I. Quantum mechanics of one-dimensional two-particle models. II. A quantum mechanical treatment of inelastic collisions

Part I

Solutions of Schrödinger’s equation for system of two particles bound in various stationary one-dimensional potential wells and repelling each other with a Coulomb force are obtained by the method of finite differences. The general properties of such systems are worked out in detail for the case of two electrons in an infinite square well. For small well widths (1-10 a.u.) the energy levels lie above those of the noninteresting particle model by as much as a factor of 4, although excitation energies are only half again as great. The analytical form of the solutions is obtained and it is shown that every eigenstate is doubly degenerate due to the “pathological” nature of the one-dimensional Coulomb potential. This degeneracy is verified numerically by the finite-difference method. The properties of the square-well system are compared with those of the free-electron and hard-sphere models; perturbation and variational treatments are also carried out using the hard-sphere Hamiltonian as a zeroth-order approximation. The lowest several finite-difference eigenvalues converge from below with decreasing mesh size to energies below those of the “best” linear variational function consisting of hard-sphere eigenfunctions. The finite-difference solutions in general yield expectation values and matrix elements as accurate as those obtained using the “best” variational function.

The system of two electrons in a parabolic well is also treated by finite differences. In this system it is possible to separate the center-of-mass motion and hence to effect a considerable numerical simplification. It is shown that the pathological one-dimensional Coulomb potential gives rise to doubly degenerate eigenstates for the parabolic well in exactly the same manner as for the infinite square well.

Part II

A general method of treating inelastic collisions quantum mechanically is developed and applied to several one-dimensional models. The formalism is first developed for nonreactive “vibrational” excitations of a bound system by an incident free particle. It is then extended to treat simple exchange reactions of the form A + BC →AB + C. The method consists essentially of finding a set of linearly independent solutions of the Schrödinger equation such that each solution of the set satisfies a distinct, yet arbitrary boundary condition specified in the asymptotic region. These linearly independent solutions are then combined to form a total scattering wavefunction having the correct asymptotic form. The method of finite differences is used to determine the linearly independent functions.

The theory is applied to the impulsive collision of a free particle with a particle bound in (1) an infinite square well and (2) a parabolic well. Calculated transition probabilities agree well with previously obtained values.

Several models for the exchange reaction involving three identical particles are also treated: (1) infinite-square-well potential surface, in which all three particles interact as hard spheres and each two-particle subsystem (i.e. BC and AB) is bound by an attractive infinite-square-well potential; (2) truncated parabolic potential surface, in which the two-particle subsystems are bound by a harmonic oscillator potential which becomes infinite for interparticle separations greater than a certain value; (3) parabolic (untruncated) surface. Although there are no published values with which to compare our reaction probabilities, several independent checks on internal consistency indicate that the results are reliable.

Melatonina, isoenzimas de glutationa S-transferases e estresse oxidante em pacu Piaractus mesopotamicus (Holmberg, 1887)

O oxigênio é fundamental para os vertebrados. No entanto, variações dos níveis de oxigênio na água podem provocar estresse oxidante em peixes porque privação de oxigênio seguida de reoxigenação forma espécies reativas de oxigênio (ERO) em células. Níveis intracelulares de ERO aumentados favorecem que moléculas de proteínas, fosfolipídios e ácidos nucleicos sofram alterações, vindo a prejudicar muitas funções celulares. No Pantanal, habitat do pacu, o nível de oxigênio varia circadianamente na água das lagoas rasas que acabam isoladas dos rios na seca. O pacu evoluiu sob a pressão contínua da exposição aos efeitos prejudiciais das ERO causados pelos pulsos de inundação. A melatonina, uma indolamina produzida na glândula pineal, influencia os níveis de atividade de enzimas antioxidantes que reduzem ERO, além de ser capaz de doar elétrons ou captar radicais livres de forma não enzimática. Os níveis de melatonina no pacu são mais altos no verão e menores no inverno. Isoenzimas de glutationa S-transferases que conjugam o tripetídeo glutationa com o 4-hidroxinonenal, aldeído derivado da peroxidação de ácidos graxos por ERO, são importantes para evitar alteração funcional de proteínas por ligação do 4-hidroxinonenal à sua estrutura. Neste trabalho procuramos relação entre estresse oxidante, níveis de atividades de glutationa S-transferase e melatonina, para estabelecer se a melatonina ajudaria pacus a superar os efeitos deletérios das espécies reativas de oxigênio. Ensaiamos atividades de isoenzimas de glutationa S-transferases no citosol de fígado de pacus mantidos em normoxia, hipoxia, reoxigenação e hiperoxia no inverno e no verão. Medimos o efeito da melatonina in vitro e in vivo sobre as atividades de isoenzimas de glutationa S-transferase. Medimos os efeitos do estresse oxidante sobre a ligação do 4-hidroxinonenal com proteínas nos fígados de pacus tratados com melatonina. Somente as isoenzimas que conjugam 4-hidroxinonenal com glutationa mostraram menor atividade no inverno em relação ao verão; outras isoenzimas de glutationa S-transferases não alteram suas atividades sazonalmente. In vitro a melatonina não alterou a atividade de isoenzimas de glutationa S-transferase que conjugam o 4-hidroxinonenal, mas inibiu outras isoenzimas de glutationa S-transferase. In vivo a melatonina aumentou a atividade encontrada no inverno das isoenzimas que conjugam o 4-hidroxinonenal para os níveis do verão. A ligação de 4-hidroxinonenal com proteínas foi menor em pacus inoculados com melatonina. Nossos resultados mostram que a melatonina pode influenciar os efeitos de ERO em fígado de pacus. Ficou claro que a melatonina do plasma mantém os níveis de atividade conjugadora de 4-hidroxinonenal do fígado em pacus e que a baixa produção de melatonina no inverno não é adequada para a conjugação do 4-hidroxinonenal em fígado de pacus.

Energy transfer in molecular collisions

Two general, numerically exact, quantum mechanical methods have been developed for the calculation of energy transfer in molecular collisions. The methods do not treat electronic transitions because of the exchange symmetry of the electrons. All interactions between the atoms in the system are written as potential energies.

The first method is a matrix generalization of the invariant imbedding procedure, ^{17, 20} adapted for multi-channel collision processes. The second method is based on a direct integration of the matrix Schrödinger equation, with a re-orthogonalization transform applied during the integration.

Both methods have been applied to a collinear collision model for two diatoms, interacting via a repulsive exponential potential. Two major studies were performed. The first was to determine the energy dependence of the transition probabilities for an H₂ on the H₂ model system. Transitions are possible between translational energy and vibrational energy, and from vibrational modes of one H₂ to the other H₂. The second study was to determine the variation of vibrational energy transfer probability with differences in natural frequency of two diatoms similar to N₂.

Comparisons were made to previous approximate analytical solutions of this same problem. For translational to vibrational energy transfer, the previous approximations were not adequate. For vibrational to vibrational energy transfer of one vibrational quantum, the approximations were quite good.

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.

Thermodynamic and kinetic behavior of an argon plasma jet. Decomposition of nitric oxide between 1300 - 1750 degrees K in an argon plasma

In the first part of the study, an RF coupled, atmospheric pressure, laminar plasma jet of argon was investigated for thermodynamic equilibrium and some rate processes.

Improved values of transition probabilities for 17 lines of argon I were developed from known values for 7 lines. The effect of inhomogeneity of the source was pointed out.

The temperatures, T, and the electron densities, n_e , were determined spectroscopically from the population densities of the higher excited states assuming the Saha-Boltzmann relationship to be valid for these states. The axial velocities, v_z, were measured by tracing the paths of particles of boron nitride using a three-dimentional mapping technique. The above quantities varied in the following ranges: 10¹² ˂ n_e ˂ 10¹⁵ particles/cm³, 3500 ˂ T ˂ 11000 °K, and 200 ˂ v_z ˂ 1200 cm/sec.

The absence of excitation equilibrium for the lower excitation population including the ground state under certain conditions of T and n_e was established and the departure from equilibrium was examined quantitatively. The ground state was shown to be highly underpopulated for the decaying plasma.

Rates of recombination between electrons and ions were obtained by solving the steady-state equation of continuity for electrons. The observed rates were consistent with a dissociative-molecular ion mechanism with a steady-state assumption for the molecular ions.

In the second part of the study, decomposition of NO was studied in the plasma at lower temperatures. The mole fractions of NO denoted by x_NO were determined gas-chromatographically and varied between 0.0012 ˂ x_NO ˂ 0.0055. The temperatures were measured pyrometrically and varied between 1300 ˂ T ˂ 1750°K. The observed rates of decomposition were orders of magnitude greater than those obtained by the previous workers under purely thermal reaction conditions. The overall activation energy was about 9 kcal/g mol which was considerably lower than the value under thermal conditions. The effect of excess nitrogen was to reduce the rate of decomposition of NO and to increase the order of the reaction with respect to NO from 1.33 to 1.85. The observed rates were consistent with a chain mechanism in which atomic nitrogen and oxygen act as chain carriers. The increased rates of decomposition and the reduced activation energy in the presence of the plasma could be explained on the basis of the observed large amount of atomic nitrogen which was probably formed as the result of reactions between excited atoms and ions of argon and the molecular nitrogen.

Lattice anomalies and magnetic states in Fe_5Si_3-Mn_5Si_3 alloys

The lattice anomalies and magnetic states in the (Fe_100-xMn_x)₅Si₃ alloys have been investigated. Contrary to what was previously reported, results of x-ray diffraction show a second phase (α') present in Fe-rich alloys and therefore strictly speaking a complete solid solution does not exist. Mössbauer spectra, measured as a function of composition and temperature, indicate the presence of two inequivalent sites, namely 6(g) site (designated as site I) and 4(d) (site II). A two-site model (TSM) has been introduced to interpret the experimental findings. The compositional variation of lattice parameters a and c, determined from the x-ray analysis, exhibits anomalies at x = 22.5 and x = 50, respectively. The former can be attributed to the effect of a ferromagnetic transition; while the latter is due to the effect of preferential substitution between Fe and Mn atoms according to TSM.

The reduced magnetization of these alloys deduced from magnetic hyperfine splittings has been correlated with the magnetic transition temperatures in terms of the molecular field theory. It has been found from both the Mössbauer effect and magnetization measurements that for composition 0 ≤ x ˂ 50 both sites I and II are ferromagnetic at liquid-nitrogen temperature and possess moments parallel to each other. In the composition range 50 ˂ x ≤ 100 , the site II is antiferromagnetic whereas site I is paramagnetic even at a temperature below the bulk Néel temperatures. In the vicinity of x = 50 however, site II is in a state of transition between ferromagnetism and antiferromagnetism. The present study also suggests that only Mn in site II are responsible for the antiferromagnetism in Mn₅Si₃ contrary to a previous report.

Electrical resistance has also been measured as a function of temperature and composition. The resistive anomalies observed in the Mn-rich alloys are believed to result from the effect of the antiferromagnetic Brillouin zone on the mobility of conduction electrons.

Classical and Quantum Effects in Plasmonic Metals

The field of plasmonics exploits the unique optical properties of metallic nanostructures to concentrate and manipulate light at subwavelength length scales. Metallic nanostructures get their unique properties from their ability to support surface plasmons– coherent wave-like oscillations of the free electrons at the interface between a conductive and dielectric medium. Recent advancements in the ability to fabricate metallic nanostructures with subwavelength length scales have created new possibilities in technology and research in a broad range of applications.

In the first part of this thesis, we present two investigations of the relationship between the charge state and optical state of plasmonic metal nanoparticles. Using experimental bias-dependent extinction measurements, we derive a potential- dependent dielectric function for Au nanoparticles that accounts for changes in the physical properties due to an applied bias that contribute to the optical extinction. We also present theory and experiment for the reverse effect– the manipulation of the carrier density of Au nanoparticles via controlled optical excitation. This plasmoelectric effect takes advantage of the strong resonant properties of plasmonic materials and the relationship between charge state and optical properties to eluci- date a new avenue for conversion of optical power to electrical potential.

The second topic of this thesis is the non-radiative decay of plasmons to a hot-carrier distribution, and the distribution’s subsequent relaxation. We present first-principles calculations that capture all of the significant microscopic mechanisms underlying surface plasmon decay and predict the initial excited carrier distributions so generated. We also preform ab initio calculations of the electron-temperature dependent heat capacities and electron-phonon coupling coefficients of plasmonic metals. We extend these first-principle methods to calculate the electron-temperature dependent dielectric response of hot electrons in plasmonic metals, including direct interband and phonon-assisted intraband transitions. Finally, we combine these first-principles calculations of carrier dynamics and optical response to produce a complete theoretical description of ultrafast pump-probe measurements, free of any fitting parameters that are typical in previous analyses.

激光功率密度对Al膜靶后表面快电子发射的影响

报道了在20 TW皮秒激光器上完成的p偏振激光与等离子体相互作用过程中产生的快电子的角分布和能谱测量结果.实验得到：当激光功率密度小于1017 W/cm^2时,电子发射没有明显定向性,在激光入射面内多峰发射;当激光功率密度大于1017 W/cm^2,小于1018 W/cm^2时,电子主要沿靶面法线方向发射;当激光功率密度达到相对论强度时,电子主要沿激光传播方向发射;激光功率密度未达到相对论强度时,靶后表面法线方向快电子能谱拟合平均温度符合共振吸收温度定标率;激光功率密度达相对论强度以上时,靶后表面法线方向

Spin-helical Dirac states in graphene induced by polar-substrate surfaces with giant spin-orbit interaction: a new platform for spintronics

Spintronics, or spin electronics, is aimed at efficient control and manipulation of spin degrees of freedom in electron systems. To comply with demands of nowaday spintronics, the studies of electron systems hosting giant spin-orbit-split electron states have become one of the most important problems providing us with a basis for desirable spintronics devices. In construction of such devices, it is also tempting to involve graphene, which has attracted great attention because of its unique and remarkable electronic properties and was recognized as a viable replacement for silicon in electronics. In this case, a challenging goal is to lift spin degeneracy of graphene Dirac states. Here, we propose a novel pathway to achieve this goal by means of coupling of graphene and polar-substrate surface states with giant Rashba-type spin-splitting. We theoretically demonstrate it by constructing the graphene@BiTeCl system, which appears to possess spin-helical graphene Dirac states caused by the strong interaction of Dirac and Rashba electrons. We anticipate that our findings will stimulate rapid growth in theoretical and experimental investigations of graphene Dirac states with real spin-momentum locking, which can revolutionize the graphene spintronics and become a reliable base for prospective spintronics applications.

Charge and spin transport in graphene devices

170 p.

Giant diamagnetism of gold nanorods

The presence of giant diamagnetism in Au nanorods, NRs, is shown to be a possible consequence of field induced currents in the surface electrons. The distance, Delta , between quantum surface energy levels has been calculated as a function of the NRs radius. Note that those electrons occupying states for which Delta > k(B)T are steadily orbiting with constant orbital moment. The diamagnetic response induced when a field is turned on remains constant during the time the field is acting. As the NRs radius increases, Delta decreases and accordingly the electron fraction available to generate constant currents decreases, consequently the surface diamagnetic susceptibility decreases towards its bulk value. The surface electronic motion induced by the axial applied field on electrons confined into a cylindrical surface accounts with extremely good quantitative agreement for the giant diamagnetism recently measured and reported.

Three-photon-excited upconversion luminescence of niobium ions doped silicate glass by a femtosecond laser irradiation

We report on the bluish green upconversion luminescence of niobium ions doped silicate glass by a femtosecond laser irradiation. The dependence of the fluorescence intensity on the pump power density of laser indicates that the conversion of infrared irradiation to visible emission is dominated by three-photon excitation process. We suggest that the charge transfer from O-2-to Nb5+ can efficiently contribute to the bluish green emission. The results indicate that transition metal ions without d electrons play an important role in fields of optics when embedded into silicate glass matrix. (C) 2008 Optical Society of America.

Density-potential mapping in the standard and quantum electrodynamical time-dependent density functional theory

131 p.

Yb：YAG晶体的合作发光现象

研究了Yb：YAG晶体的合作发光现象。当用940hm的近红外光激发时，Yb：YAG晶体有明显的上转换蓝色发光。实验发现498nm的蓝色发光强度与激发功率的平方成正比，而且Yb^3＋掺杂浓度越高，蓝色发光越强。分析表明这是Yb^3＋间强的相互作用导致的合作发光，是由于Yb^3＋在共价性的YAG基质中，它的4f^I3电子易于与近邻离子发生相互作用导致的。

V^3＋：YAG晶体的生长、色心与光谱性能研究

采用石墨电阻加热的温梯法生长了V：YAG晶体，晶体的不同部位呈现两种不同的颜色：浅绿色和黄褐色．通过对比分析不同颜色V：YAG晶体的室温吸收光谱，推断出石墨发热体高温下扩散出来的C可以起到还原作用，提高晶体中V^3＋tetra离子的浓度，同时诱导了F心的形成．在1300℃下，对不同颜色的V：YAG晶体进行真空退火处理，发现处于八面体格位中的V^3＋离子在热激发作用下与近邻的四面体格位Al^3＋离子存在置换反应，由此产生一定浓度的四面体格位V^3＋离子．同时，F心在退火过程中被完全消除，释放出来的自由电子被