisor: prof. RNDr. Petr Bouř, DSc., Institute of Organic Chemistry and Biochemistry AS CR, v.v.i. Abstract: The thesis presents a series of studies concerning magnetic circular dichroism (MCD), a spectroscopic method, which experienced an intense theo- retical development in the recent years. New computational codes opened possi- bilities to calculate MCD spectra of larger and more varied molecules than was possible in the past. In the presented studies, we took the advantage of the new computational codes to broaden the possible span of applications of the MCD technique. As an example, we present MCD as a method useful for obtaining information about the structure of fullerenes. We also studied the influence of the molecular conformation and the explicit and implicit solvent models on the MCD spectra of aromatic amino acids using the newly implemented alterna- tive computational protocol based on sum-over-states calculations. We have also theoretically predicted spectra of the nuclear spin circular dichroism (NSCD), a potential new high-resolution spectroscopy. Keywords: magnetic circular dichroism, quantum-chemical calculations, density...

Identifying the protein content in a cell in a fast and reliable manner has become a relevant goal in the field of proteomics. This thesis computationally explores the potential for silicon nitride nanopores to sense and distinguish single miniproteins, which are small domains that promise to facilitate the systematic study of larger proteins. Sensing and identification of these biomolecules using nanopores happens by studying modulations in ionic current during translocation. The approach taken in this work was to study two miniproteins of similar geometry, using a cylindrical-shaped pore. I employed molecular mechanics to compare occupied pore currents computed based on the trajectory of ions. I further used density functional theory along with relative surface accessibility values to compute changes in interaction energies for single amino acids and obtain relative dwell times. While the protein remained inside the nanopore, I found no noticeable differences in the occupied pore currents of the two miniproteins for systems subject to 0.5 and 1.0 V bias voltages. Dwell times were estimated based on the translocation time of a protein that exhibits no interaction with the pore walls. I found that both miniproteins feel an attractive force to the pore wall and estimated their relative dwell times to differ by one order of magnitude. This means even in cases where two miniproteins are indistinguishable by magnitude changes in the ionic current, the dwell time might still be used to identify them. This work was an initial investigation that can be further developed to increase the accuracy of the results and be expanded to assess other miniproteins with the goal to aid future experimental work.

Es werden die Verbindungen YMn2O5 und YFeMnO5 diskutiert. Die erstere zeigt unterhalb von TN = 45 K Ferromagnetismus und in der magnetischen Phase schwache Ferroelektrizität. Die elektrische Polarisation wird mit Symmetriebrechung durch die Spinstruktur erklärt, die zur Aufhebung der Inversionssymmetrie führt (sog. unechtes Ferroelektrikum). Isostrukturelle Ersetzung von Mn durch Fe führt zu YFeMnO5, einer Verbindung, die bei T<165 K ferrimagnetisch, jedoch nicht ferroelektrisch ist. Die Spin-Strukturen beider Verbindungen sind bereits eingehend untersucht und zeigen charakteristische Unterschiede. Für Verbindungen der Zusammensetzung YFe(x)Mn(2-x)O5 wurden Röntgenbeugungs-und Absorptionsfeinstruktur-Experimente zur Bestimmung der Kristallstrukur in Abhängigkeit vom Fe-Anteil x durchgeführt und ausgewertet. Die Ergebnisse zeigen, daß die Strukturparameter einen nahezu linearen Verlauf zwischen den aus der Literatur bekannten Grenzfällen YFeMnO5 und YMn2O5 nehmen. Fe ersetzt dabei das Mn auf der fünffach koordinierten Lage innerhalb einer Sauerstoff-Pyramide. Besonders markant ist die unterschiedliche Position von Mn bzw. Fe in dieser Umgebung. Mit Hilfe der Strukturdaten wurden kollineare DFT-Rechnungen im LSDA+U-Formalismus in skalar-relativistischer Näherung durchgeführt. Für YFeMnO5 konnte der experimentell bekannte Grundzustand im Rahmen der Näherung reproduziert werden, obgleich eine Bandlücke nur in Abhängigkeit von der U-Korrektur auftritt. Der berechnete Grundzustand von YMn2O5 gibt die komplizierte magnetische Struktur dieser Verbindung nicht wieder, weil die gewählte Elementarzelle des Gitters dafür zu klein ist. Statt dessen ist der berechnete Grundzustand hier sehr ähnlich zu dem von YFeMnO5. Eine ausführliche Untersuchung der projizierten Zustandsdichten der Metallatome ermöglicht die Diskussion der Kristallfeldaufspaltung im Zusammenhang mit deren Position innerhalb der Sauerstoffpolyeder. Durch Berechnung mehrerer Spinstrukturen in einer kristallographischen Elementarzelle mit erniedrigter Symmetrie konnten die Austauschparameter eines Heisenberg-Modells zwischen den lokalisierten Spins der Metallatome berechnet werden. Die Größenverhältisse dieser Parameter können mit den aus der Literatur bekannten Spinstrukturen in Einklang gebracht werden. Die Wechselwirkungen sind überwiegend antiferromagnetisch, in Übereinstimmung mit den GKA-Regeln für den Superaustausch. Bei YMn2O5 wird insbesondere eine der schwächeren Kopplungen in der magnetischen Struktur periodisch frustriert. Man geht davon aus, daß dies eine mögliche Ursache für das Auftreten von Ferroelektrizität in der magnetischen Phase ist. Bei YFeMnO5 ist der berechnete Wert dieser Kopplung wesentlich größer und die magnetische Struktur beinhaltet keine Frustration. Dies ist eine mögliche Erklärung für die Abwesenheit der magnetisch induzierten Ferroelektrizität in YFeMnO5. Im zweiten Teil stehen das in Perowskitstruktur kristallisierende SrTiO3 und die durch Hinzufügen von SrO daraus hervorgehenden Kristallstrukturen der sog. Ruddlesden-Popper-Phasen (RP) im Mittelpunkt. Die Daten von Nahkanten-Elektronenenergieverlustspektren (ELNES) an der Sauerstoff K-Kante in SrTiO3, SrO und einer RP-Phase wurden ausgewertet und mit DFT-berechneten projizierten Zustandsdichten (PDOS) der 2p-Orbitale der O-Atome in diesen Verbindungen verglichen. Bei ELNES-Nahkantenspektren ist ein solcher Vergleich mit Experimenten im Bereich hoher Elektronenenergien möglich, weil die Auswahlregel auch für die inelastischen Elektronenstöße zutrifft. Die Spektren zeigen für jede Verbindung charakteristische Maxima, deren Ursache die unterschiedliche nähere Umgebung der Sauerstoffatome ist. Weiterhin wurden Experimente an SrTiO3-Einkristallen unter Einfluß elektrischer Gleichströme und -felder durchgeführt. Bei Experimenten an Einkristall-Wafern waren Hinweise auf lokale Veränderungen der Kristallstruktur unter diesen Bedingungen gefunden worden. Ergänzend dazu wurden mikroskopische einkristalline Proben untersucht. Bei geringen Stromstärken zeigte sich dabei das bereits bekannte Degradationsverhalten des elektrischen Widerstands. Bei hohen Stromstärken kommt es zum elektrischen Durchbruch und dauerhafter Erniedrigung des Widerstands. Röntgenbeugungsmessungen ergaben keine Hinweise auf Veränderungen an der Kristallstruktur oder in Form von Zwillings-oder Bruchstückbildung. Im dritten Teil werden Röntgenbeugungsmessungen an CeCu2Si2-Einkristallen diskutiert. Bei der Auswertung älterer Messungen fielen nach der Strukturbestimmung charakteristische Maxima der Restelektronendichte auf, deren Ursprung nicht erklärt werden konnte und die bei mehreren Kristallen beobachtet wurden. Mit erneuten Messungen und Simulationen konnte nun gezeigt werden, daß diese Maxima von einer fehlerhaften Auswertungsmethode verursacht wurden.

The description of the magnetic properties of interacting many-particle systems has been one of the most important goals of physics. The problem is to derive the magnetic properties of such systems from quantum mechanical principles. It is well understood that the magnetization in an atom described by quantum numbers, spin (S), orbital (L), and total angular momentum (J) of its electrons. A set of guidelines, known as Hund's rules, discovered by Friedrich Hermann Hunds help us to determine the quantum numbers for the ground states of free atoms. The question ``to which extent are Hund's rules applicable on different systems such as molecules and solids?'' is still on the agenda. The main problem is that of finding the ground state of the considered system. Density functional theory (DFT) methods apparently are the most widely spread self-consistent methods to investigate the ground state properties. This is due to their high computational efficiency and very good accuracy. In the framework of DFT, usually the total energy is decomposed into kinetic energy, Coulomb energy, and a term called the exchange-correlation energy. Taking into account the relativistic kinetic energy leads to direct and indirect relativistic effects on the electronic structure of a solid. The most pronounced direct effect (although not the biggest in magnitude) is the spin-orbit splitting of band states. A well-known indirect relativistic effect is the change of screening of valence electrons from the nuclear charge by inner-shell electrons. One can ask that how relativistic effects come into play in ordinary density functional theory. Of course ordinary density functional theory does not include those effect. Four-current density functional theory (CDFT), the quantum electrodynamic version of the Hohenberg-Kohn theory is a powerful tool to treat relativistic effects. Although it is principally designed for systems in strong magnetic fields, CDFT can also be applied in situations where currents are present without external magnetic fields. As already pointed out by Rajagopal and Callaway (1973), the most natural way to incorporate magnetism into DFT is the generalization to CDFT. These authors, however, treated its most simple approximation, the spin density functional theory (SDFT), which keeps the spin current only and neglects completely correlation effects of orbital currents. By using the Kohn-Sham-Dirac (KSD) equation, spin-orbit coupling is introduced kinematically. The part of the orbital magnetism that is a consequence of Hund's second rule coupling is absent in this theory and there is not any more a one-to-one mapping of spin densities onto external fields. In solids, in particular in metals, the importance of Hund's second rule coupling (orbital polarization) and Hund's third rule (spin-orbit coupling) is usually interchanged in comparison to atoms. Thus, in applications of the relativistic CDFT to solids, the usual way has been to keep the spin-orbit coupling in the KSD equation (an extension to ordinary Kohn-Sham (KS) equation) and to neglect the orbital contribution to the total current density and approximate exchange-correlation energy functional with spin density only. This scheme includes a spontaneous exchange and correlation spin polarization. Orbital polarization, on the other hand, comes into play not as a correlation effect but also as an effect due to the interplay of spin polarization and spin-orbit coupling: In the presence of both couplings, time reversal symmetry is broken and a non-zero orbital current density may occur. Application of this scheme to 3d and 4f magnets yields orbital moments that are smaller than related experimental values by typically a factor of two. Orbital magnetism in a solid is strongly influenced by the ligand field, originating from the structural environment and geometry of the solid. The orbital moments in a solid with cubic symmetry are expected to be quenched if spin-orbit coupling is neglected. However, spin-orbit coupling induces orbital moments, accordingly. The relativistic nature of the spin-orbit coupling requires orbital magnetism to be treated within QED, and the treatment of QED in solids is possible in the frame of current density functional theory. The kinematic spin-orbit coupling is accounted for in many DFT calculations of magnetic systems within the LSDA. However, a strong deviation of the LSDA orbital moments from experiment is found in such approaches. To avoid such deviations, orbital polarization corrections would be desirable. In this Thesis, those corrections have been investigated in the framework of CDFT. After a short review for CDFT in Chapter 2, in Chapter 3, an &amp;quot;ad hoc&amp;quot; OP correction term (OPB) suggested by Brooks and Eriksson is given. This correction in some cases gives quite reasonable corrections to orbital moments of magnetic materials. Another OP correction (OPE), which has been introduced recently, was derived from the CDFT in the non-relativistic limit. Unfortunately, the program can only incompletely be carried through, as there are reasonable but uncontrolled approximations to be made in two steps of the derivation. Nevertheless, the result is quite close to the &amp;quot;ad hoc&amp;quot;ansatz. The calculated OPE energies for 3d and 4f free ions are in qualitative agreement with OPB energies. In Chapter 4, both corrections are implemented in the FPLO scheme to calculate orbital moments in solids. We found that both OPB and OPE corrections implemented in FPLO method, yield reasonably well the orbital magnetic moments of bcc Fe, hcp Co and fcc Ni compared with experiment. In Chapter 5, the effect of spin-orbit coupling and orbital polarization corrections on the spin and orbital magnetism of full-Heusler alloys is investigated by means of local spin density calculations. It is demonstrated, that OP corrections are needed to explain the experimental orbital moments. Model calculations employing one ligand field parameter yield the correct order of magnitude of the orbital moments, but do not account for its quantitative composition dependence. The spin-orbit coupling reduces the degree of spin polarization of the density of states at Fermi level by a few percent. We have shown that the orbital polarization corrections do not change significantly the spin polarization degree at the Fermi level. We also provide arguments that Co2FeSi might not be a half-metal as suggested by recent experiments. In Chapter 6, to understand recent XMCD data for Co impurities in gold, the electronic structure of Co impurities inside gold has been calculated in the framework of local spin density approximation. The orbital and spin magnetic moment have been evaluated. In agreement with experimental findings, the orbital moment is enhanced with respect to Co metal. On the other hand, internal relaxations are found to reduce the orbital moment considerably, whereas the spin moment is less affected. Both OPB and OPE yield a large orbital moment for Co impurities. However, those calculated orbital moments are almost by a factor of two larger than the experimental values. We also found that the orbital magnetic moment of Co may strongly depend on pressure.

Mit Hilfe der Dichtefunktionaltheorie wurden magnetische Eigenschaften an 3d Elementen und Legierungen und 5f Verbindungen untersucht. Dabei wurde auf die Wichtigkeit von Orbitalpolarisationskorrekturen eingegangen und diese näher erörtert. Im ersten Anwendungsteil wurden magnetische Momente und die Magnetokristalline Anisotropie Energie an 3d Elementen untersucht. Des Weiteren wurden FeCo Legierungen als mögliche Bestandteile in der Festplattenindustrie diskutiert. Im letzten Abschnitt wurden Uranverbindungen in Hinsicht auf Ihre Orbitalpolarisation untersucht.:1 Introduction 1 2 Theoretical Considerations 5 2.1 Quantum Mechanics Applied to Solids . . . . . . . . . . . . . . . 6 2.2 Density Functional Theory . . . . . . . . . . . . . . . . . . . . . 7 2.2.1 non-Relativistic DFT . . . . . . . . . . . . . . . . . . . . 7 2.2.1.1 Hohenberg and Kohn . . . . . . . . . . . . . . . 7 2.2.1.2 Kohn-Sham Equations . . . . . . . . . . . . . . 10 2.2.1.3 Local Density Approximation and More . . . . 12 2.2.2 Relativistic DFT . . . . . . . . . . . . . . . . . . . . . . . 13 2.3 FPLO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.4 Magneto-Crystalline Anisotropy Energy . . . . . . . . . . . . . . 18 2.5 Disorder within DFT . . . . . . . . . . . . . . . . . . . . . . . . 20 3 Orbital Polarisation in DFT 23 3.1 Hund’s Rules in DFT . . . . . . . . . . . . . . . . . . . . . . . . 24 3.2 An Introduction to OPC and DFT . . . . . . . . . . . . . . . . . 25 3.2.1 OPC Brooks . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.2.2 OPC Eschrig . . . . . . . . . . . . . . . . . . . . . . . . . 26 4 Transition Metals 39 4.1 Fe, Co, and Ni . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 4.1.1 Calculational Details . . . . . . . . . . . . . . . . . . . . 40 4.1.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 4.1.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 4.2 Fe1−xCox . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.2.2 Fixed Spin Moment Calculations . . . . . . . . . . . . . . 50 4.2.3 Epitaxial Bain Path . . . . . . . . . . . . . . . . . . . . . 51 4.2.4 Calculational Details . . . . . . . . . . . . . . . . . . . . 54 4.2.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 4.2.6 LSDA vs. GGA . . . . . . . . . . . . . . . . . . . . . . . 69 4.2.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 5 Uranium Compounds 75 5.1 UX, with X = (N, P, As, Sb, O, S, Se, and Te) . . . . . . . . 77 5.1.1 UN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 5.1.2 UX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 5.1.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 5.2 UM2, with M = (Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, and Zn) 90 5.2.1 Calculational Details . . . . . . . . . . . . . . . . . . . . 90 5.2.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 5.2.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 5.3 UAsSe, USb2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 5.3.1 Calculational Details . . . . . . . . . . . . . . . . . . . . 97 5.3.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 5.3.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 6 Summary and Outlook 101 A Definitions i A.1 Spherical Harmonics . . . . . . . . . . . . . . . . . . . . . . . . . i A.2 Other Definitions Used in Text . . . . . . . . . . . . . . . . . . . ii B Input Parameters for the Racah Parameter iii B.1 d-Shells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii B.2 f-Shells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v Biblography vi Acknowledgement xxiv Versicherung xxvii