Development and Application of Embedding Methods for the Simulation of Large Chemical Systems

The high computational cost of correlated wavefunction theory (WFT) calculations has motivated the development of numerous methods to partition the description of large chemical systems into smaller subsystem calculations. For example, WFT-in-DFT embedding methods facilitate the partitioning of a system into two subsystems: a subsystem A that is treated using an accurate WFT method, and a subsystem B that is treated using a more efficient Kohn-Sham density functional theory (KS-DFT) method. Representation of the interactions between subsystems is non-trivial, and often requires the use of approximate kinetic energy functionals or computationally challenging optimized effective potential calculations; however, it has recently been shown that these challenges can be eliminated through the use of a projection operator. This dissertation describes the development and application of embedding methods that enable accurate and efficient calculation of the properties of large chemical systems.

Chapter 1 introduces a method for efficiently performing projection-based WFT-in-DFT embedding calculations on large systems. This is accomplished by using a truncated basis set representation of the subsystem A wavefunction. We show that naive truncation of the basis set associated with subsystem A can lead to large numerical artifacts, and present an approach for systematically controlling these artifacts.

Chapter 2 describes the application of the projection-based embedding method to investigate the oxidative stability of lithium-ion batteries. We study the oxidation potentials of mixtures of ethylene carbonate (EC) and dimethyl carbonate (DMC) by using the projection-based embedding method to calculate the vertical ionization energy (IE) of individual molecules at the CCSD(T) level of theory, while explicitly accounting for the solvent using DFT. Interestingly, we reveal that large contributions to the solvation properties of DMC originate from quadrupolar interactions, resulting in a much larger solvent reorganization energy than that predicted using simple dielectric continuum models. Demonstration that the solvation properties of EC and DMC are governed by fundamentally different intermolecular interactions provides insight into key aspects of lithium-ion batteries, with relevance to electrolyte decomposition processes, solid-electrolyte interphase formation, and the local solvation environment of lithium cations.

Oxidative chemisorption of SO_2 on γ - Al_2O_3 and deposition of H_2-permselective SiO_2 films

The interaction of SO_2 with γ - Al_2O_3 and the deposition of H_2 permselective SiO_2 films have been investigated. The adsorption and oxidative adsorption of SO_2 on γ - Al_2O_3 have been examined at temperatures 500-700°C by Fourier transform infrared spectroscopy (FTIR) and thermogravimetric analysis (TGA). At temperatures above 500°C most of SO_2 adsorbed on the strong sites on alumina. The adsorbed SO_2 species was characterized by an IR band at 1065 cm^(-1). The equilibrium coverage and initial rate of adsorption decreased with temperature suggesting a two-step adsorption. When γ - Al_2O_3 was contacted with a mixture of SO_2 and O_2, adsorption of SO_2 and oxidation of the adsorbed SO_2 to a surface sulfate characterized by broad IR bands at 1070 cm^(-1), 1390 cm^(-1) took place. The results of a series of TGA experiments under different atmospheres strongly suggest that surface SO_2 and surface sulfate involve the same active sites such that SO_2 adsorption is inhibited by already formed sulfate. The results also indicate a broad range of site strengths.

The desorption of adsorbed SO_2 and the reductive desorption of oxidatively adsorbed SO_2 have been investigated by microreactor experiments and thermogravimetric analysis (TGA). Temperature programmed reduction (TPR) of adsorbed SO_2 showed that SO_2 was desorbed without significant reaction with H_2 when H_2 concentration was low while considerable reaction occurred when 100% H_2 was used. SO_2 adsorbed on the strong sites on alumina was reduced to sulfur and H_2S. The isothermal reduction experiments of oxidatively adsorbed SO_2 reveal that the rate of reduction is very slow below 550°C even with 100% H_2. The reduction product is mainly composed of SO_2. TPR experiments of oxidatively adsorbed SO_2 showed that H_2S arose from a sulfate strongly chemisorbed on the surface.

Films of amorphous SiO_2 were deposited within the walls of porous Vycor tubes by SiH_4 oxidation in an opposing reactants geometry : SiH_4 was passed inside the tube while O_2 was passed outside the tube. The two reactants diffused opposite to each other and reacted within a narrow front inside the tube wall to form a thin SiO_2 film. Once the pores were plugged the reactants could not reach each other and the reaction stopped. At 450°C and 0.1 and 0.33 atm of SiH_4 and O_2, the reaction was complete within 15 minutes. The thickness of the SiO_2 film was estimated to be about 0.1 µm. Measurements of H_2 and N_2 permeation rates showed that the SiO_2 film was highly selective to H_2 permeation. The H_2:N_2 flux at 450°C varied between 2000-3000.

Thin SiO_2 films were heat treated in different gas mixtures to determine their stability in functioning as high-temperature hydrogen-permselective membranes. The films were heat-treated at 450-700°C in dry N_2, dry O_2, N_2-H_2O, and O_2-H_2O mixtures. The permeation rates of H_2 and N_2 changed depending on the original conditions of film formation as well as on the heat treatment. Heating in dry N_2 slowly reduced the permeation rates of both H_2 and N_2. Heating in a N_2-H_2O atmosphere led to a steeper decline of H_2 permeability. But the permeation rate of N_2 increased or decreased according to whether the film deposition had been carried out in the absence or presence of H_2O vapor, respectively. Thermal treatment in O_2 caused rapid decline of the permeation rates of H_2 and N_2 in films that were deposited under dry conditions. The decline was moderate in films deposited under wet conditions.

The stability of traveling wave solutions of parabolic equations

A method for determining by inspection the stability or instability of any solution u(t,x) = ɸ(x-ct) of any smooth equation of the form u_t = f(u_(xx),u_x,u where ∂/∂a f(a,b,c) > 0 for all arguments a,b,c, is developed. The connection between the mean wavespeed of solutions u(t,x) and their initial conditions u(0,x) is also explored. The mean wavespeed results and some of the stability results are then extended to include equations which contain integrals and also to include some special systems of equations. The results are applied to several physical examples.

Existence, uniqueness, and stability of solutions of a class of nonlinear partial differential equations

In this study we investigate the existence, uniqueness and asymptotic stability of solutions of a class of nonlinear integral equations which are representations for some time dependent non- linear partial differential equations. Sufficient conditions are established which allow one to infer the stability of the nonlinear equations from the stability of the linearized equations. Improved estimates of the domain of stability are obtained using a Liapunov Functional approach. These results are applied to some nonlinear partial differential equations governing the behavior of nonlinear continuous dynamical systems.

Synthesis and characterization of high-spin organic materials: prototypes for the polaronic ferromagnet

The design, synthesis and magnetic characterization of thiophene-based models for the polaronic ferromagnet are described. Synthetic strategies employing Wittig and Suzuki coupling were employed to produce polymers with extended π-systems. Oxidative doping using AsF_5 or I_2 produces radical cations (polarons) that are stable at room temperature. Magnetic characterization of the doped polymers, using SQUID-based magnetometry, indicates that in several instances ferromagnetic coupling of polarons occurs along the polymer chain. An investigation of the influence of polaron stability and delocalization on the magnitude of ferromagnetic coupling is pursued. A lower limit for mild, solution phase I_2 doping is established. A comparison of the variable temperature data of various polymers reveals that deleterious antiferromagnetic interactions are relatively insensitive to spin concentration, doping protocols or spin state. Comparison of the various polymers reveals useful design principles and suggests new directions for the development of magnetic organic materials. Novel strategies for solubilizing neutral polymeric materials in polar solvents are investigated.

The incorporation of stable bipyridinium spin-containing units into a polymeric high-spin array is explored. Preliminary results suggest that substituted diquat derivatives may serve as stable spin-containing units for the polaronic ferromagnet and are amenable to electrochemical doping. Synthetic efforts to prepare high-spin polymeric materials using viologens as a spin source have been unsuccessful.

Temporal and spacial control of RNA stability in the early embryo of Drosophila melanogaster

Early embryogenesis in metazoa is controlled by maternally synthesized products. Among these products, the mature egg is loaded with transcripts representing approximately two thirds of the genome. A subset of this maternal RNA pool is degraded prior to the transition to zygotic control of development. This transfer of control of development from maternal to zygotic products is referred to as the midblastula transition (or MBT). It is believed that the degradation of maternal transcripts is required to terminate maternal control of development and to allow zygotic control of development to begin. Until now this process of maternal transcript degradation and the subsequent timing of the MBT has been poorly understood. I have demonstrated that in the early embryo there are two independent RNA degradation pathways, either of which is sufficient for transcript elimination. However, only the concerted action of both pathways leads to elimination of transcripts with the correct timing, at the MBT. The first pathway is maternally encoded, is triggered by egg activation, and is targeted to specific classes of mRNAs through cis-acting elements in the 3' untranslated region (UTR}. The second pathway is activated 2 hr after fertilization and functions together with the maternal pathway to ensure that transcripts are degraded by the MBT. In addition, some transcripts fail to degrade at select subcellular locations adding an element of spatial control to RNA degradation. The spatial control of RNA degradation is achieved by protecting, or masking, transcripts from the degradation machinery. The RNA degradation and protection events are regulated by distinct cis-elements in the 3' untranslated region (UTR). These results provide the first systematic dissection of this highly conserved process in development and demonstrate that RNA degradation is a novel mechanism used for both temporal and spatial control of development.

Dynamical stability of nascent neutron stars

This thesis presents a study of the dynamical stability of nascent neutron stars resulting from the accretion induced collapse of rapidly rotating white dwarfs.

Chapter 2 and part of Chapter 3 study the equilibrium models for these neutron stars. They are constructed by assuming that the neutron stars have the same masses, angular momenta, and specific angular momentum distributions as the pre-collapse white dwarfs. If the pre-collapse white dwarf is rapidly rotating, the collapsed object will contain a high density central core of size about 20 km, surrounded by a massive accretion torus extending to hundreds of kilometers from the rotation axis. The ratio of the rotational kinetic energy to gravitational binding energy, β, of these neutron stars is all found to be less than 0.27.

Chapter 3 studies the dynamical stability of these neutron stars by numerically evolving the linearized hydrodynamical equations. A dynamical bar-mode instability is observed when the β of the star is greater than the critical value β_d ≈ 0.25. It is expected that the unstable mode will persist until a substantial amount of angular momentum is carried away by gravitational radiation. The detectability of these sources is studied and it is estimated that LIGO II is unlikely to detect them unless the event rate is greater than 10^-6/year/galaxy.

All the calculations on the structure and stability of the neutron stars in Chapters 2 and 3 are carried out using Newtonian hydrodynamics and gravity. Chapter 4 studies the relativistic effects on the structure of these neutron stars. New techniques are developed and used to construct neutron star models to the first post-Newtonian (1PN) order. The structures of the 1PN models are qualitatively similar to the corresponding Newtonian models, but the values of β are somewhat smaller. The maximum β for these 1PN neutron stars is found to be 0.24, which is 8% smaller than the Newtonian result (0.26). However, relativistic effects will also change the critical value β_d. A detailed post-Newtonian stability analysis has yet to be carried out to study the relativistic effects on the dynamical stability of these neutron stars.

Selectivity, activity, and stability of ruthenium-carbene based olefin metathesis initiators

The olefin metathesis reaction has found many applications in polymer synthesis and more recently in organic synthesis. The use of single component late metal olefin metathesis catalysts has expanded the scope of the reaction to many new applications and has allowed for detailed study of the catalytic species.

The metathesis of terminal olefins of different steric bulk, different geometry as well as electronically different para-substituted styrenes was studied with the ruthenium based metathesis initiators, trans-(PCy₃)₂Cl₂Ru=CHR, of different carbene substituents. Increasing olefin bulk was found to slow the rate of reaction and trans internal olefins were found to be slower to react than cis internal olefins. The kinetic product of a11 reactions was found to be the alkylidene, rather than the methylidene, suggesting the intermediacy of a 2,4-metallacycle. The observed effects were used to explain the mechanism of ring opening cross metathesis and acyclic diene metathesis polymerization. No linear electronic effects were observed.

In studying the different carbene ligands, a series of ester-carbene complexes was synthesized. These complexes were found to be highly active for the metathesis of olefinic substrates, including acrylates and trisubstituted olefins. In addition, the estercarbene moiety is thermodynamically high in energy. As a result, these complexes react to ring-open cyclohexene by metathesis to alleviate the thermodynamic strain of the ester-carbene ligand. However, ester-carbene complexes were found to be thermolytically unstable in solution.

Thermolytic decomposition pathways were studied for several ruthenium-carbene based olefin metathesis catalysts. Substituted carbenes were found to decompose through bimolecular pathways while the unsubstituted carbene (the methylidene) was found to decompose unimolecularly. The stability of several derivatives of the bis-phosphine ruthenium based catalysts was studied for its implications to ring-closing metathesis. The reasons for the activity and stability of the different ruthenium-based catalysts is discussed.

The difference in catalyst activity and initiation is discussed for the bis-phosphine based and mixed N-heterocyclic carbene/phosphine based ruthenium olefin metathesis catalysts. The mixed ligand catalysts initiate far slower than the bis-phosphine catalysts but are far more metathesis active. A scheme is proposed to explain the difference in reactivity between the two types of catalysts.

General-domain compressible Navier-Stokes solvers exhibiting quasi-unconditional stability and high-order accuracy in space and time

This thesis presents a new class of solvers for the subsonic compressible Navier-Stokes equations in general two- and three-dimensional spatial domains. The proposed methodology incorporates: 1) A novel linear-cost implicit solver based on use of higher-order backward differentiation formulae (BDF) and the alternating direction implicit approach (ADI); 2) A fast explicit solver; 3) Dispersionless spectral spatial discretizations; and 4) A domain decomposition strategy that negotiates the interactions between the implicit and explicit domains. In particular, the implicit methodology is quasi-unconditionally stable (it does not suffer from CFL constraints for adequately resolved flows), and it can deliver orders of time accuracy between two and six in the presence of general boundary conditions. In fact this thesis presents, for the first time in the literature, high-order time-convergence curves for Navier-Stokes solvers based on the ADI strategy---previous ADI solvers for the Navier-Stokes equations have not demonstrated orders of temporal accuracy higher than one. An extended discussion is presented in this thesis which places on a solid theoretical basis the observed quasi-unconditional stability of the methods of orders two through six. The performance of the proposed solvers is favorable. For example, a two-dimensional rough-surface configuration including boundary layer effects at Reynolds number equal to one million and Mach number 0.85 (with a well-resolved boundary layer, run up to a sufficiently long time that single vortices travel the entire spatial extent of the domain, and with spatial mesh sizes near the wall of the order of one hundred-thousandth the length of the domain) was successfully tackled in a relatively short (approximately thirty-hour) single-core run; for such discretizations an explicit solver would require truly prohibitive computing times. As demonstrated via a variety of numerical experiments in two- and three-dimensions, further, the proposed multi-domain parallel implicit-explicit implementations exhibit high-order convergence in space and time, useful stability properties, limited dispersion, and high parallel efficiency.

Stability of Hypervelocity Boundary Layers

The early stage of laminar-turbulent transition in a hypervelocity boundary layer is studied using a combination of modal linear stability analysis, transient growth analysis, and direct numerical simulation. Modal stability analysis is used to clarify the behavior of first and second mode instabilities on flat plates and sharp cones for a wide range of high enthalpy flow conditions relevant to experiments in impulse facilities. Vibrational nonequilibrium is included in this analysis, its influence on the stability properties is investigated, and simple models for predicting when it is important are described.

Transient growth analysis is used to determine the optimal initial conditions that lead to the largest possible energy amplification within the flow. Such analysis is performed for both spatially and temporally evolving disturbances. The analysis again targets flows that have large stagnation enthalpy, such as those found in shock tunnels, expansion tubes, and atmospheric flight at high Mach numbers, and clarifies the effects of Mach number and wall temperature on the amplification achieved. Direct comparisons between modal and non-modal growth are made to determine the relative importance of these mechanisms under different flow regimes.

Conventional stability analysis employs the assumption that disturbances evolve with either a fixed frequency (spatial analysis) or a fixed wavenumber (temporal analysis). Direct numerical simulations are employed to relax these assumptions and investigate the downstream propagation of wave packets that are localized in space and time, and hence contain a distribution of frequencies and wavenumbers. Such wave packets are commonly observed in experiments and hence their amplification is highly relevant to boundary layer transition prediction. It is demonstrated that such localized wave packets experience much less growth than is predicted by spatial stability analysis, and therefore it is essential that the bandwidth of localized noise sources that excite the instability be taken into account in making transition estimates. A simple model based on linear stability theory is also developed which yields comparable results with an enormous reduction in computational expense. This enables the amplification of finite-width wave packets to be taken into account in transition prediction.

Investigations of DNA-mediated protein oxidation

DNA charge transport (CT) involves the efficient transfer of electrons or electron holes through the DNA π-stack over long molecular distances of at least 100 base-pairs. Despite this shallow distance dependence, DNA CT is sensitive to mismatches or lesions that disrupt π-stacking and is critically dependent on proper electronic coupling of the donor and acceptor moieties into the base stack. Favorable DNA CT is very rapid, occurring on the picosecond timescale. Because of this speed, electron holes equilibrate along the DNA π-stack, forming a characteristic pattern of DNA damage at low oxidation potential guanine multiplets. Furthermore, DNA CT may be used in a biological context. DNA processing enzymes with 4Fe4S clusters can perform DNA-mediated electron transfer (ET) self-exchange reactions with other 4Fe4S cluster proteins, even if the proteins are quite dissimilar, as long as the DNA-bound [4Fe4S]^3+/2+ redox potentials are conserved. This mechanism would allow low copy number DNA repair proteins to find their lesions efficiently within the cell. DNA CT may also be used biologically for the long-range, selective activation of redox-active transcription factors. Within this work, we pursue other proteins that may utilize DNA CT within the cell and further elucidate aspects of the DNA-mediated ET self-exchange reaction of 4Fe4S cluster proteins.

Dps proteins, bacterial mini-ferritins that protect DNA from oxidative stress, are implicated in the survival and virulence of pathogenic bacteria. One aspect of their protection involves ferroxidase activity, whereby ferrous iron is bound and oxidized selectively by hydrogen peroxide, thereby preventing formation of damaging hydroxyl radicals via Fenton chemistry. Understanding the specific mechanism by which Dps proteins protect the bacterial genome could inform the development of new antibiotics. We investigate whether DNA-binding E. coli Dps can utilize DNA CT to protect the genome from a distance. An intercalating ruthenium photooxidant was employed to generate oxidative DNA damage via the flash-quench technique, which localizes to a low potential guanine triplet. We find that Dps loaded with ferrous iron, in contrast to Apo-Dps and ferric iron-loaded Dps which lack available reducing equivalents, significantly attenuates the yield of oxidative DNA damage at the guanine triplet. These data demonstrate that ferrous iron-loaded Dps is selectively oxidized to fill guanine radical holes, thereby restoring the integrity of the DNA. Luminescence studies indicate no direct interaction between the ruthenium photooxidant and Dps, supporting the DNA-mediated oxidation of ferrous iron-loaded Dps. Thus DNA CT may be a mechanism by which Dps efficiently protects the genome of pathogenic bacteria from a distance.

Further work focused on spectroscopic characterization of the DNA-mediated oxidation of ferrous iron-loaded Dps. X-band EPR was used to monitor the oxidation of DNA-bound Dps after DNA photooxidation via the flash-quench technique. Upon irradiation with poly(dGdC)₂, a signal arises with g = 4.3, consistent with the formation of mononuclear high-spin Fe(III) sites of low symmetry, the expected oxidation product of Dps with one iron bound at each ferroxidase site. When poly(dGdC)₂ is substituted with poly(dAdT)₂, the yield of Dps oxidation is decreased significantly, indicating that guanine radicals facilitate Dps oxidation. The more favorable oxidation of Dps by guanine radicals supports the feasibility of a long-distance protection mechanism via DNA CT where Dps is oxidized to fill guanine radical holes in the bacterial genome produced by reactive oxygen species.

We have also explored possible electron transfer intermediates in the DNA-mediated oxidation of ferrous iron-loaded Dps. Dps proteins contain a conserved tryptophan residue in close proximity to the ferroxidase site (W52 in E. coli Dps). In comparison to WT Dps, in EPR studies of the oxidation of ferrous iron-loaded Dps following DNA photooxidation, W52Y and W52A mutants were deficient in forming the characteristic EPR signal at g = 4.3, with a larger deficiency for W52A compared to W52Y. In addition to EPR, we also probed the role of W52 Dps in cells using a hydrogen peroxide survival assay. Bacteria containing W52Y Dps survived the hydrogen peroxide challenge more similarly to those containing WT Dps, whereas cells with W52A Dps died off as quickly as cells without Dps. Overall, these results suggest the possibility of W52 as a CT hopping intermediate.

DNA-modified electrodes have become an essential tool for the study of the redox chemistry of DNA processing enzymes with 4Fe4S clusters. In many cases, it is necessary to investigate different complex samples and substrates in parallel in order to elucidate this chemistry. Therefore, we optimized and characterized a multiplexed electrochemical platform with the 4Fe4S cluster base excision repair glycosylase Endonuclease III (EndoIII). Closely packed DNA films, where the protein has limited surface accessibility, produce EndoIII electrochemical signals sensitive to an intervening mismatch, indicating a DNA-mediated process. Multiplexed analysis allowed more robust characterization of the CT-deficient Y82A EndoIII mutant, as well as comparison of a new family of mutations altering the electrostatics surrounding the 4Fe4S cluster in an effort to shift the reduction potential of the cluster. While little change in the DNA-bound midpoint potential was found for this family of mutants, likely indicating the dominant effect of DNA-binding on establishing the protein redox potential, significant variations in the efficiency of DNA-mediated electron transfer were apparent. On the basis of the stability of these proteins, examined by circular dichroism, we proposed that the electron transfer pathway in EndoIII can be perturbed not only by the removal of aromatic residues but also through changes in solvation near the cluster.

While the 4Fe4S cluster of EndoIII is relatively insensitive to oxidation and reduction in solution, we have found that upon DNA binding, the reduction potential of the [4Fe4S]^3+/2+ couple shifts negatively by approximately 200 mV, bringing this couple into a physiologically relevant range. Demonstrated using electrochemistry experiments in the presence and absence of DNA, these studies do not provide direct molecular evidence for the species being observed. Sulfur K-edge X-ray absorbance spectroscopy (XAS) can be used to probe directly the covalency of iron-sulfur clusters, which is correlated to their reduction potential. We have shown that the Fe-S covalency of the 4Fe4S cluster of EndoIII increases upon DNA binding, stabilizing the oxidized [4Fe4S]³⁺ cluster, consistent with a negative shift in reduction potential. The 7% increase in Fe-S covalency corresponds to an approximately 150 mV shift, remarkably similar to DNA electrochemistry results. Therefore we have obtained direct molecular evidence for the shift in 4Fe4S reduction potential of EndoIII upon DNA binding, supporting the feasibility of our model whereby these proteins can utilize DNA CT to cooperate in order to efficiently find DNA lesions inside cells.

In conclusion, in this work we have explored the biological applications of DNA CT. We discovered that the DNA-binding bacterial ferritin Dps can protect the bacterial genome from a distance via DNA CT, perhaps contributing to pathogen survival and virulence. Furthermore, we optimized a multiplexed electrochemical platform for the study of the redox chemistry of DNA-bound 4Fe4S cluster proteins. Finally, we have used sulfur K-edge XAS to obtain direct molecular evidence for the negative shift in 4Fe4S cluster reduction potential of EndoIII upon DNA binding. These studies contribute to the understanding of DNA-mediated protein oxidation within cells.

Stability of Electrode-Electrolyte Interfaces during Charging in Lithium Batteries

In this thesis we study the growth of a Li electrode-electrolyte interface in the presence of an elastic prestress. In particular, we focus our interest on Li-air batteries with a solid electrolyte, LIPON, which is a new type of secondary or rechargeable battery. Theoretical studies and experimental evidence show that during the process of charging the battery the replated lithium adds unevenly to the electrode surface. This phenomenon eventually leads to dendrite formation as the battery is charged and discharged numerous times. In order to suppress or alleviate this deleterious effect of dendrite growth, we put forth a study based on a linear stability analysis. Taking into account all the mechanisms of mass transport and interfacial kinetics, we model the evolution of the interface. We find that, in the absence of stress, the stability of a planar interface depends on interfacial diffusion properties and interfacial energy. Specifically, if Herring-Mullins capillarity-driven interfacial diffusion is accounted for, interfaces are unstable against all perturbations of wavenumber larger than a critical value. We find that the effect of an elastic prestress is always to stabilize planar interfacial growth by increasing the critical wavenumber for instability. A parametric study results in quantifying the extent of the prestress stabilization in a manner that can potentially be used in the design of Li-air batteries. Moreover, employing the theory of finite differences we numerically solve the equation that describes the evolution of the surface profile and present visualization results of the surface evolution by time. Lastly, numerical simulations performed in a commercial finite element software validate the theoretical formulation of the interfacial elastic energy change with respect to the planar interface.

Stability of parametrically excited differential equations

Sufficient stability criteria for classes of parametrically excited differential equations are developed and applied to example problems of a dynamical nature.

Stability requirements are presented in terms of 1) the modulus of the amplitude of the parametric terms, 2) the modulus of the integral of the parametric terms and 3) the modulus of the derivative of the parametric terms.

The methods employed to show stability are Liapunov’s Direct Method and the Gronwall Lemma. The type of stability is generally referred to as asymptotic stability in the sense of Liapunov.

The results indicate that if the equation of the system with the parametric terms set equal to zero exhibits stability and possesses bounded operators, then the system will be stable under sufficiently small modulus of the parametric terms or sufficiently small modulus of the integral of the parametric terms (high frequency). On the other hand, if the equation of the system exhibits individual stability for all values that the parameter assumes in the time interval, then the actual system will be stable under sufficiently small modulus of the derivative of the parametric terms (slowly varying).

The Design and Synthesis of Transition Metal Complexes Supported by Non-innocent Ligand Scaffolds for Small Molecule Activation

This dissertation focuses on the incorporation of non-innocent or multifunctional moieties into different ligand scaffolds to support one or multiple metal centers in close proximity. Chapter 2 focuses on the initial efforts to synthesize hetero- or homometallic tri- or dinuclear metal carbonyl complexes supported by para-terphenyl diphosphine ligands. A series of [M₂M’(CO)₄]-type clusters (M = Ni, Pd; M’ = Fe, Co) could be accessed and used to relate the metal composition to the properties of the complexes. During these studies it was also found that non-innocent behavior was observed in dinuclear Fe complexes that result from changes in oxidation state of the cluster. These studies led to efforts to rationally incorporate central arene moieties capable managing both protons and electrons during small molecule activation.

Chapter 3 discusses the synthesis of metal complexes supported by a novel para-terphenyl diphosphine ligand containing a non-innocent 1,4-hydroquinone moiety as the central arene. A Pd⁰-hydroquinone complex was found to mediate the activation of a variety of small molecules to form the corresponding Pd⁰-quinone complexes in a formal two proton ⁄ two electron transformation. Mechanistic investigations of dioxygen activation revealed a metal-first activation process followed by subsequent proton and electron transfer from the ligand. These studies revealed the capacity of the central arene substituent to serve as a reservoir for a formal equivalent of dihydrogen, although the stability of the M-quinone compounds prevented access to the PdII-quinone oxidation state, thus hindering of small molecule transformations requiring more than two electrons per equivalent of metal complex.

Chapter 4 discusses the synthesis of metal complexes supported by a ligand containing a 3,5-substituted pyridine moiety as the linker separating the phenylene phosphine donors. Nickel and palladium complexes supported by this ligand were found to tolerate a wide variety of pyridine nitrogen-coordinated electrophiles which were found to alter central pyridine electronics, and therefore metal-pyridine π-system interactions, substantially. Furthermore, nickel complexes supported by this ligand were found to activate H-B and H-Si bonds and formally hydroborate and hydrosilylate the central pyridine ring. These systems highlight the potential use of pyridine π-system-coordinated metal complexes to reversibly store reducing equivalents within the ligand framework in a manner akin to the previously discussed 1,4-hydroquinone diphosphine ligand scaffold.

Chapter 5 departs from the phosphine-based chemistry and instead focuses on the incorporation of hydrogen bonding networks into the secondary coordination sphere of [Fe₄(μ₄-O)]-type clusters supported by various pyrazolate ligands. The aim of this project is to stabilize reactive oxygenic species, such as oxos, to study their spectroscopy and reactivity in the context of complicated multimetallic clusters. Herein is reported this synthesis and electrochemical and Mössbauer characterization of a series of chloride clusters have been synthesized using parent pyrazolate and a 3-aminophenyl substituted pyrazolate ligand. Efforts to rationally access hydroxo and oxo clusters from these chloride precursors represents ongoing work that will continue in the group.

Appendix A discusses attempts to access [Fe₃Ni]-type clusters as models of the enzymatic active site of [NiFe] carbon monoxide dehydrogenase. Efforts to construct tetranuclear clusters with an interstitial sulfide proved unsuccessful, although a (μ₃-S) ligand could be installed through non-oxidative routes into triiron clusters. While [Fe₃Ni(μ₄-O)]-type clusters could be assembled, accessing an open heterobimetallic edge site proved challenging, thus prohibiting efforts to study chemical transformations, such as hydroxide attack onto carbon monoxide or carbon dioxide coordination, relevant to the native enzyme. Appendix B discusses the attempts to synthesize models of the full H-cluster of [FeFe]-hydrogenase using a bioinorganic approach. A synthetic peptide containing three cysteine donors was successfully synthesized and found to chelate a preformed synthetic [Fe₄S₄] cluster. However, efforts to incorporate the diiron subsite model complex proved challenging as the planned thioester exchange reaction was found to non-selectively acetylate the peptide backbone, thus preventing the construction of the full six-iron cluster.

Hydrothermal experiments on the thermal stability of amino substances in sediments

Aspartic acid, threonine, serine and other thermally unstable amino acids have been found in fine-grained elastic sediments of advanced geologic age. The presence of these compounds in ancient sediments conflicts with experimental data determined for their simple thermal decomposition.

Recent and Late Miocene sediments and their humic acid extracts, known to contain essentially complete suites of amino acids, were heated with H₂O in a bomb at temperatures up to 500°C in order to compare the thermal decomposition characteristics of the sedimentary amino compounds.

Most of the amino acids found in protein hydrolyzates are obtained from the Miocene rock in amounts 10 to 100 times less than from the Recent sediment. The two unheated humic acids are rather similar despite their great age difference. The Miocene rock appears uncontaminated by Recent carbon.

Yields of amino acids generally decline in the heated Recent sediment. Some amino compounds apparently increase with heating time in the Miocene rock.

Relative thermal stabilities of the amino acids in sediments are generally similar to those determined using pure aqueous solutions. The relative thermal stabilities of glutamic acid, glycine, and phenylalanine vary in the Recent sediment but are uniform in the Miocene rock.

Amino acids may occur in both proteins and humic complexes in the Recent sediment, while they are probably only present in stabilized organic substances in the Miocene rock. Thermal decomposition of protein amino acids may be affected by surface catalysis in the Recent sediment. The apparent activation energy for the decomposition of alanine in this sediment is 8400 calories per mole. Yields of amino compounds from the heated sediments are not affected by thermal decomposition only.

Amino acids in sediments may only be useful for geothermometry in a very general way.

A better picture of the amino acid content of older sedimentary rocks may be obtained if these sediments are heated in a bomb with H₂O at temperatures around 150°C prior to HCl hydrolysis.

Leucine-isoleucine ratios may prove to be useful as indicators of amino acid sources or for evaluating the fractionation of these substances during diagenesis. Leucine-isoleucine ratios of the Recent and Miocene sediments and humic acids are identical. The humic acids may have a continental source.

The carbon-nitrogen and carbon-hydrogen ratios of sediments and humic acids increase with heating time and temperature. Ratios comparable to those in some kerogens are found in the severely heated Miocene sediment and humic acid.