Beschreibung von Oberflächenphänomenen durch relativistische Clusterrechnungen unter Verwendung eines Einbettungsverfahrens

For the theoretical investigation of local phenomena (adsorption at surfaces, defects or impurities within a crystal, etc.) one can assume that the effects caused by the local disturbance are only limited to the neighbouring particles. With this model, that is well-known as cluster-approximation, an infinite system can be simulated by a much smaller segment of the surface (Cluster). The size of this segment varies strongly for different systems. Calculations to the convergence of bond distance and binding energy of an adsorbed aluminum atom on an Al(100)-surface showed that more than 100 atoms are necessary to get a sufficient description of surface properties. However with a full-quantummechanical approach these system sizes cannot be calculated because of the effort in computer memory and processor speed. Therefore we developed an embedding procedure for the simulation of surfaces and solids, where the whole system is partitioned in several parts which itsself are treated differently: the internal part (cluster), which is located near the place of the adsorbate, is calculated completely self-consistently and is embedded into an environment, whereas the influence of the environment on the cluster enters as an additional, external potential to the relativistic Kohn-Sham-equations. The basis of the procedure represents the density functional theory. However this means that the choice of the electronic density of the environment constitutes the quality of the embedding procedure. The environment density was modelled in three different ways: atomic densities; of a large prepended calculation without embedding transferred densities; bulk-densities (copied). The embedding procedure was tested on the atomic adsorptions of 'Al on Al(100) and Cu on Cu(100). The result was that if the environment is choices appropriately for the Al-system one needs only 9 embedded atoms to reproduce the results of exact slab-calculations. For the Cu-system first calculations without embedding procedures were accomplished, with the result that already 60 atoms are sufficient as a surface-cluster. Using the embedding procedure the same values with only 25 atoms were obtained. This means a substantial improvement if one takes into consideration that the calculation time increased cubically with the number of atoms. With the embedding method Infinite systems can be treated by molecular methods. Additionally the program code was extended by the possibility to make molecular-dynamic simulations. Now it is possible apart from the past calculations of fixed cores to investigate also structures of small clusters and surfaces. A first application we made with the adsorption of Cu on Cu(100). We calculated the relaxed positions of the atoms that were located close to the adsorption site and afterwards made the full-quantummechanical calculation of this system. We did that procedure for different distances to the surface. Thus a realistic adsorption process could be examined for the first time. It should be remarked that when doing the Cu reference-calculations (without embedding) we begun to parallelize the entire program code. Only because of this aspect the investigations for the 100 atomic Cu surface-clusters were possible. Due to the good efficiency of both the parallelization and the developed embedding procedure we will be able to apply the combination in future. This will help to work on more these areas it will be possible to bring in results of full-relativistic molecular calculations, what will be very interesting especially for the regime of heavy systems.

Adsorption of element 112 on a Au surface

Während der letzten 20 Jahre hat sich das Periodensystem bis zu den Elementen 114 und 116 erweitert. Diese sind kernphysikalisch nachgewiesen, so dass jetzt die chemische Untersuchung an erster Selle steht. Nachdem sich das Periodensystem bis zum Element 108 so verhält, wie man es dem Periodensystem nach annimmt, wird in dieser Arbeit die Chemie des Elements 112 untersucht. Dabei geht es um die Adsorptionsenergie auf einer Gold-Ober fläche, weil dies der physikalisch/chemische Prozess ist, der bei der Analyse angewandt wird. Die Methode, die in dieser Arbeit angwandt wird, ist die relativistische Dichtefunktionalmethode. Im ersten Teil wird das Vielkörperproblem in allgemeiner Form behandelt, und im zweiten die grundlegenden Eigenschaften und Formulierungen der Dichtefunktionaltheorie. Die Arbeit beschreibt zwei prinzipiell unterschiedliche Ansätze, wie die Adsorptionsenergie berechnet werden kann. Zum einen ist es die sogenannte Clustermethode, bei der ein Atom auf ein relativ kleines Cluster aufgebracht und dessen Adsorptionsenergie berechnet wird. Wenn es gelingt, die Konvergenz mit der Größe des Clusters zu erreichen, sollte dies zu einem Wert für die Adsorptionsenergie führen. Leider zeigt sich in den Rechnungen, dass aufgrund des zeitlichen Aufwandes die Konvergenz für die Clusterrechnungen nicht erreicht wird. Es werden sehr ausführlich die drei verschiedenen Adsorptionsplätze, die Top-, die Brücken- und die Muldenposition, berechnet. Sehr viel mehr Erfolg erzielt man mit der Einbettungsmethode, bei der ein kleiner Cluster von vielen weiteren Atomen an den Positionen, die sie im Festkörpers auf die Adsorptionsenergie soweit sichergestellt ist, dass physikalisch-chemisch gute Ergebnisse erzielt werden. Alle hier gennanten Rechnungen sowohl mit der Cluster- wie mit der Einbettungsmethode verlangen sehr, sehr lange Rechenzeiten, die, wie oben bereits erwähnt, nicht zu einer Konvergenz für die Clusterrechnungen ausreichten. In der Arbeit wird bei allen Rechnungen sehr detailliert auf die Abhängigkeit von den möglichen Basissätzen eingegangen, die ebenfalls in entscheidender Weise zur Länge und Qualität der Rechnungen beitragen. Die auskonvergierten Rechnungen werden in der Form von Potentialkurven, Density of States (DOS), Overlap Populations sowie Partial Crystal Overlap Populations analysiert. Im Ergebnis zeigt sich, dass die Adsoptionsenergie für das Element 112 auf einer Goldoberfläche ca. 0.2 eV niedriger ist als die Adsorption von Quecksilber auf der gleichen Ober fläche. Mit diesem Ergebnis haben die experimentellen Kernchemiker einen Wert an der Hand, mit dem sie eine Anhaltspunkt haben, wo sie bei den Messungen die wenigen zu erwartenden Ereignisse finden können.

Acquiring expert knowledge for the design of conceptual information systems

Conceptual Information Systems unfold the conceptual structure of data stored in relational databases. In the design phase of the system, conceptual hierarchies have to be created which describe different aspects of the data. In this paper, we describe two principal ways of designing such conceptual hierarchies, data driven design and theory driven design and discuss advantages and drawbacks. The central part of the paper shows how Attribute Exploration, a knowledge acquisition tool developped by B. Ganter can be applied for narrowing the gap between both approaches.

Conceptual knowledge discovery and data analysis

In this paper, we discuss Conceptual Knowledge Discovery in Databases (CKDD) in its connection with Data Analysis. Our approach is based on Formal Concept Analysis, a mathematical theory which has been developed and proven useful during the last 20 years. Formal Concept Analysis has led to a theory of conceptual information systems which has been applied by using the management system TOSCANA in a wide range of domains. In this paper, we use such an application in database marketing to demonstrate how methods and procedures of CKDD can be applied in Data Analysis. In particular, we show the interplay and integration of data mining and data analysis techniques based on Formal Concept Analysis. The main concern of this paper is to explain how the transition from data to knowledge can be supported by a TOSCANA system. To clarify the transition steps we discuss their correspondence to the five levels of knowledge representation established by R. Brachman and to the steps of empirically grounded theory building proposed by A. Strauss and J. Corbin.

Relativistic LCAO with Minimax Principle and New Balanced Basis Sets

Relativistic density functional theory is widely applied in molecular calculations with heavy atoms, where relativistic and correlation effects are on the same footing. Variational stability of the Dirac Hamiltonian is a very important field of research from the beginning of relativistic molecular calculations on, among efforts for accuracy, efficiency, and density functional formulation, etc. Approximations of one- or two-component methods and searching for suitable basis sets are two major means for good projection power against the negative continuum. The minimax two-component spinor linear combination of atomic orbitals (LCAO) is applied in the present work for both light and super-heavy one-electron systems, providing good approximations in the whole energy spectrum, being close to the benchmark minimax finite element method (FEM) values and without spurious and contaminated states, in contrast to the presence of these artifacts in the traditional four-component spinor LCAO. The variational stability assures that minimax LCAO is bounded from below. New balanced basis sets, kinetic and potential defect balanced (TVDB), following the minimax idea, are applied with the Dirac Hamiltonian. Its performance in the same super-heavy one-electron quasi-molecules shows also very good projection capability against variational collapse, as the minimax LCAO is taken as the best projection to compare with. The TVDB method has twice as many basis coefficients as four-component spinor LCAO, which becomes now linear and overcomes the disadvantage of great time-consumption in the minimax method. The calculation with both the TVDB method and the traditional LCAO method for the dimers with elements in group 11 of the periodic table investigates their difference. New bigger basis sets are constructed than in previous research, achieving high accuracy within the functionals involved. Their difference in total energy is much smaller than the basis incompleteness error, showing that the traditional four-spinor LCAO keeps enough projection power from the numerical atomic orbitals and is suitable in research on relativistic quantum chemistry. In scattering investigations for the same comparison purpose, the failure of the traditional LCAO method of providing a stable spectrum with increasing size of basis sets is contrasted to the TVDB method, which contains no spurious states already without pre-orthogonalization of basis sets. Keeping the same conditions including the accuracy of matrix elements shows that the variational instability prevails over the linear dependence of the basis sets. The success of the TVDB method manifests its capability not only in relativistic quantum chemistry but also for scattering and under the influence of strong external electronic and magnetic fields. The good accuracy in total energy with large basis sets and the good projection property encourage wider research on different molecules, with better functionals, and on small effects.

Electron-Nuclear Correlation in Laser-Driven Diatomic Molecules

The interaction of short intense laser pulses with atoms/molecules produces a multitude of highly nonlinear processes requiring a non-perturbative treatment. Detailed study of these highly nonlinear processes by numerically solving the time-dependent Schrodinger equation becomes a daunting task when the number of degrees of freedom is large. Also the coupling between the electronic and nuclear degrees of freedom further aggravates the computational problems. In the present work we show that the time-dependent Hartree (TDH) approximation, which neglects the correlation effects, gives unreliable description of the system dynamics both in the absence and presence of an external field. A theoretical framework is required that treats the electrons and nuclei on equal footing and fully quantum mechanically. To address this issue we discuss two approaches, namely the multicomponent density functional theory (MCDFT) and the multiconfiguration time-dependent Hartree (MCTDH) method, that go beyond the TDH approximation and describe the correlated electron-nuclear dynamics accurately. In the MCDFT framework, where the time-dependent electronic and nuclear densities are the basic variables, we discuss an algorithm to calculate the exact Kohn-Sham (KS) potentials for small model systems. By simulating the photodissociation process in a model hydrogen molecular ion, we show that the exact KS potentials contain all the many-body effects and give an insight into the system dynamics. In the MCTDH approach, the wave function is expanded as a sum of products of single-particle functions (SPFs). The MCTDH method is able to describe the electron-nuclear correlation effects as the SPFs and the expansion coefficients evolve in time and give an accurate description of the system dynamics. We show that the MCTDH method is suitable to study a variety of processes such as the fragmentation of molecules, high-order harmonic generation, the two-center interference effect, and the lochfrass effect. We discuss these phenomena in a model hydrogen molecular ion and a model hydrogen molecule. Inclusion of absorbing boundaries in the mean-field approximation and its consequences are discussed using the model hydrogen molecular ion. To this end, two types of calculations are considered: (i) a variational approach with a complex absorbing potential included in the full many-particle Hamiltonian and (ii) an approach in the spirit of time-dependent density functional theory (TDDFT), including complex absorbing potentials in the single-particle equations. It is elucidated that for small grids the TDDFT approach is superior to the variational approach.

Theoretical study of magnetism, structure and chemical order in transition-metal alloy clusters

Research on transition-metal nanoalloy clusters composed of a few atoms is fascinating by their unusual properties due to the interplay among the structure, chemical order and magnetism. Such nanoalloy clusters, can be used to construct nanometer devices for technological applications by manipulating their remarkable magnetic, chemical and optical properties. Determining the nanoscopic features exhibited by the magnetic alloy clusters signifies the need for a systematic global and local exploration of their potential-energy surface in order to identify all the relevant energetically low-lying magnetic isomers. In this thesis the sampling of the potential-energy surface has been performed by employing the state-of-the-art spin-polarized density-functional theory in combination with graph theory and the basin-hopping global optimization techniques. This combination is vital for a quantitative analysis of the quantum mechanical energetics. The first approach, i.e., spin-polarized density-functional theory together with the graph theory method, is applied to study the Fe$_m$Rh$_n$ and Co$_m$Pd$_n$ clusters having $N = m+n \leq 8$ atoms. We carried out a thorough and systematic sampling of the potential-energy surface by taking into account all possible initial cluster topologies, all different distributions of the two kinds of atoms within the cluster, the entire concentration range between the pure limits, and different initial magnetic configurations such as ferro- and anti-ferromagnetic coupling. The remarkable magnetic properties shown by FeRh and CoPd nanoclusters are attributed to the extremely reduced coordination number together with the charge transfer from 3$d$ to 4$d$ elements. The second approach, i.e., spin-polarized density-functional theory together with the basin-hopping method is applied to study the small Fe$_6$, Fe$_3$Rh$_3$ and Rh$_6$ and the larger Fe$_{13}$, Fe$_6$Rh$_7$ and Rh$_{13}$ clusters as illustrative benchmark systems. This method is able to identify the true ground-state structures of Fe$_6$ and Fe$_3$Rh$_3$ which were not obtained by using the first approach. However, both approaches predict a similar cluster for the ground-state of Rh$_6$. Moreover, the computational time taken by this approach is found to be significantly lower than the first approach. The ground-state structure of Fe$_{13}$ cluster is found to be an icosahedral structure, whereas Rh$_{13}$ and Fe$_6$Rh$_7$ isomers relax into cage-like and layered-like structures, respectively. All the clusters display a remarkable variety of structural and magnetic behaviors. It is observed that the isomers having similar shape with small distortion with respect to each other can exhibit quite different magnetic moments. This has been interpreted as a probable artifact of spin-rotational symmetry breaking introduced by the spin-polarized GGA. The possibility of combining the spin-polarized density-functional theory with some other global optimization techniques such as minima-hopping method could be the next step in this direction. This combination is expected to be an ideal sampling approach having the advantage of avoiding efficiently the search over irrelevant regions of the potential energy surface.

Finite-Elemente-Mehrgitter von Molekülen

Im Rahmen der Dichtefunktionaltheorie wurden Orbitalfunktionale wie z.B. B3LYP entwickelt. Diese lassen sich mit der „optimized effective potential“ – Methode selbstkonsistent auswerten. Während sie früher nur im 1D-Fall genau berechnet werden konnte, entwickelten Kümmel und Perdew eine Methode, bei der das OEP-Problem unter Verwendung einer Differentialgleichung selbstkonsistent gelöst werden kann. In dieser Arbeit wird ein Finite-Elemente-Mehrgitter-Verfahren verwendet, um die entstehenden Gleichungen zu lösen und damit Energien, Dichten und Ionisationsenergien für Atome und zweiatomige Moleküle zu berechnen. Als Orbitalfunktional wird dabei der „exakte Austausch“ verwendet; das Programm ist aber leicht auf jedes beliebige Funktional erweiterbar. Für das Be-Atom ließ sich mit 8.Ordnung –FEM die Gesamtenergien etwa um 2 Größenordnungen genauer berechnen als der Finite-Differenzen-Code von Makmal et al. Für die Eigenwerte und die Eigenschaften der Atome N und Ne wurde die Genauigkeit anderer numerischer Methoden erreicht. Die Rechenzeit wuchs erwartungsgemäß linear mit der Punktzahl. Trotz recht langsamer scf-Konvergenz wurden für das Molekül LiH Genauigkeiten wie bei FD und bei HF um 2-3 Größenordnungen bessere als mit Basismethoden erzielt. Damit zeigt sich, dass auf diese Weise benchmark-Rechnungen durchgeführt werden können. Diese dürften wegen der schnellen Konvergenz über der Punktzahl und dem geringen Zeitaufwand auch auf schwerere Systeme ausweitbar sein.

The Quadric Reference Surface: Theory and Applications

The conceptual component of this work is about "reference surfaces'' which are the dual of reference frames often used for shape representation purposes. The theoretical component of this work involves the question of whether one can find a unique (and simple) mapping that aligns two arbitrary perspective views of an opaque textured quadric surface in 3D, given (i) few corresponding points in the two views, or (ii) the outline conic of the surface in one view (only) and few corresponding points in the two views. The practical component of this work is concerned with applying the theoretical results as tools for the task of achieving full correspondence between views of arbitrary objects.

A comparison of the alr and ilr transformations for kernel density estimation of compositional data

In a seminal paper, Aitchison and Lauder (1985) introduced classical kernel density estimation techniques in the context of compositional data analysis. Indeed, they gave two options for the choice of the kernel to be used in the kernel estimator. One of these kernels is based on the use the alr transformation on the simplex SD jointly with the normal distribution on RD-1. However, these authors themselves recognized that this method has some deficiencies. A method for overcoming these dificulties based on recent developments for compositional data analysis and multivariate kernel estimation theory, combining the ilr transformation with the use of the normal density with a full bandwidth matrix, was recently proposed in Martín-Fernández, Chacón and Mateu- Figueras (2006). Here we present an extensive simulation study that compares both methods in practice, thus exploring the finite-sample behaviour of both estimators

Comparing methods for dimensionality reduction when data are density functions

Functional Data Analysis (FDA) deals with samples where a whole function is observed for each individual. A particular case of FDA is when the observed functions are density functions, that are also an example of infinite dimensional compositional data. In this work we compare several methods for dimensionality reduction for this particular type of data: functional principal components analysis (PCA) with or without a previous data transformation and multidimensional scaling (MDS) for diferent inter-densities distances, one of them taking into account the compositional nature of density functions. The difeerent methods are applied to both artificial and real data (households income distributions)

Los horarios laborales y su influencia en la percepción del equilibro trabajo-familia

Conciliar el trabajo y la familia es una lucha cotidiana que cada persona realiza para satisfacer las exigencias de ambas dimensiones de su vida. El no tener consciencia del problema que surge en el empleado para lograr esta conciliación y la ausencia de soluciones eficaces a éste, no sólo afecta a la organización a través de la baja productividad, el absentismo, el aumento del estrés, entre otros efectos; sino también a la vida familiar, social, física y psicológica del trabajador. Es por ello, que este proyecto de grado busca a partir de la revisión de la literatura mostrar cómo la percepción que tienen los trabajadores de su equilibrio trabajo-familia, se ve influenciada por un factor organizativo, como lo son los turnos laborales; además evidenciar las soluciones que se han implementado en las diferentes empresas de manera exitósa, para finalmente plantear estrategias que se puedan aplicar en las organizaciones facilitando el equilibrio trabajo-familia de los trabajadores.

El problema de conceptualización del terrorismo dentro de la disciplina de las Relaciones Internacionales: Un análisis desde la perspectiva histórico conceptual

Los hechos ocurridos durante el 11 de septiembre de 2001 se constituyeron como un momento fundamental en los intentos de conceptualización del terrorismo internacional dentro de la disciplina de las Relaciones Internacionales. A raíz del 9/11 tuvo lugar la resemantización del concepto de terrorismo internacional en función del terrorismo religioso y del fundamentalismo islámico. Lo anterior, marco una ruptura en el campo de experiencia y en el horizonte de expectativas del concepto mismo, pues este último adquirió un nuevo uso discursivo, y por ende, político. Por eso, ante la necesidad de emprender un análisis discursivo de los usos del concepto de terrorismo internacional, se evidencia cómo al estar inmersos en determinados juegos del lenguaje, el uso discursivo de este concepto termina por convertirse en una herramienta de acción política que promueve una forma de vida.

Exploración conceptual de la responsabilidad patrimonial del Estado frente al desplazamiento forzado.

El propósito central de la propuesta de investigación es responder a la siguiente pregunta: ¿la proliferación de respuestas teóricas al desplazamiento forzado, impulsada con la declaratoria del estado de cosas inconstitucional (ECI) en 2004, generó algún cambio en el paradigma de la responsabilidad patrimonial del Estado (REPE), que orientó al Consejo de Estado al definir la responsabilidad de las autoridades por desplazamiento forzado (DEFO), entre 2004 y 2010? Para lograrlo, comenzamos por aproximarnos a los elementos del paradigma tradicional de la responsabilidad estatal y luego tratamos de desarrollar las etapas de la teoría de las revoluciones científicas, propuesta por el profesor Thomas Kuhn. En ese orden, encontramos en primer lugar, que es posible hablar de un paradigma tradicional de la REPE pero muy difícil hallar sus contornos con absoluta precisión. Se trata de un complejo andamiaje de conceptos, creencias y valores en constante formación y redefinición. En segundo lugar, intentamos tomar consciencia de la anomalía del DEFO, esto es, apreciar de cerca sus características. Fue así como logramos evidenciar que se trata de un fenómeno fuertemente arraigado en nuestra historia, cuyas soluciones requieren esfuerzos interdisciplinares. En tercer lugar, emprendimos la exploración conceptual: buscamos dentro de una amplia urdimbre de propuestas académicas aquellas que se pudieran conectar mejor con los elementos del paradigma de la REPE. Identificamos 18 líneas de fuga teórica alrededor de los conceptos del daño, imputación y reparación. Todas apuntan hacia la ampliación de sus alcances y la búsqueda de remedios más eficaces y democráticos para las víctimas del DEFO. En cuarto lugar, contrastamos dichas propuestas con las respuestas que ofreció el Consejo de Estado a la población en desplazamiento, en sus fallos proferidos entre 2004 y 2010 en esta materia. Finalmente, después de dicha exploración encontramos que el paradigma de la REPE no fue radicalmente alterado por la proliferación de respuestas teóricas ofrecidas después de 2004. El máximo juez contencioso tomó cierta consciencia de la anomalía, exploró algunas aristas del fenómeno, pero se quedó corto a la hora de evaluar el alcance de sus herramientas tradicionales y proponer soluciones novedosas y eficaces. Presenciamos algunos cambios en el concepto y alcance de la reparación, originados en decisiones anteriores poco relacionadas con eventos de desplazamiento, que resultan insuficientes a la luz de las exigencias de la problemática del DEFO.

“Superficial Water Concessions In Light Of The General Theory of the Administrative Act” The Incidence of the Public Law’s Dogmatic Tradition of Public Law Within Environmental Law

This paper seeks the determine the ways in which anomalous decisions derived from the particularization and constitutionalization of environmental law can arise given the general theory of administrative action. This is seen through the lens of a study and characterization of administrative decisions issued by the Regional Autonomous Corporation of Cundinamarca –CAR- within the superficial water concessions procedure. It also discusses the conceptual contents of these licenses.