Effective-mass theory for InAs/GaAs strained coupled quantum dots

In the framework of effective-mass envelope-function theory, the optical transitions of InAs/GaAs strained coupled quantum dots grown on GaAs (100) oriented substrates are studied. At the Gamma point, the electron and hole energy levels, the distribution of electron and hole wave functions along the growth and parallel directions, the optical transition-matrix elements, the exciton states, and absorption spectra are calculated. In calculations, the effects due to the different effective masses of electrons and holes in different materials are included. Our theoretical results are in good agreement with the available experimental data.

Insight into the solvent effect: A density functional theory study of cisplatin hydrolysis

The solvent effect on reactions in solutions is crucial for many systems. In this study, the reaction barrier with respect to the number of solvent molecules included in the system is systematically studied using density function theory calculations. Our results show that the barriers rapidly converge with respect to the number of solvent molecules. The solvent effect is investigated by calculating cisplatin hydrolysis in several types of solvents. The results are analyzed and a linear relationship between the reaction barrier and the interaction strength of solvent-reactants is found. Insight into the general solvent effect is obtained. (c) 2006 American Institute of Physics.

Reaction Mechanisms of Crotonaldehyde Hydrogenation on Pt(111): Density Functional Theory and Microkinetic Modeling

The microkinetics based on density function theory (DFT) calculations is utilized to investigate the reaction mechanism of crotonaldehyde hydrogenation on Pt(111) in the free energy landscape. The dominant reaction channel of each hydrogenation product is identified. Each of them begins with the first surface hydrogenation of the carbonyl oxygen of crotonaldehyde on the surface. A new mechanism, 1,4-addition mechanism generating enols (butenol), which readily tautomerize to saturated aldehydes (butanal), is identified as a primary mechanism to yield saturated aldehydes instead of the 3,4-addition via direct hydrogenation of the ethylenic bond. The calculation results also show that the full hydrogenation product, butylalcohol, mainly stems from the deep hydrogenation of surface open-shell dihydrogenation intermediates. It is found that the apparent barriers of the dominant pathways to yield three final products are similar on P(111), which makes it difficult to achieve a high selectivity to the desired crotyl alcohol (COL).

Extent and limitations of density functional theory in describing magnetic systems

The performance of density-functional theory to solve the exact, nonrelativistic, many-electron problem for magnetic systems has been explored in a new implementation imposing space and spin symmetry constraints, as in ab initio wave function theory. Calculations on selected systems representative of organic diradicals, molecular magnets and antiferromagnetic solids carried out with and without these constraints lead to contradictory results, which provide numerical illustration on this usually obviated problem. It is concluded that the present exchange-correlation functionals provide reasonable numerical results although for the wrong physical reasons, thus evidencing the need for continued search for more accurate expressions.

Discrete commutative difference operator theory

The object of this thesis is to formulate a basic commutative difference operator theory for functions defined on a basic sequence, and a bibasic commutative difference operator theory for functions defined on a bibasic sequence of points, which can be applied to the solution of basic and bibasic difference equations. in this thesis a brief survey of the work done in this field in the classical case, as well as a review of the development of q~difference equations, q—analytic function theory, bibasic analytic function theory, bianalytic function theory, discrete pseudoanalytic function theory and finally a summary of results of this thesis

Developments in the Theory of X-ray Absorption and Compton Scattering.

Thesis (Ph.D.)--University of Washington, 2016-06

Visible light enhanced oxidant free dehydrogenation of aromatic alcohols using Au-Pd alloy nanoparticle catalysts

We find that visible light irradiation of gold–palladium alloy nanoparticles supported on photocatalytically inert ZrO2 significantly enhances their catalytic activity for oxidant-free dehydrogenation of aromatic alcohols to the corresponding aldehydes at ambient temperatures. Dehydrogenation is also the dominant process in the selective oxidation of the alcohols to the corresponding aldehydes with molecular oxygen. The alloy nanoparticles strongly absorb light and exhibit superior catalytic and photocatalytic activity when compared to either pure palladium or gold nanoparticles. Analysis with a free electron gas model for the bulk alloy structure reveals that the alloying increases the surface charge heterogeneity on the alloy particle surface, which enhances the interaction between the alcohol molecules and the metal NPs. The increased surface charge heterogeneity of the alloy particles is confirmed with density function theory applied to small alloy clusters. Optimal catalytic activity was observed with a Au : Pd molar ratio of 1 : 186, which is in good agreement with the theoretical analysis. The rate-determining step of the dehydrogenation is hydrogen abstraction. The conduction electrons of the nanoparticles are photo-excited by the incident light giving them the necessary energy to be injected into the adsorbed alcohol molecules, promoting the hydrogen abstraction. The strong chemical adsorption of alcohol molecules facilitates this electron transfer. The results show that the alloy nanoparticles efficiently couple thermal and photonic energy sources to drive the dehydrogenation. These findings provide useful insight into the design of catalysts that utilize light for various organic syntheses at ambient temperatures.

Au-Pd alloy nanoparticle catalyzed selective oxidation of benzyl alcohol and tandem synthesis of imines at ambient conditions

Alloy nanoparticles (NPs) of gold and palladium on ZrO2 support (Au–Pd@ZrO2) were found to be highly active in oxidation of benzyl alcohols and can be used for the tandem synthesis of imines from benzyl alcohols and amines via a one-pot, two-step process at mild reaction conditions. The first step of the process is oxidation of benzyl alcohol to benzaldehyde, excellent yields were achieved after 7 h reaction at 40 °C without addition of any base. In the second step, aniline was introduced into the reaction system to produced N-benzylideneaniline. The benzaldehyde obtained in the first step was completely consumed within 1 h. A range of benzyl alcohols and amines were investigated for the general applicability of the Au–Pd alloy catalysts. It is found that the performance of the catalysts depends on the Au–Pd metal contents and composition. The optimal catalyst is 3.0 wt% Au–Pd@ZrO2 with a Au:Pd molar ratio 1:1. The alloy NP catalyst exhibited superior catalytic properties to pure AuNP or PdNP because the surface of alloy NPs has higher charge heterogeneity than that of pure metal NPs according to simulation of density function theory (DFT)

A comment on the consistency of truncated nonlinear integral equation based theories of freezing

We report the results of two studies of aspects of the consistency of truncated nonlinear integral equation based theories of freezing: (i) We show that the self-consistent solutions to these nonlinear equations are unfortunately sensitive to the level of truncation. For the hard sphere system, if the Wertheim–Thiele representation of the pair direct correlation function is used, the inclusion of part but not all of the triplet direct correlation function contribution, as has been common, worsens the predictions considerably. We also show that the convergence of the solutions found, with respect to number of reciprocal lattice vectors kept in the Fourier expansion of the crystal singlet density, is slow. These conclusions imply great sensitivity to the quality of the pair direct correlation function employed in the theory. (ii) We show the direct correlation function based and the pair correlation function based theories of freezing can be cast into a form which requires solution of isomorphous nonlinear integral equations. However, in the pair correlation function theory the usual neglect of the influence of inhomogeneity of the density distribution on the pair correlation function is shown to be inconsistent to the lowest order in the change of density on freezing, and to lead to erroneous predictions. The Journal of Chemical Physics is copyrighted by The American Institute of Physics.

A comment on the consistency of truncated nonlinear integral equation based theories of freezing

We report the results of two studies of aspects of the consistency of truncated nonlinear integral equation based theories of freezing: (i) We show that the self-consistent solutions to these nonlinear equations are unfortunately sensitive to the level of truncation. For the hard sphere system, if the Wertheim–Thiele representation of the pair direct correlation function is used, the inclusion of part but not all of the triplet direct correlation function contribution, as has been common, worsens the predictions considerably. We also show that the convergence of the solutions found, with respect to number of reciprocal lattice vectors kept in the Fourier expansion of the crystal singlet density, is slow. These conclusions imply great sensitivity to the quality of the pair direct correlation function employed in the theory. (ii) We show the direct correlation function based and the pair correlation function based theories of freezing can be cast into a form which requires solution of isomorphous nonlinear integral equations. However, in the pair correlation function theory the usual neglect of the influence of inhomogeneity of the density distribution on the pair correlation function is shown to be inconsistent to the lowest order in the change of density on freezing, and to lead to erroneous predictions. The Journal of Chemical Physics is copyrighted by The American Institute of Physics.

Composition operators, Aleksandrov measures and value distribution of analytic maps in the unit disc

A composition operator is a linear operator that precomposes any given function with another function, which is held fixed and called the symbol of the composition operator. This dissertation studies such operators and questions related to their theory in the case when the functions to be composed are analytic in the unit disc of the complex plane. Thus the subject of the dissertation lies at the intersection of analytic function theory and operator theory. The work contains three research articles. The first article is concerned with the value distribution of analytic functions. In the literature there are two different conditions which characterize when a composition operator is compact on the Hardy spaces of the unit disc. One condition is in terms of the classical Nevanlinna counting function, defined inside the disc, and the other condition involves a family of certain measures called the Aleksandrov (or Clark) measures and supported on the boundary of the disc. The article explains the connection between these two approaches from a function-theoretic point of view. It is shown that the Aleksandrov measures can be interpreted as kinds of boundary limits of the Nevanlinna counting function as one approaches the boundary from within the disc. The other two articles investigate the compactness properties of the difference of two composition operators, which is beneficial for understanding the structure of the set of all composition operators. The second article considers this question on the Hardy and related spaces of the disc, and employs Aleksandrov measures as its main tool. The results obtained generalize those existing for the case of a single composition operator. However, there are some peculiarities which do not occur in the theory of a single operator. The third article studies the compactness of the difference operator on the Bloch and Lipschitz spaces, improving and extending results given in the previous literature. Moreover, in this connection one obtains a general result which characterizes the compactness and weak compactness of the difference of two weighted composition operators on certain weighted Hardy-type spaces.

Single atom (Pd/Pt) supported on graphitic carbon nitride as efficient photocatalyst for visible-light reduction of carbon dioxide

Reducing carbon dioxide (CO2) to hydrocarbon fuel with solar energy is significant for high-density solar energy storage and carbon balance. In this work, single palladium/platinum (Pd/Pt) atoms supported on graphitic carbon nitride (g-C3N4), i.e. Pd/g-C3N4 and Pt/g-C3N4, acting as photocatalysts for CO2 reduction were investigated by density function theory (DFT) calcu-lations for the first time. During CO2 reduction, the individual metal atoms function as the active sites, while g-C3N4 provides the source of hydrogen (H*) from hydrogen evolution reaction. The complete, as-designed photocatalysts exhibit excellent activity in CO2 reduction. HCOOH is the preferred product of CO2 reduction on the Pd/g-C3N4 catalyst with a rate-determining barrier of 0.66 eV, while the Pt/g-C3N4 catalyst prefers to reduce CO2 to CH4 with a rate-determining barrier of 1.16 eV. In addition, depositing atom catalysts on g-C3N4 significantly enhances the visible light absorption, rendering them ideal for visible light reduction of CO2. Our findings open a new avenue of CO2 reduction for renewable energy supply.

Completeness of the Coulomb wave functions in quantum mechanics

We give an explicit, direct, and fairly elementary proof that the radial energy eigenfunctions for the hydrogen atom in quantum mechanics, bound and scattering states included, form a complete set. The proof uses only some properties of the confluent hypergeometric functions and the Cauchy residue theorem from analytic function theory; therefore it would form useful supplementary reading for a graduate course on quantum mechanics.

Solution of a Boundary-Value Problem associated with Diffraction of Water Waves by a Nearly Vertical Barrier

An exact solution is derived for a boundary-value problem for Laplace's equation which is a generalization of the one occurring in the course of solution of the problem of diffraction of surface water waves by a nearly vertical submerged barrier. The method of solution involves the use of complex function theory, the Schwarz reflection principle, and reduction to a system of two uncoupled Riemann-Hilbert problems. Known results, representing the reflection and transmission coefficients of the water wave problem involving a nearly vertical barrier, are derived in terms of the shape function.