The development of efficient catalyst for water oxidation is of paramount importance to artificial photosynthesis, but before this can be achieved a deeper understanding of this reaction is essential. In nature this reaction occurs in a tetranuclear Mn-cluster which serves as the work-horse of oxygenic photosynthesis. This thesis summarises my efforts at developing molecular systems capable of mimicking this complex employing a biomimetic approach. Three different approaches towards this goal are described here-in. The first section describes a screening study, in which a number of manganese complexes were tested to see whether or not they were capable of catalysing the formation of dioxygen when treated with different oxidants (Papers I). For those reactions in which dioxygen formation was observed the reactions were repeated in labelled water and the incorporation of labelled O-atoms was studied by mass spectrometry. This allowed us to determine to what extent water was the source of the evolved dioxygen (Papers II-III). In Chapter three a reported catalyst and a derivative thereof is studied in depth. The influence of changes to the ligand on the oxygen–oxygen bond forming reaction could unfortunately not be reliably addressed, because of the instability of the complexes under “catalytic” conditions. Nevertheless, the study allowed us to revise the “carboxylate shift”-mechanism suggested in the literature (Papers IV-V). Chapter four describes the continuation of my work on ligands featuring the carboxylate ligand motif first introduced in Chapter three. In this study ligands containing multiple binding pockets were designed and synthesised (Paper VI). A better understanding of the mechanism in the natural water oxidising enzyme will facilitate the design of biomimetic complexes, this is discussed in Chapter five. In this work model complexes (Paper VII) are used to study the mechanism by which natures own water oxidising catalyst performs this reaction.

The results of kinetic isotope determination and computational studies on Noyori-type catalytic systems for the hydrogenation of ketones are presented. The catalysts examined include RuH2(NHCMe2CMe2NH2)(R-binap) and RuH(NHCMe2CMe2NH2)(PPh3)2. These complexes are active catalysts for ketone hydrogenation in benzene without addition of an external base. The kinetic isotope effect (KIE) for catalysis by RuH2(NHCMe2CMe2NH2)(R-binap) was determined to be 2.0 ± (0.1). The calculated KIE for the model system RuH(NHCH2CH2NH2)(PH3)2 was 1.3, which is smaller than the experimentally observed value but does not include tunneling effects. The complex OsH(NHCMe2CMe2NH2)(PPh3)2 is known to display autocatalytic behaviour when it catalyzes the hydrogenation of acetophenone in benzene. Pseudo first-order reaction conditions are obtained via addition of the product alcohol at the beginning of each kinetic experiment. The KIE determined using various combinations of deuterium-labeled gas, alcohol and ketone was found to be 1.1 ± (0.2). DFT calculations were used to explore the effect of the alcohol and the KIE. An induction period is observed at the start of the hydrogenation that is attributed to the formation of an alkoxide complex. A novel, diamine-orchestrated hydrogen-bonding network is proposed based on DFT calculations to explain how the alkoxide is converted back to the active catalyst. The tetradentate complexes trans-RuHCl[PPh2(ortho-C6H4)CH2NHCH2)]2 and RuHCl[PPh2(ortho-C6H4)CH2NHCMe2)]2 are known to be catalysts for the hydrogenation of acetophenone and benzonitrile in toluene when activated by KOtBu/KH. DFT studies were performed and a mechanism is proposed. The calculated rate limiting step for acetone hydrogenation was found to be heterolytic splitting of dihydrogen, which agrees well with experiment. The novel outer-sphere sequential hydrogenation of a CN triple bond and then a C=N double bond is proposed. A mechanism is proposed, which is supported by DFT studies, to explain the selectivity observed in the nucleophilic attack of amines or aziridines on palladium -prenyl phosphines complexes. Calculations on based on a palladium complex with two phosphorus donor ligands indicated that the observed selectivity would not be produced. Using two new model intermediates with either THF or aziridine substituted for a phosphine ligand trans to the unhindered side of the prenyl ligand did predict the experimentally observed selectivity.

Studies of nucleation in freezing nanoparticles usually assume that the embryo of the solid phase is completely wet by the liquid and forms in the core of the droplet. However, recent experiments and computer simulations have suggested that some nanoparticles start nucleating at the liquid-vapor interface of the drop in a pseudoheterogeneous process. The goal of the present work is to propose phenomenological models suitable for the study of surface nucleation in nanoparticle systems that can be used to understand the contributions of the various surface phenomena, such as surface and line tensions, to the nucleation barrier.<p/> The nucleation barrier for the freezing of a 276 atom gold cluster is calculated using Monte Carlo simulation techniques while previous simulation studies of a 456 atom gold cluster are extended in order to find the probability that the embryo forms in the surface or core of the nanoparticle. These calculations confirm that the crystal embryo forms at the liquid-vapor interface. Geometric studies measuring the liquid-solid and solid-vapor surface areas of the embryo suggest that it changes shape as it becomes larger and grows in towards the core of the droplet.<p/> Three phenomenological models that are based on the capillarity approximation and can account for surface nucleation are proposed. These models highlight the importance of accounting for the surface curvature contributions related to the Tolman length and the presence of the three phase contact line in calculating the nucleation free energy barrier. In some cases, the models are able to reproduce the qualitative properties of the free energy barriers obtain from simulation but numerical fits of the models generally result in estimates of the solid-liquid surface tension that are lower than the values expected on the basis of partial wetting in the bulk.<p/> Finally, a semi-phenomenological model approach to nucleation is proposed where the usual phenomenological expression for the free energy barrier is retained, but where the geometric prefactors are obtained from molecular simulation of the embryo. This method is applied to nucleation in the gold cluster and to the freezing of a bulk Lennard-Jones liquid.<p/>

Studies of nucleation in freezing nanoparticles usually assume that the embryo of the solid phase is completely wet by the liquid and forms in the core of the droplet. However, recent experiments and computer simulations have suggested that some nanoparticles start nucleating at the liquid-vapor interface of the drop in a pseudoheterogeneous process. The goal of the present work is to propose phenomenological models suitable for the study of surface nucleation in nanoparticle systems that can be used to understand the contributions of the various surface phenomena, such as surface and line tensions, to the nucleation barrier.<p/> The nucleation barrier for the freezing of a 276 atom gold cluster is calculated using Monte Carlo simulation techniques while previous simulation studies of a 456 atom gold cluster are extended in order to find the probability that the embryo forms in the surface or core of the nanoparticle. These calculations confirm that the crystal embryo forms at the liquid-vapor interface. Geometric studies measuring the liquid-solid and solid-vapor surface areas of the embryo suggest that it changes shape as it becomes larger and grows in towards the core of the droplet.<p/> Three phenomenological models that are based on the capillarity approximation and can account for surface nucleation are proposed. These models highlight the importance of accounting for the surface curvature contributions related to the Tolman length and the presence of the three phase contact line in calculating the nucleation free energy barrier. In some cases, the models are able to reproduce the qualitative properties of the free energy barriers obtain from simulation but numerical fits of the models generally result in estimates of the solid-liquid surface tension that are lower than the values expected on the basis of partial wetting in the bulk.<p/> Finally, a semi-phenomenological model approach to nucleation is proposed where the usual phenomenological expression for the free energy barrier is retained, but where the geometric prefactors are obtained from molecular simulation of the embryo. This method is applied to nucleation in the gold cluster and to the freezing of a bulk Lennard-Jones liquid.<p/>

The results of kinetic isotope determination and computational studies on Noyori-type catalytic systems for the hydrogenation of ketones are presented. The catalysts examined include RuH2(NHCMe2CMe2NH2)(R-binap) and RuH(NHCMe2CMe2NH2)(PPh3)2. These complexes are active catalysts for ketone hydrogenation in benzene without addition of an external base. The kinetic isotope effect (KIE) for catalysis by RuH2(NHCMe2CMe2NH2)(R-binap) was determined to be 2.0 ± (0.1). The calculated KIE for the model system RuH(NHCH2CH2NH2)(PH3)2 was 1.3, which is smaller than the experimentally observed value but does not include tunneling effects. The complex OsH(NHCMe2CMe2NH2)(PPh3)2 is known to display autocatalytic behaviour when it catalyzes the hydrogenation of acetophenone in benzene. Pseudo first-order reaction conditions are obtained via addition of the product alcohol at the beginning of each kinetic experiment. The KIE determined using various combinations of deuterium-labeled gas, alcohol and ketone was found to be 1.1 ± (0.2). DFT calculations were used to explore the effect of the alcohol and the KIE. An induction period is observed at the start of the hydrogenation that is attributed to the formation of an alkoxide complex. A novel, diamine-orchestrated hydrogen-bonding network is proposed based on DFT calculations to explain how the alkoxide is converted back to the active catalyst. The tetradentate complexes trans-RuHCl[PPh2(ortho-C6H4)CH2NHCH2)]2 and RuHCl[PPh2(ortho-C6H4)CH2NHCMe2)]2 are known to be catalysts for the hydrogenation of acetophenone and benzonitrile in toluene when activated by KOtBu/KH. DFT studies were performed and a mechanism is proposed. The calculated rate limiting step for acetone hydrogenation was found to be heterolytic splitting of dihydrogen, which agrees well with experiment. The novel outer-sphere sequential hydrogenation of a CN triple bond and then a C=N double bond is proposed. A mechanism is proposed, which is supported by DFT studies, to explain the selectivity observed in the nucleophilic attack of amines or aziridines on palladium -prenyl phosphines complexes. Calculations on based on a palladium complex with two phosphorus donor ligands indicated that the observed selectivity would not be produced. Using two new model intermediates with either THF or aziridine substituted for a phosphine ligand trans to the unhindered side of the prenyl ligand did predict the experimentally observed selectivity.

Let $l^2(Bbb Z)$ be the Hilbert space of square summable double sequences of complex numbers with standard basis ${e_n:ninBbb Z}$, and let us consider a bounded matrix $A$ on $l^2(Bbb Z)$ satisfying the following system of equations egin{itemize} item[1.] $lan Ae_{2j},e_{2i} an=p_{ij}+alan Ae_{j},e_i an$; item[2.] $lan Ae_{2j},e_{2i-1} an=q_{ij}+blan Ae_{j},e_{i} an$; item[3.] $lan Ae_{2j-1},e_{2i} an=v_{ij}+clan Ae_{j},e_{i} an$; item[4.] $lan Ae_{2j-1},e_{2i-1} an=w_{ij}+dlan Ae_{j},e_{i} an$ end{itemize} for all $i,j$, where $P=(p_{ij})$, $Q=(q_{ij})$, $V=(v_{ij})$, $W=(w_{ij})$ are bounded matrices on $l^2(Bbb Z)$ and $a,b,c,dinBbb C$. par It is clear that the solutions of the above system of equations introduces a class of infinite matrices whose entries are related ``dyadically". In cite{Ho:g}, it is shown that the seemingly complicated task of constructing these matrices can be carried out alternatively in a systematical and relatively simple way by applying the theory of Hardy classes of operators through certain operator equation on ${cal B}({cal H})$ (space of bounded operators on $cal H$) induced by a shift. Our purpose here is to present explicit formula for the homogeneous solutions this equation.

This study was to prepare nanoscale MgO using the homogeneous precipitation process and to investigate its destructive adsorption with dye wastewater of reactive black-5 and reactive blue-19. In addition, UV-vis Spectrophotometer, Matrix-Assisted Laser Desorption/Ionization Time of Flight Mass Spectrometry (MALDI-TOF/MS) and Gas Chromatograph/Mass Spectrometer (GC/MS) were used to analyze the intermediates resulting from destructive adsorption. Based on the results obtained, the destructive adsorption mechanisms for the treatment of dye wasterwater by nanoscale MgO were proposed in this study. In this work, the optimal operating conditions for nanoscale MgO synthesis were determined to be the following: (1) a chemical reaction time of 7 hr, (2) reaction temperature of 125¢J, (3) molar ratio of 9 for urea/MgCl2¡D6H2O, (4) water addition of 250 mL, (5) mixing intensity of 90 strokes per min, (6) calcination at 450¢J for 4 hr, (7) reflux time of 24 hr, (8) freeze-drying method, (9) two stage calcinations. Using these operating conditions one is able to prepare 2-D nanoscale MgO of hexagonal platelets with a thickness of 20-30 nm and BET surface area of 120-125 m2/g. The adsorption model of nanoscale MgO for RB-5 and RB-19 was fitted to the Langmuir equation and their adsorption capacity were 196.08 mg/g and 163.93 mg/g, respectively. Both of them were fitted to the pseudo-second-order kinetic model equation. The optimal operating conditions of nanoscale MgO for destructive adsorption of both dyes were determined to be the following: (1) an initial dye concentration of 1000 mg/L, (2) a nanoscale MgO dose of 15 g/L, (3) a vigorous mixing of 30 min, (4) no need of system pH adjustment. Under such conditions, chemical oxygen demand (COD) and American Dye Manufacturers Institute (ADMI) of RB-5 and RB-19 were lower than the textile effluent standards. According to the UV-vis spectrophotometer scanning results, the color removal of nanoscale MgO for RB-5 and RB-19 was good. At the same time, the absorbance of their second maximal peaks was decreased and some peaks were observed. Therefore, it proved that the model dyes were destroyed. Experimental results have shown that nanoscale MgO has a better performance of destructive adsorption on RB-5 than that of RB-19. This might be ascribed to the following reasons: (1) a greater molecular weight, (2) a longer molecule structure, (3) more sulfate ethyl sulfone groups for RB-5, and (4) a hard to be destroyed structure of anthraquinone for RB-19. The destructive adsorption of dye wastewater by nanoscale MgO presumably took place mainly on the surface active sites of nanoscale MgO, including anion/cation vacancies, superoxide anion, edge, corner, isolated OH, lattice bound OH and assiocited-OH groups. According to the results of MALDI-TOF/MS and GC/MS analysis, the relevant reaction mechanism for RB-5 could be divided into three stages: (1) adsorption and water-soluble groups exfoliation stage, (2) chromophor decomposition and decolorization stage, and (3) further degradation stage for light-color intermediates. On the other hand, the relevant reaction mechanism for RB-19 might involve only the adsorption and auxochrome exfoliation stage and chromophor decomposition and decolorization stage.

The sterically expanded octamethyloctahydrodibenzofluorene moiety, C29H38 (Oct), has been incorporated into ansa-metallocenes and constrained geometry catalysts (CGC's). Utilization of this sterically expanded version of fluorene has resulted in solidstate anomalies for both systems. The ansa-metallocenes Me2C(n5-C5H4) (n5-C29H36)MCl2, M = Zr, Hf and Me2C(n5-C5H4)(n5-C29H36)ZrBn2 demonstrate crystal motifs expected for ansametallocenes while Me2C(n5-C5H4)(n5-C29H36)MMe2, M=Zr, Hf exhibit diffuse diffraction, a phenomenon that is extremely unusual for organometallic complexes. This crystalline anomaly is the result of a disorder restricted to two dimensions caused by the rare pillared motif of the system. The best solution for this system consists of parallel and anti-parallel pillars present in a 60:40 ratio. The solid state anomaly observed for the Oct-CGC's occurs on a molecular level. The parent Oct-CGC, Me2Si(1-C29H36)(1-N-tBu)ZrCl2·OEt2, demonstrates an unprecedented n1 ligation to the fluorenyl-based ring. Systematic derivatization of this system via halide substitution, alkylation, and exchange of Zr for Hf has revealed that the n1 ligation persists for systems with small substituents on the metal center capable of retaining a coordinated ether. It is hypothesized that the unusual structure of this new Oct-CGC results in Me2Si(1-C29H36)(1-N-tBu)ZrCl2·OEt2/MAO (MAO = methylaluminoxane) being six times more active in the homopolymerization of 1-octene than ethylene. When compared to the prototypical Ti-CGC Me2Si(n5-C5Me4)(n1-N-tBu)TiCl2/MAO, the Oct-CGC is 85 times more reactive in the homopolymerization of 1-octene and 52 times more active in the copolymerization of 1-octene and 4-methyl-1-pentene. The high reactivity of the Oct-CGC towards alpha-olefins results in the observation of an unyielding comonomer effect in the copolymerization of these olefins with ethylene. In addition, the Oct-CGC is perhaps the most syndioselective catalyst known. With an enantiofacial selectivity of 99.7% and a remarkably high activity towards alpha-olefins, the Oct-CGC is capable of producing the highest melting syndiotactic polypropylene (Tm = 165oC, annealed = 174oC) reported thus far. The high activity and syndioselectivity of the Oct-CGC can be extended to the production of syndiotactic poly(4-methyl-1-pentene) with the highest melting point thus far reported (Tm = 215oC).

Compressible ideal-gas turbulence subjected to homogeneous shear is investigated at the rapid distortion limit. Specific issues addressed are (i) the interaction between kinetic and internal energies and role of pressure-dilatation; (ii) the modifications to pressure-strain correlation and Reynolds stress anisotropy and (iii) the effect of the composition of velocity fluctuations (solenoidal vs. dilatational). Turbulence evolution is found to be strongly influenced by gradient Mach number, the initial solenoidal-to-dilatational ratio of the velocity field and the initial intensity of the thermodynamic fluctuations. The balance between the initial fluctuations in velocity and thermodynamic variables is also found to be very important. Any imbalance in the two fluctuating fields leads to high levels of pressure-dilatation and intense exchange. For a given initial condition, it is found that the interaction via the pressuredilatation term between the momentum and energy equations reaches a peak at an intermediate gradient Mach number. The energy exchange between internal and kinetic modes is negligible at very high or very low Mach number values due to lack of pressure dilatation. When present, the exchange exhibits oscillations even as the sum of the two energies evolves smoothly. The interaction between shear and solenoidal initial velocity field generates dilatational fluctuations; for some intermediate levels of shear Mach number dilatational fluctuations account for 20% of the total fluctuations. Similarly, the interaction between shear and initial dilatation produces solenoidal oscillations. Somewhat surprisingly, the generation of solenoidal fluctuations increases with gradient Mach number. Larger levels of pressure-strain correlation are seen with dilatational rather than solenoidal initial conditions. Anisotropies of solenoidal and dilatational components are investigated individually. The most interesting observation is that solenoidal and dilatational turbulence tend toward a one componential state but the energetic component is different in each case. As in incompressible shear flows, with solenoidal fluctuations, the streamwise (1,1) component of Reynolds stress is dominant. With dilatational fluctuations, the stream-normal (2,2) component is the strongest. Overall, the study yields valuable insight into the linear processes in high Mach number shear flows and identifies important closure modeling issues.

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