Browsing by Subject "Density functional theory"
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Item Ab initio simulation methods for the electronic and structural properties of materials applied to molecules, clusters, nanocrystals, and liquids(2014-05) Kim, Minjung, active 21st century; Chelikowsky, James R.Computational approaches play an important role in today's materials science owing to the remarkable advances in modern supercomputing architecture and algorithms. Ab initio simulations solely based on a quantum description of matter are now very able to tackle materials problems in which the system contains up to a few thousands atoms. This dissertation aims to address the modern electronic structure calculation methods applied to a range of various materials such as liquid and amorphous phase materials, nanostructures, and small organic molecules. Our simulations were performed within the density functional theory framework, emphasizing the use of real-space ab initio pseudopotentials. On the first part of our study, we performed liquid and amorphous phase simulations by employing a molecular dynamics technique accelerated by a Chebyshev-subspace filtering algorithm. We applied this technique to find l- and a- SiO₂ structural properties that were in a good agreement with experiments. On the second part, we studied nanostructured semiconducting oxide materials, i.e., SnO₂ and TiO₂, focusing on the electronic structures and optical properties. Lastly, we developed an efficient simulation method for non-contact atomic force microscopy. This fast and simple method was found to be a very powerful tool for predicting AFM images for many surface and molecular systems.Item Ab-initio electronic structure and quantum transport calculations on quasi-two-dimensional materials for beyond Si-CMOS devices(2013-05) Chang, Jiwon, active 2013; Banerjee, Sanjay; Register, Leonard F.Atomically two-dimensional (2-D) graphene, as well as the hexagonal boron nitride dielectric have been and are continuing to be widely investigated for the next generation nanoelectronic devices. More recently, other 2-D materials and electronic systems including the surface states of topological insulators (TIs) and monolayers of transition metal dichalcogenides (TMDs) have also attracted considerable interest. In this work I have focused on these latter two material systems on possible device applications. TIs are characterized by an insulating bulk band gap and metallic Dirac surface states which are spin-polarized. Here, the electronic structures of bulk and thin film TIs are studied using ab-initio density functional theory (DFT). Band inversion, an essential characteristic of TIs, is shown in the bulk band structures. Properties of TI surface bands in thin film such as the critical film thickness to induce a gap, the thickness dependent gap size, and the localization length of surface states are reported. Effects of crystalline dielectric materials on TI surface states are also addressed by ab-initio calculations. I discuss the sensitivity of Dirac point degeneracy and linear band dispersion of TI with respect to different dielectric surface terminations as well as different relative atom positions of the dielectric and TI. Additionally, this work presents research on exciton condensation in TI using a tight-binding model combined with self-consistent non-local Hartree-Fock mean-field theory. Possibility of exciton condensation in the TI Bi₂Se₃ thin film is assessed. Non-equilibrium Green's function (NEGF) simulations with the atomistic tight-binding (TB) Hamiltonian are carried out to explore the performance of metal-oxide-semiconductor field-effect-transistor (MOSFET) and tunnel field-effect-transistor (TFET) based on the Bi₂Se₃ TI thin film. How the high dielectric constant of Bi₂Se₃ affects the performance of MOSFET and TFET is presented. Bulk TMDs such as MoS₂, WS₂ and others are the van der Waals-bonded layered material, much like graphite, except monolayer (and Bulk) TMDs have a large band gap in-contrast to graphene (and graphite). Here, the performance of nanoscale monolayer MoS₂ n-channel MOSFETs are examined through NEGF simulations using an atomistic TB Hamiltonian. N- and p-channel MOSFETs of various monolayer TMDs are also compared by the same approach. I correlate the performance differences with the band structure differences. Finally, ab-initio calculations of adatom doping effects on the monolayer MoS₂ is shown. I discuss the most stable atomic configurations, the bonding type and the amount of charge transfer from adatom to the monolayer MoS₂.Item Computing accurate solutions to the Kohn-Sham problem quickly in real space(2014-08) Schofield, Grady Lynn; Chelikowsky, James R.Matter on a length scale comparable to that of a chemical bond is governed by the theory of quantum mechanics, but quantum mechanics is a many body theory, hence for the sake of chemistry or solid state physics, finding solutions to the governing equation, Schrodinger's equation, is hopeless for all but the smallest of systems. As the number of electrons increases, the complexity of solving the equations grows rapidly without bound. One way to make progress is to treat the electrons in a system as independent particles and to attempt to capture the many-body effects in a functional of the electrons' density distribution. When this approximation is made, the resulting equation is called the Kohn-Sham equation, and instead of requiring solving for one function of many variables, it requires solving for many functions of the three spatial variables. This problem turns out to be easier than the many body problem, but it still scales cubically in the number of electrons. In this work we will explore ways of obtaining the solutions to the Kohn-Sham equation in the framework of real-space pseudopotential density functional theory. The Kohn-Sham equation itself is an eigenvalue problem, just as Schrodinger's equation. For each electron in the system, there is a corresponding eigenvector. So the task of solving the equation is to compute many eigenpairs of a large Hermitian matrix. In order to mitigate the problem of cubic scaling, we develop an algorithm to slice the spectrum into disjoint segments. This allows a smaller eigenproblem to be solved in each segment where a post-processing step combines the results from each segment and prevents double counting of the eigenpairs. The efficacy of this method depends on the use of high order polynomial filters that enhance only a segment of the spectrum. The order of the filter is the number of matrix-vector multiplication operations that must be done with the Hamiltonian. Therefore the performance of these operations is critical. We develop a scalable algorithm for computing these multiplications and introduce a new density functional theory code implementing the algorithm.Item First principles calculations of Raman spectra for nanostructures and improved high order forces(2015-12) Bobbitt, Nathaniel Scott; Chelikowsky, James R.; Demkov, Alexander A; Ekerdt, John G; Hwang, Gyeong S; Korgel, Brian AAdvances in computing technology coupled with theoretical developments on the electronic structure problem have laid the foundation for the rapidly growing field of computational materials science. Modern supercomputers are able to perform ab initio calculations of realistic systems containing thousands of atoms. This is an important step forward in the maturation of the field because computational insight can be used to make predictions about or predict experimental data. This dissertation aims to address contemporary theory and practice of solving the electronic structure problem for a variety of nanoscale systems, most of which are of interest for energy application such as photovoltaics or Li-ion batteries. Our calculations are performed within density functional theory using real-space pseudopotentials. In the first part, we examine nanocrystals. We calculate size-dependent properties for ZnO nanocrystals with Al and Ga dopants. Next, we calculate Raman spectra for Si nanocrystals with Li impurities and Si-Ge core-shell structures, which gives us insight into the structure of these nanocrystals. In the second portion, we examine in depth the calculation of interatomic forces within density functional theory and propose a new integration scheme which we demonstrate calculates more accurate bond lengths and vibrational frequencies and improves the stability of molecular dynamics simulations.Item First principles study of silicon-based nanomaterials for lithium ion battery anodes(2014-05) Chou, Chia-Yun Ph. D.; Hwang, Gyeong S.; Mullins, Charles B; Manthiram, Arunmugam; Ekerdt, John G; Stevenson, KeithSilicon (Si)-based materials have recently emerged as a promising candidate for anodes in lithium-ion batteries because they exhibit much higher energy-storage capacities than the conventional graphite anode. However, the practical use of Si is hampered by its poor cycleability; during lithiation, Si forms alloys with Li and undergoes significant structural and volume changes, which can cause severe cracking/pulverization and consequent capacity fading arising from the loss of electrical contacts. To overcome these drawbacks, many innovative approaches have been explored with encouraging results; however, many fundamental aspects of the lithiation behavior remain ambiguous. Hence, the focus of this work is to develop a better understanding of the lithiation process at the atomistic scale using quantum mechanical calculations. In addition, based on the improved understanding, we attempt to address the fundamental mechanisms behind the successful approaches to enhance the anode performance. To lay a foundation for the investigation of alloy-type anodes, in Chapter 3, we first examine how lithiation occurs in Si and the formation of crystalline and amorphous LixSi alloys (0 ≤ x ≤ 4); followed by assessing the lithiation-induced changes in the energetics, atomic structure, electronic and mechanical properties, and Li diffusivity. The same approach is then extended to analyze the lithiation behavior of germanium (Ge) and tin (Sn) for developing a generalized understanding on the Group IV alloy-type anodes. Along this comparative study, we notice a few distinguishing features pertain only to Si (or Ge), such as the facile Li diffusion in Ge and facet-dependent lithiation in Si, which are discussed in Chapter 4. Beyond the fundamental research, we also look into factors that may contribute to the improved anode performance, including (i) finetuning of the oxidation effects in Si-rich oxides, [alpha] -SiO [subscript 1/3] (Chapter 5), (ii) maximizing the surface effects through nano-engineered structures (Chapters 6 & 7), and finally (iii) the role of interface in Si-graphene (carbon) composites (Chapter 8).Item First-principles study of electronic and topological properties of graphene and graphene-like materials(2013-08) Jadaun, Priyamvada, 1983-; Banerjee, Sanjay; Register, Leonard F.This dissertation includes work done on graphene and related materials, examining their electronic and topological properties using first-principles methods. Ab-initio computational methods, like density functional theory (DFT), have become increasingly popular in condensed matter and material science. Motivated by the search for novel materials that would help us devise fast, low-power, post-CMOS transistors, we explore the properties of some of these promising materials. We begin by studying graphene and its interaction with dielectric oxides. Graphene has recently inspired a flurry of research activity due to its interesting electronic and mechanical properties. For the device community, graphene's high charge carrier mobility and continuous gap tunability can have immense use in novel transistors. In Chapter 3 we examine the properties of graphene placed on two oxides, namely quartz and alumina. We find that oxygen-terminated quartz is a useful oxide for the purpose of graphene based FETs. Inspired by a recent surge of interest in topological insulators, we then explore the topological properties of two-dimensional materials. We conduct a theoretical study to examine the relationship between crystal space group symmetry and the electric polarization of a two-dimensional crystal. We show that the presence of symmetry restricts the polarization values to a small number of distinct groups. There groups in turn are topologically inequivalent, making polarization a topological index. We also conduct density functional theory calculations to obtain actual polarization values of materials belonging to C3 symmetry and show that our results are consistent with our theoretical analysis. Finally we prove that any transformation from one class of polarization to another is a topological phase transition. In Chapter 5 we use density functional theory to examine the electronic properties of graphene intercalation compounds. Bilayer pseudospin field effect transistor (BiSFET) has been proposed as an interesting low-power, efficient post-CMOS switch. In order to implement this device we need bilayer graphene with reduced interlayer interaction. One way of achieving that is by inserting foreign molecules between the layers, a process which is called intercalation. In this chapter we examine the electronic properties of bilayer graphene intercalated with iodine monochloride and iodine monobromide molecules. We find that intercalation of graphene indeed makes it promising for the implementation of BiSFET, by reducing interlayer interaction. As an interesting side problem, we also use hybrid, more extensive approaches in DFT, to examine the electronic and optical properties of dilute nitrides. Dilute nitrides are highly promising and interesting materials for the purposes of optoelectronic applications. Together, we hope this work helps in elucidating the electronic properties of promising material systems as well as act as a guide for experimentalists.Item From polymer collapse to confined fluids : investigating the implications of nterfacial structuring(2009-08) Goel, Gaurav; Truskett, Thomas Michael, 1973-In the first part of this thesis, we present results from extensive molecular dynamics simulations of the collapse transitions of hydrophobic polymers in explicit water. The focus is to understand the roles that curvature and interactions associated with the polymer-water “interface” have on collapse thermodynamics. We show that model hydrophobic polymers can have parabolic, protein-like, temperature-dependent free energies of unfolding. Analysis of the water structure shows that the polymer-water interface can be characterized as soft and weakly dewetted. We also show that an appropriately defined surface tension for the polymer-water interface is independent of the attractive polymer-water interactions. This helped us to develop a perturbation model for predicting the effect of attractions on polymer collapse thermodynamics. In the second part, we explore connections between structure, thermodynamics, and dynamics of inhomogeneous fluids. First, we use molecular dynamics simulations and classical density functional theory (DFT) to study the hard-sphere fluid at approximately 103 equilibrium state points, spanning different confining geometries and particle-boundary interactions. We provide strong empirical evidence that both excess entropy and a new generalized measure of available volume for inhomogeneous fluids correlate excellently with self-diffusivity, approximately independent of the degree of confinement. Next, we study via simulations how tuning particle-wall interactions to flatten or enhance the particle layering of a model confined fluid impacts its self-diffusivity, viscosity, and entropy. Interestingly, interactions that eliminate particle layering can significantly reduce confined fluid mobility, whereas those that enhance layering can have the opposite effect. Excess entropy helps to understand and predict these trends. Finally, we explore the relationships between the effective interparticle interactions, static structure, and tracer diffusivity of a solute in a mixture. We show that knowledge of these relationships can allow one to “tune” the effective interparticle interactions of the solute in a way that increases its tracer diffusivity. One interesting consequence is that the mobility of a hard-sphere solute can be increased by adding a soft-repulsion to its interaction, effectively making it bigger.Item Functional oxide heterostructures on semiconductors(2013-08) Seo, Hosung; Demkov, Alexander A.Complex oxides exhibiting a wide variety of novel functional properties such as ferromagnetism and ferroelectricity have been extensively studied during the past decades. Recent advances in the field of oxide heteroepitaxy have made it possible to create and control hybrid oxide heterostructures with abrupt epitaxial interfaces. The oxide heteroepitaxy with the capability of controlling interface composition, strain, length scales, etc. has opened the totally new and exciting scientific avenue and has offered potential device applications to be explored. Epitaxial integration of functional oxides on semiconductor such as Si (001) and Ge(001) is of great interest, as it potentially leads to further technological development of these interesting oxide systems. In this dissertation, using density functional theory we explore physics and chemistry of novel oxide heterostructures and issues related to the integration of functional oxides on semiconductors. Oxide materials that are studied in this dissertation include polar LaAlO₃, high-k dielectric SrTiO₃, photocatalytic anatase TiO₂ and CoO, and strongly correlated magnetic oxide LaCoO₃.Item Metal-to-insulator transitions in transition metal oxides : a first principles study(2015-08) O'Hara, Andrew; Demkov, Alexander A.; Chelikowsky, James R; MacDonald, Allan H; Tsoi, Maxim; Henkelman, GraemeTransition metal oxides have received significant attention in recent decades due to their ability to display a wide range of novel functional properties. In particular, many oxides are able to undergo metal-to-insulator transitions as a function of external stimuli such as temperature, pressure, and electric field or through doping and defect formation. In the present dissertation, density functional theory is used to explore these phenomena in three systems: (1) the Peierls transition in NbO2, (2) defect formation necessary for HfO2’s resistive switching, and (3) La-doping of SrTiO3 and trap states that may limit conductivity. For NbO2, we use successive improvements to the exchange-correlation energy combined with experiment to improve understanding of the material’s band gap in the insulating phase and show it to be close to 1.2 eV for the direct gap with an indirect gap just below 1.0 eV. Furthermore, we are able to explain the orbital contributions to the dielectric function. Using a combination of transition state theory and phonon dispersion, we demonstrate that the phase transition is driven by a second-order structural transition of the Peierls type. For HfO2, we explore the nature of the metallic gettering layer used to create substoichiometric HfO2-x for resistive switching via an atomistic model of the hafnia-hafnium interface and use transition state theory to study the ability for oxygen to diffuse across the interface. Our investigation shows that the presence of hafnium lowers the formation energy of oxygen vacancies in hafnia, but more importantly the oxidation of hafnium through oxygen migration is energetically favored. In La-doped SrTiO3, the calculations are first used to corroborate optical and electrical measurements by giving values for the density of states effective mass as well as understanding the effect of La-doping on the conductivity and DC relaxation time. Motivated by the experimental observation that even after annealing in oxygen rich environments, heavily n-type doped SrTiO3 shows carrier concentrations inconsistent with dopant concentration, we explore the role that interstitial oxygen may play as a trapping state in SrTiO3. We find three meta-stable sites and that for n-type SrTiO3, interstitials with mid-gap states are favored.Item Simulation tools for predicting the atomic configuration of bimetallic catalytic surfaces(2012-12) Stephens, John Adam; Hwang, Gyeong S.Transition metal alloys are an important class of materials in heterogeneous catalysis due in no small part to the often greatly enhanced activity and selectivity they exhibit compared to their monometallic constituents. A host of experimental and theoretical studies have demonstrated that, in many cases, these synergistic effects can be attributed to atomic-scale features of the catalyst surface. Realizing the goal of designing -- rather than serendipitously discovering -- new alloy catalysts thus depends on our ability to predict their atomic configuration under technologically relevant conditions. This dissertation presents original research into the development and use of computational tools to accomplish this objective. These tools are all based on a similar strategy: For each of the alloy systems examined, cluster expansion (CE) Hamiltonians were constructed from the results of density functional theory (DFT) calculations, and then used in Metropolis Monte Carlo (MC) simulations to predict properties of interest. Following a detailed description of the DFT+CE+MC simulation scheme, results for the AuPd/Pd(111) and AuPt/Pt(111) surface alloys are presented. These two systems exhibit considerably different trends in their atomic arrangement, which are explicable in terms of their interatomic interactions. In AuPd, a preference for heteronuclear, Au-Pd interactions results in the preferential formation of Pd monomers and other small ensembles, while in AuPt, a preference for homonuclear interactions results in the opposite. AuPd/Pd(100) and AuPt/Pt(100) were similarly examined, revealing not only the effects of the same heteronuclear/homonuclear preferences in this facet, but also a propensity for the formation of second nearest-neighbor pairs of Pd monomers, in close agreement with experiment. Subsequent simulations of the AuPd/Pd(100) surface suggest the application of biaxial compressive strain as a means increasing the population of this catalytically important ensemble of atoms. A method to incorporate the effects of subsurface atomic configuration is also presented, using AuPd as an example. This method represents several improvements over others previously reported in the literature, especially in terms of its simplicity. Finally, we introduce the dimensionless scaled pair interaction, whereby the finite-temperature atomic configuration of any bimetallic surface alloy may be predicted from a small number of relatively inexpensive calculations.Item Structural phase transitions in hafnia and zirconia at ambient pressure(2010-08) Luo, Xuhui; Demkov, Alexander A.; Chelikowsky, James R.; Ekerdt, John G.; MacDonald, Allan H.; Kleinman, LeonardIn recent years, both hafnia and zirconia have been looked at closely in the quest for a high permittivity gate dielectric to replace silicon dioxide in advanced metal oxide semiconductor field effect transistors (MOSFET). Hafnium dioxide or HfO2 is chosen for its high dielectric constant (five times that of SiO2) and compatibility with stringent requirements of the Si process. As deposited, thin hafnia films are typically amorphous but turn polycrystalline after a post-deposition anneal. To control the phase composition in hafnia films understanding of structural phase transitions is a first step. In this dissertation using first principles methods we consider three phase transitions of hafnia and zirconia: monoclinic to tetragonal, tetragonal to cubic and amorphous to crystalline. Because the high surface to volume ratio in hafnia films and powders plays an important role in phase transitions, we also study the surface properties of hafnia. We discuss the mechanisms of various phase transitions and theoretically estimate the transition temperatures. We find two types of amorphous hafnia and show that they have different structural and electronic properties. The small energy barrier between the amorphous and crystalline structures is found to cause the low crystallization temperature. Moreover, we calculate work functions and surface energies for hafnia surfaces and show the surface suppression of the phase transitions.Item Theory of biomineral hydroxyapatite(2013-05) Slepko, Alexander; Demkov, Alexander A.Hydroxyapatite (HA, Ca₁₀(PO₄)₆(OH)₂) is one of the most abundant materials in mammal bone. It crystallizes in an aqueous environment within spaces between tropocollagen protein chains. However, despite its abundance and possible usefulness in the medical field this complex physical system remains poorly understood to date. We present a theoretical study of the energetics of hydroxyapatite, its electronic, mechanical and thermodynamic properties. Our mechanical and thermodynamic properties from first principles are in excellent agreement with the rare available experimental data. The monoclinic and hexagonal phases are lowest in energy. A comparison of the phonon dispersions of these two phases reveals that a phase transition occurs due to a difference in vibrational free energy. The transition is of order-disorder type. Our calculated phase transition temperature is 680 K, in decent agreement with the experimentally determined 470 K. An alternative theoretical model yields 882 K. The phase transition is mediated by OH libration modes. We also report for the first time on a peculiarity in the phonon spectrum of hexagonal and monoclinic HA. When studying the Lyddane-Sachs-Teller shifts in the spectrum close to the [Gamma]-point we identify two vibration modes showing a systematically increasing Lyddane-Sachs-Teller shift in frequency with decreasing dielectric constant. In experiment, the dielectric constant varies between 5 and 20 depending on the Ca/P ratio in the sample. The frequency shifts in the affected modes are as large as 20 cm⁻¹ as one spans the range of the dielectric constant. Thus, a simple spectroscopic analysis of a sample of bone may determine the quality of the sample in a physiological sense. We also identify the chemically stable low energy surface configurations as function of the OH, PO₄ and Ca concentration. In the experimentally relevant OH-rich regime we find only two surfaces competing for lowest energy. The surface most stable over almost the entire OH-rich regime is OH-terminated, and is currently being investigated in the presence of water and atomic substitutions on the HA surface.Item Underpotential deposition as a synthetic and characterization tool for core@shell dendrimer-encapsulated nanoparticles(2011-08) Carino, Emily V.; Crooks, Richard M. (Richard McConnell); Bard, Allen J.; Stevenson, Keith J.; Henkelman, Graeme; Mullins, C. BuddieThe synthesis and characterization of Pt core/ Cu shell (Pt@Cu) dendrimer-encapsulated nanoparticles (DENs) having full and partial Cu shells deposited via electrochemical underpotential deposition (UPD) is described. Pt DENs containing averages of 55, 147, and 225 Pt atoms immobilized on glassy carbon electrodes served as the substrate for the UPD of a Cu monolayer. This results in formation of Pt@Cu DENs. Evidence for this conclusion is based on results from the analysis of cyclic voltammograms (CVs) for the UPD and stripping of Cu on Pt DENs, and from experiments showing that the Pt core DENs catalyze the hydrogen evolution reaction before Cu UPD, but that after Cu UPD this reaction is inhibited. Results obtained by in-situ electrochemical X-ray absorption spectroscopy (XAS) confirm the core@shell structure. Calculations from density functional theory (DFT) show that the first portion of the Cu shell deposits onto the (100) facets, while Cu deposits lastly onto the (111) facets. The DFT-calculated energies for Cu deposition on the individual facets are in good agreement with the peaks observed in the CVs of the Cu UPD on the Pt DENs. Finally, structural analysis of Pt DENs having just partial Cu shells by in-situ XAS is consistent with the DFT-calculated model, confirming that the Cu partial shell selectively decorates the (100) facets. These results are of considerable significance because site-selective Cu deposition has not previously been shown on nanoparticles as small as DENs. In summary, the application of UPD as a synthetic route and characterization tool for core@shell DENs having well defined structures is established. A study of the degradation mechanism and degradation products of Pd DENs is provided as well. These DENs consisted of an average of 147 atoms per dendrimer. Elemental analysis and UV-vis spectroscopy indicate that there is substantial oxidation of the Pd DENs in air-saturated solutions, less oxidation in N₂-saturated solution, and no detectable oxidation when the DENs are in contact with H₂. Additionally, the stability improves when the DEN solutions are purified by dialysis to remove Pd²⁺-complexing ligands such as chloride. For the air- and N₂-saturated solutions, most of the oxidized Pd recomplexes to the interiors of the dendrimers, and a lesser percentage escapes into the surrounding solution. The propensity of Pd DENs to oxidize so easily is a likely consequence of their small size and high surface energy. Calculations from density functional theory (DFT) show that the first portion of the Cu shell deposits onto the (100) facets, while Cu deposits lastly onto the (111) facets. The DFT-calculated energies for Cu deposition on the individual facets are in good agreement with the peaks observed in the CVs of the Cu UPD on the Pt DENs. Finally, structural analysis of Pt DENs having just partial Cu shells by in-situ XAS is consistent with the DFT-calculated model, confirming that the Cu partial shell selectively decorates the (100) facets. These results are of considerable significance because site-selective Cu deposition has not previously been shown on nanoparticles as small as DENs. In summary, the application of UPD as a synthetic route and characterization tool for core@shell DENs having well defined structures is established. A study of the degradation mechanism and degradation products of Pd DENs is provided as well. These DENs consisted of an average of 147 atoms per dendrimer. Elemental analysis and UV-vis spectroscopy indicate that there is substantial oxidation of the Pd DENs in air-saturated solutions, less oxidation in N2-saturated solution, and no detectable oxidation when the DENs are in contact with H2. Additionally, the stability improves when the DEN solutions are purified by dialysis to remove Pd2+-complexing ligands such as chloride. For the air- and N2-saturated solutions, most of the oxidized Pd recomplexes to the interiors of the dendrimers, and a lesser percentage escapes into the surrounding solution. The propensity of Pd DENs to oxidize so easily is a likely consequence of their small size and high surface energy.Item Understanding mechanisms for C-H bond activation(2009-05-15) Vastine, Benjamin AlanThe results from density functional theory (DFT) studies into C?H bond activation, hydrogen transfer, and alkyne?to?vinylidene isomerization are presented in this work. The reaction mechanism for the reductive elimination (RE) of methane from [ ?3- TpPtIV(CH3)2H (1)] (Tp = hydridotris(pyrazolyl)borate) by oxidative addition (OA) of benzene to form [ ?3-TpPtIV(Ph)2H] (19) was investigated through DFT calculations. For 31 density functionals, the calculated values for the barriers to methane formation (Ba1) and release (Ba2) from 1 were benchmarked against the experimentally reported values of 26 (Ba1) and 35 (Ba2) kcal?mol-1, respectively. The values for Ba1 and Ba2, calculated at the B3LYP/DZP level of theory, are 24.6 and 34.3 kcal?mol-1, respectively. The best performing functional was BPW91 where the m.a.e. for the calculated values of the two barriers is 0.68 kcal?mol-1. Classic and newly proposed mechanisms for metal-mediated hydrogen transfer (HT) were analyzed with density functional theory (DFT) and Bader's "Atoms In Molecules" (AIM) analysis. Seven sets of bonding patterns that characterize theconnectivity in metal-mediate HT were found from the analysis of representative models for ?-bond metathesis ( ?BM), oxidative addition / reductive elimination (OA/RE), and alternative mechanisms. The mechanism for the formation of the alkynyl, vinylidene complex, [(PiPr3)2Rh(CCPh)(CC(H)(Ph))] (2), by the addition of two equivalents of phenylacetylene (PA) to [( ?3-C3H5)Rh(PiPr3)2] (1) was studied through DFT calculations. Two experimentally observed intermediates on the reaction coordinate are the ?2-PA, alkynyl complex, [(PiPr3)2Rh( ?2-HCCPh)(CCPh)] (Ia) and the fivecoordinate, pseudo square-pyramidal, RhIII?H complex, [(PiPr3)2Rh(H)(CCPh)2] (Ib), and were found to be in equilibrium. The relative energies of Ia, Ib, and 2 (relative to 1 + 2PA) depend on the phosphine that was used in the calculation; the predicted product is 2 with PiPr3 and PEt3 but Ia with PMe3, PMe2Ph, PMePh2, PPh3, and PH3. The equilibrium between Ia and Ib was calculated with PEt3 and one conformation of PiPr3. We investigated the mechanism for the formation of 2 from Ia, and a lower energy pathway where the ?-bound PA of Ia slips to bind through the ?-C?H bond prior to the formation of 2 through hydrogen migration was found.