Neste trabalho estudamos três diferentes sistemas de fluidos clássicos. No primeiro, esferas de poliestireno adsorvidas em água, o potencial de interação é do tipo dipolar (1/r3). As funções de correlação radial e fator de estrutura estático bem como a energia de correlação e energia livre de Helmholtz foram obtidas na aproximação das equações integral HNC. 0s resultados obtidos estão em excelente concordância com os resultados \"exatos\" de dinâmica Molecular. No segundo sistema, elétrons em superfície de hélio líquido adsorvido em um substrato, generalizamos o trabalho de Studart e Hipólito bem como o de Monarkha ao considerarmos qualquer tipo de substrato e qualquer espessura do filme de hélio. Utilizando a aproximação de Campo Auto Consistente obtivemos o fator de estrutura estático, energia de correlação e relação de dispersão. As correlações de curto alcance, responsáveis pela correção do campo local, corrigem de maneira sensível os resultados da aproximação das fases aleatórias (RPA) . No terceiro, um sistema de esferas duras carregadas, utilizamos a aproximação de Campo Auto Consistente e obtivemos o fator de estrutura estático, função de correlação de pares, equação de estado e energia de correlação. Obtivemos, pela primeira vez, a relação de dispersão deste plasma de uma componente generalizado. Este sistema é particularmente interessante pois em primeira aproximação descreve eletrólitos e sais fundidos. / We have studied in this work three different classic fluid systems. The first one, formed by polystyrene spheres adsorbed on water, can be described by a dipolar (1/r3) interaction. Theradial correlation function and static structure factor as well the correlation energy and Helmholtz free energy were obtained in the framework of the Hypernetted Chain (HNC) Integral Approximation. Our results were in excell entagreement with the \"exact\" results from Molecular Dynamics techniques. The second system consists of electrons trapped on the liquid helium films wetting a solid substrate . In this case, we have generalized the works of Studart and Hipolito, and Monarkha, by analysing the influence of the film thickness and different kinds of substrates. By using the Self-Consistent Field Approximation (SCFA), we have evaluated the static structure factor, correlation energy and plasma dispersion relation . The local field correction, responsible by the short-range correlation , modifies drastically the results from the Random-Phase Approximation (RPA). In the third system, a charged hard sphere fluid , we have determined, by using SCFA, some properties of this many-body system such as the static structure factor, pair correlation function, the equation of state and correlation energy. For the first time , we have calculated the plasma dispersion relation of this generalized one-component plasma. This system is very interesting because, in a first approximation, it can describe eletrolytes and molten salts.

A central concern within the field of molecular magnetism has been the elucidation of magneto-structural correlations. This thesis describes a variety of systems and endeavours to study the relationship between structure and magnetic properties in these systems. The first body of work (chapters 2 and 3) studies CrIII dimers, with the metal centres displaying a dialkoxo bridging moiety and latterly an additional carboxylate bridge to direct the synthesis of ferromagnetic analogues. The second section of work (chapters 4‐6) moves forward to the study of larger, heterometallic 3d‐3d compounds, through the synthesis of a large family of Anderson type MIII 2MII 5 wheels and a subsequent family of (VIVO)2MII 5 wheels. Chapter 2 describes a series of di‐alkoxo bridged Cr(III) dimers, synthesised using the pyridine alcohol ligands 2‐pyridinemethanol (hmpH) and 2‐pyridineethanol (hepH) as well as 2‐picolinic acid (picH). The structures fall into four general categories and are of formula: [Cr2(OMe)2(pic)4], [Cr2(hmp)2(pic)2X2] (where X = Cl, Br), [Cr2(L)2Cl4(A)2] (where L = hmp, A = H2O; L = hmp, A = pyridine; L = hmp, A = 4‐picoline; L = hep, A = H2O), and [Cr(hmp)(hmpH)Cl2. Magnetic studies show relatively weak antiferromagnetic exchange interactions between the Cr(III) centres and DFT calculations are used to develop magneto‐structural correlations, showing that the magnitude and sign of the J value is strongly dependent upon the orientation of the dihedral angle formed between the bridging Cr2O2 plane and the O-R vector of the bridging group, and the Cr-O-Cr-O dihedral angle. Chapter 3 builds on the work from the previous chapter with discussion of a large family of chromium(III) dimers, synthesised using a combination of carboxylate and diethanolamine type ligands. The compounds have the general formula [Cr2(R1‐deaH)2(O2CR2)Cl2]Cl where R1 = Me and R2 = H, Me, CMe3, Ph, 3,5‐(Cl)2Ph, (Me)5Ph, R1 = Et and R2 = H, Ph. The compound [Cr2(Me‐deaH)2Cl4] was also synthesised in order to study the effect of removing/adding the carboxylate bridge to the observed magnetic behaviour. Magnetic studies reveal ferromagnetic exchange interactions between the Cr(III) centres in the carboxylate bridged family with coupling constants in the range +0.37 < J < +8.02 cm‐1. Removal of the carboxylate to produce the dialkoxide‐bridged compound results in antiferromagnetic exchange between the Cr(III) ions. DFT calculations to further develop the magneto-structural correlations reveal the ferromagnetic exchange is the result of an orbital counter-complementarity effect occurring upon introduction of the bridging carboxylate. Chapter 4 reports a family of heterometallic Anderson‐type 'wheels' of general formula [MIII 2MII 5(hmp)12](ClO4)4 (where MIII = Cr or Al and MII = Ni or Zn giving [Cr2Ni5], [Cr2Zn5], [Al2Ni5] and [Al2Zn5]; hmpH = 2‐pyridinemethanol) synthesised solvothermally. The metallic skeleton describes a centred hexagon with the MIII sites disordered around the outer wheel. The structural disorder is characterised via single crystal X‐ray crystallography, 1‐3D 1H and 13C solution‐state NMR spectroscopy of the diamagnetic analogue, and solid‐state 27Al MAS NMR spectroscopy of the Al containing analogues. Alongside ESI mass spectrometry, these techniques show that structure is retained in solution, and that the disorder is present in both the solution and solid‐state. Solid‐state dc susceptibility and magnetisation measurements on [Cr2Zn5] and [Al2Ni5] reveal the Cr‐Cr and Ni‐Ni exchange interactions to be JCr‐Cr = ‐1 cm‐1 and JNi‐Ni,r = ‐5 cm‐1, JNi‐Ni,c = 10 cm‐1. Fixing these values allows us to extract JCr‐Ni,r = ‐1.2 cm‐1, JCr‐Ni,c = 2.6 cm‐1, the exchange between adjacent Ni and Cr ions on the ring is antiferromagnetic and between Cr ions on the ring and the central Ni ion is ferromagnetic. Chapter 5 focusses on planar molecules, espanding the family of heterometallic Anderson‐type 'wheels' discussed in chapter 4 to include MIII = Cr, Al and MII = Co, Fe, Mn, Cu, affording five new species of formulae [Cr2Co5(hmp)12](ClO4)4, [Cr2Fe5(hmp)12](ClO4)4, [Cr2Mn5(hmp)12](ClO4)4, [Cr2Cu5(hmp)12](ClO4)2(NO3)2 and [Al2Co5(hmp)12](ClO4)4. As per previous family members, the two MIII sites are disordered around the outer wheel, with the exception of [Cr2Cu5] where the the CuII sites are localised. A structurally related, but enlarged planar disc possessing a [MIII 6MII] hexagon capped on each edge by a CuII ion is also reported, which is formed only when MIII = Al and MII = Cu. In [AlIII 6CuII 7(OH)12(hmp)12](ClO4)6(NO3)2 the Anderson moiety contains a central, (symmetry‐imposed) octahedral CuII ion surrounded by a wheel of AlIII ions. Solid‐state dc susceptibility and magnetisation measurements reveal the presence of competing exchange interactions in the Anderson wheels family, and weak antiferromagnetic exchange between the CuII ions in [Al6Cu7]. Chapter 6 describes two heterometallic wheels of formula [(VIVO)2MII 5(hmp)10Cl2](ClO4)2∙2MeOH (where MII = Ni or Co) displaying the same Anderson‐type structure as seen in chapters 4 and 5, however the use of the vanadyl moiety has the effect of removing the disorder, with the two vanadyl ions sitting on opposing sides of the ring. The magnetic properties of both show competing antiferroand ferromagnetic interactions.

Neste trabalho estudamos três diferentes sistemas de fluidos clássicos. No primeiro, esferas de poliestireno adsorvidas em água, o potencial de interação é do tipo dipolar (1/r3). As funções de correlação radial e fator de estrutura estático bem como a energia de correlação e energia livre de Helmholtz foram obtidas na aproximação das equações integral HNC. 0s resultados obtidos estão em excelente concordância com os resultados \"exatos\" de dinâmica Molecular. No segundo sistema, elétrons em superfície de hélio líquido adsorvido em um substrato, generalizamos o trabalho de Studart e Hipólito bem como o de Monarkha ao considerarmos qualquer tipo de substrato e qualquer espessura do filme de hélio. Utilizando a aproximação de Campo Auto Consistente obtivemos o fator de estrutura estático, energia de correlação e relação de dispersão. As correlações de curto alcance, responsáveis pela correção do campo local, corrigem de maneira sensível os resultados da aproximação das fases aleatórias (RPA) . No terceiro, um sistema de esferas duras carregadas, utilizamos a aproximação de Campo Auto Consistente e obtivemos o fator de estrutura estático, função de correlação de pares, equação de estado e energia de correlação. Obtivemos, pela primeira vez, a relação de dispersão deste plasma de uma componente generalizado. Este sistema é particularmente interessante pois em primeira aproximação descreve eletrólitos e sais fundidos. / We have studied in this work three different classic fluid systems. The first one, formed by polystyrene spheres adsorbed on water, can be described by a dipolar (1/r3) interaction. Theradial correlation function and static structure factor as well the correlation energy and Helmholtz free energy were obtained in the framework of the Hypernetted Chain (HNC) Integral Approximation. Our results were in excell entagreement with the \"exact\" results from Molecular Dynamics techniques. The second system consists of electrons trapped on the liquid helium films wetting a solid substrate . In this case, we have generalized the works of Studart and Hipolito, and Monarkha, by analysing the influence of the film thickness and different kinds of substrates. By using the Self-Consistent Field Approximation (SCFA), we have evaluated the static structure factor, correlation energy and plasma dispersion relation . The local field correction, responsible by the short-range correlation , modifies drastically the results from the Random-Phase Approximation (RPA). In the third system, a charged hard sphere fluid , we have determined, by using SCFA, some properties of this many-body system such as the static structure factor, pair correlation function, the equation of state and correlation energy. For the first time , we have calculated the plasma dispersion relation of this generalized one-component plasma. This system is very interesting because, in a first approximation, it can describe eletrolytes and molten salts.