Rozprawy doktorskie na temat „Hückel molecular orbital theory”

Extended Hückel methods are known to be a useful tool in understanding surface phenomena. Important quantities about atoms and chemical bonds can be obtained from this computationally simple method, although caution must be exercised in interpreting the results. Application of Extended Hückel calculations to large metal clusters reveals the role of d orbitals in solids. Basic ideas of constructing model compounds have been developed. Several model systems for surface chemisorption processes are constructed in order to understand the surface catalyzed oxidative degradation of polyperfluoroethers. The activation of oxygen molecules can be explained. The Lewis acid character of the iron fluoride surface can be predicted. Based on these results, mechanisms of the degradation processes are discussed.

The energy of a graph began with German physicist, Erich Hückel's 1931 paper, Quantenttheoretische Beiträge zum Benzolproblem. His work developed a method for computing the binding energy of the pi]-electrons for a certain class of organic molecules. The vertices of the graph represented the carbon atoms while the single edge between each pair of distinct vertices represented the hydrogen bonds between the carbon atoms. In turn, the chemical graphs were represented by an n x n matrix used in solving Schrödinger's eigenvalue/eigenvector equation. The sum of the absolute values of these graph eigenvalues represented the total pi]-electron energy. The criteria for constructing these chemical graphs and the chemical interpretations of all the quantities involved made up the Hückel Molecular Orbital theory or HMO theory. In this paper, we will show how the chemical interpretation of Hückel's graph energy evolved to a mathematical interpretation of graph energy that Ivan Gutman provided for us in his famous 1978 definition of the energy of a graph. Next, we will present Charles Coulson's 1940 theorem that expresses the energy of a graph as a contour integral and prove some of its corollaries. These corollaries allow us to order the energies of acyclic and bipartite graphs by the coefficients of their characteristic polynomial. Following Coulson's theorem and its corollaries we will look at McClelland's first theorem on the bounds for the energy of a graph. In the corollaries that follow McClelland's 1971 theorem, we will prove the corollaries that show a direct variation between the energy of a graph and the number of its vertices and edges. Finally, we will see how this relationship led to Gutman's conjecture that the complete graph on n vertices has maximal energy. Although this was disproved by Chris Godsil in 1981, we will provide an independent counterexample with the help of the software, Maple 13.
ID: 030646262; System requirements: World Wide Web browser and PDF reader.; Mode of access: World Wide Web.; Thesis (M.S.)--University of Central Florida, 2011.; Includes bibliographical references (p. 32-34).
M.S.
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Mathematics
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Mathematical Science

Thesis (Ph. D.)--Ohio State University, 2005.
Title from second page of PDF file. Document formatted into pages; contains xxiii, 151 p.; also includes graphics (some col.). Includes bibliographical references (p. 140-151). Available online via OhioLINK's ETD Center

Thesis (Ph. D.)--Ohio State University, 2005.
Title from first page of PDF file. Document formatted into pages; contains xxxi, 309 p.; also includes graphics Includes bibliographical references. Available online via OhioLINK's ETD Center

This thesis presents the basic concepts of electronic structure theory and the chemical properties of mercury. The theoretical foundation of DFT and the consequences of relativity are also introduced. The electronic structure of Hg(II) ions, [Hg(L)n(H2O)m]q (L = HO-, Cl-, HS-, S2-) has been studied. We show, in this thesis, that the charge transfer (that is calculated from the hard-soft-acid-base principle (Pearson’s principle)), the total NBO charge and the interaction energies are strongly correlated. Our studies indicate the effect of the solvent on the global electrophilicity, the charge transfer and consequently the interaction strength between Hg(II) and ligand L. The formation constants, logK, of Hg2+−complexes are calculated. The procedure that we follow in this thesis to calculate the formation constants, logK’s, are in good agreement with the extrapolated experimental values. We introduce and explain why it is important adding water molecules explicitly during the calculations of the logK. The recommended logK value of HgS is 27.2. We examined two different types of organic compounds as sensors for heavy metal ions: lumazine (Lm) and 6-thienyllumazine (TLm). We found that the simple calculation of pKa values using DFT methods and implicit solvent models failed to reproduce the experimental values. However, calculated orbital energies and gas phase acidities both indicate that the compound TLm is inherently more acidic than the parent species Lm. We demonstrate that: (1) we need to take in our consideration the population of each tautomer and conformer during the calculations of the pKa values, and (2) thienyl group has indirect effect on the acidity of the proton on N1 in the uracil ring. Last but not least, the fluorescence spectrum of the sensors (L) and their [(L)nM(H2O)m]2+ complexes (L = Lumazine (Lm) and 6-thienyllumazine (TLm) and M = Cd2+and Hg2+) are calculated using time dependent DFT (TDDFT). The results show that TDDFT is in good agreement with experimental results. This chapter provides a new concept in the design of fluorescence turn-on/off sensors that has wider applicability for other systems. Finally, we provide a summary of the works compiled in this thesis and an outlook on potential future work.
October 2015

The continuous migration to smaller feature sizes puts high demands on materials and technologies for future ultra-large-scale integrated circuits. Particularly, the copper-based interconnect system will reach fundamental limits soon. Their outstanding properties make metallic carbon nanotubes (CNTs) an ideal material to partially replace copper in future interconnect architectures. Here, a low contact resistance to existing metal lines is crucial. The present thesis contributes to the theory and numerical description of electronic transport in metallic CNTs with metal contacts. Different theoretical approaches are applied to various contact models and electrode materials (Al, Cu, Pd, Ag, Pt, Au) are compared. Ballistic transport calculations are based on the non-equilibrium Greens function formalism combined with tight-binding (TB), extended Hückel theory (EHT) and density functional theory (DFT). Simplified contact models allow a qualitative investigation of both the influence of geometry and CNT length, and the strength and extent of the contact on the transport properties. In addition, such simple contact models are used to compare the influence of different electronic structure methods on transport. It is found that the semiempirical TB and EHT are inadequate to quantitatively reproduce the DFT-based results. Based on this observation, an improved set of Hückel parameters is developed, which remedies this insufficiency. A systematic investigation of different contact materials is carried out using well defined atomistic metal-CNT-metal structures, optimized in a systematic way. Analytical models for the CNT-metal interaction are proposed. Based on that, electronic transport calculations are carried out, which can be extended to large systems by applying the computationally cheap improved EHT. The metal-CNT-metal systems can then be ranked by average conductance: Ag ≤ Au < Cu < Pt ≤ Pd < Al. This corresponds qualitatively with calculated contact distances, binding energies and work functions of CNTs and metals. To gain a deeper understanding of the transport properties, the electronic structure of the metal-CNT-metal systems and their respective parts is analyzed in detail. Here, the energy resolved local density of states is a valuable tool to investigate the CNT-metal interaction and its influences on the transport
Die kontinuierliche Verkleinerung der Strukturgrößen stellt hohe Anforderungen an Materialen und Technologien zukünftiger hochintegrierter Schaltkreise. Insbesondere die Leistungsfähigkeit kupferbasierte Leitbahnsystem wird bald an fundamentale Grenzen stoßen. Aufgrund ihrer hervorragenden Eigenschaften könnten metallische Kohlenstoffnanoröhren (engl. Carbon Nanotubes, CNTs) Kupfer in zukünftigen Leitbahnsystemen teilweise ersetzen. Dabei ist ein geringer Kontaktwiderstand mit vorhandenen Leitbahnen von entscheidender Bedeutung. Die vorliegende Arbeit liefert grundlegende Beiträge zur Theorie und zur numerischen Beschreibung elektronischer Transporteigenschaften metallischer CNTs mit Metallkontakten. Dazu werden verschiedene theoretische Ansätze auf diverse Kontaktmodelle angewandt und eine Auswahl von Elektrodenmaterialen (Al, Cu, Pd, Ag, Pt, Au) verglichen. Die Beschreibung ballistischen Elektronentransports erfolgt mittels des Formalismus der Nichtgleichgewichts-Green-Funktionen in Kombination mit Tight-Binding (TB), erweiterter Hückel-Theorie (EHT) und Dichtefunktionaltheorie (DFT). Vereinfachte Kontaktmodelle dienen der qualitativen Untersuchung des Einflusses von Geometrie und Länge der Nanoröhren, sowie von Stärke und Ausdehnung des Kontaktes. Darüber hinaus erlauben solch einfache Modelle mit geringem numerischen Aufwand den Einfluss verschiedener Elektronenstrukturmethoden zu untersuchen. Es zeigt sich, dass die semiempirischen Methoden TB und EHT nicht in der Lage sind die Ergebnisse der DFT quantitativ zu reproduzieren. Ausgehend von diesen Ergebnissen wird ein verbesserter Satz von Hückel-Parametern generiert, der diesen Mangel behebt. Die Untersuchung verschiedener Kontaktmaterialien erfolgt an wohldefinierten atomistischen Metall-CNT-Metall-Strukturen, welche systematisch optimiert werden. Analytische Modelle zur Beschreibung der CNT-Metall-Wechselwirkung werden vorgeschlagen. Darauf aufbauende Berechnungen der elektronischen Transporteigenschaften, können mit Hilfe der verbesserten EHT auf große Systeme ausgedehnt werden. Die Ergebnisse ermöglichen eine Reihung der Metall-CNT-Metall-Systeme hinsichtlich ihrer Leitfähigkeit: Ag ≤ Au < Cu < Pt ≤ Pd < Al. Dies korrespondiert qualitativ mit berechneten Kontaktabständen, Bindungsenergien und Austrittarbeiten der CNTs und Metalle. Zum tieferen Verständnis der Transporteigenschaften erfolgt eine detaillierte Analyse der elektronischen Struktur der Metall-CNT-Metall-Systeme und ihrer Teilsysteme. Dabei erweist sich die energieaufgelöste lokale Zustandsdichte als nützliches Werkzeug zur Visulisierung und zur Charakterisierung der Wechselwirkung zwischen CNT und Metall sowie deren Einfluss auf den Transport

Solid-state nuclear magnetic resonance (SSNMR) has proven to be a useful tool in the characterization of non-covalent interactions such as hydrogen bonding and cation-π interactions. In recent years, the scientific community has manifested a renewed interest towards an important class of non-covalent interaction, halogen bonding (XB), as it has applications in various fields such as crystal engineering and biological processes. This dissertation demonstrates that NMR parameters measured in the solid state are sensitive to changes in electronic structure, which are caused by halogen bonds. A series of halogen bonded compounds exhibiting interactions between different diiodoperfluorobenzenes (p- C6F4I2, o- C6F4I2, sym- C6F3I3, p- C6H4I2) and various halogen bond acceptors have been synthesized as part of this work. These new halogen bonded compounds were characterized with a combined theoretical and experimental SSNMR, X-ray diffraction (XRD) methods. The complete multinuclear magnetic resonance spectroscopy of the nuclei involved directly in the halogen bond (13C, 14/15N, 31P, 77Se, 35/37Cl and 79/81Br) were recorded at multiple magnetic fields (4.7, 9.4, 11.75 and 21.1 T). The specialized SSNMR experiments provided high-resolution spectra of quadrupolar nuclei, which were WURST-QCPMG or solid-echo type experiments combined with the variable offset cumulative spectral (VOCS) method, as for spin 1/2 nuclei cross polarization magic angle spinning (CPMAS) experiments were usually appropriate. This dissertation will discuss successful applications of SSNMR spectroscopy to characterize halogen bonds, it will demonstrate the significant changes in NMR observables in the presence of XB interaction and thus establish that NMR parameters are very sensitive to halogen bonding interaction. Furthermore, this work explains why the NMR parameters are correlated with the halogen bonding interaction. The different trends observed between the NMR observables and the halogen bonding were further understood with a ZORA-DFT natural localized molecular orbital (NLMO) study.

Kohlenstoffnanoröhrchen (CNTs) sind vielversprechende Kandidaten für neuartige nanoelektronische Bauelemente, wie zum Beispiel Transistoren für Hochfrequenzanwendungen. Simulationen CNT-basierter Bauelemente sind dabei unverzichtbar, um deren Anwendungspotential und das Verhalten in Schaltungen zu untersuchen. Die vorliegende Arbeit konzentriert sich auf einen Methodenvergleich zwischen einem atomistischen Ansatz basierend auf dem Nichtgleichgewichts-Green-Funktionen-Formalismus und einem Modell zur numerischen Bauelementesimulation, welches auf der Schrödinger-Gleichung in effektiver-Massen-Näherung basiert. Ein Transistor mit zylindrischem Gate und dotierten Kontakten wird untersucht, wobei eine effektive Dotierung genutzt wird. Es wird gezeigt, dass die Beschränkungen des elektronischen Transports durch Quan- teneffekte im Kanal nur mit dem atomistischen Ansatz beschrieben werden können. Diese Effekte verhindern das Auftreten von Band-zu-Band-Tunnelströmen, die bei der numerischen Bauelementesimulation zu größeren Aus-Strömen und einem leicht ambipolaren Verhalten führen. Das Schaltverhalten wird hingegen von beiden Modellen vergleichbar beschrieben. Durch Variation der Kanallänge wird das Potential des untersuchten Transistors für zukünftige Anwendungen demonstriert. Dieser zeigt bis hinab zu Kanallängen von circa 8 nm einen Subthreshold-Swing von unter 80 mV/dec und ein An/Aus-Verhältnis von über 10⁶.

La Théorie de la Fonctionnelle de la Densité (DFT) combinée avec le formalisme de la Symétrie Brisée (BS) est aujourd'hui très utilisée dans le domaine du magnétisme moléculaire pour le calcul des constantes d'échange magnétique. Dans le but d'améliorer la compréhension des contributions qui participe à l'interaction d'échange caractérisant les systèmes magnétiques, nous avons mené une étude théorique systématique basée sur l'étude de deux types de modèles. Ces complexes binucléaires de cuivre(II) reliés par divers groupements pontant de type hydroxo, azoture, et chloro, ainsi que des bis-nitroxydes modèles constitués de deux groupements nitroxydes reliés par un système conjugué sont caractérisés par des couplages ferro- et anti-ferromagnétiques variés. Nous avons développé une approche théorique basée sur l'utilisation d'orbitales gelées permettant d'étudier la décomposition de l'interaction d'échange magnétique en différentes contributions telles que l'échange direct, l'échange cinétique et le mécanisme de polarisation de spin. Dans un second temps, nous avons étendu ce travail de rationalisation aux effets de solvant à l'aide de modèles implicites ou explicites. Grâce à une analyse basée sur l'approche de Hoffmann, nous avons pu déterminer les paramètres caractérisant dans les mécanismes d'échange direct et d'échange cinétique
Density Functional Theory (DFT) combined with the Broken Symmetry (BS) method is today widely used in the field of molecular magnetism for the computation of magnetic exchange coupling constants. In order to improve the understanding of the contributions involved in the exchange phenomena characterizing some magnetic systems, we propose a study based on two types of models. Copper(II) binuclear complexes connected with various bridging groups like hydroxo, azide, and chlorine, as well as small bis-nitroxide composed of two nitroxide moieties linked by a conjugated system show various ferro- and anti-ferromagnetic couplings. We have developed a theoretical approach based on the use of frozen orbitals to decompose the magnetic exchange interaction in different contributions such as the direct exchange, the kinetic exchange and mechanism of spin polarization. In a second part, we have extended this work to rationalize the solvent effects using implicit or explicit models. Through an analysis based on the Hoffmann's approach, we have determined some parameters characterizing the mechanisms of direct exchange and kinetic exchange

碩士
國立成功大學
化學系碩博士班
94
The photophysical properties of a series of cyclometalated Ir(III) complexes Ir(ppy)2(CN)2- (1), Ir(ppy)2(NCS)2- (2), and Ir(ppy)2(NCO)2- (3) (where ppy = 2-phenyl pyridine, CN = cyanide, NCS = isothiocyanate, and NCO = isocyanate) have been reported. It is concluded that time-dependent density functional theory (TD-DFT) calculations supply theoretical interpretation of the triplet excited states and the nature of photophysical behaviors reported in literature. Combined with conductive polarizable continuum model (CPCM) the calculations are valid in examining the solvent effect on excitation energies. Analysis of highest occupied molecular orbital (HOMO) and lowest unoccupied orbital (LUMO) obtained by B3LYP functional reveals effects of p-donating and/or p-accepting properties of three pseudohalogens on optical orbitals in complexes 1, 2, and 3. The origin of HOMO tuning up, results in the blue, green and yellow photoluminescence observed in experiments, can be interpreted by interaction between the lone pairs perturbed p-p*(NC) system with metal dp orbitals. We have modified the Hoffman’s orbital interaction diagram to demonstrate effects of sulfur or oxygen atoms on the energy of p(NC). The degree of HOMO tuning-up is parallel to the lone-pair contribution to the perturbed p (NC) analyzed by the natural bonding orbital (NBO) method.

The continuous migration to smaller feature sizes puts high demands on materials and technologies for future ultra-large-scale integrated circuits. Particularly, the copper-based interconnect system will reach fundamental limits soon. Their outstanding properties make metallic carbon nanotubes (CNTs) an ideal material to partially replace copper in future interconnect architectures. Here, a low contact resistance to existing metal lines is crucial. The present thesis contributes to the theory and numerical description of electronic transport in metallic CNTs with metal contacts. Different theoretical approaches are applied to various contact models and electrode materials (Al, Cu, Pd, Ag, Pt, Au) are compared. Ballistic transport calculations are based on the non-equilibrium Greens function formalism combined with tight-binding (TB), extended Hückel theory (EHT) and density functional theory (DFT). Simplified contact models allow a qualitative investigation of both the influence of geometry and CNT length, and the strength and extent of the contact on the transport properties. In addition, such simple contact models are used to compare the influence of different electronic structure methods on transport. It is found that the semiempirical TB and EHT are inadequate to quantitatively reproduce the DFT-based results. Based on this observation, an improved set of Hückel parameters is developed, which remedies this insufficiency. A systematic investigation of different contact materials is carried out using well defined atomistic metal-CNT-metal structures, optimized in a systematic way. Analytical models for the CNT-metal interaction are proposed. Based on that, electronic transport calculations are carried out, which can be extended to large systems by applying the computationally cheap improved EHT. The metal-CNT-metal systems can then be ranked by average conductance: Ag ≤ Au < Cu < Pt ≤ Pd < Al. This corresponds qualitatively with calculated contact distances, binding energies and work functions of CNTs and metals. To gain a deeper understanding of the transport properties, the electronic structure of the metal-CNT-metal systems and their respective parts is analyzed in detail. Here, the energy resolved local density of states is a valuable tool to investigate the CNT-metal interaction and its influences on the transport.
Die kontinuierliche Verkleinerung der Strukturgrößen stellt hohe Anforderungen an Materialen und Technologien zukünftiger hochintegrierter Schaltkreise. Insbesondere die Leistungsfähigkeit kupferbasierte Leitbahnsystem wird bald an fundamentale Grenzen stoßen. Aufgrund ihrer hervorragenden Eigenschaften könnten metallische Kohlenstoffnanoröhren (engl. Carbon Nanotubes, CNTs) Kupfer in zukünftigen Leitbahnsystemen teilweise ersetzen. Dabei ist ein geringer Kontaktwiderstand mit vorhandenen Leitbahnen von entscheidender Bedeutung. Die vorliegende Arbeit liefert grundlegende Beiträge zur Theorie und zur numerischen Beschreibung elektronischer Transporteigenschaften metallischer CNTs mit Metallkontakten. Dazu werden verschiedene theoretische Ansätze auf diverse Kontaktmodelle angewandt und eine Auswahl von Elektrodenmaterialen (Al, Cu, Pd, Ag, Pt, Au) verglichen. Die Beschreibung ballistischen Elektronentransports erfolgt mittels des Formalismus der Nichtgleichgewichts-Green-Funktionen in Kombination mit Tight-Binding (TB), erweiterter Hückel-Theorie (EHT) und Dichtefunktionaltheorie (DFT). Vereinfachte Kontaktmodelle dienen der qualitativen Untersuchung des Einflusses von Geometrie und Länge der Nanoröhren, sowie von Stärke und Ausdehnung des Kontaktes. Darüber hinaus erlauben solch einfache Modelle mit geringem numerischen Aufwand den Einfluss verschiedener Elektronenstrukturmethoden zu untersuchen. Es zeigt sich, dass die semiempirischen Methoden TB und EHT nicht in der Lage sind die Ergebnisse der DFT quantitativ zu reproduzieren. Ausgehend von diesen Ergebnissen wird ein verbesserter Satz von Hückel-Parametern generiert, der diesen Mangel behebt. Die Untersuchung verschiedener Kontaktmaterialien erfolgt an wohldefinierten atomistischen Metall-CNT-Metall-Strukturen, welche systematisch optimiert werden. Analytische Modelle zur Beschreibung der CNT-Metall-Wechselwirkung werden vorgeschlagen. Darauf aufbauende Berechnungen der elektronischen Transporteigenschaften, können mit Hilfe der verbesserten EHT auf große Systeme ausgedehnt werden. Die Ergebnisse ermöglichen eine Reihung der Metall-CNT-Metall-Systeme hinsichtlich ihrer Leitfähigkeit: Ag ≤ Au < Cu < Pt ≤ Pd < Al. Dies korrespondiert qualitativ mit berechneten Kontaktabständen, Bindungsenergien und Austrittarbeiten der CNTs und Metalle. Zum tieferen Verständnis der Transporteigenschaften erfolgt eine detaillierte Analyse der elektronischen Struktur der Metall-CNT-Metall-Systeme und ihrer Teilsysteme. Dabei erweist sich die energieaufgelöste lokale Zustandsdichte als nützliches Werkzeug zur Visulisierung und zur Charakterisierung der Wechselwirkung zwischen CNT und Metall sowie deren Einfluss auf den Transport.