Results of spin density functional theory (SDFT) calculations were used to construct and check features of a generally applicable semi-quantitative approach to understanding magnetic coupling in gadolinium-containing molecules, clusters, and solids. Using fragments based on structures of metal-rich lanthanide compounds, we have investigated molecular and low-dimensional extended structures, and have shown that open-d-shell clusters facilitate strong ferromagnetic coupling whereas closed-d-shell systems prefer antiferromagnetic coupling. The qualitative features can be interpreted using a perturbative molecular orbital (PMO) model that focuses the influence of the 4f 7- d exchange interaction on the d-based molecular orbitals. The f-d exchange interaction, mediated by spin polarization of both filled and partially-filled metal-metal bonding orbitals, is described for the model system Gd3I6(OPH3)12 n+ using basic perturbation methods. This approach is successful for predicting the magnetic ground state for Gd2Cl3, a semiconducting system for which calculations predict antiferromagnetic ordering of the 4f 7 moments in a pattern consistent with published neutron diffraction data. An attempt to account for the calculated magnetic energies of spin patterns using an Ising model was unsuccessful, indicating that the Ising model is inappropriate. Instead, the d-electron mediated f-f exchange interaction was interpreted using our basic perturbation theory approach. Computed density of states and spin polarization information was used to support the perturbation-theoretic analysis. This method has also been successful evaluating the ground state for Gd[Gd6FeI12]. Using the model [Gd6CoI12](OPH3)6, which has three unpaired electrons in the HOMO, the 4f moments prefer spin alignment with the unpaired electrons in the system and the ferromagnetic 4f 7 spin arrangement is the ground state. We have extended our analysis of R6X12 clusters to include nonmetal interstitial atoms, the bioctahedral cluster compounds Gd10Cl17C4 and Gd10I16C4, and Gd5(O)(OPri)5. Finally, we have shown that we can successfully predict the ground state magnetic structures of several metallic and semiconducting Gd-containing compounds, Gd2Cl3, GdB2C2,alpha-Gd2S3, Gd5Si4, and Gd5Ge4, using semi-empirical calculations which closely simulates the exchange effects exerted by the 4f electrons. In a more speculative vein, ideas concerning the incorporation of anisotropic rare-earth metal atoms to the cluster framework are touched upon.

Thesis (Ph. D.)--University of Adelaide, Dept. of Physics and Mathematical Physics, 1991. / Includes bibliographical references (leaves 135-146).

Made available in DSpace on 2016-05-17T16:50:55Z (GMT). No. of bitstreams: 0 Previous issue date: 2007-04-27. Added 1 bitstream(s) on 2016-05-17T16:54:22Z : No. of bitstreams: 1 000855676.pdf: 503229 bytes, checksum: c62a118de1f0a2d1f4f6ba7582f1a8aa (MD5) / Apresentamos a solução analítica completa para as equações de Friedmann válida na presença da constante cosmológica 'lâmbda', do parâmetro de curvatura 'capa', de matéria não-relativística (bariônica ou escura) e de radiação. Este é o modelo 'lâmbda' IND. 'gama'CDM, que exibe claramente a aceleração recente e inclui modelos particulares, como o 'lâmbda'CDM. Obtemos o conjunto completo dos geradores de simetria para o elemento de linha de Friedmann-Robertson-Walker (FRW) pela integração direta das equações de Killing. O processo de cálculo leva à função U = 'a POT. 2'H, produto do quadrado do fator de escala pela derivada temporal da função de Hubble. U constante fixa a solução maximalmente simétrica de de Sitter (dS) - com 10 geradores - em detrimento de qualquer outra solução de FRW - com 6 geradores. A interpretação física dos geradores de dS nas coordenadas comóveis não é evidente, o que exige a transcrição deles para coordenadas estáticas de dS. Nestas coordenadas, eles têm uma interpretação clara, dada a relação direta com os geradores de Poincaré via contrações de Wigner-Inönú. Um passo necessário é a construção das transformações de Robertson generalizadas entre o intervalo estático de dS e o elemento de linha de FRW para os três valores de 'capa' / Analytic expressions for solutions in the Standard Model are presented here for all combinations of 'lâmbda' = 0, 'lâmbda'diferente 0, 'capa' = 0 and 'capa'diferente'0 in the presence and absence of radiation and nonrelativistic matter. The most complete case (here called the 'lâmbda' IND. 'gama'CDM Model) has 'lâmbda'diferente 0, 'capa'diferente'0, and supposes the presence of radiation and dust. It exhibits clearly the recent onset of acceleration and reduces to the particular models such as the 'lâmbda'CDM Model. A detailed examination of the Killing equations in Robertson-Walker coordinates shows how the addition of matter and/or radiation to a de Sitter Universe breaks the symmetry generated by four of its Killing fields. The product U = 'a POT. 2'H of the squared scale parameter by the time-derivative of the Hubble function encapsulates the relationship between the two cases: the symmetry is maximal when U is a constant, and reduces to the 6-parameter symmetry of a generic Friedmann-Robertson-Walker model when it is not. As the fields physical interpretation is not clear in these coordinates, comparison is made with the Killing fields in static coordinates, whose interpretation is made clearer by their direct relationship to the Poincaré group generators via Wigner-Inönü contractions

Orientador: Ruben Aldrovandi / Banca: Sérgio Eduardo de Carvalho Eyer Jorás / Banca: Ilya Lvovich Shapiro / Bnaca: José Geraldo Pereira / Resumo: Apresentamos a solução analítica completa para as equações de Friedmann válida na presença da constante cosmológica 'lâmbda', do parâmetro de curvatura 'capa', de matéria não-relativística (bariônica ou escura) e de radiação. Este é o modelo 'lâmbda' IND. 'gama'CDM, que exibe claramente a aceleração recente e inclui modelos particulares, como o 'lâmbda'CDM. Obtemos o conjunto completo dos geradores de simetria para o elemento de linha de Friedmann-Robertson-Walker (FRW) pela integração direta das equações de Killing. O processo de cálculo leva à função U = 'a POT. 2'H, produto do quadrado do fator de escala pela derivada temporal da função de Hubble. U constante fixa a solução maximalmente simétrica de de Sitter (dS) - com 10 geradores - em detrimento de qualquer outra solução de FRW - com 6 geradores. A interpretação física dos geradores de dS nas coordenadas comóveis não é evidente, o que exige a transcrição deles para coordenadas estáticas de dS. Nestas coordenadas, eles têm uma interpretação clara, dada a relação direta com os geradores de Poincaré via contrações de Wigner-Inönú. Um passo necessário é a construção das transformações de Robertson generalizadas entre o intervalo estático de dS e o elemento de linha de FRW para os três valores de 'capa' / Abstract: Analytic expressions for solutions in the Standard Model are presented here for all combinations of 'lâmbda' = 0, 'lâmbda'diferente 0, 'capa' = 0 and 'capa'diferente'0 in the presence and absence of radiation and nonrelativistic matter. The most complete case (here called the 'lâmbda' IND. 'gama'CDM Model) has 'lâmbda'diferente 0, 'capa'diferente'0, and supposes the presence of radiation and dust. It exhibits clearly the recent onset of acceleration and reduces to the particular models such as the 'lâmbda'CDM Model. A detailed examination of the Killing equations in Robertson-Walker coordinates shows how the addition of matter and/or radiation to a de Sitter Universe breaks the symmetry generated by four of its Killing fields. The product U = 'a POT. 2'H of the squared scale parameter by the time-derivative of the Hubble function encapsulates the relationship between the two cases: the symmetry is maximal when U is a constant, and reduces to the 6-parameter symmetry of a generic Friedmann-Robertson-Walker model when it is not. As the fields physical interpretation is not clear in these coordinates, comparison is made with the Killing fields in static coordinates, whose interpretation is made clearer by their direct relationship to the Poincaré group generators via Wigner-Inönü contractions / Doutor

Thesis (Ph. D.)--University of Texas at Austin, 2000. / Vita. Includes bibliographical references (leaves 157-163). Available also in a digital version from Dissertation Abstracts.

Optimizaciones geométricas fueron llevadas a cabo con las formas cis y trans del anión [Nb2W4O19]4-. También fueron estudiadas para la forma cis varios isómeros del anión [Nb2W4O19H]3-, sugiriendo que el oxígeno enlazado a los dos átomos de Nb es el centro más básico. La determinación energética de las basicidades de los oxígenos en los hexametalatos fueron comparadas con la metodología de la distribución del potencial electrostático molecular, que es más económica computacionalmente. En el anión [V2W4O19]4-, el único OV2 fue identificado como el centro más básico. Aunque con el anión niobiotungstato, el centro más básico no soporta la carga negativa más alta.Cálculos basados en la teoría del funcional de la densidad ha sido llevados a cabo para investigar las propiedades electrónicas y magnéticas de los aniones -Keggin: [XW12O40]n-, (M= W, Mo; X= AlIII, SiIV, PV, FeIII, CoII, CoIII) y [SiM11VO40]m- (M=Mo y W). La población atómica y la distribución de la densidad electrónica calculada en los clusters estudiados mantienen la hipótesis que un anión Keggin oxidado es un clatrato XO4n- en el interior de una caja neutra M12O36. El intervalo de energía entre la banda de orbitales ocupados, formalmente deslocalizados en los ligandos oxo, y los orbitales vacíos d metálicos, deslocalizados sobre la caja, se ha encontrado independiente del ion central. Sin embargo, la substitución de un W o un Mo por un V modifica la energía relativa del LUMO y por consiguiente induce importantes cambios en las propiedades redox del cluster. De acuerdo con la más reciente determinación de rayos X del [CoIIIW12O40]5- y con la simplicidad del espectro observado para este anión, los cálculos sugieren que tiene una ligera geometría distorsionada Td. Para el cluster derivado [CoW12O40]6- el cuadruplete correspondiente al anión encapsulando un CoII, se ha hallado 1 eV más estable que la especie formada por un CoIII y 1 e deslocalizado en la pseudoesfera de los tungstenos. La reducción monoelectrónica del [CoIIW12O40]6- y [FeIIIW12O40]5- lleva a la formación de las especies "blue" 1e [CoIIW12O40]7- y [FeIIIW12O40]6-. El cluster "blue" de hierro es considerablemente antiferromagnético, y está en completa concordancia con este resultado el estado de bajo espín calculado con la aproximación "Broken Symmetry ", siendo 196 cm-1 más bajo que la solución de alto espín. Por el contrario, el anión "blue" de cobalto tiene un bajo acoplamiento ferromagnético con una diferencia S-T de 20 cm-1.[PMo12O40(VO)2]5- es un cluster altamente reducido con ocho electrones metálicos d. La naturaleza de la localización-deslocalización de los electrones d metálicos es uno de los puntos de interés de los polioxoaniones reducidos. Hemos llevado a cabo cálculos DFT que sugieren que el estado de oxidación de los átomos V es +4 y los otros seis electrones metálicos están deslocalizados entre los doce átomos de Mo. Los cálculos también proponen la evidencia de que el anión [PMo12O40(VO)2]5- debería ser paramagnético. El entorno cristalino fue introducido en los cálculos por medio de dos modelos, incrementando la tendencia a tener electrones metálicos.Los multipletes derivados de varias configuraciones excitadas del [CoIIW12O40]6- fueron calculadas usando métodos DFT. De acuerdo con la interpretación experimental del espectro, los cálculos hallan que la primera gran banda corresponde a las transiciones d-d del Co, pero es de destacar que superpuestas a estas transiciones se encuentran las transiciones de tranferencia de carga del cobalto a los wolframios. Los cálculos también demuestran la importancia de las distorsiones Jahn-Teller en los estados excitados. Con la excepción de las consecuencias derivadas de una pequeña diferencia de los orbitales d del cobalto, el espectro d-d del [CoCl4]2- es similar al del complejo del anión de Keggin. Finalmente, la energía de la transición bielectrónica fue estimada por un procedimiento basado en la teoría del campo ligando. / Geometry optimizations were carried out for the cis and trans forms of [Nb2W4O19]4-. Several isomers of the [Nb2W4O19H]3- anion were also studied for the cis form, suggesting that the oxygen bonded to two Nb atoms is the most basic center. The energetic determination of the oxygen basicities in hexametalates was compared with the indirect and less computationally demanding methodology based upon molecular electrostatic potential distributions. In [V2W4O19]4-, the unique OV2 was identified as the most basic center. Although at variance with the niobotungstate anion, the most basic center does not support the highest net negative charge.Calculations based on density functional theory have been carried out to investigate the electronic and magnetic properties of the -Keggin anions: [XW12O40]n-, (M= W, Mo; X= AlIII, SiIV, PV, FeIII, CoII, CoIII) and [SiM11VO40]m- (M=Mo and W). The atomic populations and the distribution of the electron density computed for the studied clusters support the hypothesis that an oxidized Keggin anion is an XO4n- clathrate inside a neutral M12O36 cage. The energy gap between the band of occupied orbitals, formally delocalized over the oxo ligands, and the unoccupied d-metal orbitals, delocalized over the addenda, has been found to be independent of the central ion. However, substitution of a W or a Mo by V modifies the relative energy of the LUMO and then induces important changes in the redox properties of the cluster. In agreement with the most recent X-ray determination of [CoIIIW12O40]5- and with the simplicity of the spectra observed for this anion the calculations suggest that was a slightly distorted Td geometru. For the parent cluster [CoW12O40]6- the quadruplet corresponding to the anion encapsulating a CoII was found to be 1 eV more stable than the species formed by a CoIII and 1 e delocalized over the sphere of tungstens. The one-electron reduction of [CoIIW12O40]6- and [FeIIIW12O40]5- leads to the formation of the 1 e blue species [CoIIW12O40]7- and [FeIIIW12O40]6-. The blue-iron cluster is considerably antiferromagnetic, and in full agreement with this behavior the low-spin state computed via a Broken Symmetry approch is 196 cm-1 lower than the high-spin solution. In contrast, the cobalt blue anion has a low ferromagnetic coupling with an S-T energy gap of +20 cm-1.[PMo12O40(VO)2]5- is a highly reduced cluster with eight d metal electrons. The localization-delocalization nature of d metal electrons is one of the points of interest in reduced polyoxoanions. We report DFT calculations wich suggest that the oxidation state of the V atoms is +4 and the other six metal electrons are delocalized between the 12 Mo atoms. The calculations also provide evidence that the anion [PMo12O40(VO)2]5- should be paramagnetic. The crystal environment, wich was included in the calculations by means of two models, increases the tendency to have metal electrons.Multiplet splittings for several excited configurations of [CoIIW12O40]6- were calculated using DFT methods. In agreement with the experimental interpretation of the spectrum the calculations found that the first strong band corresponds to Co d-d transitions, but it is worth noting that superposed to these transitions there are charge transfer transitions from cobalt to tungsten. The calculations also showed the importance of Jahn-Teller distortions in the excited states. With the exception of the consequences derived from a smaller splitting of d cobalt orbitals the d-d spectrum of [CoCl4]2- is similar to that of the more complex Keggin anion. Finally, the energy of the bielectronic transition 4A24T1(P) was estimated via an approximate procedure based on ligand field theory.

Bibliography : leaves 135-146 / vii, 146 leaves ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Dept. of Physics and Mathematical Physics, 1991

Made available in DSpace on 2014-06-11T19:25:34Z (GMT). No. of bitstreams: 0 Previous issue date: 2011-09-27Bitstream added on 2014-06-13T19:12:27Z : No. of bitstreams: 1 woitekjunior_m_me_ift.pdf: 9022411 bytes, checksum: 88726cc3ceec91a0d503f0b0557e5add (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Uma das características mais importantes das teorias de gauge não-Abelianas é a não-linearidade das equações de campo clássicas. Mostra-se no contexto da teoria de Yang-Mills que essa característica pode fazer com que o campo de gauge apresente comportamento caótico. Isso pode acontecer mesmo quando estivermos considerando a dinâmica do campo na ausência de fontes, isto é, o vácuo da teoria de Yang-Mills. Discutimos a relação entre os comportamentos caótico e ergódico. Em seguida, introduzimos a formulação de Berdichevsky da Mecânica Estatística Clássica para sistemas dinâmicos Hamiltonianos que são ergódicos e possuem poucos graus de liberdade. A Mecânica Estatística de Berdichevsky é usada para estudar a situação mais simples numa teoria de gauge não-Abeliana onde as variáveis de campo são caóticas e o espaço de fase correspondente tem a propriedade geométrica necessária. Mostramos que, para os propósitos desse estudo, um par de campos escalares complexos deve ser incluído no problema. Mais precisamente, analisamos o modelo de Higgs não-Abeliano; a Lagrangiana da teoria considerada possui uma simetria SU(2). A transição de uma descrição dinâmica do sistema de YangMills-Higgs (fora do equilíbrio termodinâmico) para uma descrição termodinâmica (quando ele atingiu o equilíbrio) é investigada numericamente. Mostra-se que depois de um tempo suficientemente longo as soluções numéricas se comportam de tal maneira que o sistema pode ser descrito de um jeito mais simples através de grandezas como a temperatura, calculadas de acordo com as prescriçõees da Mecânica Estatística de equilíbrio. Estas são previstas analiticamente para comparção com os resultados numéricos... / One of the most important features of non-Abelian gauge theories is the non-linearity of the classical field equations. In the context of Yang-Mills theory it is shown that this feature can cause the gauge field to show chaotic behavior. That can happen even when we are considering the field dynamics in the absence of sources, i.e., the vacuum of the Yang-Mills theory. We discuss the connection between chaotic and ergodic behaviors. Then we introduce Berdichevsky’s formulation of Classical Statistical Mechanics for Hamiltonian dynamical systems that are both ergodic and low-dimensional. Berdichevsky’s theory of Statistical Mechanics is used to study the simplest situation in a non-Abelian gauge theory where the field variables are chaotic and the corresponding phase space has the necessary geometric property. We show that, for the purposes of this study, a pair of complex scalar fields must be introduced in the problem. More precisely, we analyse the so-called non-Abelian Higgs model; the Lagrangian of the theory we are considering has a SU(2) symmetry. The transition from a non-equilibrium dynamical description of the Yang-Mills-Higgs system to a thermodynamical description when it reaches equilibrium is numerically investigated. It is shown that after a sufficiently long time the numerical solutions behave in such a manner that the system can be described by quantities like the temperature, determined in accordance with the prescriptions of equilibrium Statistical Mechanics. These are predicted analytically for comparison with the numerical results. It is verified that there is agreement between analytical and numerical predictions so that the thermalization of the Yang-Mills-Higgs system can be explained with the aid of Berdichevsky’s Statistical Mechanics. A dynamical approach to the study... (Complete abstract click electronic access below)

The concept of emergence stands in need of an update, and I propose that ontologically emergent phenomena are characterized by four necessary features: relationality, novelty, irreducibility and broken symmetry. ‘Emergence’ is a useful term to denote the varied qualitative changes that spontaneously arise as the scale and complexity of related phenomena increases. Moreover, emergent phenomena share a unique relationship with the phenomena from which they emerge, namely the emergent relation. This relation is distinct from other types of relations (i.e., identity, composition, supervenience, etc.) and moreover is not beset by the problems of causal exclusion or downward causation. Lastly, I advance this account of emergence partly as an empirical hypothesis. The epistemic resources in dynamical systems theory are uniquely suited to describe the evolution of systems that manifest emergent phenomena. This is primarily because features like novelty and broken symmetry can be given mathematically precise descriptions in dynamical systems terms. The advantage of this updated concept of emergence is its compatibility with ideas of explanation, prediction and reduction. / Thesis / Master of Philosophy (MA) / The concept of emergence is a useful one to succinctly describe the relatedness of a variety of complex phenomena in our universe. The concept of emergence however stands in need of an update. Emergent phenomena, as some would argue, are not unexplainable brute facts nor are they wholly unpredictable. I propose that ontologically emergent phenomena are characterized by four necessary features: relationality, novelty, irreducibility, and broken symmetry.

This thesis presents electronic structure calculations on problems related to the bonding in inorganic coordination compounds and clusters. A wide range of molecules with the ability to exist in different structural forms or electronic states has been selected and density functional theory is systematically applied in order to gain detailed insight into their characteristics and reactivity at the electronic level. First, we address the question of redox non-innocent behaviour of bipyridine in a series of 1st row transition metal complexes. Complexes of the type [M(2,2'-bipyridine)(mes)₂]⁰ (M = Cr, Mn, Fe, Co, Ni; mes = 2,4,6-Me₃C6H₂) and their one-electron reduced forms have been explored. The results clearly show that the anions are best described as complexes of the monoanionic bipyridine radical (S_bpy = 1/2), giving a rationale for the observed structural changes within the ligand. Likewise, we have identified dianionic bipyridine in both the complexes [Zn2(4,4'-bpy)(mes)₄]²⁻ and [Fe(2,2'-bpy)₂]²⁻. In no case have we found evidence for significant metal-to-ligand backbonding. The subject of redox-noninnocence is further revisited in a comparative study of the two complexes [M(o-Clpap)₃] (M = Cr, Mo; o-Clpap = 2-[(2-chloro-phenyl)azo]-pyridine), and their associated electron transfer series. The results indicate that all electron transfer processes are primarily ligand-based, although in the case of the Mo analogue these are coupled to substantial electron density changes at the metal. The ability of pap to form radical anions finds a contrasting case in the di- nuclear Rh complex [Rh₂(μ-p-Clpap)₂ (cod)Cl₂], where the two ligand bridges act as acceptors of strong dπ∗ backbonding from a formally Rh^–I centre. We then direct our attention to the endohedral Zintl clusters [Fe@Ge₁₀]³⁻ and [Mn@Pb₁₂]³⁻, which reveal peculiar topologies. We have probed the electronic factors that influence their geometric preferences, and propose a model based on the shift of electron density from the endo- hedral metal to the cage to account for the observed geometries. Subsequently, we reassess the electronic structure of the xenophilic clusters Mn₂(thf)₄(Fe(CO)₄)₂ and [Mn(Mn(thf)₂)₃(Mn(CO)₄)₃]^–. We conclude that these are best viewed as exchange coupled Mn^II centres bridged by closed- shell carbonylate fragments. In the closing chapter the reduction of NO₂^– to NO by the complex [Cu(tct)(NO₂)]⁺ (tct = cis,cis-1,3,5-tris(cinnamylideneamino)cyclohexane) is studied, a process that mimics the enzyme-catalysed reaction. Two viable pathways for the reaction have been traced and key inter-mediates identified. Both direct release of NO or via decomposition of a Cu-NO complex are kinetically and thermodynamically feasible.