University of Macau / Faculty of Science and Technology / Department of Mathematics

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Electron momentum spectroscopy (EMS) provides experimental atomic and molecular electronic structure information in terms of the binding energy spectrum and the experimental momentum profile (XMP), which is a direct probe of the electron momentum distribution in specific molecular orbitals. The measured XMPs permit a detailed quantitative evaluation of theoretical ab initio wavefunctions in quantum chemistry and also provide a means to investigate traditional concepts in chemical reactivity at the fundamental electronic level. This thesis reports high momentum resolution EMS measurements of the valence orbitals of H₂0, D₂0, NH₃ and H₂CO obtained using an EMS spectrometer of the symmetric, non-coplanar type operated at an impact energy of 1200eV. The measured experimental momentum profiles for the valence orbitals of each molecule have been placed on a common intensity scale, which has allowed a stringent quantitative comparison between experiment and theory. These studies now confirm earlier preliminary investigations that suggested serious discrepancies between experimental and theoretical momentum distributions. Exhaustive consideration of possible rationalizations of these discrepancies indicate that double zeta quality and even near Hartree-Fock quality wavefunctions are insufficient in describing the outermost valence orbitals of H₂0 and NH₃. Preliminary results for H₂CO also indicate that near Hartree-Fock wavefunctions are incapable of describing the outermost 2b₂ orbital. Interactive and collaborative theoretical efforts have therefore led to the development of new Hartree-Fock limit and also highly correlated (CI) wavefunctions for H₂0, NH₃ and H₂CO. It is found that highly extended basis sets including diffuse functions and the adequate inclusion of correlation and relaxation effects are necessary in the accurate prediction of experimental momentum profiles as measured by electron momentum spectroscopy. New EMS measurements are also reported for the outermost valence orbitals of NF₃, NH₂CH₃, NH (CH₃)₂, N (CH₃)₃ and para-dichlorobenzene. These exploratory studies have illustrated useful chemical applications of EMS. In particular, EMS measurements of the outermost orbitals of the methylated amines have revealed chemical trends which are consistent with molecular orbital calculations. These calculations suggest extensive electron density derealization of the so-called nitrogen 'lone pair' in the methylated amines in comparison to the 'lone pair' in NH₃. EMS measurements of the non-degenerate π₃ and π₂ orbitals of para-dichlorobenzene show different experimental momentum profiles consistent with arguments based on inductive and resonance effects. These experimental trends, both in the case of the amines and para-dichlorobenzene, were qualitatively predicted by molecular orbital calculations using double zeta quality wavefunctions. However more accurate prediction of the experimental momentum profiles of these molecules will need more extended basis sets and the inclusion of correlation and relaxation effects as suggested by the studies based on the smaller molecules. An integrated computer package (HEMS) for momentum space calculations has also been developed based on improvements to existing programs. Development studies testing a new prototype multichannel (in the ɸ plane) EMS spectrometer are described. / Science, Faculty of / Chemistry, Department of / Graduate

We exhibit long-lived resonances in scattering from two-dimensional soft cage potentials comprised of three and four Gaussian peaks. Specific low-energy resonances with very narrow width are shown to correspond to classical multiple-reflection events. These states have much larger probability densities inside the cage than outside and mimic bound states in the sense that the symmetry-breaking effect of the incident wave is relatively small. As a result we have found that isolated states display the simple symmetry characteristics of bound states. Overlapping resonances exhibit a mixing of symmetry classes leading to wave functions of lower symmetry, like those of wider resonances at higher energy. We demonstrate that at energies below the lowest resonances of two-dimensional cages, where the distance across the entrance of the cage corresponds to less than half a wavelength, the wave function may still gain access to the interior region by squeezing its wavelength in the necessary direction at the expense of the kinetic energy in the direction normal to the opening. The resulting curvature of the wave function in the donor dimension corresponds to an imaginary wavenumber, curving away from the plane defined by zero amplitude. This mechanism for passing between obstacles may be relevant for electronic and optical devices having spatial structures with dimensions comparable to the wavelengths of the energy carriers. / Graduation date: 2005

Thesis (Ph. D.)--University of Wisconsin--Madison, 1958. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

No description available.

Thesis--University of California, Berkeley, 1963. / "UC-34 Physics Distributions" -t.p. "TID-4500 (19th Ed.)" -t.p. Includes bibliographical references (p. 67-70).

This thesis describes the application of wave function-based and perturbative methods to extended systems, primarily semiconductors. In Chapter 1, I introduce the quantum chemistry problem along with current progress in the field. I then provide some requisite fundamental theory associated with the wave function-based methods and periodic boundary conditions. In Chapter 2, I describe the relationship between the traditional extended system GW method and the traditionally molecular coupled-cluster formalism through diagrammatic analysis. We find that the popular coupled cluster singles and doubles (CCSD) method contains most of the diagrams in GW theory and more, and the more accurate coupled cluster singles and doubles with perturbative triples (CCSD(T)) method contains all GW diagrams and more. Benchmarking on the GW100 test set indicates that CCSD and a number of its approximations are more accurate than GW theory. In Chapter 3, I evaluate the potential for using composite schemes to reduce the computational cost of the CCSD method. We use focal point and downfolding techniques for excited state results for the GW100 along with some sample solids. Using composite methods reduces the cost of CCSD by reducing the number of orbitals treated at a higher level of theory, which is very similar to the active space methods used in single- and multi-reference calculations. In Chapters 4 and 5, I describe how to best treat finite size effects for wave function-based methods, including the impact of including terms like the Madelung constant and which extrapolation form to use. After establishing this, we use the prescribed procedure to compare the equation-of-motion second-order M{\o}ller-Plesset (EOM-MP2) method to the MP2 method of Gr\"{u}neis and the GW method for a standard test set of 11 solid-state systems. We find that the MP2 method performs qualitatively and quantitatively poorly for extended systems, but EOM-MP2 and GW perform qualitatively well, with quantitative MAEs of 0.40 and 0.68eV, respectively relative to a zero-point corrected electronic band gap.

Thesis (PhD)--Stellenbosch University, 2001. / ENGLISH ABSTRACT: In this dissertation, we give an overview of disordered systems, where we concentrate on the theoretical calculation techniques used in this field. We first discuss the general properties of disordered systems and the different models and quantities used in the study of these systems, before describing calculation techniques used to investigate the quantities introduced. These calculation techniques include the phase formalism method used one dimension, as well as the scaling approach and field theoretic approaches leading to non-linear c-models in higher dimensions. We then introduce a complementary effective field theoretic approach based on the logarithmic derivative of the wave-function, and show how the quantities of interest are calculated using this method. As an example, the effective field theory is applied to one dimensional systems with Gaussian disorder. The average density of states, the average 2-point correlator and the conductivity are calculated in a weak disorder saddle-point approximation and in strong disorder duality approximation. These results are then calculated numerically and in the case of the density of states compared to the exact result. / AFRIKAANSE OPSOMMING: In hierdie tesis, gee ons 'n oorsig van sisteme met wanorde, waar ons konsentreer op teoretiese berekeningsmetodes wat in die veld gebruik word. Eerstens bespreek ons die algemene eienskappe van sisteme met wanorde en verskillende modelle en hoeveelhede wat gebruik word in die studie van hierdie sisteme, voordat ons die berekeningsmetodes beskryf wat gebruik word om die bogenoemde hoeveelhede te ondersoek. Hierdie berekeningstegnieke sluit in die fase formalisme wat in een dimensie gebruik word, asook die skalingsbenadering en veldteoretiese metodes wat lei tot nie-lineêr u-modelle in hoër dimensies. Ons voer in 'n komplementere effektiewe veldeteorie gebaseer op die logaritmiese afgeleide van die golffunksie, en wys hoe hoeveelhede van belang met hierdie metode bereken word. As 'n voorbeeld, word die effektiewe veldetoerie toegepas op 'n een dimensionele sisteem met 'n Gauss verdeling. Die gemiddelde digtheid van toestande, die gemiddelde 2-punt korrelator en die gemiddelde geleidingsvermoë word bereken in 'n swak wanorde saalpunt benadering en in 'n sterk wanorde duale benadering. Hierdie resultate word dan numeries bereken, en in die geval van die digtheid van toestande vergelyk met die eksakte resultaat.

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